PHD THESIS - u-bordeaux.frori-oai.u-bordeaux1.fr/pdf/2010/BUDZIK_MICHAL_2010.pdf · 2010. 12....

Numéro d'ordre de la thèse: 4041

Gdansk, 18.06.2010

PHD THESIS

BORDEAUX UNIVERSITY ECOLE DOCTORALE

DES SCIENCES PHYSIQUES ET DE L'INGENIEUR

GDANSK UNIVERSITY OF TECHNOLOGY

by Michał K. BUDZIK

TO OBTAIN THE DEGREE: PhD

IN: Mecanique et Ingenierie

SUPERVISORS:

Prof. Martin E.R. SHANAHAN (Bordeaux 1 University)

D.Sc. Krystyna IMIELIŃSKA (Gdansk University of Technology)

COORDINATOR:

PhD Julien JUMEL (Bordeaux 1 University)

FRACTURE IN ASYMMETRIC BONDED JOINTS

JURY:

Prof. A.S. WRONSKI (University of Bradford, United Kingdom) – Chairman, Reviewer

Prof. W. POSSART (University of Saarland, Germany) – Reviewer

DSc. M. WASILCZUK (Gdansk University of Technology, Poland) – Reviewer

DSc. M. SZKODO (Gdansk University of Technology, Poland) – Member

Prof. A. ZIELINSKI (Gdansk University of Technology, Poland) – Member

PhD. J. JUMEL (Bordeaux 1 University, France) – Member

Prof. M.E.R. SHANAHAN (Bordeaux 1 University, France) – Supervisor

DSc. K. IMIELINSKA (Gdansk University of Technology, Poland) - Supervisor

Within Joint-Thesis Agreement between Bordeaux University and Gdansk University of

Technology


2

Acknowledgements

I wish to thank

My supervisors:

Prof. Martin E.R. Shanahan for taking me under his wings, much precious advice, inspiration

and coordination of my research as well as friendship

and

Dr. Krystyna Imielińska for coordinating my research programme in Poland, encouragement

and friendship, valuable consultations and assistance

I am grateful

Julien Jumel, my amazing coordinator in France for his guidance and inspiration, as well as

his friendliness and partnership cooperation that made my work and life in Bordeaux much

easier

Jean Marc Olive for his commitment in the French-Polish collaboration program and creating

the opportunity for my doctoral studies in France

Prof. Andrzej Zielinski for establishing and developing the scientific contacts with LMP,

which allowed my work there

Jeremy Guitard and Lech Targan for their everyday efforts to facilitate my experimental work

Bernard Hosten, Michel Castaings and Christine Biateau for their assistance in ultrasonic

studies

The French Government for financial support (PhD grant) that enabled my stay and work in

France

My family, wife – Jadzia for her patience and support, parents, sister for believing in me

Michał K. Budzik

3

Abstract

Adhesion was studied in asymmetric bonded joints using fracture mechanics tests. The

asymmetric bonded joints consist of two different type and/or thickness materials bonded by

an adhesive. Mentions of asymmetric bonded joint tests employed so far are rare in the

literature. They are imperfect and therefore are not standardized. Accordingly three new tests

were introduced in this work to study bonded joints. The new metrological routines and

models were built for the CRT (Constant Rate Test), CFT (Constant Force Test) and the CDT

(Constant Displacement Test). The routines were validated with the new Artificial Crack Tip

test developed in this thesis. Different bonded systems were examined: the adhesives - epoxy,

cyanoacrylate, acrylic mastic, PSA; the bonded adherends - aluminium alloys, CFRP

composites and polycarbonate. The results obtained in the new tests are very promising in

terms of the accuracy and continuous observation of crack kinetics. In addition it was found

that the novel strain gauge technique, introduced in the CDT, test allows precise joint

monitoring when the adhesive is in a metastable state and a precise estimation of process

zone. Another interesting achievement of this work was describing the phenomenon of double

crack curvature in the vicinity of the strong – weak adhesion transition zone. The next

achievement was derivation of the strain energy release rate from the elastic foundation

model, which gives better understanding of the mechanics and the measurements behind

adhesive bonding. Atomic Force Microscope (AFM) and Scanning Electron Microscope

(SEM) studies were made of the bonded substrates to estimate the surface treatment effects.

The stress state in asymmetric geometry was studied using finite element analysis (FEA),

which explained the formation of the curved crack front and the origin of river patterns. The

new tests developed in this study appear promising since they offer accurate and reliable

results for the materials tested.


4

Streszczenie

W pracy przedstawiono wyniki badań asymetrycznych złączy adhezyjnych z wykorzystaniem

prób mechaniki pękania. Asymetryczne złącza klejone powstają przez połączenie dwóch

dowolnych materiałów, o innym wskaźniku na zginanie, za pomocą kleju. Zaproponowano

trzy nowe metody eksperymentalne dla których zaprojektowano i zbudowano stanowiska

badawcze. Poprawność modeli fizycznych i matematycznych wykorzystanych do interpretacji

badanych zjawisk potwierdzono wykorzystując opracowaną w pracy próbę ze sztucznym

frontem pęknięcia. Próby przeprowadzono na złączach klejonych wykorzystując kleje:

epoksydowe, cjanoakrylowy, typu Mastic i PSA, łączonymi materiałami były: stopy

aluminium, kompozyt węglowy oraz poliwęglan. Wyniki badań uzyskane przy wykorzystaniu

nowych metod wskazują na ich pewność i dokładność, dodatkowo umożliwiają ciągłą

obserwację propagującego pęknięcia. Nowa metoda pomiaru parametrów mechaniki pękania

oparta na pomiarach tensometrycznych została z powodzeniem zastosowana do złączy w

których klej znajduje się w stanie metastabilnym. W pracy zaobserwowano i przeanalizowano

zjawisko powstawania podwójnego frontu pęknięcia na granicy ośrodków o różnych siłach

adhezji, dotąd nie opisanego. Po raz pierwszy wyprowadzono równanie szybkości uwalniania

energii sprężystej wykorzystując model belki na sprężystym podłożu, co umożliwia lepsze

zrozumienie zachowania się złączy klejonych. Przeprowadzone badania z użyciem

mikroskopii sił atomowych (AFM) oraz skaningowej mikroskopii elektronowej (SEM)

umożliwiły ocenę efektów obróbki powierzchniowej stopów aluminium. W pracy dokonano

analizy naprężeń w asymetrycznych złączach adhezyjnych z wykorzystaniem metody

elementów skończonych (FEM). Analiza FEM pozwoliła na wyjaśnienie zjawiska

powstawania zakrzywionego frontu pęknięcia w badanych przełomach. Zaproponowane nowe

metody badań złączy asymetrycznych zapewniają dokładność i pewność pomiaru dla

materiałów wykorzystanych w badaniach.

Michał K. Budzik

5

Résumé

Des tests de fissuration ont été réalisés sur des joints collés asymétriques. Ces assemblages

asymétriques sont constitués de deux substrats de nature et/ou d’épaisseur différentes liés par

un adhésif. Cette géométrie d’éprouvette semble peu utilisée pour effectuer des essais de

fissuration. Elles présentent certains inconvénients et de ce fait n’ont fait l’objet d’aucune

normalisation. Dans le cadre cette géométrie d’éprouvette d’essai a été néanmoins été retenue

et utilisée dans trois configurations différentes pour la caractérisation mécanique des

assemblages collés. Des protocoles d’essai et les schéma d’analyse associés ont été définis

pour des essais de fissuration à vitesse de déplacement imposé (CRT : Constant Rate Test), à

force imposée (CFT : Constant Force Test) ainsi qu’à déplacement imposé (CDT : Constant

Displacement Test). Les analyses ont pu être étalonnées au moyen d’un étau matérialisant

artificiellement la position d’un fissure. De nombreuses configurations ont été étudiées à

l’occasion de ce travail tant du point de vue des adhésifs utilisés (epoxy, cyanoacrylate,

acrylic mastic, PSA) que du point de vue des substrats encollés (alliage d’aluminium,

composite à matrice organique, polycarbonate). Ces nouveaux tests s’avèrent prometteurs car

ils permettent de suivre de façon continu et précision la propagation de fissure au sein de la

liaison. En outre, l’analyse des déformations mesurées par extensométrie lors d’essai réalisés

à déplacement imposé (CDT) permet un suivi précis de la réponse de la couche adhésive dans

la zone contrainte et d’estimer la taille de cette dernière, y compris lorsque la colle est dans un

état métastable. Un autre résultat important de ce travail concerne l’analyse de la modification

du front de fissure celle-ci voit une diminution de l’adhésion entre les deux substrats. Enfin,

un calcul plus précis du taux de restitution d’énergie a été proposé pour prendre en compte le

caractère élastique de la couche adhésive, mais permettant aussi de mieux appréhender la

redistribution des contraintes dans la colle, et ainsi mieux interpréter les essais mécaniques

réalisés. Des analyses par Microscopie à Force Atomique (AFM) ainsi qu’au microscope

électronique à balayage (MEB) ont été effectués sur les substrats encollés pour évaluer

l’impact des traitements de surface. Des simulations numériques par la method des éléments

finis ont été réalisées pour determiner l’état de contrainte dans nos éprouvette d’essai et ainsi

expliquer la courbure du front de fissure et les faciès de rupture observés. Les nouvelles

configurations expérimentales décrites dans ce manuscript nous paraissent prometteuses car

elle offrent une amelioration très significative en terme de fiabilité et précision

comparativement aux tests présentés habituellement pour ce type de travaux.


6

NOTATION ............................................................................................................................... 8

INTRODUCTION ...................................................................................................................... 9

CHAPTER 1. BIBLIOGRAPHY ............................................................................................. 11

1.1. Historical perspective of adhesive bonding ................................................................... 11

1.2. Adhesive bonding applications ...................................................................................... 14

1.3. Structural adhesives ....................................................................................................... 19

1.4. Theories of adhesion ...................................................................................................... 29

1.5. Surface treatment of adherends ...................................................................................... 38

1.6. Mechanical testing of adhesive bonding ........................................................................ 46

1.6.1. Characterisation by failure stress ............................................................................ 47

1.6.2. Characterisation by failure energy .......................................................................... 52

CHAPTER 2. ASYMMETRIC JOINTS .................................................................................. 60

2.1. Materials and specimens ................................................................................................ 60

2.1.1. Characterization of substrates ................................................................................. 64

2.1.2. Surface preparation of the substrates ...................................................................... 65

2.1.3. AFM and SEM control of the surface ..................................................................... 67

2.1.4. Fabrication of adhesive joints ................................................................................. 69

2.2. Microscopic studies ....................................................................................................... 70

2.3. Crack path observations ................................................................................................. 70

CHAPTER 3. ADHESIVE BONDING TESTS AND ANALYSIS ........................................ 71

3.1. Constant Rate Test (CRT) .............................................................................................. 72

3.1.1. Data reduction method ............................................................................................ 73

3.1.2. Calibration of the crack length - artificial crack tip test .......................................... 76

3.1.3. Fracture of aluminium joints bonded with nanoparticle adhesive .......................... 77

3.2. Constant Force Test (CFT) ............................................................................................ 83


3.2.2. Artificial crack tip test ............................................................................................. 87

3.2.3. The (macro) fracture behaviour of different adhesives ........................................... 88

3.3. Constant Displacement (Asymmetric Wedge) Test ....................................................... 91


3.3.2. Calibration of the CDT test using artificial crack tip test ....................................... 98

3.3.4. Adhesive joint with variable adhesion properties ................................................. 102

3.3.5. Effects of The Adhesive Compliance ................................................................... 115

3.3.7. Use of the CDT test for assessment of curing time ............................................... 128

3.3.8. Temperature effects on fracture using the CDT test ............................................. 133

CHAPTER 4. MODELLING OF STRESSES IN ASYMMETRIC ADHESIVE JOINTS ... 143

4.1. FEM model .................................................................................................................. 143

4.2. Finite Element Analysis ............................................................................................... 146

4.2.1. Stress state with the straight crack front ............................................................... 146

4.2.2. Stress mixity .......................................................................................................... 147

4.2.3. Anti-plane shearing effect on fracture structure .................................................... 153

4.2.4. Crack depth ........................................................................................................... 154

DISCUSSION OF THE TESTS ............................................................................................. 159

Michał K. Budzik

7

CONCLUSIONS .................................................................................................................... 165

PERSPECTIVES .................................................................................................................... 166

APPENDICES ........................................................................................................................ 167

Appendix 1. Mode II contribution in Constant Displacement Test ................................ 167

Appendix 2. Friction dissipation in Constant Displacement Test ................................... 170

Appendix 3. List of publications ..................................................................................... 173

Appendix 4. Gantt chart of thesis progress ..................................................................... 174

REFERENCES ....................................................................................................................... 175

LIST OF FIGURES ................................................................................................................ 183

LIST OF TABLES ................................................................................................................. 190


8

NOTATION

NOTATION UNIT PARAMETER

E GPa Modulus of elasticity in tension

ν - Poisson’s ratio

I mm4 Moment of inertia

G J m-2

Strain energy release rate

Gc J m-2

Critical fracture energy

U J Elastic energy

a mm Estimated crack length

aD mm Measured crack length

F N Applied force

C mm/N Compliance

M Nm Bending moment

x,y,z - Cartesian coordinates

xi mm Strain gauge position

b mm Width

Δ mm Deflection

h mm Flexible plate thickness

H mm Rigid plate thickness

e mm Adhesive layer thickness

l, L mm Length

ε - Unit elongation, strain

R mm Curvature of bended beam

δa mm Crack depth

k GPa Elastic foundation rigidity

v mm h-1

Crack speed

f - Surface fraction

λ m-1

Wave number

A,B,C,D Calculus constants

ω - λa

η, - SBT/Winkler energy release rate ratio, II/I stress mixity ratio

θ - SBT/Winkler strain ratio

γ J m-2

Environmental dependent fracture energy

N N Normal force

ρ mm Plate curvature

V N Shear force

η MPa Shear stress

κ - III/I stress mixity ratio

ζ MPa Normal stress

Michał K. Budzik

9

INTRODUCTION

Adhesive bonding is one of the most innovative and fast developing processes of joining

structural elements. In applications such as primary aircraft structures or automobile elements

adhesive bonding competes with traditional bolting, riveting or welding. The advantages of

adhesive bonding include high strength/weight ratio, possibility to join any combination of

materials, high corrosion resistance. Some drawbacks exist such as great sensitivity to the

fabrication process, limitations on the upper continuous operating temperature (ca. 300oC),

degradation of properties during environmental (hot/wet) exposure. The success of adhesive

bonding depends on numerous factors which include the theoretical knowledge about the

adhesion (adhesion science), mechanics as well as experience in fabrication of the joints.

Adhesion science is inherently an interdisciplinary field requiring fundamental understanding

of mechanics, physics, chemistry, surfaces and materials. Adhesion as it is now interpreted

refers to a complex set of inter-connected phenomena that is far from being completely

understood. D. H. Kaelble [1] defines adhesion (lat. adhaesio-adhering) as the phenomena

causing two boundary layers of two different bodies to be held together by their attraction

forces. In general adhesion includes the set of mechanisms that allow two components

(substrates, adherends) to be held together by a third component, the adhesive or simply, glue.

Free Encyclopaedia defines the adhesive or glue as: a compound in a liquid or semi-liquid

state that adheres or bonds items together. In addition, the adhesive should assure the

required properties (strength, durability etc.) over the designed service life of the bonded

system. Modern structural adhesives have been intensely developed for over 80 years now.

Primarily they were developed for reasons of war as a fast way to produce and to bond

aircraft. Nowadays due to the need to bond modern metals, polymer and composite materials.

The development of contemporary technology and industry is closely related to the creation of

new polymeric materials, among which adhesives are playing an increasing role. Their

production is being increased at higher rates than that of other polymeric materials. Such

enhanced interest in adhesives can be attributed to several factors [2]:

1. Modern technology employs new types of materials that cannot be joined by means of

traditional mechanical methods such as welds, rivets, screws, and bolts. These materials

include different types of ceramics, glass ceramics, alloys, composites etc.

2. Newly developed adhesives characterized by high strength, heat resistance, and

noncombustibility can meet the requirements of advanced technologies.

3. Adhesion is frequently the most effective way of joining very different materials using

relatively simple equipment. The range of materials that can be cemented is practically

unlimited.

4. Application of adhesives results in the improved characteristics of the article produced,

such as improved strength.

http://en.wikipedia.org/wiki/Adhesion


10

In order to design properly bonded joint, thus assure high strength and durability of the

bonded joint, it is necessary to use appropriate testing procedures. Simple static tests do not

give sufficient information about life prediction, long time resistance, durability and

endurance of the bonded structures such as in aircraft. Fracture mechanics tests, especially the

Mode I test, are more appropriate since cleavage stress is considered as the fracture initiator.

This thesis has focused on new, reliable, mode I fracture mechanics based testing methods for

adhesive bonded joints characterization.

Although fracture mechanics is a relatively young branch of mechanics, numerous mechanical

tests have been introduced to interpret fracture behaviour of adhesive joints [3]. Most of them

are based on symmetric joint geometry. Asymmetric joints were studied only a few times

mostly in terms of physical and mathematical modelling. These studies concerned mode I/II

[4,5,6]. Mode I/III mixity conditions were reported rarely [7]. None of the test methods were

normalized or standardized. Accordingly there was the space for developing new procedures.

Furthermore the results obtained using available methods are not reliable [8] and often do not

allow continuous measurements over long times [9]. The existing models usually ignore the

adhesive and treat bonded joints as two joined materials without an intermediate layer, which

allows errors especially when the test is performed for a relatively soft adhesive, at elevated

temperature, or in a changing environment. Finally, neither crack propagation speed nor

fracture energy can be precisely estimated using the existing methods.

The present thesis has been divided into four chapters:

Chapter 1 presents the background information about the interdisciplinary science of adhesion

and the state of art in this field.

Chapter 2 outlines the experimental techniques and materials employed.

Chapter 3 describes the novel tests with physical and mathematical analysis and reports the

experimental results as well as a discussion of these.

Chapter 4 considers modelling of the asymmetric joint using a Finite Element Method so as to

estimate stress state in the joint.

The closing chapters gives conclusions and suggests future work perspectives.

Michał K. Budzik

11

Chapter 1. BIBLIOGRAPHY

1.1. Historical perspective of adhesive bonding

Over all known joining methods, adhesive bonding seems to have the longest history. The

first discovered adhesive occurs in central Italy on spear stone flakes glued to wood with

birch-bark-tar around 200,000 B.C. The use of compound glues to haft stone spears into wood

dates back to round 70,000 B.C. Evidence for this has been found in Sibudu Cave, South

Africa and the compound glues used were made from plant gum and red ochre. The Tyrolean

Iceman had weapons fixed together with the aid of glue. 6000-year-old ceramics show

evidence of adhesives based upon animal glues made by rendering animal products such as

horse teeth [10]. Archaeologists have also uncovered statues from Babylonian temples that

have ivory eyeballs glued into eye sockets. This tar-like glue has been known for almost 6000

years. Studying burial sites of prehistoric tribes dating to about 4000 B.C. foodstuffs buried

with the deceased in broken pottery vessels that had been repaired with sticky resins from tree

sap have been found. Egyptian carvings dating back 3300 years depict the gluing of a thin

piece of veneer to what appears to be a plank of sycamore. Flour paste was used to bond

together papyrus fibres that were then used as fabrics. Beeswax, tree pitches and bitumen

were used as protective coatings and adhesives. Egg whites were used to bind manuscripts at

one time and wooden objects were bonded with glues made from fish, horn, and cheese. The

period of time between 1500-1000 B.C. gave further proof that glue had become a method of

assembly. Paintings and murals showed details of wood gluing operations. A casket removed

from the tomb of King Tutankhamen shows the use of glue in its construction. Another

notable name in history who may owe his notoriety, at least in part to adhesives, is Genghis

Khan. Around the year 1000 A.D., Genghis Khan overcame all attackers because of the

exceptional power and range of the weaponry his men carried. Bows were made from

laminated lemon wood and bullhorn bonded with an adhesive whose formulation has been

lost to antiquity. During the 18th century, the technology of animal and fish glues advanced.

In the 19th century, rubber and nitrocellulose based cements were introduced. By 1900, the

U.S. had a number of factories producing glue from the aforementioned bases. The Industrial

Revolution caused an explosion in technical breakthroughs which resulted in new materials

becoming available for use in formulating adhesives. The first plastic polymer to be

synthesized was cellulose nitrate, a thermoplastic material derived from the cellulose of wood.

Its first use was in the manufacture of billiard balls, which had been made of ivory. The era of

plastics began with the introduction of bakelite phenolic, a thermoset plastic, in 1910. Within

a year adhesives using phenolic resin were on the market. The 1920´s, 30´s and 40´s saw

many new plastics and rubbers produced synthetically, many out of urgent necessity

developed during World War II. Although adhesives have been known for a very long time,

most of the technology of adhesives has been developed in the last 100 years. Nowadays,

more than 2,300,000 tonnes of adhesives are produced and used in Europe each year and this

volume is on the increase. Adhesive manufacturers offer more than 250,000 different products

for the most diverse applications – and these products are customised for virtually every

purpose [11]. This is important, because each adhesive must satisfy different requirements

depending on the application. The size of the 2007 total world market for adhesives is 10.5

http://en.wikipedia.org/wiki/Sibudu_Cave

http://en.wikipedia.org/wiki/Ochre

http://en.wikipedia.org/wiki/%C3%96tzi_the_Iceman

http://en.wikipedia.org/wiki/%C3%96tzi_the_Iceman

http://en.wikipedia.org/wiki/Animal_glue


12

million metric tons. Its value was estimated at about $US 36 billion after allowing for various

currency fluctuations. The global market leaders are North America and West Europe regions

(Fig.1.1).

Fig.1.1. Global adhesive industry by region, 2007 share demand[11].

Global adhesive demand is still dominated by paper industries (Fig.1.2). The fastest

increasing submarkets are those of sealants and particularly structural adhesives.

Fig.1.2. World Adhesive (including sealants) demand in 2007[2].

Structural adhesives market is nowadays worth ca. $US 3 billion and is developing with 5.4%

year rate [2] with modern urethane and epoxy based adhesives are playing dominant role (see

Fig.1.3).

Michał K. Budzik

13

Fig.1.3. Structural adhesive market in 2002[12].

Structural bonding may offer many advantages over more traditional joining methods. A short

summary of the features of the common joining methods can be found in the Table 1.1.

Table 1.1. General comparison of joining methods[13].

WELDING BRAZING AND

SOLDERING

MECHANICAL

FASTENING

ADHESIVE

BONDING

JOINT FEATURES

PERMANENCE Permanent joints Usually

permanent

Threaded

fasteners permit

disassembly

Permanent joints

STRESS

DISTRIBUTION

Local stress

points in structure

Fairly good stress

distribution

Points of high

stress at fasteners

Good uniform

stress distribution

over joint area

APPEARANCE Usually

acceptable. Some

dressing

necessary for

smooth surfaces

Good Surface

discontinuities

sometimes

unacceptable

Joint almost

invisible

MATERIALS

JOINED

Generally limited

to similar material

groups

Some capability

of joining

dissimilar metals

Most forms and

combinations of

materials can be

fastened

Ideal for joining

dissimilar

materials

TEMPERATURE

RESISTANCE

Very high Limited by filler

metal

High Poor to elevated

temperature

MECHANICAL

RESISTANCE

Special provision

often necessary to

enhance fatigue

resistance

Good resistance

to vibration

Special provision

for fatigue

Excellent fatigue

properties.

Electrical

resistance

reduces corrosion


14

Since this thesis is mainly devoted to load carrying structures and the methodology of their

testing, only structural bonding applications will be here presented.

1.2. Adhesive bonding applications

The biggest advantage of adhesive bonding is the possibility to join many materials without

affecting their properties. This allows bonding to be used in almost any application. The

industrial sectors which employs structural adhesive bonding include aeronautical, aerospace,

automotive, marine and off shore, construction, medical and sports.

Aeronautical and aerospace applications

Adhesives and aircraft have a long and interesting joint history. Even though flying vehicles

have progressed from glorified kites to commercial jet transports, supersonic missiles and

space vehicles, adhesively bonded structure has been crucial to virtually every one. Both

primary structure, which carries primary flight loads and failure of which could result in loss

of vehicle, and secondary structure are bonded. The military has historically led the way in the

development and application of adhesive bonding on aircraft. The earliest structural adhesive

applications were made during the First World War for bonding the wooden frames aircraft

(of biplanes), were strength was adequate but, by today’s standards, moisture resistance was

poor. This practice continues today, primarily with bombers, fighter and attack aircraft where

weight is a critical consideration, but also with support craft such as reconnaissance aircraft

and freighters. Much more so than the commercial world, military aviation is concerned with

aircraft performance. Because of this continued emphasis on adhesive bonding technology

development over the years, the airframes of modem front-line aircraft such as the B-2

bomber, the F-117, F-22, F-35, or Swedish JAS Grippen (Fig.1.4) fighters are largely

structurally bonded advanced composites [14].

Fig.1.4. JAS Grippen bonded primary elements[15].

Bonding

Bonding

Bonding

Bonding

Bonding

Michał K. Budzik

15

In addition, the use of adhesives prevents corrosion processes when different materials have

to be combined. Finally, due to uniform, plane load transfer through the adhesive, layer notch

sensitivity is reduced. The use of bonding also provides high potential for variation in styling

due to the possibility of combining different materials. In modern military and civil aircrafts,

as much as 50% of the airframe may be carbon fibre reinforced polymers (CFRP), with

adhesives being used for primary structural bonding [14].

Moreover, the average age of military and civilian aircraft is growing older at a fast pace. As

aircraft become older and accumulate more flight hours, the tendency they have to develop

corrosion problems, fatigue cracking, overload cracking etc. increases. When today’s aircraft

reach the end of their service life, fatigue cracks are found to have developed along rivet holes

and other highly stressed regions of the aircraft [16]. In order to extend the life of these

aircraft, repairs have been made to arrest these cracks [17]. Composite doublers or repair

patches provide an innovative repair technique, which can enhance the way aircraft are

maintained.

The very high cost of boosting spacecraft structure into orbit makes it cost-effective to spend

significant resources to save weight, thus is driving force behind this interest in bonding.

Exotic materials and processes that are too expensive for use on commercial aircraft are

commonplace in the space vehicle industry. Typical requirements for adhesively bonded

structure for space applications vary widely and differ substantially from those for

atmospheric vehicles. Because of widespread use of cryogenic rocket fuels, adhesives near

tank structure must maintain adequate properties at very low temperatures. At the other

extreme, adhesives have been used to bond ablative or insulative heat shields to the bottom of

re-entry vehicles since the advent of manned space flight [19]. Elevated temperature cure

epoxy film and paste adhesives supplanted the urethanes are standard today in areas of low to

moderately high temperature exposure because of their ease of fabrication and high strength.

Other adhesives such as silicone elastomers, cyanoacrylates and room-temperature epoxies

are used to bond many non-structural joints.

Automotive applications

Adhesives have been employed in the automotive industry since its beginnings, with the use

of natural resins to bond wood and fabric bodies [20]. Recent developments in synthetic resin

technology have resulted in a very wide range of adhesive materials available to the design

engineer. The drivers for the automotive industry are lightweight structures, use of mixed

materials, long term performance, crash performance and also styling and design. Since the

adhesive can improve the stiffness and strength of a joint the weight can be reduced. Adhesive

bonding can furthermore allow the realisation of combining different structural materials such

as FRP, metals, glasses and ceramics. It is quite clear that many parts of different materials

have to be brought together through bonding, sometimes together with rivets. In many

situations this is preferred to welding. Similar to aerospace bonding, galvanic processes can

be delayed or prevented when adhesives are used, in particular when different materials are

joined together. Improvement of crash performance is possible by the use of substrates and


16

adhesives with a high potential of energy absorption. Finally, diversity of styling and design

are possible due the possibility of combining different materials and components and joining

them together by bonding. Adhesives for automotive and industrial bonding are modified

acrylics/methacrylates which provide high strength and elongation properties and also bond to

thermoplastics. Other adhesives are polyurethanes, which are tough and have a high abrasion

resistance and good adhesion at low temperatures. Silicones are also used for bonding to

glass, plastics and other materials.

Marine and off-shore applications

Casein and then formaldehyde resin compositions have been used as adhesives and gap fillers

in wooden boat construction for many years [20]. Many GFRP-hulled boats, both naval and

civilian, now relay significantly on resins for laminating, stiffening, the fabrication of

sandwich panels, and for bonding attachments. Traditionally the shipbuilding industry uses

welding as the primary process for joining the different structural parts in a ship. It is well

known however that this process results in induced stresses during the fabrication stage which

in turn lead to distortion in the shape of structural components and indeed, the ship itself.

Considerable effort has thus to be expended to mitigate these weld-induced distortions leading

to increased production costs. One additional problem, in the case of aluminium, is the

significant reduction in the fatigue load capacity in welded structures [21]. As a consequence,

either the structural topology has to be designed to cope with increased stress levels or the

scantlings of the structure have to be enhanced. In either case, there is an increase in the

weight of the structure. Since structural weight needs to be minimised, especially in high

speed, high performance ships, there is a need to investigate alternative joining techniques for

aluminium structures; adhesive bonding is one of them [22,23]. Adhesive bonding offers the

opportunity to replace welding of steel structures, to reduce distortion, effectively eliminate

residual stress and to improve fatigue performance when compared to welded connections.

Avoidance of hot-work leads to safer construction practices in hazardous environments.

Adhesive bonding of composites provides well-distributed loading and maximises the

utilisation of the adherent materials. Typical adhesives in the marine industry are polyesters

which are less expensive than epoxy and are widely used in other industrial applications.

Polyester, however, is chemically weaker than epoxies and experiences a high degree of

shrinkage. Vinyl ester, which provides higher strength, modulus of elasticity and elongation

than polyesters is still less expensive than epoxy are often preferable to polyesters. For

bonding to metallic parts epoxies are typically used. In addition modern composites materials

are also very attractive for marine industries. Whole composite body boats are already in use,

like luxury CRN 128 Sima [24] boat full FRP body boat joined with adhesive bonding.

Railway applications

In rail vehicle manufacture, new components such as those made from glass-fibre reinforced

plastic (GFRP) have resulted in enormous weight reduction and have transformed the

production process. For example ADtranz (part of Bombardier Transportation company)

Michał K. Budzik

17

regional trains are manufactured using a frame structure consisting of tensile and compression

struts in a triangular arrangement. This is the lightest design for bearing structures. Due to the

frame structure, it is not necessary to weld on metal sheets to take up the shear stresses. There

are only tensile and compressive forces in the struts. In order to enclose the frame, large outer

skin elements are bonded to the supporting metal structure using moisture curing 1-C

polyurethane adhesives [25]. No complex straightening and filling work is required, as is the

case when welding is used to attach the metallic outer skin elements. The GFRP elements that

are used for the outer skin have a sandwich structure and hence provide good thermal

insulation and have very good acoustic properties. As no heat distortion occurs, contrary to

when welding, the outer skin gives the rail vehicle a ready painted/lacquered, level, smooth

and flush outer surface with no additional work having to be undertaken. Joining a metallic

framework structure with components made of fibre reinforced composite plastic can only be

economically and reliably achieved using bonding technology. In order to compensate the

different linear deformations of the structure and outer skin when they are exposed to heat, a

highly elastic, thick film of adhesive is used. The resulting bonds have high strengths, even

when subjected to repeated temperature fluctuations in the range between -40°C and +80°C

and under impact-like stress. They also have very good resistance to aging, even in moist

environments. The thickness of the bonded joint varies between 4 and 18 mm. This depends

on the size of the components, which can be up to 8.5 metres long and therefore subject the

bonded joint to very high shearing deformation. Another advantage of this type of structure is

the high damping and the positive effect on the dynamic operating characteristics and ride

comfort. Finally bonded trains are about 25% lighter than comparable conventional trains, and

they also have improved ride characteristics, lower production costs and reduced energy

requirements for operation.

Construction applications

The adhesives are used in construction industry in repair and strengthening of existing

structures and new built structures.

a) Repair and strengthening of existing structures using bonding techniques is mainly

associated with concrete structures. During the 1950’s and 1960’s an enormous amount of

new constructions were built and, as these structures age, many faults have become evident.

The repair substrate may be ordinary concrete or polymer concrete, with or without

reinforcement. If increased structural capacity is needed then external plate bonding can be an

alternative. During the 1970’s and up to the end of the 1990’s, steel plate bonding was not

unusual, however in the last decade, the use of advanced composites for external

strengthening has become quite common (see Fig.1.5) [26,27]. Also a great number of models

for debonding have been presented [28-32].

b) In new-built structures the adhesives are often used for filling voids or gaps and to fasten

secondary, non-load carrying elements. Adhesives are also used to fasten bridge bearing and

expansion joint nosing. On steel decks, skid resistant surfacing materials in the form of small

gravel-filled epoxy or polyester resins are often used. There are also examples where epoxy


18

resin systems have been used to bond precast concrete slab units directly to a steel girder

surface for a steel-concrete composite bridge (German Bonded Bridge, 1979). However, with

the increased use of new-built FRP structures requiring bonding for building and civil

purposes the situation may change. The example of a FRP structures is presented in Fig.1.6.

The Zaragoza Bridge Pavilion have all structural joints made using epoxy adhesive.

Fig.1.5. Bridge repaired and strengthened with CFRP patch (left).

Fig.1.6. Zaragoza Bridge Pavilion. Bridge build totally from cement reinforced with GFRP

(right).

Medical applications

The use of the adhesives in medical applications was for a long time restricted to the

manufacture of self-adhesive bandages (plasters, self-adhesive strips of fabric, etc.).

Adhesives are today employed in diverse areas of medicine, replacing traditional methods

with friendlier processes. For example stitches can be avoided by applying special

cyanoacrylate adhesives to quickly close skin wounds. An advantage here is that the whole

wound can be covered, so largely suppressing secondary bleeding and the risk of infection.

The use of methacrylate based adhesives has been a great success in orthopaedics for

anchoring hip socket implants to the bone. Also hip and knee implants anchored using

adhesive are in 90% of cases functional for about 15 years [25] (Fig.1.7).

Fig.1.7. One of the examples of structural bonding applications in medicine[25].

Michał K. Budzik

19

In dentistry, fillings based on UV curing acrylates have largely replaced traditional filling

materials such as amalgam. The products have a long open time (the period during which they

can be used after mixing) and bond in just a minute or so when exposed to UV light. Also

based on ceramics adhesives are used to repair broken tooth etc. (Fig.1.8) [33].

Fig.1.8. Structural adhesive application in dentistry.

Other developing markets

Sport: bonded bicycle frames, kayaks, rowing boats, rows, pole vault poles, golf clubs,

tennis rockets etc.

Nuclear energy application: radioactive waste tanks and containers, strengthening and

radiation resistance improvement of cement tanks for radioactive water

Oil and gas industry: oil tanks reconstructions, corrosion resistant barriers, repair of

pipelines, pipeline strengthening

Bonding of silicon in photovoltaic panels

1.3. Structural adhesives

Structural adhesives are based upon resins composition that polymerize to give high-modulus,

high-strength adhesive so that a load-bearing joint is formed [34]. The first structural adhesive

successfully applied was in the aircraft industry for bonding aluminium to wood. It was

polyvinyl formal composition with a phenoloformaldehyde resin. There is rarely a situation in

which a single adhesive is unique for a task. This is because adhesive are versatile and

selection does not usually, depend upon one single property, but rather balance of several

properties which more than one adhesive may be able to meet. Usually the first decision

regarding adhesive bonding is to choose the basic chemical type of adhesive, nowadays for

structural applications we can choose from:

Acrylic adhesives

Epoxy adhesives

Bismaleimide adhesives

Polyimide adhesives


20

Polyurethane adhesives

Phenolic adhesives

Silicone adhesives

Acrylic adhesives

Acrylic adhesives were developed in late 1960’s in Germany as an outgrowth of

poly(methylmethacrylate) chemistry [35]. Acrylic adhesives are nowadays large class of

specifically designed products made to meet the needs of industry in the assembly of a wide

variety of components. These adhesives are solvent-free reactive engineering adhesives and

include cyanoacrylic, anaerobic and modified acrylic adhesives [34]. The basic acrylic

monomers or oligomers contain unsaturated double bonds (vinyl groups), and consequently

cure by addition polymerization involving free-radical reaction. Free-radical producing

compounds such as peroxides, peracetic acids, and sulfones are added to acrylic resins to

initiate polymerization. Free-radical polymerization of acrylics may also be induced by UV or

visible light. These UV-curing adhesives, most of which are based on acrylic or modified

acrylic resins are of increasing commercial importance today for the rapid bonding of

electronic devices, fiber optics etc. Reactive methacrylate monomers include

methylmethacrylate, diethyleneglycol dimethacrylate and butyl methacrylate. The

polymerization reaction for the basic monomer is depicted in Fig.1.9.

Fig.1.9. Basic acrylic reaction[36].

Cyanoacrylates are one-part, highly polar thermoplastic polymers. The resin monomers

(Fig.1.10) cure in seconds when in contact with a weak base such as the moisture that is

present on most of the surfaces. Many cyanoacrylate-adhesive formulations are commercially

available, but not widely used in electronics assembly because of their poor resistance to

solvents and moisture at elevated temperatures (>70°C). Cyanoacrylates have relatively low

impact and peel strengths and may be brittle unless toughened by the addition of elastomeric

resins. Currently available liquid acrylate and methacrylate adhesives can be seen as logical

developments of the anaerobic machinery adhesives against corrosion as well as the

considerable economic advantages gained by not having to maintain very close tolerances on

the machined parts.

Michał K. Budzik

21

Fig.1.10. Cyanoacrylate monomers structure, with R is usually alkyl group[35].

Although these adhesives are still by a margin more expensive (10 to 100 times when

compared to older bonding technologies) they achieve enormous commercial success thanks

to specific benefits they offer. Major features of acrylic adhesives include [36]:

Adhesion to a variety of substrates

Water resistance

Durability

Flexibility when modified

Good low temperature properties

Excellent optical properties

Low toxicity.

Epoxy adhesives

Epoxy or epoxide resins are a group of reactive compounds that are characterized by the

presence of the epoxy group, which in the simplest epoxy compound have structure of

ethylene oxide, oxirane group (Fig.1.11):

Fig.1.11. Ethylene oxide (oxirane).

They are capable to react with suitable hardeners to form cross-linked matrices of great

strength and with excellent adhesion to a wide range of substrates. This make them ideally

suited to adhesive applications in which high strength under adverse condition is prerequisite.

Work on epoxy resins started in the mid 1920’s when in 1926 Eisleb noted the reaction of

epichlorohydrin with secondary amines and subsequent dehyrogenation with caustic [37]. The

first commercially useful epoxy resins appeared during World War II, when in 1939 Greenlee

explored the epichlorohydrin-bisphenol A synthesis route for the production of new resins

without caustic-sensitive ester linkages. Today this resins, in a range of molecular weights,

constitute the majority of all epoxy resins used. By contrast, hardeners come in a variety of

shapes and sizes. Epichlorohydrin is capable of reacting with hydroxyl (-OH) groups with the


22

elimination of hydrochloric acid. The most widely used epoxy resins are the family of

products produced by the reaction between epichlorohydrine and bisphenol A, to give

diglycidylethere of bisphenol A (DGEBA), shown in Fig.1.12. Epoxy resins react with

hardeners in stoichiometric quantities. Knowledge of the number of reactive sites is needed in

order to calculate correct ratios. For the resin this is given by the epoxide equivalent weight

(EEW), which is the quantity of resin required to yield one epoxy group. For a DGEBA type

in which n=0, the molecular weight is 340. Since we have two epoxy group per molecule,

therefore, EEW=170. Typically, pure epoxy resins available for adhesive applications are in

the range 180<EEW<310 (while for paints EEW=2000 and more!). The viscosity of epoxy

resin is primarily dependent on molecular weight. Even at low molecular weight, viscosity is

typical in excess of 6000cP, while at 190 EEW is usually around 12000cP. Stoichiometric

ratios can be calculated similarly for hardeners, from which amines are of the major interest.

Example of amine curing mechanism of epoxy is illustrated in Fig.1.13.

Fig.1.12. Bisphenol A-epichlorohydrine reaction[38].

Fig.1.13. Amine – curing mechanism of epoxies: a) initial step, formation of a secondary

amine and more hydroxyl groups; b) formation of tertiary amine; c) continued crosslinking

through reaction of hydroxyl groups[38].

Michał K. Budzik

23

Epoxy adhesives offer[36]:

Good adhesion to many surfaces

A range of mechanical properties, depending on formulation and curing

A wide range of cure characteristics (from RT to 180oC)

Low shrinkage

No by-products evolved during curing

Range of available adhesive forms (film, paste one or two component).

The epoxy adhesive are the most extensively used structural adhesives, particularly in the

transport industry. In Table 1.2 fracture resistance of the epoxy and toughened epoxy resins is

compared with different material. It has to be noted that modified epoxies (e.g. with rubber)

are at least 10 time stronger than pure epoxy resins.

Table 1.2. Values of measured Critical Fracture Energies[39].

Material Critical Fracture Energy, GIc

(J m-2

)

Inorganic glasses <10

Unmodified epoxies 70 – 175

PMMA 350 – 800

Modified epoxies 1750 – 3500

Aluminium/nylon/epoxy adhesive 7000 – 8800

Metals >17000

Bis-maleimide adhesives

In the narrow sense, bis-maleimide resin means the thermosetting resin composed of the bis-

maleimide of methylene dianiline (BMI, bis(4-maleimidopheny1)-methane) and methylene

dianiline (MDA, bis(4-aminopheny1)methane) (Fig.1.14).

Fig.1.14. The chemical structure of BMI and MDA[40].


24

Because of the addition mechanism, the resin is cured without elimination, which is a

characteristic of this resin. Bis-maleimide resin is used as a thermally stable matrix up to

204°C in which typical epoxy resins may not normally be used. However, in spite of having

an imide structure, bis-maleimides are classified as being moderately thermally stable resins.

The aliphatic structure of the resin is not stable for long periods above 232°C. If a highly

aromatic thermally stable thermosetting resin is necessary, acetylene end-capped aromatic

imide-based oligomers should be used. We can conclude that bis-maleimide adhesives offer

[36]:

High temperature capability

Excellent electrical properties

No volatiles evolved during cure, which simplifies processing and reduces porosity

Poor peel resistance, owing to their stiffness. Reinforcing required.

Polyimide adhesives

Polyimides are formed from polyamic acid or polyamic ester precursors by heating to

temperatures as high as 400°C. Polyimide precursors are synthesized by reacting equimolar

amounts of aromatic diamines with aromatic dianhydrides forming polyamic acids or

polyamic esters as in Fig.1.15a. The prepolymer from pyromellitic dianydride (PMDA) and

4.4’-oxydianiline (ODA) has been the most widely studied and used [41]. The precursors are

available as solvent solutions (generally, N-methyl-2-pyrrolidone) that can then be formulated

as adhesives, coatings, or performs by adding fillers and other additives. Curing is not the

traditional crosslinking or chain propagation using curing agents, but occurs by heating to

eliminate water and close the imide rings along the chain forming the very stable polyimide

structure (Fig.1.15b).

Fig.1.15. a) Preparation of polyamide precursor, b) curing of polyamides by imidization[43].

Michał K. Budzik

25

The process of ring closure is known as imidization and requires step curing, which, for

silver-filled paste adhesives, is typically 30 minutes at 150°C, followed by 30 minutes at

275°C [42]. In some cases, however, step cures up to 400°C are necessary to achieve

complete imidization, an example of which is: 15 minutes at 135°C, followed by 30 minutes

at 300°C, and finally 10 minutes at 400°C. The initial temperature exposure of 135°C–150°C

assures the removal of the N-methyl- 2-pyrrolidone (NMP), a solvent that is present in almost

all polyimide precursor formulations.

Main features of polyimide adhesives are include [36]:

High-temperature capability (up to 300oC)

Excellent electrical properties, e.g. radome applications

Evolution of volatile materials during cure so extraction or high processing are

needed.

Polyurethane adhesives

The development of polyurethane adhesives can be traced back to pioneering efforts of Otto

Bayer and co-workers. Bayer extended the chemistry of polyurethanes (initiated in 1937) into

the realm of adhesives by combining polyester polyols with di- and polyisocyanates (about

1940) [44]. He found that these products made excellent adhesive for bonding elastomers to

fibers and metals. Early commercial applications included life rafts, vests, airplanes, tires and

tanks. Being thermoplastic, polyurethanes are also easier to rework than epoxies.

Polyurethanes are distinguished from other polymer types in containing the repeating urethane

group throughout its structure (Fig.1.16).

Fig.1.16. Urethane group.

Typical polyurethane adhesive may contain, in addition to the urethane linkages, aliphatic and

aromatic hydrocarbons, esters, ethers, amides, urea, and allophanate groups. Polyurethanes

are formed by the addition reaction of diisocyanates or polyisocyanates with polyols through a

step-growth polymerization mechanism (Fig1.17). Accordingly, polyurethanes may be either

thermoplastic or thermoset, depending on the functionality of the monomers. Urethane

adhesives are classified as one-component or two-component adhesives. Each category

includes several different types of adhesives. Urethane structural adhesive are two-

component. These adhesives may be rigid plastics similar in modulus to standard epoxy

adhesives, with glass transition temperatures of the cured adhesive being approximately 60°C.

Two-component urethane adhesives are used to bond sheet molding compound (SMC) panels

for automotive OEM (original equipment manufacturers) and aftermarket applications. Two-

part urethanes are used as laminating adhesives in the RV (recreational vehicle) industry.


26

Fig.1.17. Basic polyurethane polymerization reaction[45].

One of the polyurethane features is good adhesion to the numerous substrates, this is due to

the following reasons:

Effective wetting of surfaces [46]

They readily form hydrogen bonds to the substrate

Their small molecular size allows them to permeate porous substrates

They form covalent bond with surfaces that have active hydrogen (Fig.1.18).

Fig.1.18. Typical mechanism for a urethane adhesive bonding covalently to a polar

surface[45].

Main polyurethane adhesive features are:

Good adhesion to variety of substrates

Good chemical resistance to solvents

Tough, flexible bonds

Available in many forms: liquids, dispersions, films, powders etc.

PREPOLYMER

H H H

NCO NCO NCO

PREPOLYMER

NH NH NH

O=C O=C O=C

Michał K. Budzik

27

Phenolic adhesives

Phenolic resins were the first totally synthetic plastics invented. They history dates back to

1853 with Gerhardt’s observations of insoluble resin formation while dehydrating sodium

salicylate [47]. The reasons for the long-term, commercial robustness of phenolic technology

include low cost, versatility, heat and flame resistance, durability, strength and stiffness, low

toxicity, and ease of processing. Adolph Baeyer is credited with the first recognition of the

general nature of the reaction between phenols and aldehydes in 1872 [47-50]. Prior to 1890,

formaldehyde was not commercially available [47]. Thus the first phenol-formaldehyde resins

were made using formaldehyde equivalents such as methylene diacetate or methylal [1,20].

The first true phenol-formaldehyde resin was made by Kleeberg at the direction of Emil

Fisher in 1891 [47,51]. The condensation polymerization reaction is shown in Fig.1.19.

Fig.1.19. Polymerization of phenol with excess of formaldehyde[52].

Phenolic resins are adaptable to many applications. The list is very long, however, the major

uses are wood binders, glass insulation binders, moulding compounds, laminates, foundry

binders, coatings, friction linings, abrasives, and oil well propants [53-58]. They have found

their way into a number of new, high technology uses such as rocket motor wear parts,

military armour, sports equipment, photoresists for computer chip manufacture, epoxy

crosslinkers, circuit board binders and microchip module packaging. There has been a

renewal of interest in the use of phenolics for aircraft construction because of their excellent

flame resistance and low smoke generating properties [59]. The formation of a phenolic resin

is often formally separated into two steps, though it probably should be three. In the three-step

model, the first step is activation of the phenol or aldehyde. The second step is methylolation,

and the third is condensation or chain extension. In addition to the clarity provided by the

formalism, these steps are also generally separated in practice to provide maximum control of

exothermic behaviour, with the strategy being to separate the exotherm from each step from

that of the others as much as possible. Main features of phenolic adhesives are:

High temperature curing (often treated as advantage – no curing in ambient

conditions)

Very brittle, requires compounded with other materials (polychloropropylen,

polyvinyl butryl, epoxides etc.)


28

High mechanic strength

Good solvent and water resistance

High thermal stability

Flame retardant (often used as a compound to epoxides, rubbers etc.).

Silicone adhesives

Silicones are a unique class of polymers due to their semi-organic molecular structure. Instead

of the normal carbon-to-carbon backbone structure of most polymers, silicones have a silicon-

to-oxygen structure that gives them advantages of very high thermal stabilities (up to 300°C,

in some cases), flexibility at subzero temperatures (-80°C), and excellent electrical properties

under both extreme conditions. The -Si-O-Si-O- backbone of silicones is referred to as

siloxane. The silicon atoms may be linked to a wide variety of aliphatic or aromatic groups, as

shown in Fig.1.20, where the radical R groups are commonly methyl (-CH3), phenyl (C6H5-),

allyl (-CH2-CH=CH2) or vinyl (-CH=CH2).

Fig.1.20. General structure for a linear silicon polymer[43].

A silicone adhesive is known to be among the most durable and flexible. There are not a lot of

heavy-duty adhesives that can serve in the same capacity as a silicone adhesive, and this is

because they come in a range of styles and are capable of joining materials like plastic, metal

and glass. Accordingly, silicone adhesives are water and high temperature resistant.

Interestingly, a silicone adhesive will also retain flexibility after curing, making it applicable

in ways other adhesives are not. This type of silicone adhesive appears quite frequently in the

building industry where it can be used to join materials that must face exposure to glaring

sunlight, freezing temperatures, water, wind and other issues that would cause traditional

adhesives to fail.

Main silicon adhesives features include:

Wide variety of possible viscosities

Good flexibility

Very good resistance to high and low temperature (-120oC – ~400

oC)

Resistance to UV and IR radiation

Resistance to oxidation.

Michał K. Budzik

29

Properties of common used structural are summarized in the Table 1.3. The variety of

properties, meting different requirements can be easily noted.

Table 1.3. Common properties of structural adhesives.

Adhesive

/Properties

CTE*

(μm/moC)

Tension

strength

(MPa)

Application

Temperature

(oC)

Young

modulus

(GPa)

Density

(kg/m3)

Acrylic 54-150 19-90 >115 0.9-4.5 0.98-1.22

Cyanoacrylate 2.5-50 >100 1.05-1.11

Epoxy 20-60 28-75 >300 2.5-5.5 1-2

Bis – Maleimiade 15-100 12 >500

Phenolic 30-45 35-63 166-205 5.5-11 <1.5

Silicone 54-300 1-30 >370 0.0006-

0.005

0.82-2.82

Urethane 1-510 0.9-29 >130 0.004-0.8 0.89-3.2

Polyamid <100 <200 <200 <10 <1.4

* Coefficient of Thermal Expansion

1.4. Theories of adhesion

An adhesive must do two things when applied to surfaces which are to be bonded. It must first

wet the surface, as manifested by spreading and making a contact angle approaching zero.

Secondly, it must harden to give a cohesively strong solid. When contact is intimated, van der

Waals forces are formed, but other intermolecular forces, such as chemical bonds, may be

formed at the time of contact or during the hardening process. If the adhesive can penetrate

the substrate before hardening then mechanical interlocking will contribute to the strength of

the joint. Molecular interdiffusion will occur when adhesive molecules would intertwine those

of substrate. Other approaches are also possible. To understand fully the basics of adhesive

bonding and to be able to conclude properly from any experiments or structure behaviour

when bonding joints appears, one must understand how adhesion is created. Of major concern

are:

Mechanical interlocking theory

Electronic theory

Weak Boundary Layer (WBL) theory

Physical adsorption theory

Diffusion theory

Chemical bonding theory.

Mechanical interlocking

The mechanical interlocking theory was first proposed by MacBain and Hopkins [60]. The

theory assumes mechanical keying, or interlocking of the adhesives into the cavities, pores


30

and asperities of the solid surface to be the major factor in determining adhesive strength.

Borroff and Wake [61] presented one of the most consistent examples presenting validity of

this theory. They measured adhesion between rubber and textile fabrics, clearly proving that

penetration of the protruding fibres into rubber was determining parameter in this specific

joint. However the possibility of producing good adhesion between smooth, polished surfaces

leads to the remark that mechanical interlocking theory cannot be used as the universal. To

overcome this difficulty, primarily by Gent and Schultz [62], Wake [63] has proposed that the

effects of both mechanical and thermodynamic interfacial interactions could be taken into

account, as a multiplying factors to estimate proper adhesion strength, G:

(1.1)

where:

α – constant

MC – mechanical interlocking component

IC – interfacial interactions component.

Therefore, due to interlocking theory, high strength of adhesive joint is achieved by increasing

both surface morphology (MC) and physicochemical surface properties of substrate and

adhesive (see Table 1.4). Work done by Packham [64] emphasized the dominant role of the

mechanical interlocking mechanism on adhesion strength, although in another study Wake

deduced that IC component may become greater than MC [63].

Table 1.4. Surface topography influence on peel energy[64].

Surface topography of copper foil Peel energy

Description Diagrammatic representation kJ/m2

Flat

Flat + 0.3 μm dendrites

3 μm high angle pyramids

Nickel foil with club-headed

modular structures

0.66

0.7

1

2.3

Another important aspect of mechanical adhesion theory is surface roughness. When

roughness is increased the actual surface area is growing by developing. In the literature we

can find a study by Wenzel on this subject [65], which defined simple roughness factor, r in

the form:

Michał K. Budzik

31

(1.2)

where:

A - true surface area

A0 - real surface area.

Thus, for a perfect flat surface r=1, when consisting of hemispheres r=2 etc. This simple

factor can define work of adhesion, Wa’ for rough surface:

(1.3)

where γ is surface free energy in the boundary between s – solid, v – vapour and l – liquid

phases.

Electronic theory

The electronic theory was proposed by Deryaguin and co-workers [66]. Authors have

suggested that an electron transfer mechanism between the substrate and the adhesive, having

different electronic band structures, can occur to equalize Fermi levels. This can lead to

double electronic layer formation at the interface, which may contribute to the adhesive

strength. Therefore, the adhesive-substrate junction can be analyzed as a capacitor. Interfacial

separation of the system leads to increasing potential difference until discharge occurs. The

separation energy, Ge is thus related to the discharge potential, Ve:

(1.4)

h – discharge distance

εd – dielectric consant

One of the interesting aspects of these theory is that it allows adhesion variation with gas, and

pressure of the gas in which the measurement is performed. In fact, Deryaguin et al. have

measured, by means of peel test significant variation in separation energy when measured in

argon and air environment with different pressure, which stays in very good agreement with

theoretical predictions. However several other analysis [e.g. 63] have not confirmed these

results, leading to the conclusion that Deryaguin was rather causal.

Weak Boundary Layer (WBL) and interphase

It is now well known that the adhesive/adherend interphase can have different properties from

the bulk adhesive and adherend. The first approach to this problem is due to Bikerman [67],

who stated that the cohesive strength of a weak boundary layer (WBL) can always be

considered as the main factor in determining the level of adhesion, even when the failure


32

appears to be interfacial. According to this assumption, adhesion energy, Ea, is always equal

to cohesive energy, Gc (WBL) of weaker interfacial layer. This theory is based on statistics,

proving that the fracture should never propagate only along adhesive/substrate interface for

pure statistical reasons and that cohesive failure near weaker interface is more favourable.

Formation of WBL is caused by many physical, physicochemical and chemical phenomena,

for example [68]:

The orientation of the chemical group or the overconcentration of chain ends to

minimize the free energy of the interface

Migration toward the interface of additives or low molecular weight fraction

The growth of transcrystalline structure, for example, when substrate acts as a

nucleating agent

Formation of pseudoglassy zone resulting from a reduction in chain mobility through

strong interactions with the substrate

Modification of thermodynamics and/or kinetics of the polymerization or cross-

linking reaction at the interface through preferential adsorption of species or catalytic

effects.

Physical adsorption theory

Physical adsorption theory [52] involves long range bonding with van der Waals forces but

also thermodynamic-spreading theory.

a) van der Waals forces

van der Waals forces, which occurs between all atoms and molecules when they are close to

each other, are the weakest of all intermolecular forces, but their strengths are adequate to

account for the strength of the adhesive joint. Physical adsorption involves van der Waals

forces across the interface. These involve attractions between permanent dipoles and induced

dipoles (Fig.1.21), and are of three types.

Epp is the potential energy, in a vacuum, of a pair of permanent dipoles separated by

distance r at their centres and is given by equation:

(1.5)

r – distance between dipole pair

μ1, μ2 – dipole moments

ε0 – permittivity of the vacuum

k – Boltzmann constant

T – absolute temperature.

Michał K. Budzik

33

Fig.1.21. van der Waals interactions[69].

If a non-polar molecule is close to a dipole, then the latter will induce a dipole (μi) in

the former. The induced-dipole moment is given by:

(1.6)

α – polarizability of the non-polar molecule

E – electric field

The potential energy of such interaction can be given by:

(1.7)

Instantaneous dipoles exist in non-polar molecules because of the fluctuating

distribution of electrons. These lead to attractive forces between molecules, without

which non-polar gases such as helium and argon would not be able to liquefy. The

potential energy of a pair of molecules, Eii is given by equation:

(1.8)

where:

α1, α2 – molecule polarizabilities

I1, I2 – ionization potentials.


34

b) Thermodynamic (spreading) theory [68]

Thermodynamic theory in its major aspect is limited to solid-liquid systems. Adhesives must

effectively wet and completely contact the surfaces to assure a strong bond. The ability to wet

a surface, wettability, is related to the ease with which a liquid spreads on a solid surface and

is essential in maximizing coverage and minimizing voids in the bondline [70]. Wettability is

measured by the equilibrium contact angle, θ, which is defined by balancing surface-tension

forces in Young’s equation.

(1.9)

where:

γsv – surface energy at solid – vapour interface

γsl – surface energy at solid – liquid interface

γlv – surface energy at liquid - vapour interface.

The measurement of contact angle (Fig.1.22) is a means of investigating adhesion by physical

adsorption. These are the weakest forces contributing to adhesive bonds, but are quite

sufficient to make strong joints.

Fig.1.22. Wettability of adhesives and contact angle.

The thermodynamic work of adhesion, Wa, is by definition the free energy change per unit

area required to separate to infinity two surfaces initially in contact surfaces, which results in

creating new surfaces. Work of adhesion can be related to a solid and a liquid phase forming

an interface across which secondary forces are acting. Free energy is given by Dupré

equation. The reversible work of adhesion in an inert medium may be expressed by:

(1.10)

i.e.

(1.11)

We can easily combine the Young and Dupré equations, to yield Young-Dupré equation in the

form:

(1.12)

Michał K. Budzik

35

The spreading coefficient, called S [71,72] or sometimes (although badly) work of adhesion

(Wa) in equation above, shows that good wetting (θ<90o) is realized when Wa is greater than 0.

Good wetting requires also using liquid with high surface tension. As Wa decreases, θ

increases from 0o to 180

o and conditions go from partial wetting to non-wetting [73]. Based

on this equation, conditions of wetting versus non-wetting are as presented in the Table 1.5

[70], and illustrated schematically in Fig.1.23.

Fig.1.23. Schematic presentation of good and bad wetting.

Table 1.5. Wetting conditions.

Complete wetting, liquid spreads spontaneously, high surface attraction

Partial wetting

Non-wetting: liquid beads up

Diffusion theory

The diffusion theory of bonding is based on the assumption that the adhesion strength of

polymers themselves (autocohesion) or to each other is due to mutual diffusion

(interdiffusion) of macromolecules across the interface, thus creating an interphase (Fig.1.24).

Fig.1.24. Adhesive – substrate interdiffusion[75].

Such mechanism was studied in details by the Russian Voyutskii [74]. The author implied

that the macromolecular chains or chain segments are sufficiently mobile and mutually

soluble. This is of great importance for many adhesion problems, such as healing and welding

process. If interdiffusion occurs the joint strength should depend on different factors, such as

contact time, temperature, nature and molecular weight of polymers etc. The reason for

diffusion is thermodynamic potential difference of molecules of both substrates. Vasenin [76]

has developed, from Fick's first law, a quantitative model of diffusion model that correlates

the amount of material, w diffusing in given x direction across a plane of unit area to the

concentration gradient, ∂c/ ∂x and the time, t:


36

(1.13)

with:

Df – diffusion coefficient.

To estimate the depth of penetration of the molecules that interdiffused into the junction

region during the time of contact, tc, Vasenin assumed that the variation of the diffusion

coefficient is constant and of form Ddtc-β

, therefore we can deduced the depth of penetration,

lp from:

(1.14)

where:

k - constant

Dd – constant characterizing the mobility of polymer chains

β – constant of order 0.5.

Finally, Vasenin assumed that the measured peel energy, G was proportional to both, the

depth penetration and the number of chains crossing the interface between the adhesive and

the substrate so thus:

(1.15)

where:

K – constant that depends on molecular characteristic of the polymer in contact.

N - Avogadro number

ρ - density

M – molecular weight of polymer.

Chemical bonding theory

The chemical bonding theory of adhesion involves the formation of covalent, ionic or

hydrogen bonds or Lewis acid-base interactions across the interface.

Covalent bonds: There is some evidence that covalent bonds are formed with silane

coupling agents [77], as well as adhesive containing isocyanate groups react with

active hydrogen atoms (such as hydroxyl group with wood or paper). In these two

examples Si-O and C-O bonds are formed. Another possibility is to react epoxide

adhesive with surface containing amine group, to create N-C bonds.

Michał K. Budzik

37

Ionic bonds: For ionic bonds the potential energy, E± of charge z1e and z2e separated

by distance r is given by equation:

(1.16)

εr – relative permittivity of the medium

ε0 – permittivity of vacuum.

Hydrogen bonds: The perfect example is bonding of water molecules contributed to

the attachment of stamps to envelopes where the adhesive (polyvinyl alcohol) and

paper (cellulose fibres) both contain –OH group. Hydrogen bonds are weak and they

are easily broken and readily formed. The bond consist of a hydrogen atom which is

bonded with to two other atoms, that is that two atoms are bridged by hydrogen. It

consist of one normal A-H bond and a longer H···B bond, forming A-H···B [78-80].

Lewis acid-base interactions: Conventional or Bronsted [81] acids are donors of

protons (hydrogen ions H+) and the base are protons acceptors. The concept dates back

to 1923. In 1938, G. N. Lewis proposed a broader definition in that an acid is an

electron acceptor and a base is electron donor [82]. Acid-base bonds are usually meet

in polymer-adhesive or polymer-paint systems [83-85]. The strength of Lewis acids

and bases (or donor-acceptor) in poorly solvating solvents (usually hexan, cyclohexan)

can be obtained from their heats of reaction (-ΔH), which are related to Ea and Ca, the

empirical parameters for acid, and Eb and Cb corresponding values for base by

equation:

(1.17)

Ea and Eb - susceptibilities of acid or base to undergo electrostatic interactions

Ca and Cb - susceptibilities of acid or base to form covalent bonds.

The chemical bond strengths are collected in Table 1.6.

Table 1.6. Bond energy of some of the common interactions.

Type of interaction Example Energy Range

kJ/mol nm

Covalent

C-C

C-O

Si-O

368

377

368

0.1 – 0.3

Ionic

Na+Cl

-

Al3+

O2-

Ti4+

O2-

503

4290

5340


38

Hydrogen bond

-OH···O=C

-OH···OH

-OH···N

F···HF

30

32

35

163

< 0.2

Lewis acid-base

BF3+C2H5OC2H5

C6H5OH+ NH3

SO2+ C6H5

64

33

4.2

Van der Waals

forces

Dipole-dipole

Dipol-induced

dipole

Dispersion

≤ 2

0.05

≤ 2

100 (retarded)

1.5. Surface treatment of adherends

Since adhesives function by surface attachment, the nature and condition of the substrate

surface are critical to the success of any bonding or sealing operation. Four common criteria

are generally recognized for an ideal bonding surface: cleanliness, continuity, stability and

wetting of the surface by the adhesive.

Cleanliness does not necessarily mean the absence of all surface films, since some surface

films are very strongly attached to the bulk substrate and offer a suitable surface for adhesion.

However, cleanliness does require the removal of unwanted or weak boundary layers such as

oil, dirt, or corrosion. The purpose of cleaning the surface is to remove any weakly attached

materials and to provide a surface that is relatively consistent from part to part.

Discontinuities on the adherend surface, whether chemical or physical, may adversely affect

the apparent strength of the joint by creating localized regions of poor bonding and stress

concentration within the joint. Discontinuities may also make surface cleaning or treating

processes non-homogeneous. These discontinuities could be due to inconsistent

manufacturing processes or chemical inhomogeneity within the substrate.

Stability of the substrate surface is important before bonding as well as after bonding.

Unwanted boundary layers could form during the time between surface preparation and

application of the adhesive, depending on the shop environment and the reactivity of the

surface. Boundary layers could also form during the time period after the adhesive is applied

and before it sets, depending on the reactivity of the surface with the components in the

adhesive or sealant. Certain boundary layers can also form after the adhesive is cured,

depending on the nature of the bond and the type of aggressive environment to which the joint

is exposed. The boundary layers that form after the assembled joint is in service may be the

most perplexing because they are often unexpected and may lead to catastrophically early

bond failure.

Michał K. Budzik

39

Wetting of the adherend surface is a required and important process in establishing adhesion.

There will be various degrees of wetting dependent on the chemistry of the surface that comes

into contact with the adhesive. Along with the wettability of the surface, surface roughness

and topology also influence the strength of bonded joints [86]. The suitability of the bonding

surface will also depend on the type and degree of cleaning or surface treatment that was

performed before application of the adhesive [87].

Surfaces of metallic, polymeric and ceramic adherends

The term surface in adhesive science is usually defined as portion of the adherend with which

the adhesive interacts. The surface is defined by both area and depth of interaction. When a

supposedly smooth solid surface is examined closely under a microscope, it is found to

contain irregularities. It is not flat and smooth but contains many surface asperities, such as

peaks and valleys, with a certain degree of roughness. A rough surface provides more bonding

area than a smooth one of the same gross dimensions. The greater effective surface area offers

a larger area for the forces of adhesion to operate, thereby providing a stronger joint. In an

ideal bonded assembly, the substrate should be the weakest link (Fig.1.25). In most

assemblies that are properly bonded, the adhesive is the weak link because the forces of

adhesion are greater than the forces holding the adhesive material together. Usually, the

internal strength of the substrate and adhesive or sealant system is well understood and can be

controlled.

Fig.1.25. The adhesive joint model, a) metal – metal joint, b) chain presentation[88].

Metallic surfaces such as steel or aluminium alloys might consist of several regions having no

clearly defined boundaries between them as shown in Fig.1.26. Virtually all common metal

surfaces exist as hydrated oxides. Even materials such as stainless steels, nickel, and

chromium are coated with transparent metal oxides that tenaciously bind at least one layer of

water. Thus, the adhesive used for these materials must be compatible with the firmly bound

layer of water attached to the surface metal oxide layer [89]. When working with metal


40

adherends, one must recognize that the nature of the surface can be significantly different for

the same type of metal.

Fig.1.26. Schematic presentation of metallic surface[89].

The situation with organic substrates, such as plastics or elastomers, is even more complex

than with metals. These materials have lower surface energies and lower tensile strength than

metals, and most importantly, polymeric surfaces are more dynamic and likely to change than

metals. There is a greater probability of variation in the surface. As shown in Fig.1.27,

polymeric surfaces have the potential for low molecular weight fragments, oxidation products,

plasticizers, processing aids, lubricants and slip aids, adsorbed water, and organic

contaminants along with various other surprises.

Fig.1.27. Presentation of polymer surface[89].

Components within the polymeric bulk material can also migrate to the surface. It is common

to find low molecular weight polymers or oligomers, plasticizers, pigments, mould release

agents, shrink control agents, and other processing aids as well as adsorbed contaminants in

the surface region. More so than with metals, the surface regions of plastics are dynamic

regions, continuously establishing new equilibrium internally with the bulk material and

externally with the surroundings. Polymers, having both polar and non-polar regions in their

molecular chain can present different chain segments at the surface depending on whether the

surroundings are polar or not. Wiping a surface with an ionic solution will cause the polar

groups to orient toward the surface. While the same treatment with a non-polar solvent, such

as hexane, can bring the non-polar components to the surface. Exposure to heat after surface

treatment could cause fresh, untreated molecular species to appear on the surface, thereby

losing the beneficial characteristics of the surface treatment. As a result of these dynamic

reactions, it is difficult to be confident about the surface of any polymeric material. The actual

Bulk plastic

Oriented layers

Migrated process aids

Mould release agent

Process oil or dust

Bulk metal

Segregation layer

Metal oxide

Hydroxide and water

Other adsorber contaminants

Process oil or dust

Michał K. Budzik

41

surface to which we are bonding is not always the surface that we anticipate. It is also

possible that the surface could change once the bond is made and the assembled joint is

placed into service. Thus, a weak boundary layer that is not present during the bonding

process may form during the joint’s operating life and contribute to a weakening of the

interface.

Ceramic materials have smooth surfaces, usually with very high surface energy. Since

ceramics have high surface energies, they are usually easy to bond under normal conditions.

However, many commercially important ceramics have glazed (glass-like) surfaces. This

glazed surface could provide another interface in the joint that must be addressed. The polar

nature of the bonds between atoms in a ceramic material means that there will likely be an

adsorbed layer of water and hydroxide ions. This layer is tightly held to the ceramic surface.

Adhesives used with ceramics, as those used with metals, must be compatible with the surface

moisture layer.

Surface preparation

The main purpose of surface preparation is to ensure that adhesion develops to the extent that

the weakest link in the joint is either in the adhesive or in the adherend. With optimum surface

treatment, failure should not occur at the interface because of a weak boundary layer or

insufficient wetting. Surface preparation can provide several principal functions:

Remove weak boundary layers that impede wetting of the substrate and create weak

links at the interface. Common weak boundary layers are greases, oils, scale, rust,

tarnish, and other oxides

Protect the substrate surface so that weak boundary layers do not develop during

processing of the joint or during aging in service

Influence the surface energy of the substrate so as to reduce the contact angle between

the adhesive and substrate

Prebond treatments are intended to provide cohesively strong and easily wettable surfaces.

Surface preparations enhance the quality of a bonded metal joint by performing one or more

of the following functions: remove contaminants, control adsorbed water, control oxide

formation, poison surface atoms which catalyze polymer breakdown, protect the adhesive

from the adherend and vice versa, match the adherend crystal structure to the adhesive

molecular structure and control surface roughness [91]. Generally surface treatments

techniques are divided into:

Passive surface preparation methods

Active surface treatment methods

Specific methods for given group of materials


42

Passive surface preparation methods

Passive methods do not actively alter the chemical nature of the surface. Passive processes

only clean the substrate and remove weak boundary layers in the form of contamination.

a) Passive chemical treatments

Passive chemical surface treatments remove soil and organic contaminants from the surface.

They include such common processes as solvent wiping, vapour degreasing, and chemical

cleaning:

Solvent cleaning is the process of removing soil and organic contaminants from a

substrate surface with an organic solvent. Where loosely held dirt, grease, and oil are

the only contaminants, simple solvent wiping alone will provide surfaces for weak to

medium strength bonds (see Fig.1.28). Solvent cleaning is widely used and should

precede any chemical or abrasive surface preparation. Perchloroethylene and

trichloroethylene are the most commonly used of the degreasing solvents. Although

non-flammable, these solvents are still toxic in both their liquid and vapour forms

Chemical cleaning methods are popular on polymeric surfaces where solvent cleaning

may degrade the part or on parts where the contamination is more easily removed by

an aqueous cleaner (e.g. salt films, dirt). Chemical cleaning is generally used in

combination with other surface treatments. The alkaline cleaners are generally used

for cleaning metal surfaces prior to bonding. The most popular types of chemical

cleaners are [92]:

Caustics (sodium or potassium hydroxide)

Silicates (sodium meta silicate)

Amines (triethanolamine, monoethanolamine)

Phosphates (trisodium phosphate, tetra potassium

pyrophosphate) [93]

Acids (phosphoric, hydrofluoric, citric, etc.) [94]

Chelates (EDTA)

b) Mechanical passive methods

Mechanical methods for surface preparation include abrasive blasting (sand or grid blasting)

[95-97], wire brushing, and abrasion with sandpaper [98], emery cloth, or metal wool [99].

These methods are most effective for removing heavy, loose particles such as dirt, scale,

tarnish, and oxide layers. Cleaning is generally required both before and after mechanical

surface preparation. Abrasive blasting is generally the preferred method for removing

contamination from most metal surfaces. It is particularly appropriate for removal of rust,

oxide layers, old coatings, and other heavy contamination. Certain low energy surfaces, such

as polyolefins and fluorocarbons, should generally not be abraded at all prior to application of

an adhesive or sealant. Abrasion and the resulting roughness on a low energy surface will

Michał K. Budzik

43

only increase the probability of air pockets being trapped in the crevices and valleys at the

interface. Also vapour-honing, ultrasonic and electrolyzing cleaning are efficient treating

methods for small, delicate parts.

Active surface treatments

Active surface treatments are chemical or physical processes that not merely clean the surface

or remove weak boundary layers, but they also transform the inherent surface chemistry. They

either improve wetting or modify the boundary layer to be more receptive to bonding.

a) Active chemical surface treatments

Chemical treatments change the physical and chemical properties of the surface to produce

one that is highly receptive to adhesion. Specific chemical treatments have been developed for

various metallic and nonmetallic surfaces. The chemicals used are acidic or alkaline in nature.

- Chemical treatment of metallic surfaces

Metal surfaces are usually some combination of oxides, sulfides, chlorides, acid salts,

absorbed moisture, oil, and atmospheric gases. The pure, bare metal surface may be very

reactive, and unwanted oxide layers and corrosion products could quickly form. Thus, the

surface preparation must not only remove the original surface, but replace it with a surface

coating that will protect the interface during further processing and during the joint’s service

life. A number of techniques have been developed to convert corrosion prone, clean surfaces

to less reactive ones. Three common conversion processes are phosphating [100-102],

anodizing [103-105] and chromating. These processes remove the inconsistent, weak surface

on metal substrates and replace it with one that is strong, permanent, and reproducible. For

aluminum, anodizing provides the most water durable adhesive joints. It is used by many

automotive and aerospace suppliers. The corrosion protection is provided by anodizing the

clean deoxidized aluminium surface in either chromic or phosphoric acid electrolytic baths. In

the USA, phosphoric acid anodizing is often used because of its lower toxicity and easier

disposal. Anodizing creates an oxide under controlled voltage and temperature conditions,

thereby creating a more protective surface [106] (see Fig.1.28).

- Chemical treatment of polymeric surfaces

The chemical modification of low energy polymer surfaces may be carried out by treatment

with chromic acid, metallic sodium complex dispersions, bleach/detergents, potassium

iodate/sulfuric acid and other mixtures. Chemical treatment of polymeric surfaces is generally

more difficult than metallic surfaces and requires special considerations. Polymeric products

often contain pigments, antioxidants, slip agents, mold release agents, etc. that can migrate to

the surface and interfere or alter a surface treatment process. Slight changes in the polymer

formulation or its fabrication process may result in changes in the surface condition and the

effectiveness of treating operations.


44

b) Active physical surface treatments for polymeric materials

Because of the main disadvantages of chemical treatments (hazardous nature and a slow,

batch type process), a number of other active surface treatments have been developed for

polymeric materials. These processes utilize the reactivity of the polymeric surface to gain

change that is favourable for adhesion. Rather than chemical solutions, these surface

modifications are usually made by physical means such as:

- Corona discharge. Corona discharge treatment is a popular method of dry surface

preparation of polymer films [107]. The purpose of the treatment is to make the polymer

surface more receptive to inks or coatings, however, it has also been used effectively as a

pretreatment for adhesives. In this method a spark or corona discharge is produced by ionizing

the air in the gap between the electrodes. The ionized particles in the air gap bombard and

penetrate into the molecular structure of the substrate. Free electrons and ions impact the

substrate with energies sufficient to break the molecular bonds on the surface of most

polymeric substrates. This creates free radicals that react rapidly with oxygen to form polar

chemical groups on the substrate surface and increase the surface energy to a point where

many adhesives, paints, and coatings can wet the substrate. Corona discharge technique was

also tried to aluminium substrates [108] without further outcome.

- Flame treatment. Flame treatment consists of exposing a surface to a gas flame for less than

several seconds. Flame treatment burns-off contaminants and oxidizes the surface of the

polymer similar to corona treatment [109]. Flame treatment is used as a surface treatment for

many low energy polymeric parts prior to bonding.

- Plasma treatment. A gas plasma treating process has been developed for surface treatment of

many polymeric materials. It is a dry process that is becoming a common method of treating

many different engineering plastics when maximum joint strength is required. Low energy

materials, such as polyolefins, polytetrafluoroethylene, polyethylene terephthalate, nylon,

silicone rubber, etc. are readily treated with gas plasma, but also epoxy based composites are

suitable to increase adhesion after plasma treatment [110]. Plasma treatment was also used to

enhance adhesion of aluminium [111]. Operationally, a plasma differs from corona and flame

treatment in that the process is completed at less than atmospheric pressure and with gases

other than air. With the plasma treatment technique, a low-pressure inert gas is activated by an

electrodeless radio-frequency discharge or microwave excitation to produce metastable

excited species that react with the polymeric surface. The plasma treatment produces changes

only to the depth of several molecular layers. Generally, only very short treating times

(seconds to minutes) are necessary. It is generally believed that the plasma treating process

provides surfaces with greater stability than chemical etch, corona, flame, or other common

polymeric treatment processes [112].

- Other methods

Michał K. Budzik

45

Ion beam etching has been used on stainless steel, graphite, and fluorocarbon surfaces

[113]

Excimer laser surface treatment has been used for preparing polyester sheet molding

compounds (SMC) for adhesive bonding in the automotive industry. The excimer laser

preparation of SMC surfaces occurs through the following stages: ablation of surface

contaminates, selective ablation of calcium carbonate filler from the SMC, and

removal of polyester resin from the SMC [114,115]

UV irradiation has also been applied as a prebond surface treatment to a variety of

plastics [116]

It must be pointed out that in structural bonding (especially of aluminium) chemical and

mechanical processes dominates. The effect of the different, common aluminium surface

preparation on the bonded joint durability is illustrated in Fig.1.28.

Fig.1.28. Effect of surface pretreatment on the performance of aluminium joints with a

toughened epoxy adhesive and subjected to ageing in water[90].

Priming to improve adhesion

One approach to improve adhesion characteristics is to intentionally introduce an interphase

region to improve initial adhesion, provide chemical stabilization against degradation in

aggressive environments, and perhaps provide for a broad transitional zone in mechanical

properties between the phases. An interphase engineered to accomplish these goals that is

applied as a separate manufacturing step is referred to as a primer.

Primers are multifunctional compounds designed to provide a means for chemically coupling

to both the inorganic surface and to the organic adhesive or coating. The most widely used


46

coupling agents are based on organosilicon chemistry, although titanates and zirconates have

also enjoyed modest technical and commercial success. An excellent (though slightly dated)

review of coupling agent technology may be found [117]. Silane coupling agents are

generally synthesized through addition of silicon hydrides to unsaturated organic molecules:

(1.18)

where X is a hydrolyzable group such as Cl-OCH2CH3, or -OCH3.

As primers for adhesive bonding, organosilanes (Table 1.7) are typically hydrolyzed in

solution to the corresponding silanol prior to application. In most cases, these silanols begin to

homopolymerize in solution and therefore have a limited shelf life. One result of this

condensation is that the structure of the final film has its origins in the solution history prior to

film deposition.

Table 1.7. Commercial silane coupling agents[13].

Organofunctional group Chemical structure

Vinyl

Chloropropyl Epoxy

Methacrylate

Primary amine Diamine Mercapto

Cationic styryl

While primers are believed to improve the performance of adhesively bonded aluminium

structures primarily through improved corrosion resistance and improved wetting of the

microscopically rough adherend surface by the adhesive, modification of the mechanical

properties of the adhesive near the substrate can have a large effect on both the stress

distribution and total strain energy [118].

1.6. Mechanical testing of adhesive bonding

Adhesion due to its complexity requires specially designed tests. Different substrates,

adhesive types - from very fragile through tough up to very plastic, surface treatments,

adhesion enhancements techniques oblige many different phenomena to occur. Among

different, industrial branches and trades, a variety of test methods for the evaluation of

adhesively bonded joints have been developed and established, including International

Organization of Standardization (ISO), European Committee for Standardization (EN) and

American Society of Testing and Materials (ASTM) standards. During last years lot of tests

were developed inside special laboratories to specifically describe adhesive joints. The spectra

Michał K. Budzik

47

of mechanical tests of the adhesive joints can be subdivided into tens of different ways only

dependent on the chosen criteria. Because of the thesis aim all tests are divided into to groups

dependent on proposed failure criteria:

Failure stress tests – in which stress in principal load direction at failure is estimated

Failure energy tests – in which energy required to separate material or materials is

estimated

1.6.1. Characterisation by failure stress

Fundamental understanding of adhesively bonded joints requires understanding the rudiments

of mechanics, the stress and strain states within the bonded joint. Generally when load is

applied to the bonded joint, the entire joint and the adhesive layer itself is subjected to

different kind of loads.

Tensile tests

One of the basic structural elements encountered in bonded joints is the straight, axially

loaded bar. The stress within loaded bar is given by the well know expression (assuming de

Saint-Venant’s rule):

(1.19)

where:

F - applied axial load

A - cross section are of loaded bar.

Axial deformation caused by applied force, F:

(1.20)

where:

L - initial bar length

E - elastic modulus (Young modulus).

Stored elastic energy, U is:

(1.21)

where:

F - applied external force


48

A - area of bar cross section

E - Young’s modulus of elasticity.

In addition to the axial deformation, which occurs due to the applied axial load, deformations

in the transverse directions are also observed, and are related to the axial strains through the

Poisson’s ratio, ν of the material. Specifically, for uniaxial loading, Poisson’s ratio is defined

as the negative of the ratio of the transverse strain, εt to the axial strain, εa:

(1.22)

with:

ν - Poisson ratio

εt - transverse strain

εa - axial strain.

Theoretically ranging from -1 to 0.5, Poisson’s ratio for most engineering materials ranges

only from around 0.2 to nearly 0.5. Poisson’s ratio can have significant effects on the stress

states present in bonded joints, giving rise to complex three dimensional stress states.

Adhesive bonding tension tests include:

ASTM D897-08 - Standard Test Method for Tensile Properties of Adhesive Bonds

[119]

One of the most commonly used adhesive tensile test method is described in ASTM D897

standard. The recommended sample geometry is shown in the Fig.1.29. Because of high

sensitivity of the test to geometrical aspects like thickness of bondline, uniformity of the

bondline, alignment of the substrates results are often cumber with large scatter [120].

Fig.1.29. Specimen configuration for adhesive tensile testing.

F

F

Michał K. Budzik

49

ASTM C297-04 - Standard Test Method for Flatwise Tensile Strength of Sandwich

Constructions [121]

The standard describes specimen used to determination of the flatwise tensile strength

sandwich constructions.

ASTM D2095-6(2008) - Standard Test Method for Tensile Strength of Adhesives by

Means of Bar and Rod Specimens [122]

The standard recommends bar or rod specimens that are easier to manufacture than those from

D897. The results from all of the tensile tests are reported as simple force, F to bonded area, A

average stress. This can be misleading since average stress differs markedly from the

maximum stress and can easily over exceeds the average value [123]. Designers usually avoid

using adhesives in a direct tensile loading mode. Overlapping, scarfing or fingering the two

pieces can increase bonded surface significantly but also change stress state, allowing

preferable shearing to occur.

Shear tests

Shear tests are very exploited and popular because of their provisional simplicity. Rudiments

of the shear are here recalled. In a simple shaft of length l and second moment of inertia, I

applied torque T will result with:

Shear stress given by:

(1.23)

T – torque

ρ – torque arm

I – second polar inertia moment of the shaft section.

Angel of twist written as:

(1.24)

L – length of the shaft

G – shear modulus of elasticity.

And stored elastic energy:

(1.25)


50

Shear tests most frequently are used to yield shear strength and modulus of the adhesive. Lap

joint test configuration is sometimes used in creep test as well as in durability approaches.

Napkin ring test [124]

The conservative way of yielding shear properties of the adhesive bond is described in both,

ISO 11003-1 [125] and ASTM E229-97 Standard Test Method for Shear Strength and Shear

Modulus of Structural Adhesives [126], which relates to so-called Napkin ring test (see

Fig.1.30).

Fig.1.30. Napkin ring test.

This test produce uniform shear stress within an adhesive layer (ca. 3% variation across the

adhesive ring) and hence is widely use for producing shear strength and modulus data [127]

although care must be taken when producing bondline.

Single Lap Joint Test

Different lap specimens configuration are recommended by ASTM D1002-05 Standard Test

Method for Apparent Shear Strength of Single-Lap-Joint Adhesively Bonded Metal

Specimens by Tension Loading (Metal-to-Metal) [128] (Fig.1.31). Results from this test must

be carefully studied since both, shear and tensile load occurs. Recently finite element studies

[129-132] described difficulties of analyzing test results from single-lap test.

Fig.1.31. Single lap test configuration (ASTM D1002).

ρ

L

T

Michał K. Budzik

51

Double Lap Joint Test

A large amount of tensile stress induced by bending deformation had led to introducing the

double-lap joint specimens. The standardized specimen configurations from ASTM D3528-

96(2008) Standard Test Method for Strength Properties of Double Lap Shear Adhesive Joints

by Tension Loading [133] is shown in Fig.1.32.

Fig.1.32. Double-lap shear adhesive specimen configurations (ASTM D3528).

The lap joint test is the most commonly used adhesive test, because test specimens are simple

to construct and resemble the geometry of many practical joints. However it must be pointed

out that stress distribution in the adhesive is not homogenous. That was primarily stated by

Otto Volkersen. The shear lag model, first published in 1938 [134], is one of the most

fundamental concepts in the transfer of load between two members joined by either discrete

connections, such as mechanical fasteners, or by a continuous layer such as an adhesive.

Solution for the shear lag model is nonuniform shear stress distribution along the bondline as

it is illustrated in Fig.1.33.

Fig.1.33. Graphical presentation of shear lag model.

And followed by equation:

(1.26)


52

where:

E1 and E2 - Young’s modulus of two bonded substrates

h1 and h2 – thicknesses of substrates

F – applied shearing force

and ω:

(1.27)

As can be noted, for the balanced adherend case where the Eihi products for the upper and

lower adherends are the same, the coefficient for the hyperbolic sine term becomes zero, and

the shear stress distribution is symmetric about the centre of the joint. Additionally followed

by Volkersens analysis and those incorporated by Emil Winkler in 1867 [135] in his elastic

foundation model, Goland and Reissner introduced a new model of lap shear geometries. The

Goland and Reissner model is an extended Volkersen model, which includes peel stresses

(according to Winkler model) (Fig.1.34).

Fig.1.34. Peel stress distribution in shear lap geometry.

This becomes particularly important, since adhesives have by far worse properties in tension

than in shearing, and peel, or opening stress, is found to be the initiator of the crack. Up to

nowadays design of adhesive bonds is focused on minimizing peel forces, which is

complicated on real structures [136] in which crack initiation and propagation is driven by the

cleavage stress at the end of the bonded region. Furthermore any static test is not very

convenient in long term, hostile environment testing. Therefore, tests based on energy

required to separate bonded substrates are numerous. Mode I fracture tests are among the

most promising, giving important data- the fracture energy in the most critical opening

(cleavage) mode.

1.6.2. Characterisation by failure energy

Historically failure energy criteria in their essence try to accommodate fracture and

delamination phenomena within the framework of continuum theory. Nowadays experimental

Michał K. Budzik

53

but also mathematical fracture mechanics is based on works of famous engineers like Griffith,

Kies, Irwin, Orowan etc. The application of classical elasticity concepts leads to infinite

stresses at the crack tip. Cracks and sharp comers give rise to singular stress and strain fields

in the material surrounding them. A singular stress has the form ζ~rλ-1

, where r is the distance

from the crack tip or corner and λ is known as the order of the singularity. If 0<λ<1, the stress

ζ ∞ as r 0. Griffith’s principal contribution is an analysis of crack stability based on

energy required to drive the sharp crack [137], i.e. supply (at least) the surface energy for the

two newly formed surfaces.

Consider the situation shown in Fig.1.35.

Fig.1.35. Joint in mode I fracture (F – applied force, Δ – vertical displacement, a – crack

length, δa – crack increment).

If the crack, of length a, is in equilibrium, the decrease of strain energy U, must be equal to

the increase of surface energy S due to crack extension, that is:

(1.28)

where:

- the crack extension force, G, which is defined as strain energy release rate

- energy spent in increasing the crack area

γ - surface free energy.

Griffith’s work dealt with very brittle glass rods. When the material exhibits ductility, as in

most metallic materials, consideration of the surface energy alone is inadequate and then the

vast majority of the released strain energy is absorbed generating plastic flow in the material

near the crack tip. Thus, catastrophic fracture occurs when the strain energy is released at a

rate sufficient to satisfy the needs of all the energy requirements, parameter Gc. Fracture

mechanics analyses relate to sharp cracks, i.e. when the local stress for fracture is reached. For

metallic materials this is usually achieved by fatigue precracking from a notch. Application of

Fracture Mechanics to polymers presents additional problems, including viscoelasticity and

the generation of sharp precracks. For adhesive bonding the latter problem is frequently

F

Δ

a δa


54

tackled by monitoring a moving, and therefore sharp, crack. Not only in ductile, but also in

near-brittle [138] materials a plastic zone develops at the tip of the crack. As the applied load

increases, the plastic zone increases in size until the crack grows and the material behind the

crack tip unloads. Hence, a dissipative term has to be added to the energy balance relation

devised by Griffith for brittle materials. In physical terms, additional energy is needed for

crack growth in ductile materials when compared to brittle materials. This was first stated by

George Rankin Irwin. Irwin's strategy was to partition the energy into two parts [139]:

The stored elastic strain energy which is released as a crack grows. This is the

thermodynamic driving force for fracture

The dissipated energy which includes plastic dissipation and the surface energy (and

any other dissipative forces that may be at work). The dissipated energy provides the

thermodynamic resistance to fracture.

Therefore, the total energy is:

(1.29)

with:

Gp - the plastic deformation dissipation (and dissipation from other sources) per unit area of

crack growth.

For brittle materials such as glass, the surface energy term dominates and G≈2γ. For ductile

materials such as steel, the plastic dissipation term dominates and G≈Gp. For polymers and

therefore adhesives, we can obtain full set of different properties.

Standard Mode I tests

The ASTM has standardized several cleavage tests for adhesives, from which all of them are

based on symmetric sample geometry.

ASTM D1062-08 Standard Test Method for Cleavage Strength of Metal-to-Metal

Adhesive Bonds test [154]

The ASTM D1062 specimen is shown in Fig.1.36. It is also referred as a compact tension

(CT) test of the adhesive joints. The test specimen is fabricated from two identical pieces of

metal that are adhesively bonded to form bondline. The load is applied off-axis, subjecting the

specimen to combined tension-bending load. The standard requires breaking force to be

registered per specimen thickness. Additionally, percentages of surface experiencing cohesive

and adhesive fracture are to be reported.

http://en.wikipedia.org/wiki/Plastic

http://en.wikipedia.org/wiki/Structural_load

Michał K. Budzik

55

ASTM D3807-98 (2004) Standard Test Method for Strength Properties of Adhesives

in Cleavage Peel by Tension Loading (Engineering Plastics-to-Engineering Plastics)

test [155]

The beam cleavage test configuration, shown in the Fig.1.37 is referred in ASTM to D3807.

The standard recommends beam like cleavage specimens. The adherend strips are required to

be semirigid, such that they can bend through an appreciable angle without failing. The results

are reported as a force per width required to propagate the failure.

Fig.1.36. ASTM D1062 cleavage test of adhesive joints (left).

Fig.1.37. ASTM D3807 cleavage test specimen (right).

ASTM D3433-99 (2005) Standard Test Method for Fracture Strength in Cleavage of

Adhesives in Bonded Metal Joints [156]

This test was initially conceived as true adhesion fracture test. The specimen geometry is

illustrated in Fig.1.38. The specimen is composed from two strips (symmetrical) which are

separated using tensile machine. D3433 test is one of the most common and widespread

fracture test of the adhesive joints and is abbreviated to DCB (Double Cantilever Beam) test.

The fracture energy can be found as:

(1.33)

with: U – elastic energy and A being surface area created by the propagating crack (∂A=∂ab

where a – crack length, b – width of the substrate – constant).

Finally, the adhesive fracture toughness in cleavage test can be yield as:

(1.34)


56

For the beam with the inertia moment define as I:

(1.35)

Fracture toughness expression becomes:

(1.36)

It is worthwhile noting that in this configuration the shear stress component is usually very

small, since a>>h. However, it should be pointed out that two values need to be estimated:

the crack length and force, both strongly affect the final toughness expression. Force can be

measured directly by the force sensor mounted to the tensile machine. The crack length is

very hard to measure directly and finally must be estimated in another way. Since the test is

designed to be made on a tension machine we must notice that due to increasing crack length,

the momentum required to separate plates is decreasing, which plays an important role in

compliance measurements. As is proven by experimental and analytical studies, also other

effects like anticlastic curvature, root rotation or residual stresses can imply even more

significant contributions to final toughness values [157,158]. Some of these problems were

solved by introducing tapered geometry, shown in Fig.1.39. The test is referred as TDCB

(Tapered DCB) and is recommended by the same ASTM standard – D3433.

Fig.1.38. ASTM D3433 test specimen (left).

Fig.1.39. ASTM D3433 TDCB test specimen (right).

Since during the test cross section of the beams or substrate varies with the crack length

increment additional factor, m occurs in the final energy release formula:

(1.37)

Michał K. Budzik

57

with factor m being:

(1.38)

Taper is chosen to vary the beam compliance, C (C=ΔF-1

), such that for given force F at

failure, fracture energy Gc is independent of the crack length, a. As can be found, TDCB is

free of crack length interpretation problem, but compliance arises the others. Since all tensile

machines have their own compliance, comparison between the results from different

laboratories give huge scatter of results [159,160]. In addition, adhesive elasticity and

viscoelastic properties allows root rotation to occur which significantly increase errors to

almost 30% in terms of fracture energy [161]. Tapered specimen geometry is not very

convenient from technological and practical points of view. Finally in situ, environmental

tests are difficult for both DCB and TDCB tests. Nowadays, hostile environment effects are

studied using aged samples are used. We must remember that ageing on unloaded samples

cannot be compared with combined environment-mechanical loading cycle e.g. because

ageing conditions require higher loads, which cannot be transferred when the structure is

mechanically loaded. Finally tapered geometry cannot be obtained for many materials e.g.

some composites or ceramics, because of the machining necessity.

ASTM D3762-03 Standard Test Method for Adhesive-Bonded Surface Durability of

Aluminium - The Wedge Test [162]

Limitations of the DCB test making use of tensile machines led to the development, first at

the Boeing company in 1980’s, of the adhesive bonding durability test referred to as the

Boeing Wedge Test, and now known as standard ASTM D3762 test. The test specimen is

shown in Fig.1.40.

Fig.1.40. D3762 wedge test configuration for durability testing.


58

In this test a double cantilever beam of the geometry identical to the DCB test is loaded by

forcing a wedge of thickness Δ between the separated beams. The fracture energy is given as:

(1.39)

with:

Δ – wedge thickness.

Contrary to the DCB and TDCB tests in wedge test the crack propagation rate is decreasing

with time leading to stable propagation. A major drawback of the wedge test is high

dependence of the fracture energy on crack length, scaled to -4th

power.

Summary of the mode I fracture tests

Of the various adhesion tests available for evaluating the fracture strength of structural

adhesive joints, the double cantilever beam (DCB) and its close relative, the (so-called

Boeing) wedge test, are amongst the most versatile, and generally yield the most reliable

information about fracture energy [163-170]. It has to be pointed out that in standards only

symmetric geometries are listed, and thus asymmetric geometry is rarely studied in the

literature. With a judicious choice of test geometry, these systems lead to relatively small

adherend strains near the crack front [157,171]. As a result, local plastic strain, which leads to

supplementary energy dissipation, is relatively limited. If the length of the opening crack

(either within the adhesive or at the interface adherend/adhesive, depending on type of failure)

is represented by a, it may be shown that the energy release rate, equivalent to fracture

energy, Gc, follows a scaling rule of the form Gc~a2. Beam analysis based on the opening

displacement and the force applied allows a, and therefore Gc, to be evaluated. However,

since the bending moment leading to failure increases linearly with a, crack growth may

accelerate and become unstable in certain cases. This problem has been countered by the

development of the more refined, tapered double cantilever beam (TDCB) test, in which

stability is restored by using profiled adherends with thickness increasing away from the

region of force application [e.g. 172]. In principle, crack length need not be measured directly,

but such obtained results were found not precise [159,160,161]. In addition it is not always

convenient, or even possible, to use profiled adherends (for instance, when testing the

adhesion properties of automotive body assembly materials). Away from tensile machine

based techniques, various techniques have been used to study crack lengths in this tests. The

most basic techniques rely on direct, or microscopic, observations of the position of the crack

tip, sometimes with the addition of paint, or other marking fluid, to the joint edges to facilitate

observation [157,173-175]. Use has been made of optical correlation [173], laser moiré [176]

and speckle interferometry [177]. Electrical techniques have also been tried, such as

measurement of crack growth through changes in electrical resistance of carbon paint applied

to the edges of non-conducting substrates [178], or by employing piezoelectric techniques

[179]. The use of a single strain gauge technique has also been reported [180]. Displacement

Michał K. Budzik

59

sensors have been employed for continuously monitoring cracks [157]. Measurement of crack

length nevertheless remains a delicate process in many practical cases. Moreover

environmental testing seems to be crucial. In reality even while wedge test is performed the

crack measurements are difficult. After the sample is loaded with wedge insertion and placed

in the environmental chamber the crack length, a should be observed and recorded. Since very

sensitive crack measurements are required, and these were not possible under hostile

environmental conditions, such approach was left. Normal, and nowadays common, method is

to remove the sample from the chamber and measure crack length manually using e.g. simple

calliper gauge or a different method described above not assuring required accuracy and

reliability. In addition, immersion-drying cycle certainly must change the adhesive behaviour

e.g. due to possible fatigue. Another problem arises due to possible loading mode mixity. In

practice, most materials to be bonded are different in geometrical, physical or chemical

meaning which implies different mechanical behaviour. For example it was found, that when

the system becomes increasingly asymmetric, a greater degree of in-plane shearing

incorporating mode II [141]. The locus of failure is also changing, shifting from cohesive in

the adhesive to interfacial along the adherend surface [142-148]. The anti-plane shearing

effect – mode I/III mixity was studied very rarely [e.g. 152,153] particularly for the

development of the mode mixity tests. Mode mixity is also suspected to change final value of

the fracture energy, since the adhesives are much stronger in shearing [149] even small mode

mixity contribution may markedly change final fracture energy. The strain energy release rate

in mode mixity conditions is given by equation:

(1.31)

Where index I, II, III corresponds to opening, in-plane shearing and anti-plane shearing

(tearing) fracture modes respectively. The effects of the mode I/II mixity were studied by

Chen et al. [150,151]. The authors have introduced energy release rate mixity factor:

(1.32)

They pointed out that when η<3% the crack front will oscillate between the adherend

interfaces. When global mode mixity increase, η<14% the crack front has increased

directional stability and propagates along one adherend only. The effects of mode III/I mixity

are ignored by the authors.


60

Chapter 2. ASYMMETRIC JOINTS

According to the literature and international standards fracture mechanics tests in the crack

opening mode I conditions are made using symmetric joint geometry, made from, in principle,

the same materials with the same dimensions.

The focus of this study was asymmetric joints (see Fig.2.1) made from two bonded plates one

being assumed rigid, of thickness H, the second elastically deformable, or flexible, of

thickness h. The asymmetric bonded joint configuration allows any materials combination to

be used. Schematic representation of the sample used, with all of the geometrical and material

features, is shown in Fig.2.1.

Fig.2.1. Asymmetric test sample.

The rigid-flexible assumption is kept by having appropriate flexural rigidity ratio of the two

bonded plates (beams):

(2.1)

where E and I are elastic modulus and second moment of inertia of the rigid (index H) and

flexible (index h) plates respectively.

2.1. Materials and specimens

To study the methodology of testing of the adhesive joints and validity of the developed

procedures different materials systems were studied. Material selected for rigid plates (in all

experiments) was aluminium-magnesium alloy AA5754. Flexible plates were made of:

aluminium-copper alloy AA2024, carbon fiber reinforced polymer - CFRP, polycarbonate -

PC. The adhesives used to bond rigid and flexible plates were: pure and nanoparticles

reinforced epoxy, acrylic mastic adhesive, cyanoacrylate adhesive and PSA type adhesive.

Aluminium-magnesium alloy AA5754-H111

The aluminium-magnesium alloy AA5754 was supplied by Alcoa (Pittsburgh, PA, USA) in

H111 condition which corresponds to strain hardening and annealing to give small increase of

Flexible adherend

The adhesive

Rigid adherend

h, Ih, Eh, l, b

H, IH, EH, L, b

e, b, Eadh, ladh Force, F

Deflection, Δ

Michał K. Budzik

61

strength. The chemical composition of AA5754 alloy to the supplier standard is given in

Table 2.1.

Table 2.1. AA5754 chemical composition.

Chemical Composition Limits Others

Weight % Si Fe Cu Mn Mg Cr Zn Ti Each Total

Minimum - - - - 2.6 - - - - -

Maximum 0.40 0.40 0.10 0.50 3.6 0.30 0.20 0.15 0.05 0.15

The magnesium concentration is usually maintained less than 4% (weight) in order to avoid

intermetallic phase Mg5Al8. Work hardened aluminium alloys tend to soften with time

because the microstructure is not stable even at ambient temperature. Therefore annealing is

(in 400oC) to the required strength (Table 2.2) and stability required operation after work

hardening. The 5754 alloy has good corrosion resistance and medium mechanical properties

and is mainly used in the shipbuilding industry, automotive bodies and as rivets. Plates of

thickness H=6 mm, width, b=25 mm, and length of L=180 mm were cut from 50 x500x6 mm

plate using milling machine. To avoid any changes in the 5754 alloy microstructure all

operations were taken in the stream of cooling liquid.

Table 2.2. Physical and mechanical properties of AA5754-H111 alloy.

Properties: Denisty

(gcm-3

)

Modulus of

Elasticity

(GPa)

Yield stress

(MPa)

Tensile

Strength

(MPa)

Coeff. of Thermal

expansion

(oC

-1)

Required: 2.66 68 100 215 24 x 10-6

Aluminium-copper alloy AA2024

The aluminium-copper alloy AA2024 was supplied by Alcoa (Pittsburgh, PA, USA). The

AA2024 series is most extensively used in aeronautic industry for plane fuselages. The

chemical composition of the alloy is shown in the Table 2.3.

Table 2.3. AA2024 chemical composition (supplier data).

Chemical Composition Limits Other

Weight % Si Fe Cu Mn Mg Cr Zn Ti Each Total

Minimum

-

-

3.8

0.30

1.2

-

-

-

-

-

Maximum 0.50 0.50 4.9 0.9 1.8 0.10 0.25 0.15 0.05 0.15

The usual heat treatment includes solution heat treatment and ageing, which gives final

structure of copper solid solution with metastable CuAl2 precipitates which gives rise to the

strength properties and hardness. Although, the corrosion resistance of AA2024 alloy is not

very good, since this alloy is particularly subjected to stress corrosion cracking due to


62

possible copper precipitates, it has good fracture toughness and good weight/strength ratio.

Also it is the cheapest of the high performance aluminium alloys. The plate was delivered in

T3 condition – solution heat treated (ca. 500oC), naturally aged and finally cold rolled. The

mechanical properties are listed in the Table 2.4.

Table 2.4. Properties of AA2024-T3 (supplier data).

Properties: Denisty

(gcm-3

)

Modulus of

Elasticity

(GPa)

Yield stress

(MPa)

Tensile

Strength

(MPa)

Coeff. Of Thermal

Expansion

(oC

-1)

Required: 2.77 73.1 260 440 22.9 x 10-6

The significant advantage of the 2024 alloy, concerning the adhesive bonding, is the fact that

is very well known and studied and, in addition, was found especially susceptible to the

porous alumina layer formation on its surface [181]. The plates of thickness h=1.6 mm, width

b=25 mm and length 120 mm, were cut from 2000x2000x1.6 clad AA2024-T3 plate with

press cutter. Then all edges were finished with milling machine in the presence of cooling

liquid and finally polished to required dimensions.

Carbon Fibre Reinforced Composite

One of the biggest advantages of adhesive joints is the possibility to join fibrous composite

materials without weakening them e.g. by holes, thermal processes etc. Two epoxy resin

matrix, orthotropic carbon fibre woven composites were used. One was delivered by the

supplier, second was fabricated by the author in Merignac Institute de Maintenace

Aeronatique (IMA). Both epoxy composites were made of 6 layers of orthogonal pre-preg

HexPly M10/42%/193P/CHS-3k/1000mm, supplied by Hexcel (Stamford, CT, USA), giving

a thickness, h of 1.22 mm. Composite made at IMA was cured in 120°C under 0.3 bar

pressure for 1 hour under the vacuum bag. The precise supplier fabrication procedure is not

known. Mechanical properties of the fabricated composite were obtained using ultrasonic

Through Transmission Method (TTM) and verified in bending tests. The detailed procedure

of the TTM method can be found in authors master thesis [182]. Young’s modulus, obtained

from 3-point bending, was evaluated at 50 5 GPa, the same like in TTM method. Poisson’s

ratio, νC was 0.05. Properties of the composites employed are summarized in Table 2.5.

Finally plates (250x200) were cut with hydraulic press, edges were polished with the emery

paper to the 120x25 mm (length x width) plates.

Table 2.5. Properties of the CFRP composites.

Properties: Denisty

(gcm-3

)

Modulus of Elasticity

(GPa)

Thickness

(mm)

Tensile Strength

(MPa)

Poisson

ratio

Supplier

IMA

1.38

1.29

77

50

1.22

1.22

850

-

0.05

0.05

Michał K. Budzik

63

Makrolon® (C16H14O3)

Makrolon® General Purpose Sheet is a polycarbonate (PC) product. Sheet was supplied by

Bayer (Sheffield Plastics, Bayer MaterialScience LLC, Sheffield, MA, USA) is a clear,

colourless polymer used extensively for engineering and optical applications. It is available

commercially in both pellet and sheet form. In the studies 5 mm thick polycarbonate plates

were used, as a flexible adherend, to observe directly, using video microscope camera,

formation and shape of the crack front. The 120x25x5 mm plates were cut from 200x200x5

mm sheets using a band saw. After cutting, edges were polished with 1200 grade emery paper

to the desired dimensions.Properties of the PC plates are listed in the table 2.6.

Table 2.6. Used polycarbonate properties (supplier data).

Properties: Denisty

(gcm-3

)

Modulus of Elasticity

(GPa)

Tensile Strength

(MPa)

Average: 1.20 2.5 65

Bostik Araldite Cristal

One of the adhesive used was a commercial DGEBA (DiGlycidyl Ether of Bisphenol A:

epoxy resin synthesized by reacting bisphenol-A with epichlorohydrin in the presence of a

basic catalyst) epoxy resin (Bostik, La Défense, Paris, France) of average molecular weight

n<700 cured with N(3dimethylaminopropyl)-1.3propylenediamine. Crosslinking of the

adhesive was effected at ambient temperature (ca. 20°C) for 48 hours under 0.3 bar pressure

and at ca. 55% RH.

Epidian 6

Epoxy resin - Epidian®6 (E6) supplied by Chemical Works (Organika-Sarzyna S.A., Nowa

Sarzyna, Poland) is second resin produced from DGEBA used in the studies. The epoxy

equivalent weight, EEW, was 188 g/equiv. and the average molecular weight - n≤700. The

hardener used was 1-butyloimidazole, used in proportion 1phr (per hundred portions of resin).

To study the nanoparticles adhesive bonded joints efficiency basic E6 resin was reinforced

with 5% (by weight) of 1-D montmorillonite (MMT) nanoparticles. Nanoparticles were

dispersed in the resin using ultrasonic sound with frequency, f=35 kHz for ca. 10 min. Curing

of both of the E6 systems was effected in 150oC for 1 hour under constant pressure of 0.3 bar.

Colle Mastic Tout Fixer

As a example of highly elastic, low elasticity modulus adhesive (Eadh ca. 200 MPa) acrylic

mastic adhesive was used, Colle Mastic Tout Fixer (Leroy Merlin, 59712 Lille, France) was


64

used. Curing was effected at ambient temperature (ca. 20°C) for 48 hours under 0.3 bar

pressure and at ca. 55% RH.

UHU® Super Glue

Cyanoacrylates posses very good mechanical properties, but are very expensive and

aggressive to the environment and human. UHU® Super Glue (UHU GmbH & Co. KG, D-

77813 Buhl, Germany) is a commercial fast curing cyanoacrylate adhesive (ethyl 2-

cyanoacrylate). Curing of the adhesive was effected at ambient temperature (ca. 20°C) for 48

hours under 0.3 bar pressure and at ca. 55% RH.

PSA adhesive

Pressure Sensitive Adhesive - PSA type adhesives are common in everyday applications.

Commercial, PSA type (caustic base) adhesive, double face scotch - Scotch Double Coated

Tape was supplied by 3M (St. Paul, MN, USA). The joint after bonding with the tape was left

for 48 hours under 0.3 bar pressure.

2.1.1. Characterization of substrates

Three point bending test and cantilever beam test were performed to evaluate bending

properties of the flexible substrates. Three different span/arm lengths (60, 80, 100 mm), three

different forces (5, 10, 20 N) and three different plates from the same materials (CFRP,

AA2024-T3) were used. Results of the test are summarized in the Table 2.7.

Table 2.7. Bending test results.

Properties: Modulus of

Elasticity

(GPa)

Yield stress

(MPa)

CFRP

AA2024-T3

50 ± 5

62 ± 5

-

200 ± 7

In addition ultrasonic TTM (Through Transmission Method) [183] was used to evaluate

mechanical properties of the flexible substrates, using device shown in Fig.2.2. Results from

TTM test are also given in the Table 2.8.

Table 2.8. Materials properties from TTM measurement.

Properties: Poisson

ratio in xy

Modulus of Elasticity in x*

(GPa)

Modulus of Elasticity in y*

(GPa)

CFRP

AA2024-T3

0.03

0.32

53.76

68.19

49.54

67.23 *

x and y being are longitudinal and transverse ordinates respectively.

Michał K. Budzik

65

Fig.2.2. Through Transmission Method device.

2.1.2. Surface preparation of the substrates

Before bonding the substrate plates were subjected to variable surface treatment affecting the

surface topography (sandblasting, abrading, polishing, electrochemical PAA process) and/or

chemical structure (PAA process). Composites plates where abraded using 400 grit emery

paper, wiped in the ethanol alcohol and dried in the stream of warm air. Procedures of

aluminium surface treatment are detailed in Table 2.9.

Within the thesis the PAA surface treatment was used for different aluminium alloys. It must

be pointed out that the influence of the alloying elements on the PAA process of aluminium is

not well known yet [184] concerning the growth of the alumina layer. When the aluminium is

electrochemically anodized, an oxide grows at the anode according to the reaction [185]:

(2.2)

And hydrogen evolves:

(2.3)

The PAA is recommended process because is less toxic than common chromic acid

anodization, in addition, the phosphoric acid electrolyte was found to give the best adhesion

properties of the porous alumina layer [186]. The pore formation mechanism is displayed

schematically in Fig.2.3 following four stages [187]. At the beginning of the anodization, the

barrier film, which consists of non-conductive oxide (R=1010

~1012

Ωcm) [188], covers the

entire surface of the aluminium (stage 1). The electric field is focused locally on fluctuations

of the surface (stage 2). This leads to field-enhanced or/and temperature enhanced dissolution

in the formed oxide and thus to the growth of pores (stage 3). Since some pores begin to stop

growing due to competition among the pores, the current decreases again. Finally, the pore

formation current maintains an stabilizes state. In this stage, pores grow in a stable manner

(stage 4). However, it is very often observed that during the stable pore growth, the current

Emitter

Sample

Receiver

Medium

- water


66

density continues to decrease slightly. This is due to diffusion limits in the long pore channels

[189,190].

Table 2.9. Aluminium surface treatment procedures.

Polishing Sandblasting Anodization

Degreasing:

96 % ethanol

Abrasion/Polishing:

Emery paper

180 400 800 1200 2400/4800

Surface cleaning:

DI water stream

Ultrasound cleaning: Drying:

Methanol bath

T=30oC

t=15 min

f=35 kHz

Ethanol rinse

Hot air stream

Water break test

AFM Bonding Sandblasting: Anodization:

Perpendicular

40 mm distance

9 μm (150 μm)

SiO2 (Al2O3)

P=3 At

10% wt. H3PO4

10 V DC

23oC

20 min

20 mm distance / parallel

Ti grid cathod

Ultrasound cleaning:

Methanol bath

T=30oC

t=15 min

f=35 kHz

Drying:

Acetone rinse

Hot air stream

Bonding Bonding AFM

Michał K. Budzik

67

Fig.2.3. Schematic diagram of the pore formation at the beginning of the anodization. Stage1:

formation of barrier oxide on the entire area, stage 2: local field distributions caused by

surface fluctuations, stage 3: creation of pores by field-enhanced or/and temperature-enhanced

dissolution, stage 4: stable pore growth.

2.1.3. AFM and SEM control of the surface

Atomic Force Microscope (AFM) (Veeco Instruments Inc., Veeco Metrology Group,

Nanoscopes, New York, USA) and Scanning Electron Microscope (SEM) (Philips-FEI, XL30

ESEM-FEG/EDAX, Amsterdam, The Netherlands) were used to study the surface topography

and structure after the PAA surface treatment.

Alumina layer topography obtained for the AA2024 alloy is shown in Fig.2.4. Profile and the

section of Al2O3 layer has been illustrated in Fig.2.5. The darker, spherical areas within this

layer indicate porosity.

The alumina topography observed for AA5754 alloy using AFM is illustrated in Fig.2.6. To

be noted is that this topography is different than for the 2024 aluminium being less peaky.

Thus the 2024 alloy offers better surface development, enhancing adhesion.

ANODE:

Aluminium

Electrolyte:

10% wt. H3PO4

+ H2O

CATHODE:

Titanium grid


68

Fig.2.4. Topography of AA2024-T3 before (left) and after anodization (right).

Fig.2.5. Alumina layer obtained on Al-Cu alloy.

Fig.2.6. Topography of AA5754-H111, before (left) and after (right) anodization.

Al2O3

2024 alloy

Michał K. Budzik

69

2.1.4. Fabrication of adhesive joints

Following the appropriate surface treatment (section 2.1.3) of the substrates the plates were

bonded using one of the adhesives described. Based on standard symmetric DCB sample

geometry a new asymmetric specimen was introduced in this work (see Fig.2.7).

Fig.2.7. Symmetric and asymmetric adhesive joints.

Routine preparation of the joint is shown by the block scheme Fig.2.8.

Fig.2.8. Block scheme o sample fabrication.

Bondline thickness, e was maintained by inserting PTFE (Teflon®) spacers of a given

thickness (depending on the test) at the two joint extremities (see Fig.2.9). The constancy of

the bondline was checked by optical microscopy.

Fig.2.9. The constancy of the bondline maintained by PTFE spacers.

e

Rigid

substrate The

adhesive

Flexible

substrate

PTFE spacers

Cutting of

substrates

Substrates

surface

preparation

Bonding

with

appropriate

adhesive

Adhesive

crosslinking

Edge

polishing

2Δ

SYMMETRIC JOINT

GEOMETRY

ASYMMETRIC JOINT

GEOMETRY Δ

Flexible

substrate

Rigid

substrate


70

After crosslinking of the adhesive sample edges were polished using abrasive emery paper of

the grit 600-2400 to permit in situ crack path observation from the sample side (see Fig.2.10).

Fig.2.10. Flight-view of the side-camera observations made during the tests.

2.2. Microscopic studies

Atomic Force Microscopy (see section 2.1.3) was used to study the effects of PAA surface

treatment on surface topography. Optical Microscopy (OM), Scanning Electron Microscopy

(see section 2.1.3) were used to observe the quality of the adhesive joints, crack paths inside

the adhesive and interlayers but also for fractography. The optical microscope was Leica

Reichert MEF4M (Leica Camera AG, Wetzlar, Germany) coupled with Canon Power Shot

G5 photo camera (Canon Inc., Tokyo, Japan). For SEM and OM studies edge of the samples

were abraded using 200- 2400 grit paper and polished using alumina polishing powder.

Fracture surfaces were left untouched after fracture. Samples used for SEM study were

sputtered with gold – platinum conductive layer in order to allow electron flow.

2.3. Crack path observations

In situ crack path observations (see Fig.2.10) were made using one of the three camera

systems:

a) Canon D40 Photo Shot Camera (Canon Inc., Tokyo, Japan) - used in the test with

polycarbonate substrate and in CRT and CFT

b) Digital Micro Camera (Dino-Lite Pro-IS Production S.A., St. Genis Pouilly, France) –

used in the elevated temperature CDT test

c) CCD (Charge – Coupled Device) camera Ikegami ICD 47E (Ikegami Tsushinki Co.,

Ltd., Tokyo, Japan) – used in variable adhesion tests with CFRP substrate.

Polished

side Tracking

Camera

JOINT

Michał K. Budzik

71

Chapter 3. ADHESIVE BONDING TESTS AND ANALYSIS

In order to study the adhesive joint strength and the efficiency of adhesive bonding for given

materials systems the following tests were introduced and performed: Constant Rate Test

(CRT), Constant Force Test (CFT) and Constant Displacement Test (CDT). The CRT and

CDT tests were previously run for symmetric joints (DCB test and Wedge Test respectively),

accordingly introducing new asymmetric specimen required the development of entirely new

tests (features and metrology model in both cases and completely new metrology for CDT

test). The CFT test is entirely new test developed in this thesis. The Catia v5 (Dassault

Systems, Vélizy-Villacoublay, France) environment was used to design the test features.

Finite Element Method (FEM) using Caste3M (French Atomic Energy Commissariat, Gif-

sur-Yvette, France) was employed to analyze stress state within the joint introduced by the

proposed geometry of the joint. Additionally analytical model were proposed to study

background effects of the proposed tests. Proposed test are based on energy release rate

(Fig.3.1) consideration which are used here to evaluate the fracture energy.

Fig.3.1. Energy Release Rate principle (Δ-separation distance, F-applied force, a-crack length,

δa-crack length increment, U-stored elastic energy).

The strain energy release rate, for the cases when either displacement, Δ or applied force, F

are resulting in e.g. plate separation can be calculated as:

(1.30)

Crack propagation criteria are:

G=Gc – threshold

G<Gc – crack stabilization

G>Gc – unstable crack growth.

At threshold, G=Gc – is named critical energy release rate, fracture energy, fracture toughness

or like in the adhesion fracture tests – the work of adhesion forces.

F

Δ


72

3.1. Constant Rate Test (CRT)

Constant Rate Test is closely related to the standard DCB test. The modification are

asymmetric sample geometry and data reduction method and test interpretation. Flexible

substrate deflection, Δ and applied force, F are recorded and used directly to calculate joint

fracture properties. The setup was built using universal tensile machine adopted to fix

specimen and the force as well as displacement sensors (see Fig.3.2).

Fig.3.2. Constant Rate Test sample (a) and principle of the test (b).

The rigid adherend (1) is fixed to tensile machine frame with screws. The flexible adherend

(2) is connected by the hinge (4) to the force sensor (5) and tensile machine crosshead with

the steel chain (Ф 4mm). In addition, displacement sensor (6) is mounted under the flexible

beam to permit direct plate deflection measurements. Test begins with crosshead move up to

the moment when strain energy stored in the flexible beam exceeds critical fracture energy,

this initiate crack propagation. Since tensile machine crosshead speed is kept constant during

the test the deflection Δ is increasing linearly with time, thus only force F is unknown. The

5

To tensile machine

crosshead

6

Tensile Machine frame

1 4

2

3

dΔ/dt = const

a)

b)

Michał K. Budzik

73

Δ = f(t)

F = f(t)

a = f(t)

z

x

force measurement was carried out using strain gauge force sensor Instron with 500N load

carrying capacity (Instron, Norwood, USA). Plate deflection measurements were made using

LVDT (Linear Variable Differential Transformer) sensor Peltron PSzl 20 (Peltron Ltd.,

Warsaw, Poland). This test was found previously (in symmetric specimens) to be very rate

dependent which is particularly pronounced when the adhesive is highly viscoelastic.

Therefore brittle adhesives were chosen for CRT. The CRT routine is illustrated in Fig.3.3.

Fig.3.3. CRT test routine.

3.1.1. Data reduction method

The CRT test was analysed using Euler-Bernoulli simple beam theory (SBT) [191]. The test

physical model is based on that of cantilever beam and is shown in Fig.3.4.

Fig.3.4. Constant Rate Test physical interpretation.

Using general fracture energy balance proposed by Griffith:

(3.1)

where:

G – fracture energy

U – strain energy release rate

a – crack length

b – constant (width of the beam).

Irwin – Kies fracture mechanics compliance criteria can be used to evaluate fracture energy:

(3.2)

where:

PC

F = f(Δ)

A/D

converter Displacement

sensor, Δ

Force sensor, F (V)

(V)


74

F – applied force

C – compliance:

(3.3)

Δ – beam deflection at the point of applied force.

Bending moment, M distribution along the longitudinal x beam direction due to the applied

force, F:

(3.4)

Governing simple beam theory equation is given by:

(3.5)

where:

Eh – Young modulus of flexible adherend

Ih – second moment of inertia of the beam cross section.

Equation (3.5) is double integrated with appropriate boundary conditions to yield the solution

in terms of plate deflection. The boundary conditions are:

(3.6)

(3.7)

Following the coordinates from Fig.3.4, for simple beam model we can write down the

deflection of the beam equation:

(3.8)

From which compliance is evaluated:

(3.9)

Now:

(3.10)

Michał K. Budzik

75

Substituting (3.10) to (3.2) we obtain:

(3.11)

with Ih:

(3.12)

From (3.8) and (3.12) we may find apparent crack length:

(3.13)

It must be noticed, that the crack length equation is correct only when force and displacement

are measured in the same line, as was made in the studies. Finally, (3.11) and (3.13) gives

fracture energy:

(3.14)

Errors of crack length and energy release rate estimations were calculated using error

propagation method [192]. Following the rule:

(3.15)

Crack length estimation error is found:

(3.16)

Error of energy release rate estimation, G can be written as:

(3.17)

Finally, the energy release rate error in Constant Rate Test is found:


76

(3.18)

3.1.2. Calibration of the crack length - artificial crack tip test

In order to compare the estimated crack length, a calculated using (3.13) with the real –

established and directly measured crack length, aD artificial crack tip test was developed, in

which a moving clamp was introduced to simulate the moving crack front (Fig.3.5). The same

aluminium adherends as described above, of thicknesses 6 and 1.6 mm were employed.

Instead of bonding them together with an adhesive, a simple screw-based, collar-like

clamping system was devised, which could be slid over the joint section, i.e. both adherends

were placed together, as though bonded, and secured at aD equivalent to crack-length,

measured directly with calliper gauge (see Fig.3.5). This technique permitted both, the

fabrication of artificial joints, described here, by the clamping of unbonded aluminium plates

at a desired value of aD, before the test, and also the reconstitution of bonded samples, either

partially or totally separated during prior tests, both to corroborate crack-length evaluation

and check that plastic adherend deformation had not occurred during a test. However, due to

the imposed, straight crack-front parallel to the y axis in this technique, any effects due to

anticlastic bending, or other phenomena leading to non-rectilinear fracture fronts are

necessarily neglected [177]. Similarly, any possible influence of a deformable elastic

foundation ahead of the crack front, or root rotation, is neglected [167,173,193,194].

Fig.3.5. Scheme of the artificial crack tip test.

The artificial crack tip test was performed for the range of the beam lengths, aD from 35 to

105 with 10 mm step, three times for each length for three different AA2024 plates. The

results of this test were used to find out crack length calibration curve (Fig.3.6) and are listed

in Table 3.1.

Force

sensor

LVDT

displacement

sensor

Machine

frame

aD

Moving

clamp

Michał K. Budzik

77

30 40 50 60 70 80 90 100 110

30

40

50

60

70

80

90

100

110

a (

mm

)

aD (mm)

a = 1.0089 aD

R2 = 99.97%

Fig.3.6. CRT calibration curve.

Table 3.1. Results of artificial crack tip test.

Direct crack length

aD (mm)

Estimated crack length

a (mm)

Standard deviation

σd(a)(mm)

35 35.9 0.8

45 46.6 0.5

55 54.4 0.6

65 63.3 0.4

75 75.3 0.2

85 84.9 0.5

95 98.4 1.0

105 108.0 0.4

3.1.3. Fracture of aluminium joints bonded with nanoparticle adhesive

The aim of this study was to compare the micro and macro scale behaviour of the

aluminium/aluminium adhesive joints bonded with two epoxy adhesives: pure and reinforced

with clay nanoparticles. Moreover, the focus was on the novel use of the constant (deflection)

rate test to study adhesion/adhesives efficiency. Nanoparticle reinforcement is a new trend in

the manufacturing of advanced adhesives with improved fracture resistance [195-197]. The

reason to use clay reinforcement is that the particles are natural, thus ecological, moreover

they are cheapest available nanoparticles. In addition density of MMT is much less than those

of metallic or ceramic particles, and are likely to increase strength of the joints [198,199].

Materials and specimen preparation

Aluminium alloys used were: AA2024 (Al-Cu) (upper, flexible plate, h=1.6 mm) and

AA5754 (Al-Mg) (lower, rigid plate, H=6 mm). The plates were bonded along ladh=70 mm


78

with two adhesive systems. First was epoxy resin - Epidian®6, the second system was the

same resin reinforced with 5% of 1-D montmorillonite nanoparticles. Prior to bonding plates

were degreased, abraded, and electrochemically treated with PAA. Bondline thickness for all

samples was 600±40 μm (measured with optical microscope). Before the test samples were

precracked by insertion of the wedge between two bonded plates. The force sensor was

Instron with 200 N capacity and LVDT displacement sensor Peltron PSzl. The temperature

during tests was 20±2oC, and ca.55±5% RH. Two displacement/deflection rates were used:

vD=0.485 mmh-1

- fast, and vD=0.248 mmh-1

- slow with the corresponding numbers I and II

respectively for both adhesive systems (Fig.3.7). In addition, macro (Digital Camera Canon

D40), microoptical (Leica MEF 4M with Canon Power Shot G5) and SEM views of fractured

surfaces were made.

0 1 2 3 4 5 6 7 8 9 10 11 12

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Dis

pla

cem

en

t,

(m

m)

Time, t (h)

Epoxy I

Epoxy II

Epoxy + Nano I

Epoxy + Nano II

vD = 0.485 (mm h

-1)

vD = 0.248 (mm h

-1)

Fig.3.7. Specimen deflection vs. time for two adhesive systems and two displacement rates.

Macromechanics of fracture

Crack growth rate in the adhesive joints was evidently dependant on the adhesive system used

to bond the plates. Crack propagation plots are shown in Figs.3.8a and 3.8b. To be noted are:

nonlinear graph profile (Fig.3.8b) followed by quasi-constant crack growth (vc=const.) and

distinct difference in the behaviour of the two material systems at lower displacement rate

(constant crack growth rate regime). Crack growth rate of the Epoxy+Nano II (lower

displacement rate) specimens is markedly lower than one of the pure resin samples. This was

also found during macrographic studies of fracture surfaces. Three distinct crack speed

sections were found (see Fig.3.9). The advantage of the epoxy system strengthened with

nanoparticles over pure epoxy adhesive is illustrated in Figs.3.10. and 3.11. showing the

average fracture energy and crack growth rate vs. strain rate for the two adhesive joints

studied in this work. The difference is ca. 30% in terms of fracture energy in favour for MMT

reinforced adhesive. In addition, crack rate is in this case smaller, thus using of the MMT

reinforcement results in better joint performance.

Michał K. Budzik

79

Fig.3.8. Crack increment vs. time plots. Nonlinear graph profile (in square) followed by quasi-

constant crack growth (vc~const) (left). Nonlinear part of the graph at the onset of crack

growth (t=0-1.5h) (right).

Fig.3.9. Macrographic view of fracture surfaces: River patterns regions (inside white boards)

and three distinct crack speed sections indicated with white arrows: I – fast crack speed

(probably during wedge insertion), II – medium – decreasing crack speed (probably nonlinear

part of Fig.3.8), III – stable crack growth (linear part of Fig.3.8).

Fig.3.10. Average minimum fracture energy for aluminium bonded with reinforced and pure

epoxy adhesive (left).

Fig.3.11. Crack growth rate vs. deflection rate for the two systems: with and without

nanoparticles (right).

0

20

40

60

80

100

Fra

ctu

re e

nerg

y, G

Ic m

in (J

m-2

)

Epoxy + Nano

Epoxy

0.25 0.30 0.35 0.40 0.45 0.50

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

vc (

mm

h-1

)

vd (mm h

-1)

Epoxy

Epoxy + Nano

I I

I III

CRACK DIRECTION

25 m

m

70 mm

Riv

er p

att

erns

regio

ns

0 1 2 3 4 5 6 7 8 9 10 11 12

0

5

10

15

20

25

30

35

40 Epoxy I

Epoxy II

Epoxy + Nano I

Epoxy + Nano II

Cra

ck in

cre

me

nt,

a (

mm

)

Time, t (h)

0 1

0

5

10

15

Epoxy I

Epoxy II

Epoxy + Nano I

Epoxy + Nano II

Cra

ck in

cre

me

nt,

a (

mm

)

Tme, t (h)


80

Micromechanics of fracture

The illustration of fracture surfaces are shown in Figs.3.12 and 3.13 for the two epoxy

systems at lower and higher strain rates. The centre of the specimens was selected for optical

examination. No difference in the fracture surface profile of the two adhesive systems was

noted for the same strain rate. However, there is a marked difference in the appearance of

fracture surfaces depending on the crack growth rate for both materials. The higher the

deflection rate the coarser the fracture surface which implies that microstructural effects are

more present at lower deflection rate (fine fracture surface). Accordingly, very slow

deflection rate is recommended in further study of microstructural effects. The explanation is

time dependant nature of the mechanical properties of epoxy-based materials. Excessively

high deflection rate does not allow micromechanical effects to take place at least from optical

microscope observations. Therefore SEM studies using 200x-4000x magnification were

carried out, where the differences are more pronounced. Results of these observations are

shown in Figs.3.14 and 3.15 Brittle fracture was found in all of the observations. Noteworthy

is the difference in fracture surfaces between pure epoxy and MMT modified resins where the

former gives bigger active fracture surface area due to visible 1-D nanoparticles and thus

additional surface development. It has to be pointed out that fracture surface depends on crack

speed, and thus at higher speed giving smooth, almost glassy surface while rough when the

crack speed is low.

Fig.3.12. Optical micrographs of fracture surface of E6 resin, after lower (left) and higher

crack growth rate (right).

Fig.3.13. Optical micrographs of fracture surface of E6 with nanoparticles, after lower (left)

and higher crack growth rate (right).

Michał K. Budzik

81

I – FAST

II – TRANSITION

III - STABLE

Fig.3.14. SEM fractographs of pure DGEBA epoxy for different crack speeds regimes (in

columns) and for different magnifications (in rows: 200-500-1000x).


82

I – FAST

II – TRANSITION

III - STABLE

Fig.3.15. SEM fractographs of epoxy reinforced with 5% of MMT 1-D nanoparticles for

different crack speeds (columns) and magnifications (rows). Arrows indicates nanoparticles.

In addition, microscopic studies disclosed some interesting phenomena, difference between

fracture surfaces at the sample side and in the middle of the sample. Difference was

particularly marked in the fast crack propagation regions (see Fig.3.8). The fractographs

Michał K. Budzik

83

indicates possible high anti-plane shearing stress and thus mode mixity regions near the

sample side edges which results in river patterns (see Figs.3.15 and 3.16).

Fig.3.16. SEM fractographs made at the middle of the sample (left) and near the side edge

(right). Arrows indicates features of the river patterns phenomena.

Fig.3.17. Side view of Fig.3.16 made using optical microscope.

3.2. Constant Force Test (CFT)

Constant Force Test (CFT) is a new test introduced within the thesis. Differences between

CFT and the standard DCB test are in sample geometry and loading conditions. In this test

only flexible substrate deflection, Δ, is recorded during the test, the applied force, F, is kept

constant. The test setup was designed in Catia v5 (Dassault Systems, Vélizy-Villacoublay,

France) environment using Mechanical Design tool. The schematic illustration of the test and

its principle are shown in Fig.3.18. The rigid adherend (1) is fixed to the frame using screws.

The flexible adherend (2) is connected by a hinge, placed at the one of the flexible plate

extremities (see Fig.3.2), with the mass (4) by a steel chain (Ф4 mm). A displacement sensor

(3) is mounted to the frame so that the sensor tip is touching the flexible adherend exactly

under applied force. This permits direct plate deflection measurements in the point of the

highest deflection, in addition simplifying data reduction.

CRACK DIRECTION

100 μm


84

a = f(t)

x

z

F = const

Δ = f(t)

Fig.3.18. Schematic representation of the CFT test.

The test begins by hanging an appropriate mass, thus applying constant force, F. When the

strain energy stored in the flexible substrate achieves the critical value of the fracture energy,

the crack begins to propagate, in CFT, initially at a slow rate. The crack accelerates with time

as the crack length, a, increase and thus bending moment grows. The crack position is

manifested by the change of deflection of the flexible substrate, Δ which is the only variable

to be measured. Deflection was measured with 10 mm range RDP DCTH 200 AG LVDT

(Linear Variable Differential Transformer) sensor (RDP Electronics Ltd., Wolverhampton,

UK). The block scheme of the built metrological circuit is illustrated in Fig.3.19. In addition

the CFT test, in principle, allows full characterization in one test of the crack speed, v vs.

fracture energy, GC.

Fig.3.19. Block scheme of metrological circuit.


In the CFT test crack propagation is manifested by the change of the flexible plate deflection,

Δ. The physical model of the test, shown in Fig.3.20, is based on the cantilever beam. The

Euler-Bernoulli simple beam theory (SBT) mathematics was used for data reduction.

Fig.3.20. Constant Force Test physical model.

PC

Δ=f(t)

Displacement

sensor, Δ

(V) A/D

converter

3

Clamps

4

1

2

Michał K. Budzik

85

The distribution of the bending moment, M, along x due to the applied force, F is:

(3.19)

The governing equation of the simple beam theory SBT is:

(3.20)

The plate deflection is found from double integration of (3.20) with appropriate boundary

conditions. The boundary conditions used are:

(3.21)

(3.22)

Finally, the plate deflection along the x:

(3.23)

Because the LVDT sensor is measuring the deflection exactly under the applied force, F, it

can be written:

(3.24)

With the second geometrical moment of inertia of the flexible plate section:

(3.25)

We can write the estimate of crack length:

(3.26)

In order to find the fracture energy, the classical Irwin-Kies relation can be used:

(3.27)


86

where C is compliance (Δ/F).

Now using (3.24):

(3.28)

(3.29)

Thus:

(3.30)

Finally, the energy release rate is given by:

(3.31)

It should be noted that the formula is exactly the same as for the Constant Rate Test. Thus the

change is in that F is now constant, which gives the metrological advantage of measuring only

one variable. In addition, the CFT test is compliance (e.g. machine, chains etc.) effect free.

Estimation of the CFT method error was achieved using propagation of errors. Crack length,

a, error:

(3.32)

(3.33)

Error of energy release rate estimation, G:

(3.34)

Michał K. Budzik

87

(3.35)

3.2.2. Artificial crack tip test

To verify assumption about the mathematical and physical model the artificial crack tip test,

described previously (see section 3.1.2) was performed. Schematic presentation of the made

test is illustrated in Fig.3.21.

Fig.3.21. Artificial crack test in Constant Force Test configuration.

Three aluminium AA2024 plates were used. Four different force values were applied. The test

was performed for the range of crack lengths, aD, from 35 to 105 mm with 10 mm step

(measured with calliper gauge). Since plates were used instead of beam elements, equation

3.24 was verified. Results are illustrated in the left of Fig.3.22. The calibration curve is

illustrated on the right of Fig.3.22. All data from the artificial crack tip test are summarized in

the Table 3.2.

Fig.3.22. Linear force – deflection relation (left) and crack length calibration curve (right).

30 40 50 60 70 80 90 100 110

30

40

50

60

70

80

90

100

110

120

a (

mm

)

aD(mm)

a = 1.069 aD

R2 = 99.92 %

0 2 4 6 8 10

0

5

10

15

20

25

30

35

40

F = 3.0356

R2 = 99.86 %F =

4.5

271

R2 =

99.9

8 %

F =

7.0

236

R2 =

99.

82 %

F =

11.6

75

R2 =

99.9

5 %

F =

20.0

7

R2 =

99.7

6 %

areal

= 40 mm

areal

= 50 mm

areal

= 60 mm

areal

= 70 mm

areal

= 80 mm

Fo

rce,

F (

N)

Deflection, (mm)

LVDT

displacement

sensor

aD

Artificial crack tip

Δ

Mass, F


88

Table 3.2. Results of artificial crack tip test for CFT configuration.

Direct crack estimate, aD

(mm)

Estimated crack length, a

(mm)

Standard deviation, σd(a)

(mm)

35 37.3 0.4

45 51.4 0.4

55 58.0 0.7

65 66.6 0.3

75 79.9 0.2

85 90.8 0.9

95 105.3 0.5

105 113.7 0.7

3.2.3. The (macro) fracture behaviour of different adhesives

In order to find out the features of the Constant Force Test when applied to real joints, the test

was used to evaluate fracture properties of different popular adhesive systems. Three different

adhesives were used: cyanoacrylate adhesive, acrylic mastic and PSA double face Scotch®.

The reasons to choose those adhesives adhesive are their different behaviour in loaded

conditions as well as their common commercial use. In addition, they can be competitive in

many fields to epoxy adhesives. Particularly PSA adhesives are nowadays extensively

developed for practical reasons (easy, fast application) and their possible applications in

structural bonding. In fact, PSA adhesives promise such easiness of application that all

engineers wish to have, still their strength and durability must be improved. The aim of this

comparative study of several different adhesives was to consider macro scale behaviour of the

aluminium/aluminium adhesive joints. The focus was also on the novel Constant Force Test

to study adhesion/adhesives efficiency. It must be pointed out that the CFT test and

characteristics obtained are presented for the first time within this work (to own knowledge).

Materials and specimen preparation

Aluminium alloys used were: AA2024 and AA5754. The plates were bonded along ladh=70

mm. Prior to bonding plates were degreased, abraded, and electrochemically treated with

PAA. The bondline thickness, e, for all samples was 200±10 μm. Before the test

cyanoacrylate samples were precracked by insertion of the wedge between two bonded plates.

Mastic and PSA adhesives did not require this operation. The conditions of the test were:

20±2oC, and ca. 55±5% RH.

Crack behaviour

The crack increment, δa vs. time, t characteristics are shown in Fig.3.23. To be noted is the

significant difference in the crack increments between elastic adhesives (mastic and PSA) and

brittle (cyanoacrylate). The crack growth rate in the adhesive joints tested was evidently

Michał K. Budzik

89

dependent on the adhesive system. I is worth noting that the crack growth rate accelerates

almost immediately from the onset of the load.

Fig.3.23. Crack increment for cyanoacrylate (Cyanoacrylate), acrylic mastic (Mastic) and

double face scotch (PSA) adhesives (left).

Fig.3.24. Crack speed characteristics. Vertical lines corresponds to the estimated time of

overall failure due to accelerating crack growth (right).

The observations from crack propagation are manifested in crack speed characteristics. It

must be pointed out that the value of the measurable crack speed is limited by time intervals

used between two measurements. Here measurement were taken every 45 seconds, thus the

maximum measureable speed is δa/45s (in practice ca. 50 mm/h).

Fracture energy

Fracture energy, Gc vs. crack speed, v are the data most required from fracture tests (Fig.3.25)

and are rarely presented in the literature in continuous form. Cyanoacrylate adhesive

possesses the best fracture characteristics, giving smooth, linear curves with small gradient.

The same linear relation can be observed for the mastic adhesive but for 2 times smaller

energy values. The PSA adhesive shows the worst characteristics. PSA was found most

sensitive to crack speed, promising the smallest energy and inhomogeneous energy transfer.

Although fully quantitative studies were not the main interest here, it must appreciated that for

the crack speed range presented, cyanoacrylate adhesive has about 200-260 Jm-2

fracture

energy, with mastic 25-40 Jm-2

and PSA 0.8-20 Jm-2

. This shows the abilities and versatility

of the CFT test in measuring fracture properties of the adhesive joints.

1 10

0.1

1

10

100

Cyanoacrylate

Mastic

PSA

Cra

ck

sp

eed

, v

(m

mh

-1)

Time, t (h)

0.1 1 10

0

5

10

15

20

25

30

Cra

ck

in

cre

men

t,

a (

mm

)

Time, t (h)

Cyanoacrylate

Mastic

PSA


90

Fig.3.25. Fracture energy characteristics for the tested materials.

Nonlinear effects

In the CFT test, nonlinear behaviour and/or elasticity of the adhesive was manifested (see

Fig.3.26).

Fig.3.26. The example of creep behaviour (or adhesive elastic deformation) at the beginning

of the observed in mastic adhesive. On right, close up of elastic foundation region.

This effect can be related to many different molecular phenomenon. From a modelling

standpoint this could be approached with combination of parallel springs, possessing some

vertical stiffness and deforming under any applied load. In the case of a soft adhesive, where

the observed effects are particularly pronounced a process zone (see Fig.3.27) [194,200,201]

is created earlier. Process zone is defined as a zone in front of the crack tip affected by applied

load and in the study was not estimated. This effect should be studied because it can lead to a

wrong estimation of crack length and fracture energy. Basically we consider this zone (of

d2Δ/dt

2<0) as being due to adhesive time-dependent strain, rather than crack growth.

Nonlinear effects at the beginning of the test can be related to phenomena such as: Payne or

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

2

4

6

8

10

12

Cra

ck in

cre

me

nt,

a (

mm

)

Time, t (h)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.0

0.2

0.4

0.6

0.8

1.0

Experiment

a = 1.047 t0.2403

Cra

ck in

cre

me

nt,

a (

mm

)

Time, t (h)

1 10 100

10

100

Cyano

Mastic

PSA

Fra

ctu

re e

nerg

y,

Gc (

Jm-2

)

Crack speed, v (mmh-1)

Michał K. Budzik

91

Mullins effects, adhesive relaxation or adhesive creep under constant applied force. However,

presented here briefly elastic interpretation of the initial adhesive behaviour which may be

very promising, and could possibly allow direct fracture energy estimation using the classical

Dugdale model.

Fig.3.27. Schematic representation of the process zone.

3.3. Constant Displacement (Asymmetric Wedge) Test

Constant Displacement Test (CDT) is an asymmetric version of the popular Boeing Wedge

Test. The test setup was designed using Catia v5 environment and is schematically illustrated

in Fig.3.28. The rigid substrate (6) is fixed to the aluminium block/wall (7) using screws. The

pin (8) is used to place and assure vertical position of the sample. The wedge (3) of

aluminium of thickness, Δ is pushed by the screw based system (1 and 2) while guides assert

appropriate wedge position. If necessary vertical position of the entire system allows water

immersion tests. The test begins as the wedge is inserted manually to the desired position,

which results in the elastic deformation of the flexible plate (4) and the propagation of crack

continue at its self-determined rate. The test stops when strain energy stored within the

flexible adherend achieve value of the adhesive (5) minimum fracture energy, Gc. Within this

thesis novel crack length measurement method is reported. The upper surface of the flexible

beam was instrumented with series of strain gauges attached along the direction of crack

propagation. Strain gauges used were Vishay Micro-Measurements, reference EA-13-060LZ-

120/E (Vishay, Malvern, PA, USA) of nominal resistance 120Ω. Strain gauges were

connected in Wheatstone quarter-bridge circuit using Vishay Micromesures 2100 System

Multi Channel Signal Conditioner/ Amplifier with ten modules of Model 2120 B Strain

Gauge Conditioner/Amplifier, and one module of Model 2110 B Power Supply.

PROCESS

ZONE


92

Fig.3.28. Schematic representation of the CDT test.

The CDT test metrological routine is shown in Fig.3.29.

Fig.3.29. CDT metrological circuit.


Cantilever beam physical model and simple beam theory (SBT) mathematics were used to

analysis the Constant Displacement Test (see Fig.3.30).

Fig.3.30. Physical model of CDT.

a(t)

x

R

z Δ=const

Strain gauge Wheatstone

bridge

A/D

converter

PC

ε = f(t)

(Ω) (V)

1

2

3

4

5

6

7

8

4

3

6

Michał K. Budzik

93

Governing equation of SBT is:

(3.36)

With bending moment, M distribution:

(3.37)

Double integration of equation with appropriate boundary conditions yield the solution in

terms of plate deflection. The boundary conditions are:

(3.38)

(3.39)

plate deflection along the x:

(3.40)

Since displacement not force is applied to separate bonded plates, we can write:

(3.41)

Finally we obtain relation between crack length and wedge thickness, Δ:

(3.42)

Energy balance method was used to evaluate the energy release rate, G:

(3.43a)

(3.43b)

where terms corresponds to: work, W, done by force F to propagate the crack (=0), change in

elastic energy, U, due to crack propagation and adhesion energy to create new crack

increment, δa.


94

The elastic energy is given by:

(3.44)

From (3.44) and (3.41):

(3.45)

Now, change of the elastic energy due to propagating crack – the energy release rate can be

found:

(3.46)

with

- geometrical second inertia moment of flexible adherend section.

From (3.43), we obtain (the minus sign is the convention used, since the energy is releasing-

giving out from the systems):

(3.47)

Energy release rate expression in asymmetric CDT:

(3.48)

It has to be pointed out that energy in asymmetric test is different from symmetric by the

factor of 2. In addition, like in the symmetric version of the test, G is very sensible to crack

length, a with scaling of -4th

power.

Crack length and energy release rate estimation from strain measurements

To obtain results in terms of the crack length and fracture energy strain measurements were

performed. Strain in the upper layer of flexible member (absolute value is given since upper

layer is submitted to compression):

(3.49)

With inversed beam radius, R(x)-1

:

Michał K. Budzik

95

(3.50)

Strain can found as:

(3.51)

Thus, only one strain gauge based at xє<0, a> is required to find out the actual crack position

and to measure crack length growth. Due to possible misalignment error e.g. inappropriate

strain gauge bonding, singular strain gauge properties or possible failure of the single gauge

using test can be unsuccessful or lead to misinterpretation. From (3.51) linear relation

between measured strain |εs(x)| and strain gauge position x, can be noted. This allows one

parameter linear regression analysis and thus a series of strain gauges were used.

(3.52)

Therefore, combining the data from the various strain gauges in their different relative

positions (x) with respect to the crack front, an accurate, and potentially continuous

assessment of crack length can be obtained.

Now, criteria for best α, (for n – strain gauges, with i for ith

gauge):

(3.53)

where:

|εs(x)|th - theoretical strain value at x

|εs(x)|exp - experimental value of strain at x.

This yields:

(3.54)

The minimum criteria is kept if, first derivation of the sum over α is equal 0, so:

(3.55)

The best estimation of α can be written:


96

(3.56)

Thus, statistically, best crack length is:

(3.57)

Strain estimation will include the error of Δα and thus:

(3.58)

To calculate error of our estimation propagation of error method was used assuming no error

on x, thus:

(3.59)

with:

yi = |εs(xi)|exp.

We can write:

(3.60)

And:

(3.61)

Hence all y have equal weight, so Δy1= Δy2 =...Δyn=Δy:

(3.62)

The best estimation of the strain standard deviation is given for n-1 strain gauges:

(3.63)

Michał K. Budzik

97

From definition of α:

(3.64)

(3.65)

(3.66)

So:

(3.67)

And finally the estimation error, Δα:

(3.68)

Crack length error will be therefore:

(3.69)

So:

(3.70)

The energy release rate error:

(3.71)

Finally:


98

(3.72)

3.3.2. Calibration of the CDT test using artificial crack tip test

Artificial Crack Tip Test technique was employed in order to estimate the accuracy of the

strain gauge technique developed here, without using an actual adhesive joint. Strain gauges

were bonded in place along the central line of the thin adherend, at values of x of 16, 26, 36

and 46 mm (Fig.3.31).

Fig.3.31. Artificial crack tip test principle.

Strain measurements were made for two wedge thicknesses, Δ - 4.6 and 9.7 mm, and six beam

lengths, aD: from 35-100 mm (measured directly using calliper gauge). The example of the

crack lengths estimation by a single gauges, using eq.3.51 are shown in the left of Fig.3.32.

On the right of the Fig.3.32 crack estimation-strain gauge position linear relation is shown. In

addition, eq.3.52 was verified. Results are illustrated in Fig.3.33 (left). Experimental results

are summarized in Table 3.3, and are shown in Fig.3.33 (right) as a crack length calibration

curve.

Screw system

a

Clamps

x1 x2

x3

x4

y

x

z

x

Michał K. Budzik

99

Fig.3.32. Verification of eq.3.51 (left). Estimated crack length value, a vs. strain gauge

position, x relation (right).

Fig.3.33. Verification of eq.3.52 (left). Crack length calibration curve, a vs. aD (right).

Table 3.3. Results of the crack length estimation with artificial crack tip test.

Direct measurement, aD

(mm)

Strain gauge estimate, a

(mm)

Standard deviation, σd(a)

(mm)

35 33.7 0.3

50 49.2 0.4

65 63.8 0.4

75 74.9 0.4

85 86.9 0.4

100 101.2 0.5

3.3.3. Surface treatment effect in CDT test

In order to verify the CDT method two different surface treatment of the aluminium plates

were employed. The aluminium surfaces were prepared either by simple abrasion or by

electrochemical treatment. Bondline thickness was maintained at ca. 0.35. Five longitudinal

strain gauges were fixed. The values of x1 to x5 were respectively 35, 45, 55, 75 and 85 mm.

Initially, two strain gauges are within the limits of the bonded region, and three without, as is

15 20 25 30 35 40 45 50

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.0010

0.0011

0.0012 Experimental points

|s(x)|= 2.53668* 10 -5

x

R2

=0.99986

Ab

solu

t st

rain

, |

s(x)|

Gauge position, x (mm)

= 4.54 mm

a = 75 mm

30 40 50 60 70 80 90 100

30

40

50

60

70

80

90

100

a (m

m)

aD (mm)

a = 1.0017 aD

R2 = 99.96%

40 42 44 46 48

74.0

74.1

74.2

74.3

74.4

74.5

74.6

74.7

74.8

74.9

75.0

75.1

75.2

x1 = 16 mm

x2 = 26 mm

x3 = 36 mm

x4 = 46 mm

Cra

ck l

eng

th,

a (m

m)

Time, t (s)

15 20 25 30 35 40 45

74.0

74.2

74.4

74.6

74.8

75.0

Cra

ck

len

gth

est

imati

on

, a (

mm

)

Strain gauge position, x (mm)

a = 0.0227x + 73.7388

R2 = 99%


100

shown in Fig.3.34. The wedge thickness, Δ was 4.5 or 9.7 mm. Two tests for each of the two

surface treatments were effected at 20 2°C, and at an ambient humidity of ca. 55% RH.

Fig.3.34. Schematic representation of tested sample.

Crack propagation

The evaluation of crack propagation kinetics can be virtually continuous with this strain gauge

technique, leading to detailed crack monitoring. Fig.3.35 represent crack length increment, δa,

vs. time, t, for the abraded and the PAA treated wedge tests.

0 50 100 150 200 250 300 350 400 450 500 550 600

0

2

4

6

8

10

Anodized

Abraded

Cra

ck

in

cre

men

t,

a (

mm

)

Time, t (h) Fig.3.35. Crack length increment, δa with time, t.

Δ

85

35

45

55

75

a(t0)=67 mm ladh(t0)=33 mm

y

x

z

x

R~εs-1

Michał K. Budzik

101

Noise on the measurement (electric) of a is typically less than 0.1 mm, and at worst less than

0.2 mm. This noise has been removed for aesthetic reasons, since it only essentially thickens

the graphic line. Error bars, shown for various values of time, t, were calculated using (3.69)

and those associated. As can be seen, estimated errors are similar for the two treatments and

reasonably independent of crack length, being of the order of ±0.5 mm. The general features

of wedge tests results are present in both cases, viz. continuously increasing crack length, a(t),

with time, t, and concomitant decrease of da(t)/dt, as strain energy release rate diminishes.

This is a typical trait of adhesive fracture, as first exemplified with elastomers many years ago

[e.g. 202,203]. Despite these overall trends, there are second order changes in gradient, with

slight ups and downs, which are presumably related to a degree of inhomogeneity of the

adhesive joint. Such effects are rarely reported in the literature, presumably quite simply

because most techniques for measuring crack length cannot be employed in continuous mode,

in contrast to the present method. Other advantage of using strain gauge technique is

possibility to check if any plastic deformation of the substrate occurs during the test. This will

be manifested by non-zero strain signal after finished test. The reconstituted joint led to

reproducible surface strain values, and did not reveal any permanent set. The most dangerous

situation is at the beginning of the test, when the crack length/wedge thickness ratio is the

smallest. Of course, as the crack progresses, this value, corresponding to the value of surface

strain at the moving crack front, quite rapidly decreases. Notwithstanding, e.g. for the PAA

treated joint, is ca. 0.26, which is well below the yield limit of aluminium 2024 alloy.

In a correctly designed test procedure, this potential exceeding of the elastic limit of the

adherend should, needless to say, be avoided.

Fracture

Fracture, or adhesion energy, Gc, was evaluated for continuously increasing a(t) using (3.48).

Corresponding crack growth rates, d(a)t)/dt, were also calculated from tangents to the a vs. t

curves. In Fig.3.36, Gc vs. v=d(a)t)/dt results are presented for the two systems corresponding

to simple abrasive of substrates and PAA treatment. The calculated error bars include

systematically errors on E, h, Δ as well as random errors. This is to show the potential

precision on Gc obtainable from crack length measurement with the strain gauge method

presented here. Without these errors error bar is of the size of the experimental point. Various

observations may be made. Firstly, overall the fracture energies are relatively low for this type

of joint. However, the adhesive used was a general-purpose, pure epoxy resin, and not a

specialised material (modified etc.), so this is not too surprising (see Table 1.2). Secondly,

clearly the PAA surface treatment gives a considerably higher fracture energy than simple

abrasive treatment, for any given crack growth rate. At the lower end of the rate scale studied,

fracture energy is ca. 80% greater for PAA, at the other extreme, ca. 20%. This suggests that

the relation between effective energy of adhesion and surface treatment is not simply

multiplicative, as often suggested for elastomers [202,203]. Superficially at least, fracture

appeared to be interfacial for the abraded aluminium surfaces, but distinctly cohesive within

the adhesive for the PAA pre-treatment. Again, this is not surprising as good adhesion to

aluminium generally requires adequate surface treatment. The results on real joints in this

context are presented to corroborate findings with the artificial wedge tests.


102

1E-4 1E-3 0.01 0.1 1 10

60

70

80

90

100

110

120

Fra

ctu

re e

ner

gy

, G

c(J

m-2

)

Crack speed, v (mm h-1)

Abraded

Anodized

Fig.3.36. Fracture energy vs. crack speed characteristic of Al/Al bonded plates with pure

DGEBA resin after different surface treatment.

3.3.4. Adhesive joint with variable adhesion properties

Strain gauge method developed has been extended, in order to investigate crack growth

behaviour in the case of variable adherend surface pre-treatment. The basic idea is to alter the

surface treatment of one and the same adherend, but in separate zones, prior to bonding, with

a knowledge that one treatment is likely to produce markedly better adhesion than the other.

Simple measurement of the fracture energy on each surface is relatively easy and should hold

no surprises. Nevertheless, the fact that it is possible to vary surface pre-treatment on one and

the same adherend could prove useful in order to obtain more reliable comparative data on the

quality of adhesion different surface preparations and/or ageing conditions, eliminating, or at

least reducing, experimental scatter due to the use of separate joints (individual, slightly

different adherends, reproducibility of curing temperature and pressure, etc.). However,

principal aim here was to consider crack behaviour near the transition from one surface pre-

treatment to another.

In this study CFRP composite material with Eh=50 GPa was bonded to an aluminium plate to

form the joint. Adherends were bonded along 105 mm, as shown in Fig.3.37. Two strain

gauges were attached to the outer surface of the flexible, composite plate, along the centre line

and in the positions shown. The values of x1 and x2 were respectively 15 and 25 mm. The

figure suggests that one strain gauge initiates within the bonded length of the assembly, but in

practice, the adhesive bond was pre-cracked from the wedge end, so both gauges were

effectively in the de-bonded section. The adhesive used was a commercial epoxy resin

Araldite Cristal. Bondline thickness was maintained at 350 25 μm. Two different surface

Michał K. Budzik

103

treatments of the aluminium were used prior to bonding. In both cases, the aluminium to be

bonded was abraded with 1200 grade emery paper. This was the only treatment for parts of

the surface, and is represented by P (polishing). These parts were then carefully protected

with adhesive tape, and the remaining surface to be bonded was sandblasted, using SiO2 grit

(referred as SB). Finally, an aluminium wedge, of thickness Δ of 3 mm, was inserted. Tests

reported here were based on two separate assemblies, results being found reproducible.

Experiments were effected at 20 2°C, and at an ambient humidity of ca. 55% RH.

Fig.3.37. Geometry of asymmetric wedge test sample with strain gauges (dimensions in mm).

(a) Side view. (b) Top view showing position of the strain gauges. (c) Top view showing the

relative position of the wedge and one of the zones of sandblasting.

Crack length and fracture energy

Fig.3.38 represents an example of crack length, a, vs. time, t, for the composite/aluminium

assembly whilst fracture is occurring in the vicinity of the SB/P transition. It is usual in wedge

tests to observe an asymptotically decreasing crack speed, da/dt. This is due to a constantly

decreasing (strain) energy release rate, G. However, Fig.3.38 presents three distinctive

sections: from t=0 to ca. 20 hours, the usual decrease in da/dt is observed, and then from ca.

20 to ca. 40 hours, crack growth accelerates. Finally, from ca. 40 hours onwards, da/dt

decreases again, albeit with a couple of minor oscillations. These results are perhaps more

clear when presented as da/dt vs. t., as shown in Fig.3.39. The initial high crack speed near

t=0, and due to a relatively high value of G in the early stages of fracture, becomes attenuated,

only to pick up again from ca.20 hours, with a peak of ca. 0.6 mmh-1

near t=40 hours.

Thereafter, the crack speed again decays.

15

25

Δ

ladh(t0)=105 mm a(t0)=30 mm

Composite The adhesive

Aluminium

SB P

Wed

ge

Approximate Zone of Interest

y

x

z

x

a)

b)

c)


104

Fig.3.38. Crack length, a, vs. time, t, for the composite/aluminium assembly in the vicinity of

the transition from SB to P surface treatment. The transition is occurring between ca. 20 and

40 hours (left).

Fig.3.39. Results of Figure 3.38 expressed as crack speed, da/dt, vs. time, t (right).

Clearly this ―U‖ shape of the da/dt vs. t plot is related to the surface treatment transition. In

order to understand the basic physics of what is occurring, we propose the following

explanation. Although the wedge test is usually considered to be 2 dimensional, in fact there

are some non-negligible 3D effects [177,204]. This phenomenon is essentially related to

anticlastic curvature of the bent adherend. We therefore assume, in the present case, that the

crack front is curved (convex towards the intact side of the fracture front) and may be

approximated to a circular arc of low profile, such that we may write , using the

nomenclature of Fig.3.40, R being the radius, δ the depth of the crack front, and b the joint

width, as before. The arc subtends a (small) angle of 2α. Consider the line AB, which cuts the

arc in two places and represents a transition between surface treatments of the aluminium

surface, sandblasting, SB, and polishing, P.

Fig.3.40. Model for curvilinear crack front traversing the frontier between SB and P treated

aluminium.

b

δ

y

SB P

A

B

R

α θ

aF*

a*

0 20 40 60 80 100 120

30

31

32

33

34

35

36

37

38

Sandblasted

Transition

Polished

Cra

ck

len

gth

, a (

mm

)

Time, t (h)

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sandblasted

Transition

Polished

Cra

ck

sp

eed

, v

(m

m h

-1)

Time, t (h)

Michał K. Budzik

105

We take the SB treatment to be on the right hand side of AB. The central part of the arc, to the

left of the intersections with the line AB in the figure, subtends an angle 2α, where

. It is thus readily shown, for , that to a good approximation:

(3.73)

where represents the distance along the x axis between the wedge and the SB/P transition,

and is crack length, the asterisk denoting that we have, arbitrarily, defined crack length as

being the distance between the wedge and the fracture front taken at the joint edges. In other

words, the (projected) width of the crack front on the left of AB is given by

, with the remainder,

, on the right of AB, and thus,

by hypothesis, the former is in the P zone and the latter in the SB zone. With and

representing respectively fracture energy in the region pre-treated by sand-blasting and that

following simple polishing, we can write an expression for the (average) fracture energy, ,

whilst the crack front finds itself cut by line AB:

(3.74)

which is a function of crack length, , such that

and

, with intermediate values of

for

. Generally, as the crack

length, , increases, growth rate decreases since energy release rate, G ~ a-4

. However,

as the crack front encroaches on the zone of simple, polished surface treatment, the intrinsic

fracture energy decreases, since , such that for a given value of energy release rate

G, crack speed should increase, other things being equal. Thus, there are two antagonistic

effects, both being exacerbated by increasing a. If the decrease in intrinsic is more

significant than the effect of increased crack length, the crack will accelerate, contrary to the

behaviour of classic wedge tests, which decelerate due to diminishing G. Thus a graph of

crack length, a, versus time, t, will change from concavity towards the time axis to convexity,

and the junction of the concave and convex sections of the curve, at an inflexion point where

or possibly at an abrupt change of gradient

corresponds to

. Assuming that δ remains a constant, when , the crack front is totally on the

polished surface. Henceforth, is no longer a mixture of and , albeit smaller, and

simply equals . Thus crack growth rate will again decrease monotonically. Again, an

inflexion point may be expected. From these two inflexions on the graph of a vs. t, it should

thus be possible to estimate the depth of the curved crack front, δ. If the crack front negotiates

a transition from bonding on the polished treatment, P, to that on the sandblasted treatment,

SB, one may expect a similar effect. However, unfortunately, the added effect of fracture on

the sandblasted surface, thus leading to higher , will only decrease the crack growth rate


106

even further than that due uniquely to increasing a, viz. G ~ a-4

. Thus, at best, one may expect

a slight reduction in da/dt, but no change in overall features of the curve from concavity to

convexity. Returning to Figures 3.38 and 3.39, we can see that the scenario described above,

and the scheme of Figure 3.40 can explain the observed features of crack speed, da/dt, vs.

time, t. Estimation of the positions of the inflexions in Fig.3.39 leads to two corresponding

values of a, and by difference, we estimate the crack depth, δ, to be ca. 2.3 mm. (Note that we

cannot reasonably estimate an error on da/dt, since the error bars correspond to position and

not to gradient). The value of 2.3 mm is quite plausible and entirely consistent with values

found earlier on a similar system [177]. Further work on a system with a transparent adherend

is envisaged, in order to corroborate this effect, although results from [177] already lends

credibility. However, the system will necessarily be different due to (at least one) different

surface treatment.

Fracture energy assessment

The data of Fig.3.38 have been used to calculate the fracture energy, , of the

aluminium/composite assembly in the vicinity of the surface treatment transition, where no

distinction is made as to whether this quantity is pure or , or whether (3.74) is

applicable. This has been done using the now standard equation for fracture energy, obtained

from an asymmetric wedge test, in which one adherend may be considered to be rigid viz.:

(3.75)

The evolution of vs. time, t, is shown in Fig.3.41.

0 20 40 60 80 100 120

125

150

175

200

225

250

275

300 Sandblasted

Transition

Polished

Fra

ctu

re E

nerg

y, G

c (J

m-2

)

Time, t (h)

Fig.3.41. Fracture energy, , vs. time, t, in the vicinity of the transition zone.

Michał K. Budzik

107

As in Fig.3.38, the two representative error bars at 0 and 100 hours correspond to estimates of

systematic errors on a, obtained using propagation of errors theory. Also as before, relative

errors, neglecting possible misestimates of Eh, Δ and h are far smaller, and would be difficult

to discern in the figure. Fig.3.41 shows anticipated behaviour: a decrease of with time as G

diminishes with crack growth, followed by a steeper decrease as the crack transfers from the

SB to the P treated aluminium surface. Finally, a further decrease with time occurs, but at

much lower values of and at a lower rate of change, because the crack front is entirely in

the P region.

Fig.3.42. Fracture energy, , vs. crack speed, v=da/dt, in the vicinity of the transition zone.

For , f=1 (I) and

for, f=0 (II). The intermediate cases (examples)

correspond to f=0.54 and 0.27, as shown schematically below (III).

Fig.3.42 represents fracture data in the more conventional manner, viz. vs. crack speed,

v=da/dt. The data at the top and at the bottom (accentuated by solid lines in the figure) follow

1E-4 1E-3 0.01 0.1

125

150

175

200

225

250

275

300 Sandblasted

Transition

Polished

Fra

ctu

re e

nerg

y, G

c (J

m-2

)


I

III

II

Sandblasted Polished

I III

II

Crack growth


108

the expected monotonic increase, which is well known for polymeric adhesives [201,205].

However, at first sight, this portrayal is surprising, since appears to be three-valued in

places. Indeed it is. The upper curve, or maximal fracture energy for a given fracture rate,

may be interpreted as the fracture energy, , and corresponds to fracture purely in the

SB region. Similarly, the lower curve is attributable to failure in the P zone, where

(minimal energy). The data points in the intermediate region apparently indicate a decrease in

fracture energy with increasing crack speed, which is highly unlikely under the present

conditions of stable crack growth. In fact, each data point in this region corresponds

effectively to a different type of assembly. The reason for this is that at each point, the relative

contribution from each of and is different, as given by (3.74) (or possibly a more

accurate version thereof). Since the and curves appear reasonably parallel, it is

reasonable to suppose that through each point, we should be able to pass a curve parallel to

the maximal and minimal curves. This has been done in Fig.3.42 for two cases to demonstrate

the principle (heavy dotted lines). To clarify the situation, we may write (3.74) in a simpler

form as:

(3.76)

where f represents the fraction of surface (failure front) SB involved in the separation, and

therefore (1 – f ) corresponds to the fraction of P. Let us consider (arbitrarily) the crack speed

of v=0.1 mmh-1

. As shown by the (light) dotted lines on the graph in Fig.3.42, this

corresponds to values of and respectively of ca. 265 and 152 Jm-2

. The equivalent

experimental value of for v=0.1 mm h

-1, corresponding to the intermediate case, in the

transition zone, and also shown with a dotted line, is equal to ca. 225 Jm-2

. Alternatively, we

may take the known value of joint width, b, the estimated value of crack front depth, δ (see

above), and together with (3.74) and (3.76) a knowledge of crack position, estimate f (ca.

0.54). Accepting the experimental values and above, (3.76) predicts a value of the

intermediate of ca. 215 Jm

-2. The procedure may be repeated, but for a crack speed, v, of

0.3 mmh-1

, and we find experimental and predicted values of respectively of 205 and 200

Jm-2

(f=ca. 0.27). (The relative data are also indicated by dotted lines in Fig.3.42). Given the

simplicity of the model for crack front shape, the agreement is really quite acceptable.

Fracture surfaces

The results presented in Fig.3.43-3.45 are a visual assessment of fracture surfaces, and

corresponds to a photograph of the side view of a composite/aluminium joint after fracture, in

the vicinity of the transition zone from SB to P treatment. The crack proceeded from the right

towards the left in the photograph. It is clearly visible that the fracture surface changes

radically at the frontier between the two surface treatments. The thin band between the

composite and the aluminium is the adhesive layer, which adheres to the latter when SB

treated, separation occurring at, or near, the adhesive/composite interface.

Michał K. Budzik

109

Fig.3.43. Photographs of side of fractured joint in the vicinity of the transition zone between

sandblasted (SB) and polished (P) surfaces. The fracture front comes from the right.


polished (SB) and sandblasted (P) surfaces. The fracture front comes from the left.

Fig.3.45. SEM micrographs of the side of surfaces near the fracture zone in the SB treated

region. (a) The macroscopically interfacial failure at the adhesive composite interface is in

fact a cohesive failure within the adhesive, but near the interface, whereas (b), the

adhesive/aluminium interface remains intact.

ALUMINIUM

COMPOSITE

ADHESIVE

ADHESIVE (a) (b)

COMPOSITE COMPOSITE

ADHESIVE

ALUMINIUM

ADHESIVE

ALUMINIUM

P SB P SB

New crack

initiation Initial crack

side

ALUMINIUM ALUMINIUM SB P SB P

COMPOSITE

COMPOSITE

ADHESIVE ADHESIVE

2 mm 2 mm


110

However, when the fracture front enters the region of P surface treatment, there is a relatively

rapid deviation of crack path, with separation occurring at, or near, the adhesive/aluminium

interface. Opposite situation occurs when the crack is coming from polished to sandblasted

region, like in Fig.3.44. This suggests strongly that the SB treated aluminium presents better

adhesion to the adhesive than does the composite, but that the P surface has poorer adhesion.

This may be expected from the nature of the surface treatments, but corroboration from

energetic considerations follows a description of the transition behaviour. Fig.3.45 shows

details (pictured from the side) of the fracture zone near the SB treated aluminium, obtained

by scanning electron microscopy (SEM). It is clear that the macroscopically interfacial failure

at the adhesive/composite interface is, in fact, a cohesive failure within the adhesive, but near

the interface. This weakness in the interfacial region, or interphase, was first proposed by

Bikermann in the context of a weak boundary layer (WBL) [67], and later discussed by

Sharpe and also others [206,207]. It is also clear that the adhesive/aluminium interface

(interphase?) remains intact, when the latter has received the SB treatment.

Direct observation of double crack curvature phenomenon

Direct observation of the phenomenon of the double crack curvature was studied using

transparent flexible adherend - polycarbonate plate (PC). Variable, promising different

surface properties, surface treatment of aluminium plate was used prior to bonding. Primarily

aluminium was polished. This was the only treatment of the surface represented by P in

Fig.3.46.

Fig.3.46. Scheme of the experiment principle.

Camera

20 20 20 20

Camera

ladh(t0) = 80 a(t0)=35

PC

Aluminium

Δ =

5

z

x

y

x

P PAA P PAA

Michał K. Budzik

111

Finally, PAA treatment was made on entire sample protecting polished regions with

waterproof scotch tape, thus obtaining variable treatment. The anodized surface regions are

represented by PAA. After removing the tape, both PC and aluminium were lightly rinsed

with C2H5OH before bonding. Both plates were than bonded with epoxy adhesive, Araldite

Cristal plate leaving initial separation (crack length), a=35 mm. Measured adhesive thickness,

e was 0.4 mm. Two tests were run, thus 8 transition zones were observed. Two aluminium

wedges were used. The wedge thickness, Δ was changed during the test from 5 to 9 mm to

force crack propagation towards all transition zones. The scheme of the experiment is shown

in Fig.3.46.

Crack propagation in the vicinity of transition zone

Crack propagation was recorded with Canon D40 photo camera (from the side view) and with

micro USB camera Dino - top view. The interval time between two camera frames was set at

15 min. Experiments were effected at 23±2°C, and at an ambient humidity of ca. 55% RH.

Results are shown in Figs.3.47 and 3.48.

Fig.3.47. Crack propagation in the vicinity of the transition, STRONG/WEAK, zone. Crack is

coming from anodized (PAA) surface to polished (P). Arrows indicates regions of crack front

initiation.

Fig.3.48. Crack propagation in the vicinity of the transition, WEAK/STRONG, zone between

polished (P) and anodized (PAA) surfaces. Arrows indicates regions of crack front initiation.

PAA

P

CR

AC

K

P

PAA

CR

AC

K


112

Based on results from direct observations, as well as from previous measurements, model of

crack propagation in the vicinity of transition zone was proposed (see Fig.3.49). Crack

propagation stages are detailed in Table 3.4.

Fig.3.49. Stages of crack propagation in the sample with variable adhesion properties.

Table 3.4. The crack propagation stages in the vicinity of transition zones.

a) Crack nucleation in STRONG* adhesion zone

b) Crack propagation, with increasing depth of the crack

c) STRONG – WEAK transition

d) Beginning of crack propagation in the WEAK**

zone with higher speed. Decrease of

crack curvature in the STRONG zone

e) Propagation of double crack curvature with an increase of curvature in the WEAK

zone

f) Crack establishment in the WEAK zone

g) Propagation of the crack in the weak zone with higher speed then in the STRONG

zone and lower energy consumption

h) Crack arrests close to the WEAK – STRONG transition. Crack propagation requires

new energy portion – e.g. increase of wedge thickness

i) Decrease of crack curvature without propagation of the front

j) Nucleation of the crack in the STRONG adhesion zone from almost straight crack

front

k) Beginning of crack propagation in STRONG zone

l) Normal propagation of the crack *STRONG – e.g. PAA or sandblasted,

**WEAK – e.g. polished

a) b) c) d) e) f)

g) h) i) j) k) l)

STRONG

WEAK

STRONG

Michał K. Budzik

113

Behaviour of crack front near transition zones

The behaviour of the crack front of the crack of length, a, vs. time, t, near the transition zone

separating strong adhesion S (e.g. sandblasted or anodized) and weak adhesion P (e.g.

polished) surface treatments on the aluminium surface prior to bonding was considered. The

validity of equation 3.74 was assumed describing the effective, or mean overall, fracture

energy, , when the (sharp, linear) transition of surface treatment traverses the curved

fracture front of Fig.3.39:

(3.77)

Fracture occurs when the strain energy release rate, G, is equal to , and the basic relation

for fracture is given by:

(3.78)

where U represents stored elastic energy, b is sample width and a is crack length. In the

asymmetric wedge test, is given by (3.74) which we write as

=ka-4

, where k=3ECΔ2h

3/8,

since it is only variations of a that are presently of interest.

From (3.74) and (3.78), we may write the threshold for fracture as:

(3.79)

Since the analysis leading to (3.74) is based on 2D analysis, it does not allow for any crack

front curvature, which amounts to variability of a=a(y), and there is therefore some doubt as

to what value of a should be used, although a* has previously been defined as the crack length

at the joint edge. Notwithstanding this detail for the moment, (3.79) is differentiated with

respect to time, t, and arranged to give:

(3.80)

where v=da*/dt=da/dt, assuming that it is permissible to equate the two derivatives (an

additive constant between them). For the moment, δ is constant.


114

Now, when the crack front first reaches the S/P transition, a*=(a

*- δ). Evaluation (3.80) at this

point leads to:

(3.81)

Thus, since k, v and a are finite and positive, provided GcS>GcP, and dGcS/v>0 , which is

clearly the case, d2a/dt

2=∞. The experimental data suggest strongly an inflexion point,

corresponding to d2a/dt

2=0 , rather than a sharp change in da/dt (d

2a/dt

2=∞). This in turn

suggests that δ varies (if only slightly) as the S/P frontier is encroached upon, since this will

permit the denominator of the first term on the right hand side of (3.81), i.e. the term in

in (3.80) to remain finite. Clearly δ cannot decrease, or contact with the

transition will be lost, and so δ must increase. From a purely intuitive, physical, point of view,

this also seems reasonable, since adhesion is less good in the P region, and with a similar

local moment, or value of G, the anticlastic effect is likely to become exacerbated, increasing

δ. A sketch of the expected scenario is given in Fig.3.50. As the crack front encroaches onto

the zone of lower adhesion, separation occurs more readily, leading to a bubble-like failure

area.

Fig.3.50. Suggested sketch of crack front bubbling as it encounters the sharp transition

between SB and P treated aluminium.

The same consideration can be given to the case, occurring later, when the entire crack front

is just on the P region, i.e. when a*=aF

*, but simple substitution into (3.81) reveals that this

situation leaves d2a/dt

2 finite (and possibly 0) under expected conditions. Thus the

paradoxical multi-valued fracture energy curves may be explained. Clearly the model leading

to (3.74) has its limitations but the physical reason for the relatively smooth transition

between types of fracture behaviour occurring on what amounts to a step function in surface

treatment can be successfully explained and is fulfilled by the experimental observations.

S P

Michał K. Budzik

115

3.3.5. Effects of The Adhesive Compliance

The aim of this study was to consider effects of elastic foundation [135] and root rotation

[167,193,200] by using an extension of the strain gauge method previously presented. It must

be appreciated that the following is aimed at both a better appreciation of the intricacies of the

CDT test, and an analysis of the interpretation of results specifically in the context of the

strain gauge method adopted. An asymmetric wedge configuration was adopted in which both

adherends were from aluminium alloy. The flexible adherend was (initially) bonded to the

rigid member along length, ladh=60 mm. This left an initial effective crack length, a, as shown

(see Fig.3.50). Either 8 or 10 strain gauges were attached, along the central line of symmetry,

onto the outer surface of the flexible plate, with at least three being in front of the crack, or in

the so-called free zone, the remainder being in the (initially) bonded zone. Two adhesives

were used. One was a epoxy resin Bostik Araldite Cristal second acrylic mastic. Adhesives

thicknesses, e were maintained in the range of 0.2-0.8 mm. Prior to bonding, all substrate

surfaces were prepared by polishing and degreasing with acetone. In the case of bondline

thickness, e=0.2 mm, surfaces were subsequently sandblasted, with Salox Al2O3. For bondline

thickness, e=0.8 mm, and for the mastic joints, after polishing surfaces were treated by

phosphoric acid anodisation (PAA). Experiments were undertaken either at ambient

temperature, ca. 23°C, or elevated temperature, 50°C. Both conditions were achieved using

Memmert D 06061 Model 500 oven cabin (Memmert GmbH + Co. KG D-91107 Schwabach,

Germany).

Data reduction method

General deflection equation (simple beam theory - SBT) is 2-dimensional and does not allow

for any transverse effects (y in Fig.3.51). Also, due to use of simple beam theory, no

allowance is made for flexibility of the system near the crack front but in the bonded part (x >

a), particularly within the adhesive layer. This may give rise to some vertical displacement of

the flexible beam within the bonded zone, and thus lead to root rotation as was shown,

probably, in CFT test and was presented by other authors [173,208-210]. In Fig.3.52, a sketch

of a flexible beam, rigidly clamped (the brick wall) at x=a SBT (SBT-simple beam theory), but

bonded by a sufficiently soft adhesive as far as aW (W-Winkler) is presented.


116

Fig.3.51. Schematic representation of samples tested.

With the insertion of a wedge of thickness, Δ, not only does the beam flex upwards but the

bonded area, aW<x<aSBT, also deforms as shown in Fig.3.52.

Fig.3.52. Schematic presentation of Winkler (aWinkler) and cantilever beam (aSBT) crack

lengths. The difference between these crack lengths gives the transition zone between open

crack and measurable elastic foundation effect.

Assuming the section, aW<x<aSBT, to be elastic and to possess foundation stiffness, k (Nm-2

),

in the z direction, a load of q (Nm-1

) can be represented as:

Δ

R

PROCESS

ZONE

aWinkler

aSBT

z

x

L

Δ

z

x

e h

a ladh

l

b

STRAIN GAUGES

y x

x = a

M

F z

x

k

Michał K. Budzik

117

(3.82)

Moments equilibrium equation (F is only acting shear force):

(3.83)

Force equilibrium equation:

(3.84)

The bending moment is given by:

(3.85)

where θ is the angle of Euler – Bernoulli beam model:

(3.86)

Application of standard equations describing the equilibrium of forces and couples and the

bending moment relation, M, leads to two 4th

order differential equations:

For 0< x<a:

(3.87)

with general solution:

(3.88)

And for : a< x<+∞:

(3.89)

with solution:

(3.90)

Equation 3.90 has only two constants of integration because the possible solution in is

physically unrealistic, and has therefore been eliminated. The constant, or wave number, λ, is

given by:


118

(3.91)

In the present case, k is interpreted as:

(3.92)

where νadh and Eadh are respectively Poisson’s ratio and Young’s modulus of the adhesive, and

e is adhesive thickness. The bracketed terms in νadh are to allow for essentially plane strain

conditions existing in a thin adhesive layer (e/b<<1). The correction is not negligible, since an

adhesive could easily have a Poisson’s ratio of 0.4, leading to ca. twice the value of k given

by the simpler, often used, expression

.

To find out 6 constants of (3.88) and (3.90) we need derivations up to the 3th

order for both,

free and bonded zone:

For 0<x<a:

(3.93)

(3.94)

(3.95)

(3.96)

For a<x<∞:

∞

(3.97)

∞

(3.98)

∞

(3.99)

∞

(3.100)

Michał K. Budzik

119

Required boundary conditions are:

For x=0:

(3.101)

(3.102)

Finally, from continuity conditions when x=a, we have:

(3.103)

(3.104)

(3.105)

(3.106)

Therefore constants are:

(3.107)

(3.108)

(3.109)

(3.109)

(3.110)

(3.111)

By deriving the standard beam equation one further time with respect to x, and using

equilibrium of moments (dM/dx+F=0 with F as the (shear) force exerted by the wedge on the

beam), we have:


120

(3.112)

Thus:

(3.113)

when equation (3.96) has been substituted. Now, elastic energy is:

(3.114)

and using (3.109), we obtain expression:

(3.115)

Which may is used to find out the strain energy release rate, G:

(3.116)

Substituting second moment of inertia, Ih:

(3.117)

With , Ih – inertia moment defined before.

Also useful are expressions for surface strain of the upper surface of the flexible adherend, εs,

which we find from derivation of equations 3.88 and 3.90 and the constants. It is in the main

negative, therefore we use its absolute value. Strain in free zone:

(3.118)

(3.119)

(3.120)

Strain in bonded zone :

Michał K. Budzik

121

∞

(3.121)

∞

(3.122)

For comparison, strain equation of SBT theory is:

(3.123)

Note that, in the limit of (infinite rigidity, k, within the intact joint), equation (3.120)

becomes equation of simple beam theory (3.123) as would be expected.

To compare both models ratio θ, is introduced, representing the ratio of surface strains, for

given values of x and a, expected from the SBT and the Winkler (W) interpretations:

(3.124)

Thus we may see that there is a simple proportionality between the two estimated values of

strain in the free zone, independent of x, yet dependent on crack length a (λ, from equation

3.91 is a constant of the system). Clearly, for high values of λa (rigid adhesive and/or large

crack length), , and little distinction exists between the two models. However, for

smaller values of λa, the difference may be significant. By rearrangement of SBT equation,

we may isolate crack length, aSBT, as estimated from SBT, as a function of (measured) surface

strain, , at a given x (and given Δ and h). From (3.124), we see that the same strain

(measurement) will give rise to a different estimate of crack length, aW, from the Winkler

theory:

(3.125)

We take as the real, or best estimate of crack length and finally, we may also define the

ratio η, representing the ratio of estimates of fracture energy obtained from the two

approaches:

(3.126)

Again, as , the ratio of fracture energy estimates tends towards unity, but for lower

values of λaW, SBT tends to overestimate strain energy release rate, and therefore fracture

energy.


122

Results and interpretation

The experimental set-up described in previous section allows to obtain values of strain of the

flexible adherend on the unbonded side along the centre line, and at distances xi from the

inserted wedge. Due to continuous monitoring, it is possible to follow the evolution of

(surface) strain with time. Although time dependency is not the principal aim of the present

study, an example for a joint made with acrylic mastic is given in Fig.3.53 (left), in

which vs. time, t, is given for 8 different strain gauges (here numbered 1-8).

Fig.3.53. Left: surface strain, |εs(x)| , at various values of x, vs. time, t. Right: |εs(x)| vs. x for a

given time shown by the bold vertical dotted line on the left part of the figure.

Strain measurements are reported over three minutes. What is observed over the first ca. 20

seconds can be construed as transient behaviour during loading. Thereafter, there is some

crack growth, or possibly viscoelastic accommodation of the adhesive, exemplified by

changing strain, the system approaching stability towards three minutes. More significant is

the fact that strain clearly depends on the position of the strain gauge in question. The greatest

strain is at xi=45 mm (strain gauge 3), and the least at xi=91 mm (strain gauge 8), with the

others being intermediate. If we take a given value of time, here ca. 0.025 h we can plot

vs. xi as shown in Fig.3.53 (right). It can be seen how the strain at first increases, more

or less linearly, from xi=0 (where is necessarily 0, as shown by the initial point, not in

fact, a measurement) up to its maximum, and then decreases beyond xi=45 mm. Up to 45 mm,

we have strain in the unbonded (or debonded) area, linearly increasing in agreement with

equation (3.119) (or its simple beam theory counterpart). Somewhere in the range between 45

and 67.5 mm, there will (presumably) be a maximum, which should correspond to the crack

front. Beyond that value of x, surface strain would be expected to become immediately zero,

if simple beam theory is applied. However, it can be seen that strain only slowly decreases

with x, strongly suggesting an effect of elastic foundation.

Having seen semi-quantitatively the effect of elastic foundation, the objective now is to obtain

the best interpretation of the results quantitatively, and thus obtain a good estimate of crack

length. Other advantages of the elastic foundation treatment will also become manifest.

A

A

A-A

0.00 0.01 0.02 0.03 0.04

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010 x

1= 29 x

2= 37 x

3= 45 x

4= 59

x5= 67.5 x

6= 75.5 x

7= 83.5 x

8= 91

Str

ain

, S

(x)

Time, t(h)

0 20 40 60 80 100

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

Str

ain

,

s(x

)

x (mm)

FREE BONDED

CR

AC

K

Michał K. Budzik

123

Interpretation of strain gauge measurements

The theory presented has been applied quantitatively to results obtained both with the epoxy

resin and with the acrylic mastic and essential findings presented in Fig.3.54-3.58 These

represent static results, i.e. crack growth rate is sufficiently slow to be neglected during

measurement. Various features are present in these figures to a greater or lesser extent. In all

cases, experimental results show that (negative) surface strain initially increases acceptably

linearly from the origin, corresponding to the position of the wedge. This observation is in

agreement both with the SBT model and the Winkler theory and is explained by the linearly

increasing bending moment. Following this, strain decreases with x, in Fig.3.54 very abruptly

becoming effectively zero, suggesting to a good approximation the validity of the SBT.

Fig.3.54. Results of (negative) surface strain, |εs(x)| vs. distance, x, from wedge for the epoxy

adhesive with a 0.2 mm thick bondline (ambient temperature) (right).

Fig.3.55. As for Fig.3.53, but at 50°C (left).

It may be considered that this case, with a rigid adhesive and thin bondline, shows the most

inflexible elastic foundation. On heating the same system to 50°C (Fig.3.55), the gradient of

the initial linear portion decreases, and what is more, the reduction of (negative) strain after a

maximum, is more gradual. Clearly the modulus of the adherend (aluminium alloy) does not

change significantly over this temperature range of less than 30°C, but that of the epoxy

adhesive does. Thus, despite the use of a thin bondline (its thermal expansion is negligible

here), reduction in elastic modulus is clearly sufficient to change observed behaviour.

Reduced absolute surface strain in the unbonded region can be attributed to the root rotation

allowed by the bonded portion, and follows from the Winkler treatment. Figs.3.56 and 3.57

show results for a 0.8 mm bondline. At ambient temperature, some effect of elastic foundation

may be seen, due to the fourfold increase in joint thickness. This is, however, limited. At

50°C, the initial gradient is reduced and the drop in strain after the maximum more gradual, in

keeping with the findings with a 0.2 mm bondline. There is even some (very slight and

therefore possibly insignificant) suggestion that surface strain becomes positive (i.e. negative

strain becomes negative in the figure).

0 10 20 30 40 50 60 70 80 90

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

Str

ain

, -

s(x)

x (mm)

Experiment

Winkler

SBTcorrected

SBT

= 2.8 mm

aWinkler

= 54.5 mm

aSBT

= 56.5 mm

= 0.55

0 10 20 30 40 50 60 70 80 90 100

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

Str

ain

, -

s(x)

x (mm)

Experiment

Winkler

SBTcorrected

SBT

e = 0.2 mm

T = 50o C

= 2.8 mm

aWinkler

= 55 mm

aSBT

= 63.5 mm

= 0.11


124

Fig.3.56. Results of (negative) surface strain, -εs(x), vs. distance, x, from wedge for the epoxy

adhesive with a 0.8 mm thick bondline (ambient temperature) (right).

Fig.3.57. As for Fig.3.56, but at 50°C (left).

In Fig.3.58, we see a very marked effect of the elastic foundation. After the maximum of

(negative) strain, there is a gradual decrease over more than 20 mm. Given the comment about

negative strain above for the 0.8 mm thick epoxy resin, it may at first appear surprising that

this is not observed here, but closer inspection of the theory shows that the distance at which

positive surface strain appears is dependent on the wavenumber, λ, which in turn depends on

the adhesive Young’s modulus, Eadh. A smaller value of λ implies a larger wavelength, and

thus positive strain appears further from the crack front, too far to be visible in our case.

0 20 40 60 80 100

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022 Experiment

Winkler

SBTcorrected

SBT

Str

ain

, -

s(x

)

x (mm)

MASTIC

e = 0.4 mm

= 2.6 mm

aWinkler

= 53 mm

aSBT

= 74.3 mm

= 0.0477

Fig.3.58. Results of (negative) surface strain,-εs(x), vs. distance, x, from wedge for the acrylic

mastic with a 0.4 mm thick bondline (ambient temperature).

The results presented in Figs.3.54-3.58 may be analysed in the light of the theory presented

above. Beam, or crack length, aSBT, as obtained from the SBT interpretation implies an

encastré attachment, as if the bonded portion of the joint were embedded in a brick wall

(Fig.3.52). This leads to overestimation of crack length, compared to the Winkler theory

(aW<aSBT). The physical reason is that in reality, the bonded region presents some flexibility,

0 10 20 30 40 50 60 70

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Str

ain

, -

s(x)

x (mm)

Experiment

Winkler

SBTCorrected

SBT

e = 0.8 mm

= 3.2 mm

aWinkler

= 35.8 mm

aSBT

= 40 mm

0 20 40 60 80 100

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

Str

ain

, -

s(x)

x (mm)

Experiment

Winkler

SBTCorrected

SBT

e = 0.8 mm

T = 50oC

= 3.2 mm

aWinkler

= 52.5 mm

aSBT

= 59.3 mm

= 0.1451

Michał K. Budzik

125

allowing root rotation. Attachment of the free beam is thus less restrained (the beam is not

exactly parallel to the substrate at the crack front, as is assumed in SBT) leading to lower

values of (absolute) surface strain in the former. This in turn suggests a lower applied bending

moment (larger R in Fig.3.52) which, in the case of SBT implies a higher value of crack

length, a. Mathematically, we consider (3.124), which gives the ratio of .

The ratio θ was already included in (3.125) in order to estimate the Winkler crack length, aW,

but assuming SBT, we use the simpler equation, viz.:

(3.127)

in which θ has been neglected. (Note that (3.125) and (3.129) are independent of x since εs(x)

is linear in x). From (3.125) and (3.129), we may calculate , which

quantifies the overestimation of crack length from SBT theory. As may be seen in Fig.3.59,

for large values of the product λaW, the difference is relatively slight, the ratio being close to

unity, but for small values (i.e. short crack for a given value of λ) it can be very significant

(aW has been taken as the true crack length). In any dynamic experiment, this means that the

overestimation of crack length will actually decrease, since crack length itself is increasing.

Fig.3.59. Crack length overestimation due to assumption of SBT

From the experimental results, it is possible to use regression analysis to obtain the best fits of

the data to both SBT and Winkler interpretations. For the former, only the initial linear data

are used. For the latter, all data are used and therefore the requisite value of λaW, for a given

system (crack length included) can be found. This was done using a Matlab® programme.

Returning to Figs.3.54-3.58, three calculated lines were added, viz. SBT, Winkler, and

SBTcorrected. The first (open circles) is simply application of linear regression to the

experimental points assumed to correspond to the separated part of the wedge test. The second

(continuous heavy line) corresponds to application of the Winkler theory. This, of course, is

0 20 40 60 80

1.0

1.2

1.4

1.6

1.8

2.0

1

/3

aW


126

valid over the entire joint, unbonded and bonded portions. It can be seen that obverse surface

strain is expected to become momentarily positive, after the decrease from its maximum

(absolute) value corresponding to the crack front (except in the case of the soft acrylic mastic,

Fig.3.58, where the dip is off scale). This effect cannot be truly confirmed from our results,

but a strong suggestion is nevertheless present in Figs.3.56 and 3.57. Within the limits of

experimental error, the trend of surface strain behaviour upstream of the crack front correlates

well with theory. This is particularly the case for the results obtained with the acrylic mastic.

As can be seen from the data inset in Figs.3.54-3.58, the SBT and Winkler estimates of crack

length are different, as expected, with aW<aSBT. The more supple is the elastic foundation, the

greater is the difference. The third line, SBTcorrected, corresponds to a simple calculation of the

expected strain/position relationship, using SBT but assuming the Winkler estimate of crack

length to be valid. As can be seen, this treatment overestimates strain, only slightly for a rigid

elastic foundation, but quite considerably so for a flexible foundation.

In Fig.3.60, a microscopic side view of an acrylic mastic bond is presented, both before and

after insertion of the wedge. It can be seen that the initial thickness of the adhesive of 0.4 mm

increases after wedge insertion.

Fig.3.60. Zone near crack front, on bonded side, in acrylic mastic bond, before (upper) and

after (lower) wedge insertion. Extension of the adhesive layer perpendicular to the interface is

due to imposed displacement and effect of elastic foundation.

The wedge being on the left hand side, it can be seen that the extension of the mastic, without

fracture, increases from right to left.

Effect on strain energy release rate

Clearly, the aim of the wedge test is to estimate the fracture energy, principally in mode I, of

adhesive bonds, Gc, or equivalently the critical strain energy release rate for given conditions.

In this study, actual fracture has been avoided in the main since the aim was to evaluate

Δ

Δ

Michał K. Budzik

127

different interpretations of the basic test. As such, values of fracture energy for the systems

studied are not presented here, but rather compare estimates of strain energy release rates

corresponding to fracture energies if the crack were to propagate. In order to compare

equivalents, we first consider the five systems corresponding to Figs.3.54-3.58 with their

assumed correct cracks length, viz. those calculated using Winkler theory. Values of the ratio

of energy release rate , as given by equation 3.126, are presented in Fig.3.61.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Epoxy, e = 0.2 mm

Epoxy, e = 0.2 mm, 50oC

Epoxy, e = 0.8 mm


Mastic, e = 0.4 mm

Fig.3.61. Ratio, (equation (18)) of SBT to Winkler values of the strain energy

release rate using Winkler values of the crack length, aW.

It is clear that in all cases, use of SBT leads to an overestimate of strain energy release rate,

and that this effect is seriously increased by the supple nature of the adhesive layer. However,

this is perhaps an unfair comparison. The SBT approach already presents an error, which may

be significant if the adhesive layer is soft. It produces an estimate of crack length, aSBT, which

is too large. Thus we are justified in comparing the strain energy release rates of the two

approaches using calculations based on respective estimates of crack length. (3.126) becomes:

(3.128)

(3.129)

where refers to the fact that each calculation of G uses its corresponding value of the crack

length, a. Equation 3.129 make use of introduced before factor θ, in order to avoid using

different crack lengths in the same formula. Values of are presented in Fig.3.62, and show

convincingly that the two errors in SBT are effectively self-compensating, at least in the cases

studied. These results show that there are still things to be learnt from the wedge test in the

vicinity of the crack front. This approach should prove promising to look at such phenomena

as crazing and cavitation in the adhesive layer.


128

0.0

0.2

0.4

0.6

0.8

1.0

Epoxy, e = 0.2 mm


Epoxy, e = 0.8 mm


Mastic

~


release rate, each using own values of crack length, a.

Effects of deformation of the adhesive layer perpendicular to the interface, using an approach

first suggested by Winkler in the 19th

century where here analyzed. The Winkler model (W)

was used in conjunction with a strain gauge method, previously reported, allowing detailed

information of strain within the flexible member of an asymmetric wedge test to be accurately

determined. A comparison between the two approaches, W and SBT was made. An important

finding was that when calculating crack length from the SBT treatment, using only data from

the free part of the adhesive bond, this approach led systematically to overestimations. If

corrected crack lengths are used, then strain energy release rate is overestimated. However,

when using SBT with its own erroneous estimate of crack length, the errors incurred would

appear to be self-compensating, at least in the cases studied! It should be noted that use of

SBT may indicate a crack length beyond the actual value, where the adhesive is significantly

strained but not broken. The effect may be compared to crazing or cavitation. Findings do not

invalidate use of SBT analysis, which is reassuring, but the present treatment should lead

potentially to more insight into fracture, in the deformed, but still intact adhesive zone.

3.3.7. Use of the CDT test for assessment of curing time

The theory discussed in the previous section was used to study the behaviour of the structure

bonded with the long time curing adhesive. Basically, as an adhesive cures, it is expected to

get harden and thus its modulus increases. Change of parameter λ, or simply change of the

adhesive mechanical properties, with time was expected, thus giving λ=f(t) or more strictly,

Eadh=f(t). The flexible adherend used was CFRP composite with Eh=75 GPa. The rigid or

thick plate was Hydronalium AA5754. Prior to bonding the aluminium surface was polished

and then anodized using the described PAA process. The composite plate was abraded, using

400 grit paper, then wiped in acetone and carefully dried in a stream of warm air (max. 50oC).

Plates were bonded using Araldite GY784BD epoxy adhesive. The measured adhesive

thickness was e=0.31 mm and found constant along the bonded zone. Crosslinking was

effected at ambient temperature (ca. 23°C) for 24 hours under a low constant pressure of ca. 4

Michał K. Budzik

129

bar (to avoid air trapping and voids) and at ca. 55 % RH. The crack length, which was kept

constant during the test, was a=65 mm while the plates were bonded along ladh=45 mm. Six

strain gauges were attached to the exposed side of thin substrate. Three in the so-called free

zone, and three in the bonded zone. To avoid any crack propagation a thin aluminium wedge

of thickness Δ=1.6 mm was used. The wedge was inserted, between separated plates, to the

desired position (2 mm from the CFRP plate extremity) and then, after ca. 5 seconds

removed, preventing any crack propagation. This operation was repeated for two samples

every day for 15 consecutive days.

Fig.3.63. Schematic representation of tested samples. Bonded and free zones are separated

with dash line.

Strain behaviour

The test results of the tests performed are shown in Figs.3.64-3.66 in terms of the flexible

plate strain change. Visible change, increase in free, decrease in bonded zone, of the strain is

related to the change of the adhesive state. Although this change can come from many

different phenomena, we assume that during crosslinking the adhesive changes its mechanical

properties. Fig.3.65 correspond to the measured strain distribution (circles) along the joint, at

the beginning and end of the test. Using Matlab® Fitting tool, the Winkler model strain was

added (dashed and solid line). Experimental and Winkler model curves agree well, thus

proving that the method presented can be successfully used to study effects of the adhesive

crosslinking.

BONDED

ZONE

FREE

ZONE

STRAIN GAUGES

x

y

b

32.5

42.5

52.5

69.5

75.5

82.5


130

Fig.3.64. Instrumented wedge test results for the adhesive subjected to slow crosslinking.

Vertical line indicates position of the crack front. Note evolution of the strain with time

(arrows indicating the direction of change) in both zones.

Fig.3.65. Interpretation of experimental data (points) with Winkler based model at the

beginning (solid line) and end of the test (dashed line). Vertical line represents crack position.

Fig.3.66 considers the situation as described previously, this time adding SBT and Winkler

model estimations of the crack length. It must be appreciated that the change of the adhesive

state, due to reticulation, when the joint is treated as an encastré (SBT) is manifested by the

decrease of the crack length. In Winkler, change of the adhesive state is seen via a change of

the λ parameter – with time increase, adhesive stiffness does the same.

Process zone after

2 days

0 10 20 30 40 50 60 70 80 90 100 110

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

0.00040

0.00045

Str

ain

, -

S(x

)

x (mm)

t= 2 days

Winkler, t = 2 days

t = 15 days

Winkler, t = 15 days

FREE ZONE

BONDED

ZONE

Process zone

after 11 days

0 10 20 30 40 50 60 70 80

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

Str

ain

, -

S(x

)

x (mm)

t = 12 days

t = 8 days

t = 6 days

t = 2 days

BONDED

ZONE

FREE

ZONE

Michał K. Budzik

131

Fig.3.66. Comparison between Winkler and SBT model. Vertical lines represent: real or

Winkler crack length (solid), crack length obtained with SBT estimation after 15 days of

curing (dashed), and SBT after 2 days of curing (dotted).

Curing time estimation

From Figs.3.67-3.69, the time required to cure the adhesive can be estimated. It should be

noted that all of the parameters presented here can be used to evaluate curing time. Strain

gauges based in the bonded zone provide estimation of the exact size of the process zone as

well as the value of the characteristic adhesive parameter, λ. This is even more valuable, since

the CDT employed was successfully performed in non-destructive mode. Returning to

Figs.3.67-3.69, the curing time using Winkler and SBT approach is manifested in different

forms as mentioned previously. Using the Winkler model, we observe changes of the λ

parameter which correspond to the adhesive state or more clearly to the size of the process

zone (see Fig.3.67).

Fig.3.67. Change in the adhesive parameter, λ, during crosslinking. Three stages of

crosslinking can be found (left).

Fig.3.68. Apparent change of the crack length estimated using simple beam theory, aSBT, as a

function of time (right).

2 4 6 8 10 12 14

65

67

69

71

73

75

77

Cra

ck

len

gth

, a

SB

T(m

m)

Time, t (days)

2 4 6 8 10 12 14

0.1

0.2

0.3

0.4

0.5

0.6

m

m-1

)

Time, t (days)

dλ/dt↑ dλ/dt=0

STAGE I STAGE II STAGE III

a = 65 mm

aSBT = 67 mm

aSBT = 76.5 mm

0 10 20 30 40 50 60 70 80 90 100 110

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

0.00040

0.00045 t = 2 days

SBT, t = 2 days

Winkler, t = 2 days

t = 15 days

SBT, t = 15 days

Winkler, t = 15 days

Str

ain

, -

S(x

)

x (mm)


132

The change of the wave number is however not linear. This, in fact, stays in good agreement

with some recent theory [e.g. 222]. As was shown, polymer crystallization gradient varies

with time. It is small in the initial stage (stage I), than accelerates (stage II) to a certain

crystallization speed (known as critical crystallization speed, vc). After achieving vc,

crystallization gradient decrease, and after short time reaches 0 (stage III). In Fig.3.67 similar

situation can be observed, related to the change of λ. However the marked acceleration, in

stage II, is not understood.

Fig.3.69. Variation of Energy Release Rate, G, with curing time. Vertical line represents the

end of the crosslinking period.

Fig.3.70. Schematic presentation of change of crack length during crosslinking. Not that the

real crack length remains constant, whereas estimated crack length changes due to neglect of

adhesive properties in SBT.

Δ

PROCESS

ZONE

Δ

z

x

aWinkle

r aSBT↓

R↓

|εs|↑ PROCESS

ZONE

t =

0

t = ∞

aSB

T

aWinkler

R

z

x

|ΔaSBT|>0

2 4 6 8 10 12 14

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

En

erg

y R

ele

ase

Rate

, G

I (J

m-2

)

Time, t (days)

Michał K. Budzik

133

In Fig.3.68 SBT crack length variation with time is presented. In the SBT treatment, the

change of the adhesive state (crosslinking), from soft to rigid is manifested by the apparent

decrease in crack length (or more correctly SBT model crack length overestimation). This

effect was expected and stays in agreement with previous statements when using the Winkler

model. The observed change in apparent crack length is linearly dependent on time. Also

energy release rate evolution, shown in Fig.3.69, was found approximately linear. The energy

release rate for both SBT and Winkler models was found to be the same, when crack lengths

applied corresponded to the given model estimation. Therefore, the curing time can be

estimated from both models (SBT or Winkler), although intuitively the Winkler model is

closer to the truth in this situation (Fig.3.70). The change of adhesive properties was observed

during the adhesive crosslinking using the strain gauge technique and interpretation with the

Winkler model. The length of the process zone decrease with time from ca. 60 to 5 mm (see

also Fig.3.65) is explained by the change of the adhesive properties with time. It must be

emphasized that the actual crack length remained unaltered throughout, since the conditions

of wedge insertion were carefully controlled. 11 days curing time can be finally recommended

as a curing cycle for a given adhesive system.

3.3.8. Temperature effects on fracture using the CDT test

One of the aims of the thesis was development of the fracture test, which can be successfully

applied for in situ, continuous measurements in complex mechanical-environmental loading

conditions. Therefore, the CDT test developed was performed to study fracture at ambient

(ca. 24oC) and elevated temperature (40

oC). In this test, two aluminium plates were used.

Prior to bonding, aluminium surfaces were polished and sandblasted with Salox Al2O3 grit.

The adhesive used was commercial epoxy resin Araldite Cristal. Plates, of now standard

lengths, thicknesses and widths, were bonded along ladh=70 mm. Crosslinking was effected at

ambient temperature (ca. 23°C) for 24 hours under 0.3 bar pressure and at ca. 55 % RH, and

dried for 24 hours at 50oC in ventilated Memmert D 06061 Model 500 oven cabin (Memmert

GmbH, Schwabach, Germany). Thickness of the adhesive layer was e=0.2 mm. Initial crack

length, was a=35 mm. Such prepared samples were left for 5 days in ambient conditions to

avoid any secondary effects of curing. Nine strain gauges were attached to the outer surface,

as shown in Fig.3.71. One additional strain gauge was left mechanically unloaded, thus

serving as a dummy gauge (to register temperature effect only). Before the test, samples were

precracked with a 3 mm thick wedge. Wedges of thickness, Δ=4.8 and 6.8 mm, were then

inserted to separate the two bonded plates. In order to observe fracture at elevated

temperature, the CDT setup and Dino Microcamera (used to register in situ fracture features

in different conditions) were placed in the Memmert oven cabin. Four tests were carried out.

Each of the tests started in ambient or room conditions (T=24oC, RH=60%). The crack was

then left to propagate until its speed reached ca. 0.01 mmh-1

. Subsequently the temperature

was increased to T=40oC with the heating rate of 0.5

oC/min. The sample was left in this

conditions to the moment of crack propagation arrest.


134

Fig.3.71. Schematic representation of tested sample.

Microscopic features of fracture in different conditions

Figs.3.72-3.74 are visual assessments of the crack propagation and fracture in both tested

conditions. The first remark must be made about multiple crack fronts. In ambient conditions,

the crack propagates via bridges created between the substrates which are particularly visible

in the bottom left of Fig.3.72. In ambient conditions these bridge zones, as observed, occur

and thus could be attributed to the process zone. Propagation observed in elevated

temperature conditions takes place in a different manner. The crack propagates through the

created fibrils of polymer (see Fig.3.73), which span the space between aluminium plate and

the adhesive layer, resulting in craze-like zones [215,216] (Figs.3.72 and 3.73). These zones,

as was observed, can expand to about 10 mm in length. This particular, elevated temperature

propagation, feature was found only in globally defined process zones. This means that the

strain recorded within the craze zone was higher than after in respect to the wedge position. In

addition, this zone was found to possess the ability to post cure and recover elastic properties

after a decrease of temperature, providing zones of certain strength. This is shown in Fig.3.74.

It was observed, that while removing (from between separated plates) the wedge at elevated

temperature the plates returns to parallel, initial, positions in respect to rigid adherend. The

situation looked different when the wedge was left between separated plates and the entire

system was cooled down to ambient temperature. Thus, removing the wedge did not change

the flexible member position (Fig.3.74). This strongly suggest that some modification to the

adhesive occurred.

b

BONDED

ZONE

FREE

ZONE

STRAIN GAUGES

86.5

95

79

23

x

y

31

39

46.5

55

64

71

Michał K. Budzik

135

Fig.3.72. Crack propagation sequences recorded in room temperature condition, T=24

oC (left)

and at the elevated temperature T=40oC (right).

Fig.3.73. Feature of fracture in elevated temperature – the adhesive crazes in the bonded zone

(indicated with arrows).

Fig.3.74. Sample cooled down with wedge between separated plates. Wedge was removed

after cooling down.

Results of strain measurements

In the following, new and intriguing results have been obtained. Discussion presented here is

not definitive since several points are still unclear and require further investigative work.

ALUMINIUM

ALUMINIUM

ADHESIVE

100 μm

ALUMINIUM

ADHESIVE

ALUMINIUM

ALUMINIUM

ADHESIVE

200 μm

T = 24oC

TIM

E

T = 40oC CRACK DIRECTION


136

Figs.3.75-3.78 refer to the results of the direct strain gauge measurements. As can be noted (as

also stated in previous studies) process zone length increase with increase of temperature.

Also the adhesive elastic properties (we assume that change of temperature does not affect the

aluminium properties) change with temperature. Of particular interest here is the possibility to

obtain results and crack position while two parameters that are changing with time, λ and

crack length a.

Fig.3.75. Strain profiles of the sample tested in ambient temperature at the beginning and end

of the test. The crack propagation from solid to dotted line (left).

Fig.3.76. Strain profiles of the sample tested in elevated temperature at three stages:

beginning, middle and at the end of the test. Solid. dashed and dotted line corresponds to the

crack position at the given stage respectively (right).

Fig.3.77. Strain profiles of the samples tested in ambient temperature at the beginning and end

of the test for the 6.8 mm wedge. The crack propagation from solid to dotted line (left).

Fig.3.78. Strain profile of the sample tested in elevated temperature at three stages: beginning,

middle and at the end of the test. Solid, dashed and dotted line corresponds to the crack

position at the given stage respectively (right).

Graphical, precise, crack length estimation

Experimentally obtained strain evolution, and crack propagation in time (illustrated in

Fig.3.79a) are the most important findings obtained in this study. When the crack is passing a

strain gauge position, the maximum value of strain response (since the corresponding bending

moment has his maximum at this moment of time) is expected (here it is for 95 mm long

crack and strain gauges bonded at this position, with the respect to the wedge).

0 10 20 30 40 50 60 70 80 90 100 110

0.0000

0.0005

0.0010

0.0015

0.0020

= 6.8 mm

T = 40oC

t = 0

t = 24 h

t = 170 h

Su

rfac

e st

rain

, -

s

x (mm)

0 10 20 30 40 50 60 70 80 90

0.0000

0.0005

0.0010

0.0015

0.0020

t = 0

t = 24 h

Su

rface s

train

, -

s

x (mm)

= 6.8 mm

T = 24oC

0 10 20 30 40 50 60 70 80 90

0.0000

0.0005

0.0010

0.0015

0.0020

t = 0 h

t = 48 h

t = 100h

Su

rfac

e st

rain

, -

s

x (mm)

= 4.8 mm

T = 40oC

0 10 20 30 40 50 60 70 80 90

0.0000

0.0005

0.0010

0.0015

0.0020

t = 0 h

t = 22 h

Su

rfac

e st

rain

, -

s

x (mm)

= 4. 8 mm

T = 24oC

Michał K. Budzik

137

Fig.3.79. a) Strain evolution with progressing crack. Signals from three strain gauges located

at: x1=23 mm and x6=64 mm (already passed by the crack) and x10=95 mm (passed during the

test). Last gauge signal presents evolution of signal in neighbourhood of the gauge. Estimated

process zone, or elastic foundation zone of ca. 14 mm. b) Fracture surface after the test with

visible process zone (left), close-up of the process zone (right).

Knowing the exact position of all strain gauges used, finding the maximum value of the

recorded strain (for the gauge at defined xi) we can calibrate measurements to give the exact

position of the crack front at any time, t, for any adhesive and his state, thus, crack length,

a=xi at this moment. This was successfully achieved and an example is shown in Fig.3.79a.

Moreover, using such data, we can precisely estimate the size (length) of the process zone,

which in the present study was ca. 14 mm length. The direct observation of the surface after

fracture supports experimental results (Fig.3.79b). Left of a Fig.3.79b is close up of the

deformed part of the adhesive, in fact, showing some details of ductile fracture. The crack

lengths recorded during the study are summarized in Fig.3.80. It must be pointed out that for

the same sample, crack length decreased when the test was stopped at elevated temperature,

and started once more at ambient (after cooling down). This is possibly due to post cure and

-εs(x=95 mm)=max

-εs(x=95 mm)=min

ELASTIC FOUNDATION ZONE

a)

b)

ca.14 mm

77.5 80.0 82.5 85.0 87.5 90.0 92.5 95.0 97.5 100.0 102.5 105.0

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

x1 = 23 mm

x6 = 64 mm

x10

= 95 mm

Su

rface s

train

, -

s(xi)

Crack length, a (mm)

= 6.8 mm

T = 40oC


138

recovery of certain zones within the aluminium/the adhesive interface (also, the typical

fracture energy value should decrease with increasing temperature).

Fig.3.80. Crack length evolution during the test (note the joint behaviour in Fig.3.74).

Kinetics of crack propagation

Crack kinetics measurements are shown in Figs.3.81-3.83 for the situation when the wedge of

thickness, Δ=6.8 was used (representative for all tests made). What can be easily noted is

stable, slow crack growth at ambient temperature and fast, unstable crack growth at elevated

temperature. The structure, bonded with the tested adhesive, submitted only to 16oC of

temperature, will suddenly fail, although while testing without mechanical loading, will resist,

probably, for hundreds if not thousand of hours.

Fig.3.81. Crack propagation in time for different test conditions (left).

Fig.3.82. Crack propagation kinetic in ambient test condition (right).

Comparing crack speed characteristics (Figs.3.82 and 3.83), differences between propagation

in different conditions are even more pronounced. Stable crack slowing down may be

observed at ambient temperature, while five specific crack speed regions (marked in Fig.3.83)

were found for the elevated temperature propagation. Primarily (stage I), the crack slow down

1E-3 0.01 0.1 1 10 100

0

5

10

15

20

25

30

35

= 6.8 mm, T = 24oC

= 6.8 mm, T = 40oC

Cra

ck

in

cre

men

t,

a (

mm

)

Time, t (h)

0.01 0.1 1 10

0.01

0.1

1

10

100

1000

= 6.8 mm

Cra

ck

sp

eed

, d

a/d

t (m

m h

-1)

Time, t (h)

T = 24oC

60

65

70

75

80

85

90

95

100

105

110

= 6.8 mm

T = 40oC

= 6.8 mm

T = 24oC

= 4.8 mm

T = 40oC

Cra

ck l

eng

th,

a (m

m)

t = 0

t = end

= 4.8 mm

T = 24oC

ADHESIVE RECOVERY

Michał K. Budzik

139

as would be expected in any condition. Second stage (II) shows some crack length

acceleration, possibly due to additional, temperature driven, stress relief. In third stage (III),

the crack slows down once more after stress relief. Fourth stage (IV) can be treated as a

transition stage, between normal, elevated temperature propagation speed, and acceleration

due to approaching sample extremity (stage V) with some signs of stick-slip propagation. In

fact, acceleration in stage V can be provided using entire Winkler model, in which, deflection

is written as a symmetric equation with stress growth at both elastic foundation extremities.

Fig.3.83. Crack propagation kinetics in elevated temperature. Five specific regions were

noted: I. Linear speed decrease, normal for propagation at constant temperature, II. Increase

of the crack speed, possibly due to the adhesive stress relief, III. Normal, stable crack

propagation. IV. Transition, stick-slip like zone, V. Acceleration of the crack close to the

sample extremity.

Fracture energy comparison, Gc

The previous findings were also emphasized in fracture energy analysis. Figs.3.84 and 3.85

show energy release rate as functions of time and crack speed respectively. Although Fig.3.84

does suggest normal – stable energy release Fig.3.85 is more unusual. Here, second order

changes are more pronounced and once more, five specific zones of crack propagation in

40 60 80 100 120 140 160

0.01

0.1

T = 40oC

Cra

ck s

pee

d,

v (

mm

h-1

)

Time, t (h)

= 6.8 mm

I II III IV V

1 10 100

0.01

0.1

1

T = 40oC

Cra

ck s

pee

d,

v (

mm

h-1

)

Time, t (h)

= 6.8 mm


140

elevated temperature can be found. Accordingly, and contrary to the accepted model, some

part of the graph shows decrease of fracture energy with increase of crack speed. This may

show, that some of the environmental conditions, providing crack acceleration, are more

important than simple, mechanical considerations.

Fig.3.84. Energy Release Rate change with time (left).

Fig.3.85. Change of the energy release rate with the crack speed. Stages I-V like in Fig.3.83

(right).

In Fig.3.86, three dimensional visualisation of the entire crack propagation process is

presented. Such data are presented for the first time within this thesis, and are mainly due to

use of the CDT technique developed here.

Fig.3.86. Energy- Crack- Speed curve for elevated temperature propagation. Zone IV of ca.

12.5 mm length.

The complex problem described (but not solved here), requires separate, more complex and

detailed studies. However, provisionally, in agreement with theory (time-temperature

superposition) [223], properties of the polymers e.g. elevated temperature fracture energy can

7580

85

90

95

100

105

30

40

50

60

70

80

90

100

110

0.1

1

Ene

rgy

Rel

ease

Rat

e, G

c (J

m-2

)

Crack speed, v (mm h-1 )

Crack length, a (m

m)

T = 40oC

= 6.8 mm

0.01 0.1 1 10 100

20

40

60

80

100

120

140

160 = 6.8 mm, T = 24

oC

= 6.8 mm, T = 40oC

En

erg

y R

ele

ase

Rate

, G

c (

J m

-2)


I

II III IV

V

0 20 40 60 80 100 120 140 160 180 200

20

40

60

80

100

120

140

160

= 6.8 mm, T = 24oC

= 6.8 mm, T = 40oC

En

erg

y R

ele

ase

Rate

, G

c (

J m

-2)

Time, t (h)

Michał K. Budzik

141

be shifted from e.g. ambient temperature fracture. Herein, for a given environment the

following formula can be written:

(3.130)

where:

v – crack speed

α , β – system constants

γ – environment dependent energy release rate.

Using part of Fig.3.85 (ambient condition curve and stage III of elevated temperature

propagation – stable crack growth at elevated temperature) and following equation 3.130, the

shifted fracture energy vs. crack speed can be plotted (for elevated temperature) as shown in

Fig.3.87. Such based data shows, that in the case studied, the energy required to propagate the

crack at elevated temperature is ca. 3.6 times smaller than for the same adhesive system but

tested in ambient conditions.

0.01 0.1 1 10 100

40

50

60

70

80

90

100

110

120

130

140

150

Gc = 29.88 v

0.1146+ 25.2

Gc = 29.88 v

0.1146+ 90.15

T = 24oC

T = 40oC

En

erg

y R

ele

ase

Rate

, G

c (J

m-2

)


= 6.8 mm

Fig.3.87. Interpretation of temperature effect with highlighted region used for elevated

temperature interpretation.

Testing of adhesive joints in hostile environments has only rarely been reported. Generally,

environment impact was limited to joint behaviour analysis after aging. This can easily lead a

to mismatch with the real problem of the joint reliability. Although after degradation, decrease

of material properties can be observed [224-226], the critical changes are achieved after many

hours of extreme exposure. When structures are loaded both, environmentally and

mechanically, the majority will not survive until degradation moment, e.g. few degrees

heating can critically change the system behaviour. Accordingly, change of the joint operating

temperature can provide many changes in mechanical properties of the system. Complex,

simultaneous mechanical-environmental tests are therefore required. However complex

loading conditions imply many phenomena. Despite complexity it was proven that the

technique developed here, taking advantage of standard strain gauges, is reliable and can be

used for such studies. In addition, the wedge test is particularly suitable for the assessment of

structural adhesive fracture energies. However, this test is often analysed using simple beam


142

theory (SBT), whereby it is assumed that one or both adherends may be treated as encastré

cantilever beams, in their unbonded portions. However, when the adhesive layer is

particularly deformable either due to its low elastic modulus or significant thickness or both,

the encastré part may be far from rigid, leading to an effect of root rotation, or elastic

foundation. This must be taken into account and is part of developed here CDT technique.

Michał K. Budzik

143

s

t n

2

1

Chapter 4. MODELLING OF STRESSES IN ASYMMETRIC ADHESIVE

JOINTS

Finite element analysis approach was introduced to study asymmetric test configuration and

its effects. Different geometrical aspects of the flexible member and the adhesive were

analyzed. Moreover, it must be pointed out, that all elements of the modelled bonded joint

undergoes classical, proportional Hook's law.

4.1. FEM model

Bonded adhesive joint was designed using Cast3m (Development Team, Laboratoire de

Mécanique Systèmes et Simulation, Commissariat Français à l'Energie Atomique) program in

3-dimensional Cartesian geometry with a high level interpreted language: GIBIANE.

Finite Elements (FE)

CUB8 elements were used for the adhesive layer design. They main feature are eight corner

nodes with eight Gauss points. CUB8 corresponds to solid three dimensional elements and are

perfectly suited for elastic analysis. The plate was represented by the COQ4 elements which

are four nodes, four Gauss points elements devoted to the Mindlin-Reissner plates. COQ4

gives advantage of taking transverse shear into account (nb. analogically to Timoshenko’s

beam element). It must be appreciated that both introduced elements takes advantage from

square shape function. This is important aspect for estimation of searched values between the

element nodes. Some of the FE features are summarized in Table 4.1.

Table 4.1. Details of finite elements used in the studies.

Element Presentation Stress or Force Deformation

COQ 4

4 nodes, 3 D element

Local orientation:

N11- normal force in 11

N22 - normal force in 22

N12 - normal force in 12

M11- bending moment in 11

M22- bending moment in 22

M12 - bending moment in 12

V1 - shear force in 1

V2 - shear force in 2

Local orientation:

εss – plane elongation in ss

εtt – plane elongation in tt

γst – shearing in st

γtn – shearing in tn

γsn – shearing in sn

ρss – curvature in ss

ρtt – curvature tt

ρst – curvature st

CUB 8

8 nodes, 3 D element

Global orientation:

ζxx - stress in x

ζyy - stress in y

ζzz - stress in z

ηyz - stress in yz (shear)

ηxz - stress in xz (shear

ηxy- stress in xy (shear

Global orientation:

εxx – plane elongation in x

εyy – plane elongation in y

εzz – plane elongation in z

γyz – shearing in yz

γxz – shearing in xz

γxy – shearing in xy

z

x

y


144

To cast the results within the global coordinate system x, y, z stresses and deformations of

shell element has to be changed. That was made using following the formulas shown below.

(4.1)

(4.2)

(4.3)

(4.4)

(4.5)

(4.6)

(4.7)

(4.8)

(4.9)

(4.10)

(4.11)

(4.12)

where:

h – thickness of modelled shell element

k = 1 for the upper plate surface

= 0 for the middle plane

= -1 for the bottom plate surface.

Mesh

The mesh was built from 50x50 (length x width) finite elements (FE) with increasing length

of the element and constant element width equal to the adhesive width divided by number of

elements, thus sb=b/50. Length of the element was increasing, starting from the crack front

(for plate in both directions), with the first element being of length s1=100 μm (see Fig.4.1).

Michał K. Budzik

145

Fig.4.1. Details of designed mesh.

Boundary conditions

At x=0 constant displacement, Δ was imposed (see Fig.4.1). Thus:

(4.13)

The bottom plane of the adhesive was modelled as built in (brick in Fig 4.1) so thus rigid

adherend was not modelled in the studies. All movements: displacements or rotations are

blocked.

(4.14)

(4.15)

(4.16)

where u with appropriate index is beam displacement in the given direction.

The plate-adhesive interface was modelled using COLLER procedure (operator), which

defines shell (or plate) - volume elements junction. This procedure allows the rotation from

shell elements (e.g. COQ4) to the volume element (e.g. CUB8) nodes. Function allows to

bond two surfaces leaving possibility for the edge rotations and displacements without

sn=sn-1+(Σsn-1)/ladh

h e

ladh (50 FE) a (50 FE)

b (

50 F

E)

z

x

x

y

zadh

s1


146

separation between bonded elements. This fact is very important while studying asymmetric

geometry with one relatively flexible member. One important parameter was taken into

account, the flexible adherent eccentricity with respect to the adhesive layer. Normally,

bended plate is represented in finite element by its mean plane, so that no interfacial stresses

exists. In practice the bottom side of the plate is in contact with the adhesive which implies

different load transfer than from mean plate (e.g. shear and results). Adhesive displacement is

therefore:

(4.17)

where ux, uz are local beam displacements along x and z and θy is the local beam rotation. This

eccentricity generates many coupling between vertical reaction and bending momentum,

membrane effects and others.

4.2. Finite Element Analysis

In order to study different systems which can be used within the experiment, the plate-

adhesive configuration was varying during the finite element analysis. Parameters, their

notation and range which were studied are summarized in Table 4.2.

Table 4.2. Parameters tested during studies.

Parameter Designation Value Unit

Crack depth δa 0-3.5 mm

Plate Thickness h 1-5 mm

Adhesive thickness e 0.01-1 mm

Plate Young modulus E 5-200 GPa

Adhesive Young modulus Eadh 0.01-5 GPa

Plate Poisson coefficient ν 0.01-0.45 -

Adhesive Poisson coefficient νadh 0.1-0.499 -

Length of the free zone a 10-100 mm

Length of the bonded zone ladh 20 mm

Width of the plate b 5-50 mm

Imposed displacement Δ 1-9 mm

4.2.1. Stress state with the straight crack front

For experimental results interpretation common assumption is that the crack front is straight,

and does not change shape during propagation. Stress distribution, for the cleavage, in- and

anti-plane loading modes within the adhesive and crack front are shown in Fig.4.2. As can be

seen, stress distribution is heterogeneous along the crack front, with high concentration in the

middle of the adhesive width of mode I and II. However, near to the sample edge certain

mode III stress should be noted.

Michał K. Budzik

147

σzz

THE ADHESIVE

CRACK FRONT

-10 -5 0 5 10

0

50

100

150

200

250

300

350

400

Str

ess,

zz (M

Pa

)

y (mm)

σxz

-10 -5 0 5 10

30

35

40

45

50

55

60

Sh

ea

rin

g s

tre

ss,

xz (

MP

a)

y (mm)

σyz

-10 -5 0 5 10

-40

-30

-20

-10

0

10

20

30

40

Te

ari

ng

str

ess,

yz (

MP

a)

y (mm)

Fig.4.2. Stress state within the adhesive and at the straight crack front for three common

loading modes (input data like in Table 4.3).

4.2.2. Stress mixity

As was found previously, different stresses exists within the adhesive layer and at the crack

front. In order to study stress mixity in the studies, two, stress driven stress-mixity factors are

introduced:

a) II/I stress mixity (in-plane shearing component), defined as:


148

(4.18)

b) III/I stress mixity (tearing, anti-plane shearing component):

(4.19)

where I, II, III corresponds to fracture modes.

During former analysis (section 4.2.1) it was found that the in-plane shearing stress, play the

most important role in the middle of the sample. Therefore, mode II/I was analyzed only at

this point. Contrary, tearing stress can be neglected in the middle of the sample width

(Fig.4.2), but the value of tearing stress at the sample board can play important role. Therefore

sample board was chosen for further mode III/I stress analysis. All data (constants) used for

the FEA studies of mode mixity are collected in Table 4.3.

Table 4.3. Mode mixity test panel.

Parameter Notification Value Unit

Plate Thickness h 1.6 mm

Adhesive thickness e 0.2 mm

Plate Young modulus E 70 GPa

Adhesive Young modulus Eadh 4.5 GPa

Plate Poisson coefficient ν 0.3 -

Adhesive Poisson coefficient νadh 0.45 -

Length of the free zone a 35 mm

Length of the bonded zone ladh 20 mm

Width of the plate b 25 mm

Imposed displacement Δ 4 mm

a) In-plane shearing contribution

The effects of the geometry on the modes II/I mixity are illustrated in Figs.4.3-4.7. It must be

appreciated, that the adhesive properties, not bonded plate, are playing dominant role in stress

II/I mixity. However some variation can be found for all of tested parameters of the plate,

generally change in mode mixity is small (please note the vertical scale). One of the important

findings is the crack length effect (Fig.4.3). Because of high heterogeneity of stress mixity at

the crack front for small crack lengths, initial crack of the length ca. 30 mm can be

recommended and was used in experimental part of the thesis. From geometrical aspects (we

are most of the time forced to used material of given properties) important is plate width.

Highest stress homogeneity is obtained for wider plates, although, global mode II/I mixity

also increases. In the studies these effects were balanced by using plate of 25 mm width.

Michał K. Budzik

149

Fig.4.3. Slight increase of the shearing component with crack length.

Fig.4.4. Plate width effect on I/II mode mixity (left). Plate width effect n I/II mode mixity

(right).

Fig.4.5. Plate Young modulus effect (left). Adhesive Young modulus effect (right).

20 40 60 80 100 120 140 160 180 200

10

12

14

16

18

20

(

%)

Plate Young modulus, E (GPa)

0 1 2 3 4 5

2

4

6

8

10

12

14

Adhesive Modulus, Eadh

(GPa)

-0.4 -0.2 0.0 0.2 0.4

11

12

13

14

15

b=5

b=20

b=50

y/b

10 20 30 40 50

11.8

12.0

12.2

12.4

12.6

12.8

13.0

13.2

13.4

13.6

Width, b (mm)

10 20 30 40 50 60 70 80 90 100

12.6

12.8

13.0

13.2

13.4

13.6


CRACK LENGHTS RANGE IN

THE EXPERIMENTS


150

Fig.4.6. Plate thickness effect (left). Adhesive thickness effect (right).

Fig.4.7. Poisson ratio effect of the plate (left) and the adhesive (right).

Anti-plane shearing (tearing) stress contribution

Results of the FEM analysis of the mode III/I mixity at the sample board are shown in

Figs.4.8-4.13.

Fig.4.8. Increase of the tearing component with the crack length.

10 20 30 40 50 60 70 80 90 100

6

8

10

12

14

16

18

20

22

(

%)


0.1 0.2 0.3 0.4

12.6

12.8

13.0

13.2

13.4

13.6

13.8

14.0

(

%)

Plate Poisson ratio,

0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

25

30

Poisson ratio, adh

1 2 3 4 5

12.0

12.5

13.0

13.5

14.0

14.5

15.0

15.5

Plate thickness, h (mm)

0.2 0.4 0.6 0.8 1.0

8

10

12

14

16

18

20

22

24

Adhesive thickness, e (mm)

Michał K. Budzik

151

Fig.4.9. Tearing stress factor distribution along the normalized sample width (left) and

variation of the mode mixity with the sample width (right).

Fig.4.10. Plate Young modulus effect (left). Adhesive Young modulus effect (right).

Fig.4.11. Plate thickness effect (left). Adhesive thickness effect (right).

1 2 3 4 5 6 7 8 9 10

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

(

%)

Plate thickness, h (mm)

0.0 0.5 1.0 1.5 2.0

12

13

14

15

16

17

(

%)

Adhesive thickness, e (mm)

20 40 60 80 100 120 140 160 180 200

8

10

12

14

16

18

(

%)

Plate Young modulus, E (GPa)

0 1 2 3 4 5

0

2

4

6

8

10

12

14

(

%)

Adhesive Young modulus, Eadh

(GPa)

-0.4 -0.2 0.0 0.2 0.4

0

10

20

30

40

50

60

b = 5 mm

b = 20 mm

b = 50 mm(

%)

y/b5 10 15 20 25 30 35 40 45 50

6

8

10

12

14

16

(

%)

Plate width, b (mm)


152

Fig.4.12. Poisson ratio effect of the plate (left) and the adhesive (right).

In the modes III/I mixity near the adhesive side board (contrary to modes II/I mixity) more

important are plate properties. This is result of well known membrane effects. In fracture tests

often plates are used instead of rectangular bars. Such adherend geometry implies many

additional effects, like rotations at the plate extremities etc. which finally results in additional

stress components which are transferred by the adhesive layer. This effects arises when the

used plate is of small rigidity ratio to the rigidity of the adhesive. It must be appreciated that

choosing right sample geometry to be tested can be crucial in many aspects and should be

somehow balanced process. Change of any of tested parameters impose additional effects on

the load transfer in the system and can cause additional phenomena to occur. Sample

geometry should be easy to produce and enable comparison with the tests which were made

up to the time. All tested sample features and geometry used within the thesis are detailed in

Table 4.4. Geometrical effects on the stress state is detailed in Table 4.5.

Table 4.4. Features of the sample used within the thesis.

Parameter Notation Value Unit

Crack length a 40-105 mm

Width b 25 mm

Plate Young modulus E 50-77 GPa

Plate thickness h 1.6 mm

Plate Poisson ratio ν 0.05-0.3 -

Adhesive Young modulus Eadh 0.02-4.5 GPa

Adhesive thickness e 0.2-0.8 mm

Adhesive Poisson ratio νadh 0.45-0.49 -

Imposed displacement Δ 1.6-9.7 mm

Table 4.5. Features of chosen geometry.

y\mode component η (δa = 0 – δa = 1.5) (%) κ (δa = 0 – δa = 1.5) (%)

y = 0 13.3 – 13.5 0

y = ± 12.5 20 – 16 (but small stress level) 11 - 9

0.1 0.2 0.3 0.4

0

10

20

30

40

50

60

70

(%

)

Plate Poisson ratio,

0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

25

(

%)

Adhesive Poisson ratio, adh

Michał K. Budzik

153

4.2.3. Anti-plane shearing effect on fracture structure

Figure 4.13 illustrates the mode III/I stress mixity, obtained with FEM analysis, in the

adhesive near the sample board. It must pointed out, that the stress level, when the crack

length is small, is at this stage very high (see Fig.4.2).

6 8 10 12

0

2

4

6

a = 10 mm

a = 50 mm

a = 100 mm

(

%)

y (mm)

Fig.4.13. Tearing component at different stages of crack propagation (FEM analysis).

As was noted previously [e.g. 217], cleavage-tearing stress mixity can create river patterns

phenomenon in brittle materials, i.e. epoxies. This effect was observed during microoptical

studies of the fracture surfaces of the Epidian6 (DGEBA) adhesive (Fig.4.14a). Epidian6 was

tested in the CRT test on slow strain rate tensile machine. All tested samples (also with MMT

nanoparticles) indicates the river pattern phenomenon near the side board. This characteristic,

microstructural, feature was never recorded in the adhesive joints test and within this study is

related to the FEM analysis which indicates high modes III/I mixity near the side board of the

adhesive. In Fig.4.14 a and b graphical analysis of the fracture surface is made. Using river

patterns found at the fracture surface, detailed studies of the stress state at the crack front can

be deduced. This short study indicates curved crack front. This findings stays with agreement

with the finite element studies (e.g. Fig.4.2) where high mode I stress concentration is based

in the middle of the sample width. While this stress is decreasing, moving from the centre of

the plate, mode III – anti-plane shearing plate increases. Mode I concentration can result with

the crack front curvature (studied in the next section), while mode III/I mixity in the side of

the adhesive result in river patterns phenomenon, which was observed during direct,

microscopic, observations.


154

Fig.4.14. Optical micrographs of river patterns observed during the test on macro a) and

microscale b). Graphical interpretation of the surface features.

4.2.4. Crack depth

As can be seen from Fig.4.2 some stress heterogeneity occurs when the straight crack front.

Mode I stress, which drive the crack propagation is concentrated in the centre of the adhesive

width. This can result in creation of the curved crack front, where the stress state will be more

homogenous. One of the variable introduced to the analysis was crack depth, δa. Crack depth

is defined as a difference between crack length at the middle of the sample and crack length at

edge (see Fig.4.14) [204], thus δa=acentre-aside. The origin of the phenomenon is unknown but

mostly referred to the anticlastic bending effect [177,218,219]. It must also appreciated that in

bonded joints stress-strain state varies along the crack front, from plane-strain in the middle

(at y=0) to plane-stress on the side of samples (at y=± b/2). Crack length of the crack with

curved front can be defined as:

(4.20)

where n is parameter defining crack front shape.

In this study n=2 was assumed, thus giving parabolic crack front. Crack front curvature is

important parameter for the crack length estimation but often ignored by researchers. The

energy release rate, G from definition is strongly crack dependent function [204]. Ignoring

crack front curvature effect can lead to misinterpretation of the results. It was found that

energy release rate can be overestimated to ca. 40% [177]. Direct evidence of the parabolic

crack front is shown on Fig.4.15 and was found by the author while studying in all test for all

tested samples.

a)

LO

CA

L C

RA

CK

DIR

EC

TIO

NS

GLOBAL CRACK DIRECTION

MODE I

MO

DE

III

b)

PR

OV

ISIO

NA

L C

RA

CK

FR

ON

T

400 μm 100 μm

Michał K. Budzik

155

Fig.4.15. Curved crack front for two bonded with epoxy adhesive aluminium plates. Picture

made with micro camera system (Dino-Lite).

In order to study crack front curvature sample with features detailed in Table 4.6 was

analyzed.

Table 4.6. Crack depth test panel.

Parameter Designation Value Unit

Crack length a 35 mm

Width b 25 mm

Plate Young modulus E 70 GPa

Plate thickness h 1.6 mm

Plate Poisson ratio ν 0.3 -

Adhesive Young modulus Eadh 4.5 GPa

Adhesive thickness e 0.2 mm

Adhesive Poisson ratio νadh 0.45 -

Imposed displacement Δ 4 mm

Results of the qualitative analysis, made with Cast3M code are shown in Fig.4.16 in form of

three nominal stresses and their distribution in the adhesive layer. More quantitative results of

stress distribution along the crack length are shown in Figs. 4.17-4.19. Stress at two positions

were analyzed: at the middle of the width of the adhesive, and at the adhesive board (right

side of the figures). Qualitative comparison reveals that homogeneity of the stress increase

while the crack depth is increasing up to some moment, in the present study ca. 1.5 mm. From

quantitative studies can be found, that the same stress level is obtained when the crack depth

is 2.75 mm (red bold line), or 0.8 mm (blue bold line) for cleavage and in-plane shearing

modes. Homogeneity of the mode III stress is never obtained. Direct microscopic

observations yield that the crack length is ca. 2.3 mm deep (green bold line). This value is of

course closer to the mode I stress homogeneity, mode which is driving the crack. Thus, the

difference between FEM analysis and direct observation (ca. 0.45 mm) may be suspected to

come from the stress heterogeneity or from the complex stress state along the crack front.

Crack front

curvature

δa

Wed

ge

25

25


156

σzz σxz σyz

Fig.4.16. Finite Element Analysis result. Stress state in the adhesive layer. In columns:

cleavage, in- and anti-plane shearing stress respectively. In rows arising crack depth, from 0-

1.5 mm. Arrows indicate change of stress level.

δa=0

δa=0.5

δa=1

δa=1.5

Michał K. Budzik

157

Fig.4.17. Cleavage stress distribution. Opening stress, ζzz vs. crack depth, δa (left) curves

showing linear relation on sample board and in the middle (right). Solid line indicate crack

depth for which stress at the width centre and side are of the same value, dashed line for

experimental value.

Fig.4.18. In-plane shearing stress distribution along the crack length (left).Shearing stress at

the crack front vs. crack depth indicating linear relations on side and in the middle of the

sample (right). Solid line indicate crack depth for which shearing stress at the sample centre

and side are of the same value.

Fig.4.19. Anti-plane shearing stress along sample width (left). Tearing stress at the crack front

vs. crack depth indicating linear relations on side and in the middle of the sample (right). Bold

lines indicate crack depth for the situation described previously.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

10

20

30

40

50

60

Tea

rin

g s

tres

s,

yz (

MP

a)

Crack depth, a (mm)

yz

(y = 0) = 14.627 a+36.193

R2 = 99.96%

yz

(y = 12.5) = 0

y = 0

y = ± 12.5 mm

-10 -5 0 5 10

-40

-30

-20

-10

0

10

20

30

40

a = 0 mm

a = 0.5 mm

a = 1 mm

a = 1.5 mm

Teari

ng

str

ess

, y

z (

MP

a)

y (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

30

40

50

60

70

80

90

y = 0

y = ± 12.5 mm

xz

(y = 12.5) = 14.627 a+36.193

R2 = 99.99%

xz

(y = 0) = -6.936 a+54.4123

R2 = 99.99%

Crack depth, a (mm)

Sh

eari

ng

str

ess

, x

z (M

Pa)

-10 -5 0 5 10

30

35

40

45

50

55

60

a = 0 mm

a = 0.5 mm

a = 1 mm

a = 1.5 mm

Sh

eari

ng

str

ess

, x

z (M

Pa)

y (mm)

0.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

50

100

150

200

250

300

350

zz

(y=±12.5) = 93.282 a - 27.239

R2 = 99.28 %

zz

(y=0) = -50.089 a + 367.488

R2 = 99.98 %

Crack depth, a (mm)

Str

ess

,

zz (

MP

a)

y = 0

y = ± 12.5 mm

-10 -5 0 5 10

0

50

100

150

200

250

300

350

400

a = 0 mm

a = 0.5 mm

a = 1 mm

a = 1.5 mm

Str

ess

,

zz (M

Pa)

y (mm)

2.75


158

Final studies were made in order to find out effects of the crack depth impact on the stress

mixity along the crack front. This results are shown in Figs.4.20 and 4.21. Like previously

analysis were made for the centre of the adhesive for modes II/I mixity, and for the adhesive

board in case of modes III/I mixity. As can be seen, mode mixity is not changed by the crack

depth, although some relation can be found. Linear increase of the modes II/I mixity can be

seen (Fig.4.20) but with very small (0.2%) change for the analyzed crack depth range.

Contrary, modes III/I decreases with crack depth increase with power low. This change is

3.5% for the analyzed crack depth range.

Fig.4.20. Effect of the crack depth on stress mixity factors distribution. Shearing stress

component (left). Tearing mode component (right).

Fig.4.21. Slight, linear increase of the shearing component with the crack depth increase in

the middle of the tested sample (left). Decrease of the tearing stress component with the crack

depth at the side of the sample (right).

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

13.4

13.5

13.6

a, (mm)

= 0.001382a + 0.1338

R2 = 99.82 %

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

(

%)

a (mm)

= -0.02421a0.5268

+0.1253

R2 = 99.69 %

-10 -5 0 5 10

10

11

12

13

14

15

16

17

18

19

20

21

a = 0 mm

a = 1.5 mm

y (mm)

-10 -5 0 5 10

0

2

4

6

8

10

12 a = 0 mm

a = 1.5 mm

(

%)

y (mm)

Michał K. Budzik

159

DISCUSSION OF THE TESTS

Three new, asymmetric bonded joints tests were introduced: Constant Rate Test (CRT) – with

constant deflection rate loading condition, Constant Force Test (CFT) with constant force

loading condition and Constant Displacement Test (CDT) – with constant displacement

loading condition. Results were interpreted using physical cantilever beam model and

mathematical simple beam theory. Validation of the test procedures was made using proposed

Artificial Crack Tip Test. Accurate and continuous measurements of crack propagation in the

adhesive joints were introduced. Particularly in the CDT test novel instrumented wedge

technique was introduced. For the three tests original setups were designed (using Catia v5

environment) and built. Winkler elastic foundation model was extended and used in adhesive

bonding joints. Original tests applications were proposed. Fracture of the bonded joints was

studied in micro and macro scale using the developed metrological procedures as well as

atomic force microscope (AFM) and scanning electron microscope (SEM) techniques. The

asymmetric joints geometry was analysed using finite element method analysis (FEA).

Comparison of the tests

The three tests introduced in this work promise precise and correct crack increment

measurements. The errors of the crack increment were of marking point size and were

removed from the graphs for aesthetic reasons. Systematic relative errors of the methods

presented are listed in Table C.1.

Table C.1. Possible parameters error.

Test Relative error (%)

Eh b h F Δ α

CRT

CFT

CDT

max 10

max 10

max 10

0.2

0.2

0.2

max 3.1

3.1

3.1

0.02

0.02

-

0.5

0.5

max 1.7

-

-

max 2.5

Estimation

procedure

3 point

bending test,

representative

population

Calliper gauge,

representative

population

Calliper gauge,

representative

population

Force sensor

calibration,

electric noise

Sensor

calibration,

for CDT

calliper gauge

Statistical,

electric

noise

Fig.C.1 illustrates crack length calibration curves of the three new tests obtained in the

artificial crack tip test. All tests possess linear characteristic of the estimated crack length, a

vs. reference crack length, aD, so that:

(C.1)

with α – constant.


160

40 50 60 70 80 90 100

40

50

60

70

80

90

100

110

Est

imate

d c

rack

len

gth

, a

(m

m)

Reference crack length, aD (mm)

aCDT

=1.0017 aD

R2 = 99.96 %

aCFT

=1.069 aD

R2 = 99.92 %

aCRT

=1.0089 aD

R2 = 99.97 %

Fig.C.1. Crack length calibration curve of the tests.

The best precision is assured by the strain gauge technique, where the estimated crack length

can be treated as the real crack length. The less precise test is constant force. The CFT test

overestimates apparent crack length by 6.9 %.

Crack propagation behaviour

a) CRT test: in the test a constant displacement rate of the bonded plate is maintained during

the entire test. The CRT characteristic feature is linear relation between separation rate and

the crack speed. Thus one test will give one fracture energy for one crack speed, although the

separation rate will be changed during testing. The CRT test is susceptible to the adhesive

properties and highly rate dependent [220]. When the adhesive was brittle, like Epidian 6 or

cyanoacrylate the test was performed without problem. However, when the adhesive was

more ductile and tough the test could not be performed, leading to the substrates plastic

deformation which is important limitation in the applications of the CRT test.

b) CFT test: the test starts by applying constant force to the flexible plate extremity. The

initial crack growth rate is low, and increasing with time which can be critical in certain cases.

Due to the crack acceleration this test unstable, particularly when brittle adhesives are tested,

e.g. for dentistry. In this test viscoelastic properties of the adhesive and flexible substrate are

important, since at the beginning there is a possibility of the adhesive creep. The initial value

of applied force should be estimated using different method.

c) CDT test: the test starts with the wedge insertion causing adhesive break. Crack growth rate

is maximum at the test beginning and decreasing with time. Therefore the basic results and

information about adhesive fracture toughness can be found after relatively short time,

Michał K. Budzik

161

although the propagation may continue even several months [221]. The test gives possibility

of long time durability testing although can particularly suffers of the adhesive relaxation.

The comparison of the crack increment behaviour, δa in time, t for the tests studied is

illustrated schematically in Fig.C.2.

C

rack

in

cre

men

t,

a

Time, t

CRT

CFT

CDT

Fig.C.2. Crack increment behaviour of the new developed tests.

Tests applicability

a) CRT: The design is limited by the tensile machine adaptation. The designed feature (size

250x250x30mm) enable only horizontal sample position. The adaptation of facilities for

environmental tests are more complicated than for CDT and CFT tests. The test can be

performed on any flexible substrate. Environmental test are possible, although displacement

and force sensors require correct protection. Testing brittle adhesives is preferred. Tough

adhesives should be avoided due to possibility of the flexible adherend plastic deformation (at

least in the configuration studied).

b) CFT: The designed setup enable horizontal and vertical sample positioning. Size of the

entire set up is compact (size 200x200x300 mm including water tank) but not as small as for

the CDT. Test can be performed on any flexible substrate. Environmental tests can be

performed, although displacement sensor needs to be protected correctly. The test was found

not suitable to very brittle adhesives where the critical damage appeared faster (ΔtCD) than the

interval time (ΔtIT) between two measurements (see Fig.C.3). Electrical circuit with crack

increment feedback would be the best in this test.


162

Fig.C.3. Schematic representation of situation from CFT test when damage time, ΔtCD is

shorter than interval time, ΔtIT.

c) CDT: Designed setup was compact (60x60x250 mm) thus giving operational advantage. In

addition the test can be performed on any flexible substrate to which strain gauge can be

attached. Any environmental test can be performed, although strain gauges needs to be

protected correctly. All systems could be tested includes brittle and ductile adhesives, variable

surface treatments, crosslinking adhesives etc. Interpretation of the results is very precise

although the metrology is the most complicated from all presented tests.

Tests requirements

All introduced tests are using standard testing laboratory equipment. It must be pointed out

that to run CRT and CFT tests special equipment is bought at once. In the CDT test the

flexible adherend needs to be instrumented each time with new, at least two strain gauges,

although some limited reutilization of the instrumented flexible substrates is possible.

Required equipment to run single experiment is detailed in Table C.2.

Table C.2. Special equipment required to run a single test.

CRT CFT CDT

Devoted setup/

features complicity

Tensile machine

Force sensor

Displacement sensor

required/limited

design

required

required

required

required/easy

-

-

required

required/medium

-

-

-

ΔtIT

Cra

ck

in

cre

men

t,

a

Time, tΔtCD

Michał K. Budzik

163

Strain gauges

Wheatstone bridge

Signal conditioning

Post processing

-

-

required

required

-

-

required

required

required/at least 2

required

required

required

Major advantages

Features need to be

bought only once,

fast testing

Features need to be

bought only once,

multichannel

Fast accurate testing,

multichannel

Major drawbacks

Required expensive

tensile machine, one

machine – one tested

sample

- Expensive

Wheatstone bridge,

limited reusability of

samples

Summary of the experimental results

Aluminium anodization

1. Electrochemical Phosphoric Acid Anodization (PAA) applied to two different aluminium

alloys gives different surface topographies – more developed in Al-Cu alloy, although Al-Mg

alloys was affected. The alumina layer was found thicker on Al-Cu.

2. Employed PAA process gives rise of the adhesion energy over simply abraded of ca. 60 %

as was proved in the CDT test. In addition PAA change the fracture nature from adhesive to

cohesive.

Constant Rate Test

1. The constant rate test was found sensitive enough to study microstructural effects in the

adhesive joints.

2. The clay nanoparticle-modified epoxy adhesive gives higher fracture energy as well as

smaller crack growth rate over the pure adhesive. The results were confirmed with the fracture

surface studies.

3. Crack propagation rate and fracture energy of the adhesive joint are rate dependant.

4. The advantage of the epoxy/nanoparticle reinforced system is more exposed when plate

deflection rates used in the test are low.

5. The fast crack rates in the asymmetric joint geometry provides river pattern phenomenon at

the sample side boards.

Constant Force Test

1. CFT test was found precise and reliable for crack length estimations.

2. CFT test was employed successfully for testing of the adhesive joints providing precise,

continuous fracture observations.


164

3. The crack speed during the test accelerates to unidentified asymptote (sound of speed in the

given material?).

4. The crack speed and deflection rate were found linearly related.

5. The cyanoacrylate adhesives are characterized be the highest and the least crack speed

dependant fracture energy.

6. The observed nonlinear effects were assigned to creep or elastic deformation of the

adhesive.

Constant Displacement Test

1. CDT test was found precise and reliable for crack length estimations.

2. Surface treatment effect was successfully studied with the CDT test.

3. Double crack curvature phenomenon in the vicinity of the adhesion transition zone was

observed and successfully explained. In addition crack front behaviour in the studied

condition was proposed.

4. Observations of the crack path in the vicinity of the adhesion transition zone were made

illustrating that the crack is able to change the path from the interface to the cohesive fracture

without breaking the adhesive.

5. The interpretation of the soft adhesives behaviour was made using adopted to the adhesive

joints Winkler model.

6. Extended theory was successfully applied to study of the adhesive in metastable state.

7. Energy release rate was derivated from the Winkler model giving better inside into the

fracture mechanics of the adhesive joints.

8. The simple beam theory was found to overestimate the apparent crack length, although not

incorporating errors to energy release rate. The energy release rate derivated from Winkler

and SBT theory was found equal at least in situation studied.

10. The SBT model was found sufficient to study macroscale behaviour of the adhesive joints.

Finite Element Analysis

1. The proposed model was found reliable to study stress state as a function of the sample

geometry.

2. Proposed plate geometry provides ca. 13.3 % and 0% of the interfacial shearing and tearing

stress contribution respectively in the middle of the crack tip. The rest is opening stress.

3. The high value of the tearing stress near the side boards of the sample was found to be

responsible for the river patterns phenomenon.

4. The crack opening stress distribution provides the crack front curvature.

Michał K. Budzik

165

CONCLUSIONS

1. The novel tests designed in this work are promising in that they offer accurate, reliable

and continuous crack propagation observations.

2. The confirmation of this reliability was assessed by the simple beam theory (SBT) and

the Winkler elastic foundation model. It was found that the SBT overestimates the

apparent crack length which required correction for the experimental crack length.

However the extended Winkler model proved that this overestimation which appeared

to require correction is selfcompensating in terms of the strain energy release rate.

3. Among different materials systems studied in the Constant Force Test the

cyanoacrylate-bonded-joints gave the most promising results.

4. The novel Constant Rate Test allowed precise estimation of the improvement of the

adhesion efficiency in the aluminium joints bonded with nano-particle-reinforced

adhesive compared to the pure epoxy (30% improvement in fracture energy and 25%

slower crack propagation).

5. In all the tests performed using the different materials systems the existence of the

curved crack front was confirmed. This phenomenon helped to explain the fracture

behaviour at the boundary of the weak/strong adhesion zones.

6. The finite element method and analysis were found useful in studying the stress state

in the asymmetric bonded joints and allowed the explanation of the two phenomena:

the formation of the crack front curvature and the river patterns.


166

PERSPECTIVES

The following future tasks can be proposed:

1. Performing of durability tests for different materials systems used in the shipbuilding

industry where lack of the information about the durability and reliability of the

adhesive joints is main reasons of their limited applications.

2. Simplification of the existing (developed Constant Rate Test, Constant Force Test and

Constant Displacement Test) and their interpretation.

3. Development of the new, fracture mechanics based tests for particular applications,

e.g. axissymmetric samples.

4. Fracture modelling using finite element method and finite difference method –

although adhesion is a very complex phenomenon the finite element based methods

can provide many step forward in this field. For example studying adhesive joints

under complex mechanical loading can be very expensive or impossible but can be run

with finite element code. In addition fracture criteria as well as viscoelastic properties

of the adhesives and their effect on the structure behaviour can be considered.

5. Fractography based studies – the fractographic analysis is a very important tool for the

future adhesive bonding design and can provide big step forward in this field. The

knowledge about the microscale behaviour of the adhesive bonding has rarely been

reported.

6. The extended studies of new adhesives and surface treatment using Atomic Force

Microscope and Scanning Electron Microscope should be performed giving the

possibility of direct measuring of the adhesion forces.

Michał K. Budzik

167

APPENDICES

Appendix 1. Mode II contribution in Constant Displacement Test

Since the CDT test, in principle, invoke a degree of mode II fracture in addition to the

principal mode I. Simple analysis is presented showing, that the former contribution is

negligible.

Consider the geometry shown in Fig.A.1.1, which represents two thick substrates bonded such

that failure is occurring parallel to the interface, in mode II, due to the application of force, Fx

(the lower adherend is considered fixed). If the force is stationary, but the crack grows by an

increment δa, the elastic strain energy density in the volume abh (where b is width) is

reduced, since Fx decreases, although the volume involved increases to (a+δa)bh. The net

result is a reduction in overall stored energy, and it is this that drives the crack in mode II,

requiring energy GII b δa.

Fig.A.1.1. Close-up of the beam/wedge contact zone.

From an energy balance, it can be shown that the mode II fracture energy, GII, is given by:

(A.1)

With, compliance:

(A.2)

Since:

(A.3)

Therefore:

(A.4)

α F

Fx = F sinα

Fz = F cosα


168

Now consider the wedge/beam contact zone magnified in Fig.A.1.2. Assuming friction to be

negligible, the vertical force, Fz is, in fact, the vertical component, Fcosα, of the contact force,

F , normal to the beam (although the difference is very small for small α).

Fig.A.1.2. Model for mode II fracture

Similarly, there also exists a (small) horizontal component, Fx.

(A.5)

where:

(A.6)

From simple beam theory:

(A.7)

For situation studied (Fig.A.1.1):

(A.8)

We obtain:

(A.9)

Thus:

(A.10)

For small values of α valid is relation:

(A.11)

with:

(A.12)

Fx

a δa

h

Michał K. Budzik

169

we obtain:

(A.13)

The energy release rate is:

(A.14)

Finally in the present context, we may estimate the relative importance of mode II fracture

compared with mode I, from the ratio and the mode mixity rate from wedge – beam contact:

(A.15)

The worst case corresponds to the following values: h=1.6 mm, Δ=9.7 mm and a=75 mm.

These values lead to a ratio of mode II to mode I fracture energies of ca. 1.5 x 10-6

. Clearly,

neglect of mode II in this asymmetric test is of no consequence, although it may be with other

geometries.


170

Appendix 2. Friction dissipation in Constant Displacement Test

During CDT test, due to propagating crack, wedge/beam friction can occurs. This situation

can leads to possible friction energy dissipation. Simple analysis is presented showing, that

the wedge/beam friction in particular cases should not be neglected .

Consider situation like in Fig.A.2.1. The crack is propagating towards x, changing the radius

of the beam curvature, R and length of bended arm S. The point A due to crack growth moves

to the A’ position. Because beam and wedge stays in touch during entire process some energy

is lost for additional friction work.

Fig.A.2.1. CDT test and the close-up of the wedge/beam friction region.

From the SBT:

(A.13)

Δ

a

s α

x

z

Fx

Φ

A'

Fz

A

α

F

R

Michał K. Budzik

171

(A.14)

The change in bended arm:

(A.15)

(A.16)

(A.17)

(A.18)

Finally:

(A.19)

For incremental growth of crack, δa:

(A.20)

(A.21)

Since along the x, crack growth is δa, beams slides on the wedge, from A to A':

(A.22)

The normal force at the wedge/beam contact:

(A.23)

Assuming Guillaume Amontons low of friction:

(A.24)


172

We can write:

(A.25)

Work of the friction forces (on A-A' way) is:

(A.26)

Giving:

(A.27)

The strain energy:

(A.28)

(A.29)

(A.30)

(A.31)

Finally the work of adhesion forces is |δU|-Φ|δs|. The relative importance of friction

dissipation compared with energy release rate:

(A.32)

The worst case corresponds to the following values: aluminium wedge-aluminium plate

system, μ=1.2, using wedge of thickness, Δ=4 mm, and assuming a=35 mm, the friction

component can be ca. 5.5% of the strain energy.

Michał K. Budzik

173

Appendix 3. List of publications

Table A.1. List of publications

JOURNALS FROM JCR LIST

Journal: Title: Authors: Year

International

Journal of

Adhesion and

Adhesives

Accurate and Continuous

Adhesive Fracture Energy

Determination using an

Instrumented Wedge Test

M. Budzik , J. Jumel , K. Imielińska,

M.E.R.Shanahan

2009

Journal of

Adhesion

Fracture in Composite/

Aluminium Joints of Variable

Adhesive Properties


M.E.R.Shanahan

2009

Journal of

Adhesion Science

and Technology

Effect of Adhesive Compliance

in the Assessment of Soft

Adhesives with the Wedge Test


M.E.R.Shanahan

2010

(accept

ed)

OTHER REVIEWED JOURNALS

Material

Engineering

Properties of Al/CFRP composite

adhesive bonding

M. Budzik , J. Jumel , K. Imielińska

2007 in

Polish

Material

Engineering

Crack propagation in the variable

adhesion properties condition


M.E.R.Shanahan

2009 in

Polish

Advances in

Material Science

Fracture of aluminium joints

bonded with epoxy adhesive

reinforced by MMT nanoparticles

M. Budzik , R.Pilawka,J. Jumel , K.

Imielińska, M.E.R.Shanahan

2009

BOOK CHAPTERS:

Modern

technologies and

energy conversion

ed. W.

Przybylskiego

Defect detection in Al/CFRP

composite bonded joints using

ultrasonic technique

M.Budzik 2008 in

Polish

CONFERENCES, ABSTRACTS, POSTERS:

Mechanics –

Gdańsk 2007 –

Poland

Defect detection in Al/CFRP

composite bonded joints using

ultrasonic technique

M. Budzik , J. Jumel , K. Imielińska 2007

Euradh – Oxford-

Great Britiain

A strain gauge technique to

monitor crack propagation in

wedge test


M.E.R.Shanahan

2008

Colloque national

MECAMAT

Ecole de

mécanique des

matériaux-

Aussois-France

Essais de fissuration sur adhésif

au moyen d'un essai de clivage en

coin instrumente, mise en œuvre

et application.


M.E.R.Shanahan

2009

Swissbonding

2009-Zurich-

Switzerland

A novel technique for precise

crack length measurement in the

DCB or wedge test

M. Budzik ,J. Jumel , K. Imielińska,

M.E.R.Shanahan

2009

Colloque national

MECAMAT

Ecole de

mécanique des

matériaux-

Aussois-France

Adhesive monitoring with

instrumented wedge test

M. Budzik ,J. Jumel , K. Imielińska,

M.E.R.Shanahan

2010


174

Appendix 4. Gantt chart of thesis progress

Michał K. Budzik

175

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[4] Erdogan F., Sih G.C., ASME Journal of Basic Engineering, 1963, 85D, 519–527.

[5] Parmigiani J.P., Thouless M.D., Engineering Fracture Mechanics, 2007, 74, 2675-2699.

[6] Chen B., Dillard D.A., Int. J. Adhes. Adhes., 2001, 21,357- 368.

[7] Shu L., Yuh J. Ch., Xiankui Z., 2004, 41, 6147–6172.

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LIST OF FIGURES

Fig.1.1. Global adhesive industry by region, 2007 share demand[11]. .................................... 12

Fig.1.2. World Adhesive (including sealants) demand in 2007[2]. .......................................... 12

Fig.1.3. Structural adhesive market in 2002[12]. ..................................................................... 13

Fig.1.4. JAS Grippen bonded primary elements[15]. ............................................................... 14

Fig.1.5. Bridge repaired and strengthened with CFRP patch (left). ......................................... 18

Fig.1.6. Zaragoza Bridge Pavilion. Bridge build totally from cement reinforced with GFRP

(right). ....................................................................................................................................... 18

Fig.1.7. One of the examples of structural bonding applications in medicine[25]................... 18

Fig.1.8. Structural adhesive application in dentistry. ............................................................... 19

Fig.1.9. Basic acrylic reaction[36]. .......................................................................................... 20

Fig.1.10. Cyanoacrylate monomers structure, with R is usually alkyl group[35]. ................... 21

Fig.1.11. Ethylene oxide (oxirane). .......................................................................................... 21

Fig.1.12. Bisphenol A-epichlorohydrine reaction[38].............................................................. 22

Fig.1.13. Amine – curing mechanism of epoxies: a) initial step, formation of a secondary

amine and more hydroxyl groups; b) formation of tertiary amine; c) continued crosslinking

through reaction of hydroxyl groups[38]. ................................................................................ 22

Fig.1.14. The chemical structure of BMI and MDA[40]. ........................................................ 23

Fig.1.15. a) Preparation of polyamide precursor, b) curing of polyamides by imidization[43].

.................................................................................................................................................. 24

Fig.1.16. Urethane group. ......................................................................................................... 25

Fig.1.17. Basic polyurethane polymerization reaction[45]. ..................................................... 26

Fig.1.18. Typical mechanism for a urethane adhesive bonding covalently to a polar

surface[45]. ............................................................................................................................... 26

Fig.1.19. Polymerization of phenol with excess of formaldehyde[52]. ................................... 27

Fig.1.20. General structure for a linear silicon polymer[43]. ................................................... 28

Fig.1.21. van der Waals interactions[69]. ................................................................................. 33

Fig.1.23. Schematic presentation of good and bad wetting. ..................................................... 35

Fig.1.24. Adhesive – substrate interdiffusion[75]. ................................................................... 35

Fig.1.25. The adhesive joint model, a) metal – metal joint, b) chain presentation[88]. ........... 39

Fig.1.26. Schematic presentation of metallic surface[89]. ....................................................... 40

Fig.1.27. Presentation of polymer surface[89]. ........................................................................ 40

Fig.1.28. Effect of surface pretreatment on the performance of aluminium joints with a

toughened epoxy adhesive and subjected to ageing in water[90]. ........................................... 45

Fig.1.29. Specimen configuration for adhesive tensile testing. ................................................ 48

Fig.1.30. Napkin ring test. ........................................................................................................ 50

Fig.1.31. Single lap test configuration (ASTM D1002). .......................................................... 50

Fig.1.32. Double-lap shear adhesive specimen configurations (ASTM D3528). .................... 51

Fig.1.33. Graphical presentation of shear lag model. ............................................................... 51

Fig.1.34. Peel stress distribution in shear lap geometry. .......................................................... 52

Fig.1.35. Joint in mode I fracture (F – applied force, Δ – vertical displacement, a – crack

length, δa – crack increment). .................................................................................................. 53

Fig.1.36. ASTM D1062 cleavage test of adhesive joints (left). ............................................... 55


184

Fig.1.37. ASTM D3807 cleavage test specimen (right). .......................................................... 55

Fig.1.38. ASTM D3433 test specimen (left). ........................................................................... 56

Fig.1.39. ASTM D3433 TDCB test specimen (right). ............................................................. 56

Fig.1.40. D3762 wedge test configuration for durability testing.............................................. 57

Fig.2.1. Asymmetric test sample. ............................................................................................. 60

Fig.2.2. Through Transmission Method device. ....................................................................... 65

Fig.2.3. Schematic diagram of the pore formation at the beginning of the anodization. Stage1:

formation of barrier oxide on the entire area, stage 2: local field distributions caused by

surface fluctuations, stage 3: creation of pores by field-enhanced or/and temperature-enhanced

dissolution, stage 4: stable pore growth.................................................................................... 67

Fig.2.4. Topography of AA2024-T3 before (left) and after anodization (right). ..................... 68

Fig.2.5. Alumina layer obtained on Al-Cu alloy. ..................................................................... 68

Fig.2.6. Topography of AA5754-H111, before (left) and after (right) anodization. ................ 68

Fig.2.7. Symmetric and asymmetric adhesive joints. ............................................................... 69

Fig.2.8. Block scheme o sample fabrication. ............................................................................ 69

Fig.2.9. The constancy of the bondline maintained by PTFE spacers...................................... 69

Fig.2.10. Flight-view of the side-camera observations made during the tests. ........................ 70

Fig.3.1. Energy Release Rate principle (Δ-separation distance, F-applied force, a-crack length,

δa-crack length increment, U-stored elastic energy). ............................................................... 71

Fig.3.2. Constant Rate Test sample (a) and principle of the test (b). ....................................... 72

Fig.3.3. CRT test routine. ......................................................................................................... 73

Fig.3.4. Constant Rate Test physical interpretation.................................................................. 73

Fig.3.5. Scheme of the artificial crack tip test. ......................................................................... 76

Fig.3.6. CRT calibration curve. ................................................................................................ 77

Fig.3.7. Specimen deflection vs. time for two adhesive systems and two displacement rates. 78

Fig.3.8. Crack increment vs. time plots. Nonlinear graph profile (in square) followed by quasi-

constant crack growth (vc~const) (left). Nonlinear part of the graph at the onset of crack

growth (t=0-1.5h) (right). ......................................................................................................... 79

Fig.3.9. Macrographic view of fracture surfaces: River patterns regions (inside white boards)

and three distinct crack speed sections indicated with white arrows: I – fast crack speed

(probably during wedge insertion), II – medium – decreasing crack speed (probably nonlinear

part of Fig.3.8), III – stable crack growth (linear part of Fig.3.8). ........................................... 79

Fig.3.10. Average minimum fracture energy for aluminium bonded with reinforced and pure

epoxy adhesive (left). ............................................................................................................... 79

Fig.3.11. Crack growth rate vs. deflection rate for the two systems: with and without

nanoparticles (right). ................................................................................................................. 79

Fig.3.12. Optical micrographs of fracture surface of E6 resin, after lower (left) and higher

crack growth rate (right). .......................................................................................................... 80

Fig.3.13. Optical micrographs of fracture surface of E6 with nanoparticles, after lower (left)

and higher crack growth rate (right). ........................................................................................ 80

Fig.3.14. SEM fractographs of pure DGEBA epoxy for different crack speeds regimes (in

columns) and for different magnifications (in rows: 200-500-1000x). .................................... 81

Michał K. Budzik

185

Fig.3.15. SEM fractographs of epoxy reinforced with 5% of MMT 1-D nanoparticles for

different crack speeds (columns) and magnifications (rows). Arrows indicates nanoparticles.

.................................................................................................................................................. 82

Fig.3.16. SEM fractographs made at the middle of the sample (left) and near the side edge

(right). Arrows indicates features of the river patterns phenomena......................................... 83

Fig.3.17. Side view of Fig.3.16 made using optical microscope. ............................................. 83

Fig.3.18. Schematic representation of the CFT test. ................................................................ 84

Fig.3.19. Block scheme of metrological circuit........................................................................ 84

Fig.3.20. Constant Force Test physical model. ........................................................................ 84

Fig.3.21. Artificial crack test in Constant Force Test configuration. ....................................... 87

Fig.3.22. Linear force – deflection relation (left) and crack length calibration curve (right). . 87

Fig.3.23. Crack increment for cyanoacrylate (Cyanoacrylate), acrylic mastic (Mastic) and

double face scotch (PSA) adhesives (left). ............................................................................... 89

Fig.3.24. Crack speed characteristics. Vertical lines corresponds to the estimated time of

overall failure due to accelerating crack growth (right). .......................................................... 89

Fig.3.25. Fracture energy characteristics for the tested materials. ........................................... 90

Fig.3.26. The example of creep behaviour (or adhesive elastic deformation) at the beginning

of the observed in mastic adhesive. On right, close up of elastic foundation region. .............. 90

Fig.3.27. Schematic representation of the process zone. .......................................................... 91

Fig.3.28. Schematic representation of the CDT test. ................................................................ 92

Fig.3.29. CDT metrological circuit. ......................................................................................... 92

Fig.3.30. Physical model of CDT. ............................................................................................ 92

Fig.3.31. Artificial crack tip test principle................................................................................ 98

Fig.3.32. Verification of eq.3.51 (left). Estimated crack length value, a vs. strain gauge

position, x relation (right). ........................................................................................................ 99

Fig.3.33. Verification of eq.3.52 (left). Crack length calibration curve, a vs. aD (right). ........ 99

Fig.3.34. Schematic representation of tested sample.............................................................. 100

Fig.3.35. Crack length increment, δa with time, t. ................................................................. 100

Fig.3.36. Fracture energy vs. crack speed characteristic of Al/Al bonded plates with pure

DGEBA resin after different surface treatment. ..................................................................... 102

Fig.3.37. Geometry of asymmetric wedge test sample with strain gauges (dimensions in mm).

(a) Side view. (b) Top view showing position of the strain gauges. (c) Top view showing the

relative position of the wedge and one of the zones of sandblasting. .................................... 103

Fig.3.38. Crack length, a, vs. time, t, for the composite/aluminium assembly in the vicinity of

the transition from SB to P surface treatment. The transition is occurring between ca. 20 and

40 hours (left). ........................................................................................................................ 104

Fig.3.39. Results of Figure 3.38 expressed as crack speed, da/dt, vs. time, t (right). ............ 104

Fig.3.40. Model for curvilinear crack front traversing the frontier between SB and P treated

aluminium. .............................................................................................................................. 104

Fig.3.41. Fracture energy, , vs. time, t, in the vicinity of the transition zone. ................... 106

Fig.3.42. Fracture energy, , vs. crack speed, v=da/dt, in the vicinity of the transition zone.

For , f=1 (I) and for, f=0 (II). The intermediate cases (examples)

correspond to f=0.54 and 0.27, as shown schematically below (III). ..................................... 107


186


sandblasted (SB) and polished (P) surfaces. The fracture front comes from the right. .......... 109


polished (SB) and sandblasted (P) surfaces. The fracture front comes from the left. ............ 109

Fig.3.45. SEM micrographs of the side of surfaces near the fracture zone in the SB treated

region. (a) The macroscopically interfacial failure at the adhesive composite interface is in

fact a cohesive failure within the adhesive, but near the interface, whereas (b), the

adhesive/aluminium interface remains intact. ........................................................................ 109

Fig.3.46. Scheme of the experiment principle. ....................................................................... 110

Fig.3.47. Crack propagation in the vicinity of the transition, STRONG/WEAK, zone. Crack is

coming from anodized (PAA) surface to polished (P). Arrows indicates regions of crack front

initiation. ................................................................................................................................. 111

Fig.3.48. Crack propagation in the vicinity of the transition, WEAK/STRONG, zone between

polished (P) and anodized (PAA) surfaces. Arrows indicates regions of crack front initiation.

................................................................................................................................................ 111

Fig.3.49. Stages of crack propagation in the sample with variable adhesion properties. ....... 112

Fig.3.50. Suggested sketch of crack front bubbling as it encounters the sharp transition

between SB and P treated aluminium. .................................................................................... 114

Fig.3.51. Schematic representation of samples tested. ........................................................... 116

Fig.3.52. Schematic presentation of Winkler (aWinkler) and cantilever beam (aSBT) crack

lengths. The difference between these crack lengths gives the transition zone between open

crack and measurable elastic foundation effect. ..................................................................... 116

Fig.3.53. Left: surface strain, |εs(x)| , at various values of x, vs. time, t. Right: |εs(x)| vs. x for a

given time shown by the bold vertical dotted line on the left part of the figure. ................... 122

Fig.3.54. Results of (negative) surface strain, |εs(x)| vs. distance, x, from wedge for the epoxy

adhesive with a 0.2 mm thick bondline (ambient temperature) (right). ................................. 123

Fig.3.55. As for Fig.3.53, but at 50°C (left). .......................................................................... 123

Fig.3.56. Results of (negative) surface strain, -εs(x), vs. distance, x, from wedge for the epoxy

adhesive with a 0.8 mm thick bondline (ambient temperature) (right). ................................. 124

Fig.3.57. As for Fig.3.56, but at 50°C (left). .......................................................................... 124

Fig.3.58. Results of (negative) surface strain,-εs(x), vs. distance, x, from wedge for the acrylic

mastic with a 0.4 mm thick bondline (ambient temperature). ................................................ 124

Fig.3.59. Crack length overestimation due to assumption of SBT ......................................... 125

Fig.3.60. Zone near crack front, on bonded side, in acrylic mastic bond, before (upper) and

after (lower) wedge insertion. Extension of the adhesive layer perpendicular to the interface is

due to imposed displacement and effect of elastic foundation. .............................................. 126


release rate using Winkler values of the crack length, aW. ..................................................... 127


release rate, each using own values of crack length, a. .......................................................... 128

Fig.3.63. Schematic representation of tested samples. Bonded and free zones are separated

with dash line. ......................................................................................................................... 129

Michał K. Budzik

187

Fig.3.64. Instrumented wedge test results for the adhesive subjected to slow crosslinking.

Vertical line indicates position of the crack front. Note evolution of the strain with time

(arrows indicating the direction of change) in both zones. .................................................... 130

Fig.3.65. Interpretation of experimental data (points) with Winkler based model at the

beginning (solid line) and end of the test (dashed line). Vertical line represents crack position.

................................................................................................................................................ 130

Fig.3.66. Comparison between Winkler and SBT model. Vertical lines represent: real or

Winkler crack length (solid), crack length obtained with SBT estimation after 15 days of

curing (dashed), and SBT after 2 days of curing (dotted). ..................................................... 131

Fig.3.67. Change in the adhesive parameter, λ, during crosslinking. Three stages of

crosslinking can be found (left). ............................................................................................. 131

Fig.3.68. Apparent change of the crack length estimated using simple beam theory, aSBT, as a

function of time (right). .......................................................................................................... 131

Fig.3.69. Variation of Energy Release Rate, G, with curing time. Vertical line represents the

end of the crosslinking period. ............................................................................................... 132

Fig.3.70. Schematic presentation of change of crack length during crosslinking. Not that the

real crack length remains constant, whereas estimated crack length changes due to neglect of

adhesive properties in SBT. .................................................................................................... 132

Fig.3.71. Schematic representation of tested sample.............................................................. 134

Fig.3.72. Crack propagation sequences recorded in room temperature condition, T=24oC (left)

and at the elevated temperature T=40oC (right). .................................................................... 135

Fig.3.73. Feature of fracture in elevated temperature – the adhesive crazes in the bonded zone

(indicated with arrows). .......................................................................................................... 135

Fig.3.74. Sample cooled down with wedge between separated plates. Wedge was removed

after cooling down. ................................................................................................................. 135

Fig.3.75. Strain profiles of the sample tested in ambient temperature at the beginning and end

of the test. The crack propagation from solid to dotted line (left). ......................................... 136

Fig.3.76. Strain profiles of the sample tested in elevated temperature at three stages:

beginning, middle and at the end of the test. Solid. dashed and dotted line corresponds to the

crack position at the given stage respectively (right). ............................................................ 136

Fig.3.77. Strain profiles of the samples tested in ambient temperature at the beginning and end

of the test for the 6.8 mm wedge. The crack propagation from solid to dotted line (left). .... 136

Fig.3.78. Strain profile of the sample tested in elevated temperature at three stages: beginning,

middle and at the end of the test. Solid, dashed and dotted line corresponds to the crack

position at the given stage respectively (right). ...................................................................... 136

Fig.3.79. a) Strain evolution with progressing crack. Signals from three strain gauges located

at: x1=23 mm and x6=64 mm (already passed by the crack) and x10=95 mm (passed during the

test). Last gauge signal presents evolution of signal in neighbourhood of the gauge. Estimated

process zone, or elastic foundation zone of ca. 14 mm. b) Fracture surface after the test with

visible process zone (left), close-up of the process zone (right). ........................................... 137

Fig.3.80. Crack length evolution during the test (note the joint behaviour in Fig.3.74). ....... 138

Fig.3.81. Crack propagation in time for different test conditions (left). ................................ 138

Fig.3.82. Crack propagation kinetic in ambient test condition (right). .................................. 138


188

Fig.3.83. Crack propagation kinetics in elevated temperature. Five specific regions were

noted: I. Linear speed decrease, normal for propagation at constant temperature, II. Increase

of the crack speed, possibly due to the adhesive stress relief, III. Normal, stable crack

propagation. IV. Transition, stick-slip like zone, V. Acceleration of the crack close to the

sample extremity. ................................................................................................................... 139

Fig.3.84. Energy Release Rate change with time (left). ......................................................... 140

Fig.3.85. Change of the energy release rate with the crack speed. Stages I-V like in Fig.3.83

(right). ..................................................................................................................................... 140

Fig.3.86. Energy- Crack- Speed curve for elevated temperature propagation. Zone IV of ca.

12.5 mm length. ...................................................................................................................... 140

Fig.3.87. Interpretation of temperature effect with highlighted region used for elevated

temperature interpretation....................................................................................................... 141

Fig.4.1. Details of designed mesh........................................................................................... 145

Fig.4.2. Stress state within the adhesive and at the straight crack front for three common

loading modes (input data like in Table 4.3). ......................................................................... 147

Fig.4.3. Slight increase of the shearing component with crack length. .................................. 149

Fig.4.4. Plate width effect on I/II mode mixity (left). Plate width effect n I/II mode mixity

(right). ..................................................................................................................................... 149

Fig.4.5. Plate Young modulus effect (left). Adhesive Young modulus effect (right). ........... 149

Fig.4.6. Plate thickness effect (left). Adhesive thickness effect (right).................................. 150

Fig.4.7. Poisson ratio effect of the plate (left) and the adhesive (right). ................................ 150

Fig.4.8. Increase of the tearing component with the crack length. ......................................... 150

Fig.4.9. Tearing stress factor distribution along the normalized sample width (left) and

variation of the mode mixity with the sample width (right). .................................................. 151

Fig.4.10. Plate Young modulus effect (left). Adhesive Young modulus effect (right). ......... 151

Fig.4.11. Plate thickness effect (left). Adhesive thickness effect (right). .............................. 151

Fig.4.12. Poisson ratio effect of the plate (left) and the adhesive (right). .............................. 152

Fig.4.13. Tearing component at different stages of crack propagation (FEM analysis). ....... 153

Fig.4.14. Optical micrographs of river patterns observed during the test on macro a) and

microscale b). Graphical interpretation of the surface features. ............................................. 154

Fig.4.15. Curved crack front for two bonded with epoxy adhesive aluminium plates. Picture

made with micro camera system (Dino-Lite). ........................................................................ 155

Fig.4.16. Finite Element Analysis result. Stress state in the adhesive layer. In columns:

cleavage, in- and anti-plane shearing stress respectively. In rows arising crack depth, from 0-

1.5 mm. Arrows indicate change of stress level. .................................................................... 156

Fig.4.17. Cleavage stress distribution. Opening stress, ζzz vs. crack depth, δa (left) curves

showing linear relation on sample board and in the middle (right). Solid line indicate crack

depth for which stress at the width centre and side are of the same value, dashed line for

experimental value. ................................................................................................................. 157

Fig.4.18. In-plane shearing stress distribution along the crack length (left).Shearing stress at

the crack front vs. crack depth indicating linear relations on side and in the middle of the

sample (right). Solid line indicate crack depth for which shearing stress at the sample centre

and side are of the same value. ............................................................................................... 157

Michał K. Budzik

189

Fig.4.19. Anti-plane shearing stress along sample width (left). Tearing stress at the crack front

vs. crack depth indicating linear relations on side and in the middle of the sample (right). Bold

lines indicate crack depth for the situation described previously. .......................................... 157

Fig.4.20. Effect of the crack depth on stress mixity factors distribution. Shearing stress

component (left). Tearing mode component (right). .............................................................. 158

Fig.4.21. Slight, linear increase of the shearing component with the crack depth increase in

the middle of the tested sample (left). Decrease of the tearing stress component with the crack

depth at the side of the sample (right). ................................................................................... 158

Fig.C.1. Crack length calibration curve of the tests. .............................................................. 160

Fig.C.2. Crack increment behaviour of the new developed tests. .......................................... 161

Fig.C.3. Schematic representation of situation from CFT test when damage time, ΔtCD is

shorter than interval time, ΔtIT. ............................................................................................... 162

Fig.A.1.1. Close-up of the beam/wedge contact zone. ........................................................... 167

Fig.A.1.2. Model for mode II fracture .................................................................................... 168

Fig.A.2.1. CDT test and the close-up of the wedge/beam friction region. ............................. 170


190

LIST OF TABLES

Table 1.1. General comparison of joining methods[13]. .......................................................... 13

Table 1.2. Values of measured Critical Fracture Energies[39]. ............................................... 23

Table 1.3. Common properties of structural adhesives. ........................................................... 29

Table 1.4. Surface topography influence on peel energy[64]. .................................................. 30

Table 1.5. Wetting conditions................................................................................................... 35

Table 1.6. Bond energy of some of the common interactions. ................................................. 37

Table 1.7. Commercial silane coupling agents[13]. ................................................................. 46

Table 2.1. AA5754 chemical composition. .............................................................................. 61

Table 2.2. Physical and mechanical properties of AA5754-H111 alloy. ................................. 61

Table 2.3. AA2024 chemical composition (supplier data). ...................................................... 61

Table 2.4. Properties of AA2024-T3 (supplier data). ............................................................... 62

Table 2.5. Properties of the CFRP composites. ........................................................................ 62

Table 2.6. Used polycarbonate properties (supplier data). ....................................................... 63

Table 2.7. Bending test results. ................................................................................................ 64

Table 2.8. Materials properties from TTM measurement. ....................................................... 64

Table 2.9. Aluminium surface treatment procedures. .............................................................. 66

Table 3.1. Results of artificial crack tip test. ............................................................................ 77

Table 3.2. Results of artificial crack tip test for CFT configuration. ....................................... 88

Table 3.3. Results of the crack length estimation with artificial crack tip test. ........................ 99

Table 3.4. The crack propagation stages in the vicinity of transition zones........................... 112

Table 4.1. Details of finite elements used in the studies. ....................................................... 143

Table 4.2. Parameters tested during studies. .......................................................................... 146

Table 4.3. Mode mixity test panel. ......................................................................................... 148

Table 4.4. Features of the sample used within the thesis. ...................................................... 152

Table 4.5. Features of chosen geometry. ................................................................................ 152

Table 4.6. Crack depth test panel. .......................................................................................... 155

Table C.1. Possible parameters error. ..................................................................................... 159

Table C.2. Special equipment required to run a single test. ................................................... 162

Table A.1. List of publications ............................................................................................... 173

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