INFORMATION TO - University of Toronto T-Space Response of Sic@) ReinfOrced Al Based Foam Material...

INFORMATION TO USERS

This manuscript has been reproduœd from the microfilm master. UMI films the

text directly from the original or copy submitted. Thus, some thesis and

dissertation copies are in typewriter face, while others may be from any type of

cornputer printer.

The quality of this reproduction is dependent upon the quality of the copy

submitted. Broken or indistinct print, colored or poor quality illustrations and

photographs, pnnt bleedthrough, substandard margins, and improper alignment

can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete manuscript and

there are missing pages, these will be noted. A b , if unauthonzed copyright

material had to be removed, a note will indicate the deletion.

Oversize materials (e-g., maps, drawings, charts) are reproduced by sedioning

the original, beginning at the upper lefi-hand corner and continuing from left to

right in equal sections with small overlaps. Each original is also photographed in

one exposure and is included in reduced fom at the back of the book.

Photographs included in the original manuscript have been reproduced

xerographically in this copy. Higher quality 6" x 9" black and white photographic

prints are available for any photographs or illustrations appearing in this copy for

an additional charge. Contact UMI directly to order.

Bell & Howell Information and Leaming 300 North Zeeb Road, Ann Amr, MI 48106-1346 USA

800-52 1-0600

Tende Response of

SiC(p) Reinforced Al Based

Foam Material

BY

Devin, Hon Wah Siu

A thesis submitted in conformity with the requirements

for the Degree of Master of Applied Science

Department of Metallurgy and Matzials Science

University of Toronto

@Copyright by Devin, Hon Wah Siu (1998)

National Library 1+1 ,,na, Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibliographic Services services bibliographiques

395 Wellington Street 395. nie Wellington Ottawa ON K l A O N 4 Ottawa ON K I A ON4 Canada Canada

Your tüe Votm r e t ë r m

Our Notre f8f&e17C8

The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in microfonn, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de

reproduction sur papier ou sur format électronique.

The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or othenvise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.

Tensile Response of Sic@) ReinfOrced Al Based Foam Material

Devin, Hon Wah Siu

Master of Applied Science, January 1999

Department of Metailurgy and Materials Science, University of Toronto

Tensile properties of aluminum foam material reinforced by Sic particles were studied fkom both

experimental and compter simulation aspects. A unique methodology was developed to carry

out the uniaxial tensile tests and analyze the foam ce11 image during the failure process. The

experimental work dernonstrated that this materiai possesses normal characteristics of a stress-

strain curve of conventionai metallic materials but the failure occurred in a stepwise manner.

Resdts fiom the finite element simulation show that large Sic particles and high SIC particle

volume fiaction increase tensile stifhess and decrease Von Mises stress which decreases the

liability to plastic deformation. Sirnilarly, smaller foam ce11 and thicker ce11 wall lead to a higher

tensile stiffness and lower Von Mises stress distribution. Therefore, it is recommended to

produce Al foam with larger Sic particle ( 2 0 p ) and higher particle volume fiaction (15%) in

order to manufacture products with the best tensile response.

O

Acknowledgements

This author wouId like to sincerely thank his supe~sors, Professor Zhinll Wang and Professor

J.M. T o m for their advice and encouragement throughout the course of this thesis. Special

thanks are due to Mr. L. D. Kenny for the supply of his research paper and materiais for the

experimental work. Thauks are also due to author's research group members, Dr. T. Yip, Dr. S.

Ip, Mr. Y. Fu, Mr. J. Yan, Mr. N. Hai and Dr. 2. Yang for al1 the valuable discussion and

collaborations.

Finally, the author is indebted to Alcan International Ltd. and the Ontario Govenunent for the

financial support through the award of research scholarship.

Table of

List of Figures

1. Introduction

Content

Overview

Alirmuiurn Foam Production

Mechanical Behaviour of Aiurninurn Foam

Deformation Behaviour and Strengthening Mechanisrn of PMMC

Factors Mecting the Mechanicd Properties of A1Uminu.m Foam

Consideration of Present Research

Objectives

2. Experimental

Overview

Materials

Specimen Design and Preparation

Design of Griping System

Image Capturing and Digitizing System

Mechanical Testing

Finite Element Modeling

Page #

v

3. Results and Discussion

3.1 Mechanical Testing

3.1.1. S t f i e s s

3.1.2. Stress strain Curve

3.1 -3. Ce11 Shape Stress Strain Curve

3.1.4. Observations during foam failure

3.2.1. Effect of addition of S ic particles

3.2.2. Effect of Sic particle size on tensile properties

3 -2.3. Influence of particle area fiaction on tensile properties

3.2.4. Effect of foam ce11 size on tensile properties

3.2.5. Effect of foam ce11 wall thickness on tensile properties

3.2.6. Verification of modeling results

4. Conclusion

Reference

LIST OF FIGURES

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure l.6a

Figure 1.6b

Figure 1.7

Figure 1.8

Figure 1.9

Figure 1.10

Figure 1.1 1

Figure 1.12

Figure 1.12

Figure 1.13

Structure of open ceU foam

Structure of close ce1 foam

General methods of metallic foam production

Schematic diagram for Ai /Sic foam production

Graph showing the operating window for Al foam production

Flexure compressive / tensile stress-straïn c w e

Typical compression curve for metal foam

Typical tensile curve for metal foam

A schematic of compression test

Typical Compression C u v e fiom Alcan

Compression Curve fkom Gibson

Mechanism of foam deformation

2-D Hexagonal Honeycomb foam configuration

(a) Setup for t$ calculation

(b) Plateau Border Area

Micrograph show slip bands formation on the ceIl wall

Photo shows foam sam~les with different density

Figure 2.2a

Figure 2.2b

Figure 2 . 2 ~

Figure 2.3

Figure 2.4

Figure 2.5a

Figure 2.5b

Figure 2.6a

Figure 2.6b

Figure 2.7

Figure 2.8

Figure 2.9a

Figure 2.9b

Figure 2.10

Figure 2.1 1

Figure 2-12

Figure 2.13

Figure 2.14

Figure 2.15

Schematic of the tension sample

Front view of the foam materiais

Side view of the foam materials showing samples with different thichess.

Schematic shows the holes distribution on the grip area of the specimen

Procedures of specimen preparation

Side view of Upper Gnp

Front view of Upper Gnp

Side view of the plate

Front view of the plate

Schematic of a wood alloy grip

Experimental setup for uniaxial test

Mesh setup with particles

Mesh setup without particles

Comparison between FEM rnodel and actuai foam sample

Comparison of particles distribution in modeling setup and actual foam

sarnple.

FEM mesh setup of a 12 particle model with particle radius = 0.5 mm

FEM mesh setup of a 20 particle model with particle radius = 0.387 mm

FEM mesh setup of a 36 particle mode1 with particle radius = 0.289 mm

FEM mesh setup of a 64 particle model with particle radius = 0.2 17 mm

Figure 2.16 FEM mesh setup of a 36 particle mode1 with foam ce11 radius = 4.5 mm

Figure 2.17 FEM mesh setup of a 36 particle model with foam cell radius = 5.0 mm



Figure 3.1.1.1 StZhess of foam specimens with density 0.19gkc

Figure 3.1.1.2 Stifiess of foam specimens with density 0.32gkc

Figure 3.1 .S. 1 Load deflection curve from MTS chart recorder

Figure 3.1.2.2 Stress-Strain C w e of Specirnen S2

Figure 3.1.2.3 A load-deflection curve of specimen s3 showing the stepwise failure after UTS.

Figure 3.1.3.1 Image captured frorn video showing instant tirne during the tensile test

Figure 3.1.3.2 Stress-Strain Curve for specimen el0 1.

Figure 3.1.3.3 Images of foam cell taken from different regions.

Figure 3.1.3.4 A typical Image Stress-Strain Curve of specimen EL0 1 .

Figure 3.1.4.1 Comparison of ce11 before and after transcellular fracture of specimen ELOI.

Figure 3.1.4.2 Comparison of ce11 before and after intercellular fracture of specimen EL07.

Figure 3.2.1.1 The Von Mises Stress distributions of single-phase foam composite

Figure 3 -2.12 The Von Mises Stress distributions of particle-reinforced

Figure 3.2.1.3 Full view of figure 3.2.1.1

Figure 3.2.1.4 Full view of figure 3.2.1.2

Figure 3.2.1.4 Ce11 wall of single-phased foam.

vii

Figure 3 2 1 . 5 CelI wall of particle enforced foam

Figure 3.2.2.1 The Von Mises stress distribution a 12 particles model with particle radius =

0.500 mm

Figure 3.2.2.2 The Von Mses stress dishibution a 20 particles model with particle radius =

0.387 mm


0.289 mm


0.21 7 mm

Figure 3.2.2.5 Stress distribution axes for FEM model.

Figure 3.2.2.6 Comparison of relative Von Mises Stress dong L-L direction

Figure 3.2.2.7 Cornparison of relative Von Mises Stress dong T-T direction

Figure 3.2.2.8 Comparison O f Von Mises Stress statistics of models with different particle size

of S i c

Figure 3.2.2.9 shows a graphical cornparison of the stiffiess for the four models against r/R ratio.

Figure 3.2.3.1 The Von Mises stress distribution a 36 particles model with area &action = 3.0%

Figure 3.2.3.2 The Von Mises stress distribution a 36 particles model with area fiaction = 6.3%

Figure 3.2.3.3 The Von Mises stress distribution a 36 particles mode1 with area fraction = 6.8%

Figure 3.2.3.4 The Von Mises stress distribution a 36 particles model with area hction = 8.0%

Figure 3.2.3 -4 The Von Mises stress distribution a 36 particles model with area fraction = 9.3%

Figure 3.2.3.6 Comparison of Von Mises Stress distribution of FEM models under different area

fiaction in L-L direction

viii

Figure 3.2.3 -7 Comparison of Von Mises Stress distribution of FEM models under different area

fiaction in T-T direction

Figure 3.2.3 -8 Comparison of statistics of Von Mises Stress of FEM models under different area

fiaction in L-L direction.

Figure 3.2.3.9 A plot of stiffhess against particle area fiaction.

Figure 3.2.4.1 The Von Mises stress distribution a 36 particles model with foam ce11 radius = 4.5

mm


mm


LIlLn

Figure 3.2.4.4 The Von Mises stress distribution a 36 particles model with foam cell radius = 5.8

mm

Figure 3.2.4.5 Comparison of Von Mises Stress distribution of FEM models with different ce11

size in L-L direction.


size in T-T direction.

Figure 3.2.4.7 A plot of tensile stiRhess against relative foam density.

Figure 3.2.4.8 A plot of stiffness-to-weight ratio against Rp/Rc ratio.

Figure 3.2.5.1 The Von Mises stress distribution a 36 particles model with foam ce11 wall

thickness = 4.0 mm

Figure 3.2.5.2 The Von Mises stress distribution a 36 particles model with foam ce11 wail

thickness = 3.4 mm


thickness = 2.8 mm

Figure 3.2.5.4 The Von Mises stress distribution a 36 particles model with foam ceIl wall

thickness = 2.2 mm


thickness = 2 -8 mm


thickness = 1.4 mm


size in L-L direction-

Figure 3.2.5.8 Comparison of Von Mises Stress distribution of FEM models with different cell

wall thickness in T-T direction.

Figure 3.2.6.1 Experimentai result fi0111 Alcan

Figure 3.2.6.2 Determination of best fit of figure 3.2.6.1

Figure 3.2.6.3 Verification of modeling and experimental data with available data fiom Alcan.

Foarn, in general, is defined as a three-dimensional interconnected network of solid struts

or plates that form the edges and faces of cells. [1.1] StructuraUy, foam can be classifïed into

open ceIl foam and close cell foam. In open cell foam, the cells are comected by open face ce11

edges only (Figure 1.1) whereas cells in the close ce11 foam are packed closely together such that

each ce11 is seaied off from its neighbours. (Figure 1.2)

Figure 1.1 Example of open ce11 foam [l .1] Figure 1.2 Example of close ce11 foarn [l .l]

Materiais such as polymers, glasses and metak have been used to produce solid foams.

Production of solid metallic foam was first patented by Sosnik [1.2] in 1948 by using the idea of

vaporizing rnercury from a mercury aluminum alloy to produce a foarned aluminum. Since

then, many other methods have been proposed which involves casting, metallic deposition,

powder metallurgy and sputter deposition [1.3]. In the past fifty years, metallic foarns have been

developed and becoming a group of new engineering materiais.

1. introduction 1

Although many techniques for foam production were proposed, they have certain

limitations in regard to processing parameters such as foaming temperature range, production of

composite foam and cost. However, most of the techniques are concentrated on the production

of Al foam due to its structural efficiency and other exceptional properties. In 1992, ALCAN

developed a unique patent on manufachiring aluminum foam by introducing air and silicon

carbide particles into the molten aliiminum [ 1.41. The Al foam produced is particularly stable and

easy to manipulate. Moreover, the properties of foam such as the ceiI size, composition of the

composite, volume hc t ion of Sic particles as well as the size of particles can be easily

controlled during the production process.

The advantages of aluminum foam are mainly its structural efficiency and production

cost (Table 1.1). However, this ultralight metallic foam also possesses unique combinations of

properties such as high impact energy absorption capacity, hi& acoustic insulation properties,

low thermal cunductivity and f~e-resistant ability.

Table 1.1 Cost and Process cornparison for al1 available process. [1.5]

Manufacturer Alcan Shinko Wire Fraunhofer ERG (Aploras) Mepura

Process Liquid Al + gas Liquid Ai + TiH2 Solid Al + TiH2

P* Wcc) 0.08 - 0.38 0.2 1 0.35 - 0.7 0.16 - 0.32

P*/PS (-1 0.03 - 0.14 0.08 O. 13 - 0.26 0.06 - 0.12

Faces Closed Closed Closed Open

Celt Size 4-18 6 3 2-5

COS^ ($/Kg) 5-10 300 10,000

1. Introduction 2

With al1 these unique properties, there has been an interest on applying Al foam as shock

and impact absorber for packaging purposes, light weight cores for panels for structural

applications, sound insulators, thermal insulators and flame arresters.

1.2 Aluminum Foam Production

In general, al1 the foam production techniques c m be classified into four categories,

namely casting, metailic deposition, powder metdurgy, and sputter deposition (Figure 1.3).

Figure 1.3 General methods of metallic foarn production [1.3]

Foaming by casting c m be divided into four categories, namely foaming in metal, casting

around granules, investment casting and incorporating hollow sphere in melts. Foaming in metals

involves decomposing a blowing agent (e.g. TiH or Zr&) into metal rnelts to evolve gas, which

eventually expands to form molten foam. Molten foam is then cooled and cast to form solid

foam[l.8]. The disadvantages of this process include non-uniforrnity of ce11 distribution,

undesirable large size cell, short tirne interval between adding a foaming agent to the molten

rnetal and foam formation, and the process rnust be done in the temperature range of 450 to

480°C. Foarning by casting rnetal around granules involves introducing molten metals into a

casting mould with granules such as sodium chloride [1.9]. After the metal is cast around the

granules, the granules are then leached out to form a porous metal. Granules can also be

1. Introduction z

incorporated into metal melts directly. After thorough &g, it is then cast into a suitable

mould [l . IO]. Metallic foam can also be produced by investment casting that involves making a

refiactory spongy lattice mould fiom a spongy plastic component. Molten metals are then cast in

this rehctory modd to form a structure having the same structure as the original spongy plastic

[l.ll].

Foaming by metallic deposition is simply by coating a metallic cover to a polyurethane

strand by electrodeposition [1.12]. This technique consists of îhree stages, ngidization,

electroless preplating, and electroplating. Rigidization involves coating a ngid layer of epoxy to

provide support for metallic deposition. A thin layer of rnetal is then coated on the foam surface

in an electroless plating solution to enhance the conductivity and provide surface roughness for

subsequent metd deposition. Metals such as copper, nickel, silver and gold can then be

electrodeposited onto the substrate up to the desirable thickness. Although, the final product

from this process is exceptionally uniform and has a hi& degree of porosity, the cost is

extremely expensive compared to other processes.

Metallic foam can also be manufactured by powder metallurgy techniques such as Slurry

Foaming, Sintering Slurry Saturated Sponge, Loose powder sintering and Fibre Metallurgy.

Sluny Foaming and Sintering Slurry Sahirated Sponge both involve using slurry consisting of

the fme metal powder as starting matenal. Metallic foam is obtained by firing of Iiquid foam that

is formed by whipping the slurry with foaming agent dispersed in an organic vehicle [1.13].

While metallic foarn by Sintering Slurry Saturated Sponge technique is made by sintering of

metallic slurry with sponge-like materials such as plastic sponge which acts as a temporary

support structure for metallic foams. The metallic foam is obtained by decornposing and

removing the organic sponge-like material during sintering. The resulting metallic foam has an

1. Introduction 4

uniform high porosity metallic structure. Metallic foam can be manufactured by using metallic

powder [1.14] and fibres [l. 151 instead of using slurry as a starting material. Spacing agent,

which is decomposed and evaporated d u ~ g sintering, is normally added to achieve hi&

porosity. Due to the formation of aluminum oxide at the sintering temperature, sintering is not

used for aluminum powder. Therefore, aluminum foarn is normally made fiom a slurry technique

but the strength of the £inal product is much lower which limits its application.

Production of metallic foam by Sputter deposition [1.16] is comparatively a newer

process that involves depositing a metai body containhg atoms of entrapped inert gas onto a

substrate. When the metal body is heated above the metal melting point for a penod, the

entrapped gas expands and forms individual celis. A closed cellular structure is formed d e r

cooling the foam body. The porosity is controlled by the amount of entrapped gas in the metal

body that can be m e r controlled by the pressure of the inert gas, temperature of the substrate

and the negative bias voltage placed on the substrate. This method is feasible for preparing foam

fiom al1 materials not just limited to metallic foam. However, the production cost is also

expensive.

Among al1 the foaming techniques mentioned above, production cost, foaming

temperature range, stability of foam for manipulation, ability to scale up for large scale

production and the production costs have lirnited the M e r development into a massive

production process. In 1992, Jin, Kenny and Sang proposed a patent for manufacturing particle

stabilized aluminurn foam. This process involves introducing gas and finely divided silicon

carbide particles into an aiuminurn melt at above the liqcidus temperature. After proper rnixing,

a stable foam foms on the swface of the rnelt which c m be drawn off on a conveyïng belt and

cast into a solid foam slab as shown in Figure 1.4.

I . Introduction 5

Figure 1.4 Schematic diagram for Al /Sic foam production

In term of process control and product quality control, parameters such as the gas flow

rate, diameter of gas orifice of the rotating shaft, nature of particle, size of particle, volume and

volume fiaction of particle. Particle size and volume fraction of particle affect foaming ability

d u d g Al foarn production in tems of mixing of Al melt, viscosity of melt, foam stability and

particle setting. Based on these considerations, an operating production window was defined

with respect to the particle size and volume fkaction(Figure 1.5).

1. introduction 6

Figure 1.5 Graph showing the operating window for Al foam production

The volume fiaction of particles is typicaily below 25% and the optimal range is Eom 5%

to 15%. This is because the low particle volume &action contributes to low foam stability while

high particle volume fraction results in a hi& melt viscosity. In both cases, foam formation is

not difficult. In ternis of particle size, smail particles create mixing problem while large particles

cause settling problems. Therefore, although, foaming occurs over a particle size range fiom 1 to

1 OOprn, it is preferably in the range of about 1 to 20 ~.LXX.

The addition of Sic particdate not only can stabilize the foam during production, but

also affect the mechanical properties of the solid foarn. The strengthening effects should be

similar to the situation of Sic particles in Aluminum Metal Mattiv Composite or simply PMMC.

Therefore, the particle shape, the aspect ratio, volume fiaction and size of the particles should be

related to the strength of this foam composite.

1. Introduction 7

As described in the patent, the closed-ce11 foam from this process has a high strength-to-

weight ratio, Low thermal conductivity, hi& impact energy absorption capacity, good electrical

conductivity and high absorptive acoustic properties. Hence, the potential applications include

structural panels, thermal insulator, packaging material for high temperature application, and

sound insulator.

1.3 Mechanical Behaviour of Aluminum Foam

Two foreseeable applications for alurninum foam composite are rnainly as core materiais

of sandwich panels for structural purposes and as packaging materials for energy absorption.

Therefore, most of the recent researches are focus on the study of mechanical properties such as

energy absorption capacity, compressive strength and flexure properties L1.6, 1.71. The studies

f?om Grenestedt [1.7] dso take a fuaher step on investigating fracture mechanism of this foam

material.

The flexure, i.e. a three point bending, results fiom Grenestedt 11.71 are based on the

theory that the compressive and tensile stresses are a function of the strains measured on the

compressive and tensile surfaces, plus the imposed moment. By assumùig that the normal strain

varying linearly dong y-axis, Grenestedt proposed the following equation to determine the

compressive/tensile stress on the surface of the foam:

Where o(et) is the tensile stress, ct is the tensile strain, q, is the compressive strain and M is the

moment of inertia.

1. Introduction 8

By measuring the maximum compressive strain and moment appiied experimentally,

&(cb) and M(sb) respectively, a flexure compressive / tensile stress-strain curve is detennined

(Figure 1.6). It clearly shows that the tensile stress is higher than the compressive stress in both

elastic and plastic regions. Although, this is the oniy study on the tensile propeaies of this foam

composite, it is resiricted to the surface and does not consider the mechanical properties in the

b u k One of the reasons is that this foam composite is not a conventional continuous materiai.

The foam density varies between the bulk and the surface. Therefore, it is inappropriate both

experimentally and theoretically to assume that the normal strain varies linearly across the

sample. In other words, the surface properties may not tnily represent the properties of the bulk.

Hence, the r e d t s obtained fiom this experimental setup do not measure the true tensile strength

and thus cannot define the behaviour of this foam composite.

Strain, e

Figure 1.6 FIexure compressive / tensile stress-strain curve

1. Introduction 9

Mechanical properties of the foam composite in compression have been studied based on

block samples with the skin lefi intact during the compression testing. It is believed that the foam

would be used comrnerciaiiy in this manner. Figure 1.7 depicts a typical setup for compression

test.

I I I 1 -r

Figure 1.7 A schematic of compression test

Although this test configuration is considered f?om a practical point of view, it does not

tndy reflect the compression properties of this material. The reason is that the properties of the

skin deviate from the bulk in terms of foam size and density. Therefore, the compressive

responses obtained would include both the skin and buik properties. This results in over-

estimating the properties such as compressive modulus, compressive yield stress and strength.

Moreover, the sample design is not according to the ASTM standard for testing foam material

and hence the results fiom different sources are not comparable.

Figure 1.8 and Figure 1.9 show the compressive curve of Al foam material fiom Aican

fiom two different sources of studies. The shape of the cuves are comparable to a certain extent.

In general, a stress-strain cuve for compression can be roughly divided into four different

regions :

1. Introduction

Linear elistic region

PIastic region with characteristic upper and lower yield points

Plateau region

Final region

Figure 1.8 Compression Curve tiom Alcan Figure 1.9 Compression Curve fiom Gibson

The deformation mechanisms for single-phase foam composite (effect of particles are not

taken into account) were proposed by Gibson and Ashby [1.1] for each region. Ln the linear

elastic region, linear elasticity is controlled by ce11 wall bending and ce11 face stretching. As the

stress is Uicreaçed up to certain critical value, cells start to coliapse and ceIl wall fracture occurs.

This is known as the plateau region. Yielding o c c h g in this region is caused by the formation

of plastic hinges. After most of the cells have collapsed, the matenal reaches its final region. Ce11

walls touch each other and further loading leads to compression of the solid duminum. This

results in a rapid increase in stress in this region.

Gibson and Ashby [l. 11 developed a mode1 to simulate the stifhess of foam matenal in

both tensile and compression aspects within the linear elastic region by assuming the foam as

1. Introduction I I

honeycomb structure. In this model, the mechanism of deformation is proposed to be attnbuted

by ce11 wal1 bending, edge contraction and membrane stretching, and enclosed gas pressure

(Figure 1.10). In the case of the aluminum foam, the pressure difference between the enclosed

ceIl and the ambient pressure is negligible, thus the gas pressure effect can be neglected.

Therefore, the stifXhess of the foam is mainly dependent on the material properties on the edge

and the ce11 wall.

Cell Wall Bending Edge contraction and membrane stretching Enclosed gas pressure

Figure 1.10 Mechanism of foam deformation (ref. 1.1 )

By considering the energy balance on the workdone on deforming the foam by a smail

incrernent of 6, the relative stiffness of the foam is found to be related to the relative density of

the foam which is expressed in the following equation:

Where E' is the stifiess of the foam, Es is the stiffriess of the solid matenal, 4 is the volume

fiaction of solid contained in the ce11 edge, P' is the foam density and p is the density of solid.

The first term of this equation represents the contribution of ce11 edge while the second term

1. Introduction 12

represents the contribution of the ce11 wall to the stiffhess. Therefore, for open cells, where el,

the equation is expressed as a more general form of:

where ai is a constant related to the geometrical shape of the foam cel1. al approaches to unity if

the foam structure is a honeycomb type.

Similarly, if the foam is closed to a tetrakaidecahedra structure, equation (1.2) become as

follows:

Where a2 is a structural dependant constant. For an isotropie cell, and a2 is found to be 0.35 for

fcc structure, 0.19 [ 1.191 for cubic structure and 0.3 5 [1.20] for tetrakaidecahedra.

The volume fraction of solid in the ce11 edge is directly related to the geometrical

configuration. Moreover, the solid fraction in the cell edge and solid fiaction in the ce11 wall have

the following equation:

Solid fiaction in the ce11 edge + solid hc t ion in the ce11 wall= 1

Figure 1.1 1 depicts the relationship between the solid fiaction in the ce11 wail with the

geometrical configuration. By knowing the actual shape o f the foam cell, the stiffhess of the

foam can be roughiy estimated.

1. Introduction 13

2-D Hexagonal Honeycomb - lncreasing Solid Fraction in CeIl Wa1fs.f

Figure 1.1 1 2-D Hexagonal Honeycomb foam configuration.[ 1 -201

Based on a hexagonal honeycomb consideration, Simone and Gibson[l.ZO], also derived

an equation for predicting 4 on a 2D model (figurel. 12) The equation is as followed:

Figure 1.12 (a) Setup for 4 calculation, @) Plateau Border Area.[1.20]

Equation 1.2 and 1.4 provide an ideal 2D model for estimating the stiffhess of regular

isotropie hexagonal honeycomb foam without considering the effect of the SiC particles.

However, this mode1 is used as a frame of reference for v e m g the result of the fhite element

analysis in this report.

Compared to stiffhess, the available literatures on the inelastic properfies are not as

extensive. In general, most researches are carried out based on the compression instead of tensile

properties. The plastic defonnation properties of Ai foam under compression Vary between the

Alporas foam and Alcan foam C1.211. Figure 1.13 depicts a cornparison of the stress-strain

cunies by these two foams. Both foams show a sudden decrease in stress after the small elastic

region. Slips bands are formed in the plastic deformation region. The Alporas foam has a flatter

plastic region, which indicates the systematic formation of deformation bands [1.2 1, 1-22]. On

the other hand, Alcan foam has a progressively increasing plastic region in which a localized

band at roughly rnid-height and progressed outward only as the band of initially collapsing cells

approached densification [1.22]. Grenestedt reported tbat this plastic region is between 2% to

25% of the straïn. Stresses slowly increased accompanied by ce11 wdls bending and fiacturing.

0.2 0.3

Compressive Strain, E 1-1

Figure 1.13 Cornparison of compressive results between Alcan f o m and Alporas foarn. [1.2 11

1. Introduction 15

A general mode1 was proposed by Gibson[l .l] based on the dimensional analysis. The

equation is as follows:

Where co, os, p*, p,, 4 are the yield strength of the foam, yield strength of the solid,

density of the foam, density of solid and solid volume fraction on the ce11 edge. The fint term of

the equation represents the component of open foam while the second term relates to the

component of closed ce11 foam.

Simone and Gibson also performed a finite element modeling of closed-ce11

tetrakaidecahedral foam with an elastic-perfectly plastic ce11 wall solid [1.20]. The polynomial fit

to the finite element analysis data is:

Where c,i , oys, p*. pr, $ are the plastic strength of foam, yield strength of solid, density

of foam, density of solid and soiid volume fiaction on the ce1 edge.

Beyond the plastic region, the flow stress elevated tremendously during compression.

This is due to the full collapsed of the ce11 walls and the cell walls touching each other, which is

similar to cornpressing a solid material. The densification of foam resuits in a higher yield stress

p.171.

1. Introduction 16

1 ADetonnafjom Behaviour and Stmngthening khanism of PMMC

The deformation behaviour and strengthening mechanisrn of particle reinforced metal

matrix composites (PMMCs) are weii published in recent years. AI-Sic is one of the most

comrnon PMMCs. The addition of SiC particles to the Al matrix strengthens the metal matrix

signincantly. These ceramic particles strengthen the makk by acting as a load carrier to share

part of the extemal load fiom the metal ma&. Since the stiffhess of the ceramic particles is

much higher than that of the matrix, the overall stifiess increases as a function of the volume

fî-action of the particles in the composite.

However, most importantly, the introduction of the particles to the metal matrix creates

tremendous stress distribution, which becomes the main obstacle to dislocation movement. This

high stress distribution is attributed by the formation of dislocation density between the particles

and metal matrix during cooling [1.23,1.24]. The large ciifference in the coefficient of thermal

expansion (CTE) leads to a compressive residual stress on the particle and tensile stress on the

matrix. These messes may be released by the formation of dislocations which become the barrier

for the dislocation movement and hence strengthens the material.

Wang and CO-workers 11.25-1 -271 showed that an uneven distribution of particles in the

matrix create clustering which gives arise to localized dislocation density because of deformation

incompatibility and hence produces a hi& localize tnaxial stress state. The high stress state by

creating a lower Von Mises equivalent stress delays plastic deformation and therefore strengthen

the matenal. The strengthening effect is dependent on shape, size, volume fiaction, and

distribution of particles in the matrix.

1. introduction 17

The alurninum foam with addition of Sic is considered as PMMCs. Sic particles can be

found in both ce11 edge and cell w d . Particles present in the ce11 c m retard the plastic

defonnation during ce11 wali slretching.

1.5 Fadom Afbcüng the Mechanical-Behaviour of Aiuminum Foam

The three main factors that detennine the mechanical properties of foam composite are

foam density, foam ce11 structure, and the properties of the material that makes the ce11 wall. The

foarn density, as mentioned before, is ckectly related to both the elastic and plastic properties of

the metd foam. The foam ce11 structure refers to ce11 shape and ce11 size, ce11 wall thickness, ce11

wall curvature, and defects such as wiggle in the ce11 structure [1.17, 1.1 81. Grenestedt proved

that the effect of ce11 wall wiggle on stiffhess was less signifiant in closed ce11 foam than in

open ce11 foam[l.i]. The main reason is that the deformation of closed ce11 foam is not mainly

by bending but to a certain extent by stretching which reduces the effect of wiggle during elastic

deformation. The material properties of the ce11 wdl such as the presence of the Sic particulate

will affect the mechanical behaviour of foam material. Volume fraction, particle shape, particle

size and distance between particles are some of possible parameters that can affect the foam

properties. Since there is no theory to predict such effects, a cornputer simulation is one of the

possible solutions to determine the influence of particulate influence on the foarn properties.

1.6 Consideration of P-nt Research

Although the production and applications of Al foam are well understood, the snidy of

the mechanical properties of this matenal is still under development. A very good example is that

Gibson [1.5], Kemy [1.6], and Grenestedt [1.7] have published their studies in this field.

However, their efforts mainly covered the compression and flexure testing of the materials.

There is no particular methodology to perform out uniaxial test, especially the tensile test. 1. Introduction 18

Moreover, no standard mechanical testhg method or ASTM standard is available or proposed for

such kind of rnetal foam composite. One of the reasons is due to the weakness of the foam

material, which is easily collapsed when it is gripped. This makes the t ende test almost

impossible. Therefore, it has been decided to develop a standard method which includes grip

design, sample shape consideration as well as procedures on performing uniaxial

compression/tensile test on this foam matenal.

Since the Al foam entrains many Sic particles, this materiai c m also be considered as a

Particdate Metai Matrix Composite (PMMC). Hence, the interactions between the particles with

the matrix vil1 d e f ~ t e l y affect the mechanical properties of the foam. However, studies are not

available on this subject matter.

The size and the volume fraction of Sic particles are two of the major production

parameters during the Aican foam production process. These two parameters are also linked

directly to the mechanical properties of the foam material. Due to the complicated smcture of

this material, it is difficuit to derive an empirical model to represent its mechanical properties.

Finite element analysis is one of the alternatives to this problem. A 2D FEM model will be

developed to investigate the effect of S i c particle size and volume fraction on the stiffness of the

foam material. Firstly, the influence of the particle volume fraction is examined by changing the

number of particles under constant particle size. Similarly, the effect of particle size is

investigated by using different sizes of paxticle under constant volume fiaction. The influence of

the foam ce11 size and the ce11 wall thickness are aiso studied under constant particle size and

volume fiaction. These two variables are linked directly to the foam density.

1. Introduction 19

The objective of the present work is to study in detail the effects of S i c particles on the

mechanical responses of aluminum foam in order to provide additional information for refining

the AL foam production process. ln addition, attempt to develop a standard method to perforrn

uniaxial t ende test wiU be made.

The nnite element method will be used to study the relationship between stress

distribution and stiffhess of the foam with SiC partkle size, volume fraction, foam ce11 size and

ce11 wall thickness under the influence of external loads using linear eiastic formulation.

Mechanical tests of foam sarnples with different foam densities will be carried out under video

r n o n i t o ~ g to observe the defornation as well as the failure process under uniaxial loading

condition.

1. introduction 20

2.1 Ove~-ew

Most of literatures are focused on testing of the compression properties of the al foam

matenal. There is no testing procedure or method recommended for this material. Moreover, the

choice of the specimen size and shape are at the researchers' discretion. The only closest testing

method that can be found is that fiom the ASTM for semi-flexible cellular Urethanes 12.11.

Three major problems m u t be solved when teshg al foam material:

1. Al foam is easily collapsed when gripped, th is makes tende testing almost

impossible.

2. Alignment problem. Since the specimen is relatively weak, any rnisalignment may

create a torque, which can seriously affect the experirnental results.

3. Testing of specimens with different thickness, the grïps has to be flexible enough to

accommodate different specimen thichess.

Problem #1 can be solved by strengthening the grip area of the specimen. Problem #2 and

#3 can be solved by designing special grips.

2.2 Made-

Two foam materials were obtained fiom Alcan International Limited, Kingston, Ontario.

The material information and the properties of Sic particles used in the foam material are

sumrnarized in the tables 2.1 and 2.2. Figure 2.1 shows a cornparison of the two foam samples.

Table 2.1 Summary of material information

Table 2.2 Surnmary of properties of Aluminum (359.0 9Si-0.6Mg) [2.2] and Sic particles [2.3]

h

Figure 2.1 Macrograph showing foam samples with different density.

2.3 Specimen Design and Preprafion

The onginai duminum samples were received in

Specimens were cut according to the shape in Figure 2.2a.

Identification

26/01/93#2

10/02/96 #6

Poisson's ratio Elastic Modulus ( G N ~ ~ ~ )

the

Volume Fraction of Particles

10

15

blocks.

Composite

A359+lOv%SiC

A359 +15vO/o SIC

Density (g cm'

The shape and dimension of the

Approximate Average

Particle Size

13

I l

Average Foam

Density (glcc) 0.19

0.32

Coefficient of thermal expansion ( K I )

specimen were based on the standard test method for cellular materials fiom ASTM handbook

[2.1]. The actual dimension of the sample is 1.5 times the recommended specimen size fiom the

2, Experimental 22

Volume Fraction of Voids (%)

93

88

ASTM standard. Since the foam ce11 size for both sarnples are different due to clifference in foam

density, the thickness of test specimen of foam with a density of 0.19 g/cc was cut to 1.5 inches.

On the other hand, the thickness of specimen with a density of 0.32 g/cc was cut to 1 inch. Figure

2.1 shows the schematic and the dimensions of the test specimen. Figures 2.2b and 2 . 2 ~ depict

the actual specimen.

Schematic for tension specimen

Grip area

Figure 2.2a Schematic of the tension sample.

~+e 2.2b Front view of the foam materials. Figure 2 . 3 ~ Side view of the foam materials showing sarnples with different thickness.

The grip area of the specimen is weak and will collapse when gripped during the tensile

test. In order to avoid any failure in this area, epoxy is used to fiIl the empty spaces in the foam

2. Experimental 23

cells. Holes were drilled on the s d a c e of the specimen (Figure 2.3), which allow epoxy to fil1

through the core part of the specimen at the grip area. These holes when filied with epoxy

provide additional suppoa to prevent the collapse of this region during the tensile test.

Rectangular paper molds with dimension 1 . 5 ~ 1 ~ 3 in3 and 1 . 5 ~ 1 . 5 ~ 3 in3 were made for the 0.32

g/cc and 0.19 glcc foam respectively.

0.8430 Hda IO bc fillecl with epaxy

0.3750 1

1

0.7500 -

Figure 2.3 Schematic showing the holes distribution on the grip area of the specimen

Resin and hardening agents were properly rnixed with the required proportion and poured

into the mold. The tensile specimen was carefùily inserted into the mold until it was fully fitted

into die mold (figure 2.4). The specimens together with the mold were set in a vertical position

for 24 h o u for curing. The paper mold was removed after curing and the surfaces of the grip

area were polished. Two sets of foam samples with different density were prepared. Each set

contains about 15 specirnens. After curing, the epoxy not only filled the ernpty space on the

surface of the grip area but also filied the holes at the center of the grip area to provide additional

support to this area The strengthening process is similar to the idea of a continuous fiber in a

metal matrix composite or steel bars in the concrete.

2. Experimental

Foam Specimen

Holes to be filled with epoxy

Foam Specirnen

Mold Mdd

Figure 2.4 Procedures of specimen preparation

2.4 Design of the gnpping system

In order to solve the aiignment probIem as well as to accommodate specimens with

thickness, two different grips were designed. The upper grïp is adjustable such that it can fit

specimens with thickness ranging fiom %" to 3" (figure 2.5). The lower grip is a wood alloy

l3.i~-

The upper grip consists of three major components, namely, grip, plate and screws. The

grip provides a t tachent to the MTS machine and space for griping specimen. The plate acts as a

spacer to fill the space between the specimen and the grip. Depending on the thickness of the

specimen, different sizes of plates wilI be used. For exampIe, a specimen with 1.5" thickness

(density=O.l9g/cc) requires two 1" plates to fill the gap on both sides of the grip (figure 2.5a).

Figure 2.6a and 2.6b depict the schematics of the steel plate. Three holes are drilled to allow

screws to fix into them. This design ensures the proper alignment, prevents slipping between

screws and plate, as well as allowing a firm attachrnent and hence a stronger force to the plate.

2. Experirnental 25

The groves on the other side of the plate prevent slipping between the plate and specimen. These

aiso Uicrease the stress that is added onto the foam specimen to obtaùi a stronger grip on the

specimen. The screws on both sides of the grip are used to tighten the specimen. However, by

changing the depth of the screws, it is possible to align the specimen vertically even if the

surface of the specimen is not flat.

Figure 2.5; Side view of Upper Grïp Figure 2.5b Front view of Upper Grip

Figure 2.6a Side view of the plate Figure 2.66 Front view of the plate

The construction of the lower grip is known as a woods alloy grip, involves a small

induction h a c e , woods alloy and water cooling arrangement (figure 2.7). The induction

h a c e is used to melt the woods alloy to a molten state. The foam specimen is inserted into the

liquid woods alloy, whose melting is about 7S°C. Water is then introduced into the grip to

solidi@ the woods ailoy. The foam specimen is blended with the woods alloy, which forms a

very strong grip on the specimen. Moreover, the specimen is evenly surrounded by woods alloy

2. Experimental 26

under hydrostatic stresses and hence, it will be aligned verticaliy. If the upper grip design is

adopted as the lower grip, it is not easy to align the specimen in a vertical position. Stress or

torque wiil be inwduced due to misalignment between the upper and lower grip.

--- ,- - - . - - - - - - a - . . . . . - , . .-. -..----*-a- . - . . - ., -.., -i- .c.i.-.--'- .+ . . , _ . .. ... Induction Furnace

Anachment to the

Figure 2.7 Schematic of a wood ailoy grip

2.5 Image captunng and digitking system

An image capturing and digitizing system (ICD) was especially designed to observe the

shape of the foam change under the uniaxial tensile test. Figure 2.8 shows a schematic of the

ICD system. It consists of a digital lens/camera, a super VHS-VCR, a monitor and a computer,

with an image-capturing card. The image of a foam ce11 is shot via the digital camera. The image

is observed via the monitor and recorded in a super VHS-VCR for future analysis. The

instantaneous time generated dirough a digital character generator is also recorded onto the

videotape. By knowing the strain rate, it is able to determine the shape of the foam at a particular

strain tevel is determined. The failure of the foam can also be studied using this technique.

Images of foam ce11 during the tensile test was monitored and captured in JPEG format

through the computer. During the test, a digital counter, which indicated the tirne during the test,

was recorded on the videotape together with the foam image. Consequently, it was possible to

2. Experirnental

obtain the shape of the foam sample as a fiinction of the . Moreover, since the strain rate was

kept constant during the tensile test, the strain on the specimen cm be expressed as followed:

Therefore, it is possible to relate the shape of the foam ce11 to strain level at a particular

moment during the tende test. By selecting certain strain level on a stress-- c w e , it is

possible to find out the corresponding time and hence the shapes of foam ce11 at that particular

instant. Consequently, a plot of stress-strain c w e with change in foam ce11 size can be obtained.

Since this is an innovative plot, it is named as Image Stress-strain curve in this study.

Experimental Setup Foam Sample

Epoxy Filied Mg ital Mdeo Recorder

Woa& Alloy Grip

Figure 2.8 ExperirnentaI setup for uniaxial test

2.6~Mechanniical:wtîg - - -

Tende tests of the foam specimens were carried out on a MTS 810 servo-hydraulic

mechanical testing system. Al1 tests were based on a stroke control mode in order to obtain an

accurate control over the strain rate. The stmh rate was at 1.18~10" s-'. MTS extensometer

mode1 634.25E-24 was used to acquire strain measurements. The load a d strain information

were plotted on a graph paper from a chart recorder. The graph was converted to a stress-strain

c w e according to the cross-sectional area of the specimen as well as calibration of load on the

MTS machine and extensometer

The generd experimental procedures are sumrnarized as follows:

Cut specimens according to the dimension specified in figure 2.1. The thickness of the foarn specimen with density of 0.19 gkc is 1.5" while the specimen thickness for density of 0.32 g/cc is 1".

Holes are drilled on both side of the grip area of the specimen.

Specimen is completely inserted into a paper mold with liquid epoxy and cured for 24 hours. (Figure 2.4)

The paper moid is removed and the surface of the specimen in the grip area is polished.

Specimen is set vertically according to the setup shown in figure 2.5.

Woods alloy in the lower grip is heated until cornpletely melted.

Specimen is carefully loaded into the woods alloy bath in the lower grip.

Woods alloy is then cooied and solidified by flowing cold water into the grip.

Extensometer is attached to the testing zone (gauge length area).

10. Lens and digital camera are set in focus.

11. The time and the MTS machine are started at the same tirne. The whole process of tensile test is performed under video recording.

12. Images are captured using Pentium PC with software called MOCHA by Jendel Scientific.

2. Experimental 29

The main objective of this shidy is to investigate the effect of the four major parameters,

namely particle size, particle volume fiaction, cell size and ce11 wall thickness, on the elastic

properties of Al foam. Models were developed based on varying one of the four parameters and

keeping the others constant. The study was divided into four categories and four models were

built in each category. Table 2.3 summarizes the rnodeling conditions for each category. Von

Mises stress distributions and stifkess are the two main indicators to measure the effect of these

parameters on the mechanical properties of the foam composite. Results fiom models that lead to

a lower value of Von Mises stress and/or a higher value of stifikess are considered to improve

mechanical properties of the foam material. A mode1 without addition of particles was used to

ver@ the effect of the particles. Figures 2.9a and 2.9b show two FEM mesh setups that was used

to compare the effects of particle addition to the model.

Table 2.3 Summary of modeling conditions for four scenarios.

1 II III IV

Particle Size Area Fraction Ce11 Ske Ce11 Wall Thickness

Particle size V V C C

Number of particle V C C C

SiC area fiaction C V C C

Ce11 size C C V C

Ce11 wall thickness C C V V

Foam density C C V V

Weight (W) C C V V

V=Variable, C=Constant

Figure 2.9a Mesh setup with particles Figure 2.9b Mesh setup without particles

The stress analysis of these models was based on the Finite Element Method (FEM). The

programming code used was by a commercial software package, EMRCNISA, fiom the

Engineering Mechanics Research Centre based in Michigan. Figure 2.1 0 show a cornparison

between the FEM model and the real foam matrix. Due to the conditions, oniy a quarter of the

models, that is the bottom left hand quadrant, was adopted in the computation (figure 2.9).

Appropriate boundary conditions were necessary for this simplification. The right hand side of

the quarter model was constrained in the x-direction, i.e. 6 x = O, while the top side of the quarter

model had to be constrained in the y-direction, Le. S y = O. Quadnlateral 4-nodal elements were

adopted to f o m meshes as they gave considerable consistency and an accurate representation of

the outcorne as compared to triangular 3-noded elements. Uniaxial tensile loading was applied, at

each of the nodes at the bottom edge of the model. Typical values were based on 1000N per unit

lengtl of the bottom surface side.

Full View of FEM Model

Figure 2.10 Cornparison between FEM model and actual foarn sample

Due to the randomness of ce11 and particle distribution in this foarn material, assumptions

have to be made for the present research. The assumptions are as follows:

1. Circular S i c particles

2. Circular foam c e l

3. Particles are distnbuted evenly around the ce11 edge

4. Both Al and Sic are isotropie

5. Interface at particle and matrix is a continuum

The aspect ratio of S ic particles was fixed at unity, i.e. circular which could eliminate the

effect of the aspect ratio. Foam cells were assumed circular in the model, which simplie the

influence of ce11 shape and orientation. Particles were assumed to be evenly distributed dong the

ce11 edge. Two-dimensional models were used because plane strain conditions were sufficient to

represent the behaviour of the specimen under loading.

2. Experirnental 3 2

Figure 2.1 1 Cornparison of particles distribution in modeling setup and actual foam sarnpIe[l.6].

The aim of category I was to study the effect of particle size on the stifkess of the foam

under uniaxial tensile loading. Therefore, parameters such as the particle volume fiaction or

equivalent area fraction in 2D, foam ce11 size, ce11 wall thickness as well as foam density were

kept constant. As the particle size changes, the number of particles must change in order to

compensate the change in area. The relationship between paaicle size and number of particles in

the metal matrix under a constant area fraction are described by the following equation:

Where rl and r2, are the radii of Sic particles. nl and n* are the number of Sic particles in the

foam composite in the different models.

The modeling summary of Category 1 is summarized in table 2.4. The particle area

fiaction, ce11 size, ce11 wall thickness as well as foam density were kept constant. The particle

2. Experimental 33

size and number of particles followed the relationship in equation 2.1. The mesh setups for each

scenario were found fiom Figures 2.12 to 2.15 (located at the end of this chapter).

Table 2.4 shows the rnodeiing summary of FEM analysis on the Category 1.

Scenarïo No. of particles Particle radius r/R Particle area Densi mm. (r) fiaction g h m Y

R- radiuspof foam ce11 which is 5mm.

Category II was designed to investigate the influence of the area fiaction of particles by

varying particle size. Therefore, the number of particle was kept at 36. The ce11 wall thickness

and the cell size were kept at 2mm and 4.5mm respectively. Although the foam density also

varied slightly, it was less than 1% (about 0.83 percentage) and hence it was considered constant.

Moreover, the mode1 setups in this category are quite similar to that of Figures 2.12 to 2.1 5

except for changing the particle size, therefore, detail mesh setups are not shown.

Table 2.5 shows the modeling surnmary of the FEM analysis on the Category II.

Scenario No. of Particle Particle Area r/R Density particles radius fhction g/m.mL

1 36 O .200 3 .OO% 0.044 f .51

Category III aimed at determining the effect of ce11 size on the foam properties.

Parameters, such as number of particles, particle size, and ce11 wall thickness, were kept at 36,

2. Experimental 34

0.2885mm and 4mrn respectively. Four models were developed and the modeling parameters are

summarized in table 2.6. The mesh setups are shown on Figures 2.16 to 2.19 (located at the end

of this chapter).

Table 2.6 shows the modeling summary of the FEM analysis on the Category m.

Scenario No. of Particle Particle Area Ce11 SLze r/R Densi? particles radius hction mm s/mm

mm.(rl

Category IV focuses on examining the effect of ce11 wafl thickness on the mechanical

properties of the foam matenal. The number of particles, particle size, and ce11 size were kept at

36,0.2885mm and 4.5rnm respectively. Six models were developed and the modeling parameters

are summarized in table 2.7.

Table 2.7 shows the modeling summary of the FEM analysis on the Category IV.

Scenario No. of Particle radius Particle area Ce11 Wall r/R Density partides mm.@> fiaction Thickness dmm

Fifieen specimens were prepared for tensile testing according to the developed

experirnental setup under a constant strain rate of 1 x 1 0 ~ s*'. Ten foam specimens with densities

0.19gkc and 0.32g/cc were tested successfully and the stifkess data of these specimens were

determined fkom the slope of the Stress-Strain. Table 3.1.1 and figure 3.1.1.1 summarize the

results of specimens with a density of 0.19gIcc. The average stifiess was 297.4 MPa with a

standard deviation of 94.3 MPa. Table 3.1.2 and figure 3.1.1.2 list the stifhess results for

specimsns with a density of 0.32g.k~. The average stiffness was 1,167.9 MPa with a standard

deviation of 583.8 MPa. These stiffriess results were substituted into equation 1.2 to determine

the voIurne fraction of solid in the ce11 edge. Equation 1.2 c m be modified as followed:

The 4 vaiues for foam densities of 0.19 g/cc and 0.32 g/cc are 1 and 0.98 respectively.

Hence, the f values are O and 0.02. According to the figure 1.1 1 in Chapter 1, the lower the f

value, the more chcular the foam ce11 shape. Therefore, the foam cells of both foam specimens

tend to be more circular than hexagonal. This verified that the assumption for circular ce11 shape

3. Results and Discussion 44

for the FEM mode1 is vaiîd. This observation is dso consistent with result on the compressive

foam properties reported by Kemy [1.6].

The randomness in the stifiess data reflects the heterogeneous character of this foam

material. Unlike normal metals, foam materials have relatively random properties mainIy due to

this non-continuous nature as well as to their non-uniform foam ce11 size and shape. The foam

ce11 size normally falls into a distribution depending on its density and original production

technique. Therefore, the mechanical properties of specimens taken fkom different locations of

the same block of material may vary.

Table 3.1 Summary of the stiffiiess of the foam samples with a density of O.l9g/cc

Sarnple el01 el02 el03 et04 el05 El06 el07 sl s2 s3 Average Stiffiiess m a ) 378.8 270.5 420.8 158.7 192.4 384.8 390.8 310.0 198.4 268.7 297.4

Table 3.2 Surnrnary of the sti£hess of the foam sampies with a density of 0.32g/cc

Samde es01 es03 es04 es05 Es07 es08 es09 Es10 es11 es12 Average

Stiffness of foam specimens (Density=O.l9glcc)

O 2 4 6 8 I O 12

Specimens

Figure 3.1.1.1 Stiffhess of foam specimens with density 0.19gkc


Stiffness of foam specimens (Density=O.3Zglcc)

O 2 4 6 8 1 O 12

Specimens

Figure 3.1.1 -2 Stifiess of foam specimens with a density of0.32gkc

3.7.2 Stress strain curve

Figure 3.1.2.1 depicts a typical tensile load deflection curve for a specirnen with a density

of 0.19gIcc. Figure 3.1.2.2 shows a plot of the engineering stress against the strain curve. The

stress-strain curve indicats that this material has an obvious linear elastic region. It yielded at

about 0.58 MPa and its ultimate tensile stress was at 0.66 MPa. After reaching its uItimate tensile

stress, this material failed in a stepwise marner. This discrete phenornenon is even more obvious

in figure 3.1.2.3. The applied load was distributed by the ce11 walls within the specimen.

However, the load distribution was not uniforrn because both ce11 size and ce1 wall thickness

were not uniform within the specimen. This non-uniformity lead to localized stress

concentration, which resulted in plastic deformation. This eventually lead to localized necking

and ce11 wall rupture. Each step loss in the stress represented a ce11 wall rupture. After the rupture

of the ce11 wall, another stress concentrated zone formed, which yielded, and eventually rupture.

This process continued until ail ce11 walls were ruptured. The formation of Iocdized deformation

zone would lead to the relaxation of the stress at other locations. 3. Results and Discussion

Figure 3.1.2.1 Load deflection curve fiom MTS chart recorder

Stress Strain Cuwe (s2)

0.005 0.01 0.045 0.02 0.025 0.03 0.035

Strain

Figure 3.1.2.2 Stress-Strain Curve of Specimen S2


Strain

Figure 3 -1.2.3 A toad-deflection curve of specimen s3 showing the stepwise failure after UTS.

3.1.3 Cell Shape Stress Strain

The Image Stress Strain curve is a

Cuwe

curve showing foam ce11 shape as a function of stress

or main. As mentioned in the experirnental section, the images of the foam cells were recorded

as a function of time during the tensile test (Figure 3.1.3.1). Since the test was carried out under a

constant strain rate, it is possible to estimate the time of a particular strain level, by sirnply

dividing the strain by the strain rate. Tables 3.1.3.1 to Table 3.1.3.3 summarized the strain and

the correspondhg t h e .

TabIe 3.1.3.1 Strain and time of linear deformation region - - --

Time (sec.) O 135 206 300 Strain 0.00000 0.00159 0.00243 0.00354

Time (sec.) 473 547 600 664.5 - -

Strain 0.00559 0.00646 0.00709 0.00785

Tirne (sec.) 665 666 667 668 Strain 0.00785 0.00787 0.00788 0.00789


By searching the time recorded on the video (bottom left hand corner of figure 3.1.3.1),

the image of the foam cells at that ce& time could be located and captured via the computer as

either JPEG or TIFF format file. Therefore, it was possible to obtain an image at a particdar

strain level.

-

Figure 3.1.3.1 Image caphued fiom video showing instant time during the tensile test

Figure 3.1.3.2 shows a stress strain curve for specimen EL0 1. The curve was divided into

linear eiastic, plastic and mechanical failure regions. Four images were captured fkom each

region. Figure 3.1.3.3 shows the images captured for each region. By plotting these images along

with the stress-strain curve, the ce11 shape stress-strain cuve as shown in Figure 3.1.3.4 is

obtained.

The main purpose of this plot is to illustrate the change in the ce11 shape with respect to

the change in the stress/strain change. However, since the total change in strain was very small

before failure (0.8 percent), the shape change during elastic and plastic deformation at this

magnification was not obvious compared to when the ce11 started to rupture. Images captured in


the mechanicd failure region showed clearly, how a crack developed propagated and fmally

resulted in ce11 rapture. This real-time image analysis technique c m be usefid in studying failure

mechanism of any experiments that require a relationship between shape and strain (or stress).


Stress - Strain Curve for Sample EL01 700000

Figure 3.1 -3 -2 Stress-Strain Curve for specimen el0 1 .

Elastic Deformation Region

T= O s T= 135s

Plastic Deformation Region

Mechanical Failure Reg ion

Figure 3.1 -3.3 Images of foam ce11 taken fkom different regions.


Stress - Strain Curve for Sample EL01

0.00000 0.00200 0.00400 0 . m 0.00800 0.01000 0.01200 0.01400 0.01600

Strain

Figure 3.1.3.4 A typical Image Stress-Strain Curve of specimen EL0 1.

3.1.4 Observafions dunng foam failure

The images in figure 3.1.3.4 show a process of typical tramcellular fkacture in which a

crack develops and propagates within the ceIl. Figure 3.1.4.1 depicts a cornparison of cells before

and afier transcellular fiacture. This is the most common type of fracture observed among both

types of foam specimens. However, intercellular fracture in which cracks develop dong the ce11

walls, was also observed (figure 3.1.4.2). This type of fracture could be amibuted to the surface

crack, which created a weak point for fiacture to occur. The ultimate tensile stress (UTS) for

EL01 was 0.93 MPa while UTS for EL07 was 0.72 MPa. This confirms that surface defects

3. Resutts and Discussion 52

cûüld be a potential weak site for failure initiation. The irregularity on the surface, such as the

variation in ce11 size and cracks, makes the material properties inconsistent and contribute to the

fussiness of the material. Therefore, this material cannot be used by itself as a structural

material. It requires a harder surface such as metal plate to strengthen it and to prevent failure

from the surface. Another alternative couid be as described in Chapter 2, section 2.3 and by

figure 2.4 by coating the foam surface with an epoxy. This is not only eliminates most of the

surface defects but aiso strengthens the material by filling up the surface of the cell. If M e r

strength is required, holes could be drilled into the center and filled with epoxy. The advantage

of using an epoxy is that the matenal is strengthened without adding extra weight and hence it

can maintain its high strength to weight ratio. Moreover, the composite surface is more workable

and the surface finish is much better.


Transcellular Fracture

Foam Sample Before Fracture

Foam Sample After Fracture

Figure 3.1 -4.1 Cornparison of ceil before and after transcellular fracture of specimen EL0 1.


Intercellular Fracture

- Foam Sample Before Fracture

Foam Sample Afier Fracture

Figure 3.1.4.2 Cornparison of ce11 before and after intercellular fracture of specimen EL07.


3.2 Finb eîement modehg

The size and the volume fiaction of Sic are the two major parameters determinhg the

foamability of Al foam (figure 1 S). The operation window for foam production is in the range of

particles size between 1 to 20pm and of particle volume fiaction of 5 to 15% volume fiaction.

However, these two parameters piay a significant role on the mechanical properties of the foam

material because S i c particles in an Al matrix is a typical strengthening mechanisrn for metal

ma?rix composite (MMC). By using the finite element method (FEM) on MMC, it will be

possible to predict the optimum combination of these two parameters in order to produce a

stronger material. The FEM c m also provide information on how the foam ce11 size and ce11 wall

thickness affect the foam properties.

Since the Von Mises stress can be taken as a yielding critenon, Le. the higher this stress,

the matenai becomes more liable to plastic deformation and hence weaker. Therefore, the major

objective of FEM rnodeling is to seek a combination of modeling parameters that has the lowest

Von Mises stress distribution in order to decrease the possibility for plastic deformation. The

stiffhess of the model is another indicator for selecting a suitable configuration because the

higher the stiffhess, the better it is when using it as a structural material. Since one of the

advantages of the foam matenal is its high strength-to-weight ratio, this wodd inevitably be a

good indicator for choosing a better combination of modeling parameters. Therefore, in this

shidy an attempt will be made to find a suitable combination of modeling parameters in order to

achieve low Von Mises Stress distribution, high stifiess and high strength-to-weight ratio.

3.2.1 Effect of addition of Sic particles

The aim of this section is to confimi the strengthening effect of the addition of Sic

particles to the foam. The Von Mises stress distribution and stiffness of the FEM model with and

without Sic particles additions are compared.


The Von Mises stress distributions of single-phase foam composite and particle-

reinforced foam are depicted in Figures 3.2.1.1 and 3.2.1.2 respectively (located at the end of this

chapter). Figures 3.2.1.3 and 3.2.1.4 show the full view for the two cases. These two figures

represent only one quarter of the model. Tende load was applied verticdy for both cases. The

colour scale at the right hand side of the figure denotes the computed stress level, which

increases f?om the bottom to the top. Comparing the stress distribution in both figures, the

single-phase foam has a hornogeneous stress distribution while the particle-reinforced foam has a

relatively heterogeneous distribution. The stress levels in particle-reinforced foam, in general, are

lower than that for the single-phased foam, except the stress level at the particle and particle-

matrix interface. For example, the maximum stress level for the single-phased foam between the

voids ranged fkom 265.1 to 330.e MPa. However, the stress at similar location ranged fiom 176.6

to 264.6 MPa in the particle-reinforced foam. As mentioned before, a lower Von Mises stress

level will decrease the possibility for plastic deformation that may lead to catastrophic failure.

The addition of Sic particles also redistributes the stress near the foam ce11 wall. Figures

3.2.1.4 and 3.2.1.5 show zoomed images near the ce11 wall area. The red-coloured area represents

the highest stress level, which is also the weakest zone of the foam. The stress levels at the red-

coloured area ranged fiom 526.1 to 59 1 -4 MPa and 705.1 to 793.1 MPa for single-phased foam

and particle-reinforced foam, respectively. Although the stress level at the ce11 wall for the

particle-reidorced foam is much higher, these high stress levels are concentrated within the

particles. The stress levels of the surroundhg matrix are relatively less than that of the single-

phased foam at the same location. Such stress redistribution decreases the stress that the metal

matrix has to accommodate around the cell wall area. Therefore, the Al matrix at the ce11 wall

area is less liable to plastic deformation. Moreover, since the tensile strength of the Sic particles

(1.5GPa) is much higher than that of the Al matrix, they can carry a much higher stress prior to 3. Results and Discussion 57

plastic d e f o d o n . The existence of particles in the weak zone reinforces the matrix in this area

by shifting much of the load to particles and decreasing the Von Mises stress in the Al matrix.

Hence, the addition of SiC strengthens the foam composite.

Figure 3 -2.1.4 Celt wall of singIe-phased foam. Figure 3.2.1.5 Ce11 wall of particle reinforced foam

3.2.2 Effect of Sic particle size on tensiie properties

The objective of this part of study is to obtain an insight into the relationship between the

size of the SIC particle and mechanical properties of the foam. From such information, it will be

enable us to refine an operating window in ternis of particles strengthening for Al foam

production. Four two-dimensional FEM models with various particle sizes under were developed

for cornparison. Other modeling parameters, such as, area fraction, foarn cell size and ce11 wall

thickness, were al1 kept constant. Von Mises stress distribution and foam stifbess are the two

indicators for selecting the most suitable particle size among the four rnodels.


The results of the FEM analysis are summarized in Figures 3.2.2.1 to 3.2.2.4 (located at

the end of thir chapter). In order to compare the effect of particle size on the ma&, the relative

Von Mises Stresses dong the vertical and horizontal directions (defhed in figure 3.2.2.5) are

plotted against the distance fiom the lefi-hand corner of the model. A cornparison of the Von

Mises Stress for the four models in LL direction is shown in figure 3.2.2.6. The relative Von

Mises Stress decreases with an increase in particle size. Similady, the plot of the relative Von

Mises Stress in the TT direction in figure 3.2.2.7 confinns this observation. In order to M e r

support the above results, the average, standard deviation and maximum relative Von Mises

stresses fiom the four models are compared in Figure 3.2.2.8. It indicates that by using larger Sic

particles, the Von Mises stress on average decreases. Models with larger particles also have a

lower standard deviation for the relative Von Mises stress, which indicates that the stress

variation is lower than that of smaller particle. Finally, the model with largest particles also

possess a lowest maximum Von Mises stress which means

deformation.

L

that it is the least liable to plastic

Particle

L Figure 3.2.2.5 Stress distribution axes for FEM rnodel.


Comparison of Stress Distribution of foams with different Particle Size (L-L direction)

Figure 3.2.2.6 Comparison of relative Von Mises Stress dong L-L direction

Comparison of Stress Distribution of foams with different Particle Size (T-T direction)

Figure 3.2.2.7 Comparison of relative Von Mises Stress aiong T-T direction


Comparison of Von Mises Stresses on Models with different particle size of SIC

Figure 3.2.2.8 Comparison o f Von Mises Stress statistics on models with different particle size of Sic

The stiffhess of the models was calcdated based on the average strain level at the bottom

of the mode1 where the extemal forces were appiied. The results are summarized in table 3 2.2.1.

The value r/R is the ratio between the radius of Sic particle and the radius of the foarn cell. The

smaller the ratio, the smaller the particle sizes. Figure 3.2.2.9 shows a graphical cornparison of

the stiffness for the four models agauist r/R ratio. The upper bound in the graph represents the

stiffiness of pure aluminum while the iower bound represents the stiffness of foarn without

particles. The result of this analysis incikates that the stiffriess increases with increase in particle

size. In fact, the stifniess increases by about 32% with an increase in particle size by 130%.

Al1 the above proved that larger particles existing on the surface of foam ce11 have a

stronger strengthening effect than that of the smaller particles. Therefore, it will more preferable

to use particles of 20 p. 3. Results and Discussion

Table 3.2.2.1 Summary of t ende stiffaess of ail FEM models. The radius (R) was 4.5 mm.

1 II 111 IV Num ber of particles 12 20 36 64 r (mm) 0.500 0.387 0.289 0.21 7 r/R 0.100 0.077 0.058 0.043 E (GPa) 36.12 31 -40 28.04 27.33

Effect of particle size on Foam Stiffness

0.04 0.05 0.06 0.07 0.08 0-09 O. 1 0.1 1 0.1 2

Particle radius to Cell radius ratio (RplRc)

Figure 3.2.2.1 O shows a graphical cornparison of the stiffkess for the four models against r/R ratio

3.2.3 Influence of parficle area fraction on tensile properties

The airn of this section is to determine the influence of the particle volume fraction (area

fraction in 2-D) on the tensile properties of Al foam. Four 2D models were developed with area

fractions ranging fiom 3% to 7.00%. The Von Mises stress distribution and tende stifiess

arnong the models were compared in order to provide information to refme the operating window

for the production of AI foam.

Figures 3 .S.3.l to 3.2.3.5 (located at the end of this chapter) show the Von Mises stress

distribution for the corresponding models. Similar to the previous section, the relative Von Mises

stress in L-L (figure 3.2.3.6) and T-T (figure 3.2.3.7) for al1 the four models are ploaed for


cornparison. It is found that the Von Mises stress distribution decreases with increase in area

hction.

The statistics of the Von Mises stress are also compared in figure 3.2.3.8. The maximum

stress, average and standard deviation of the Von Mises stress decrease with increase in area

fraction. This indicates that a higher particle area fiaction will reduce the model's stress level as

well as smooth out the stress variation.

Both the above evidences proved that the mode1 with a higher area eaction reduces the

Von Mises stress level, which decreases the possibility of plastic deformation. Hence, the

material is strengthened. This result is in agreement with and consistent to the previous results

and publications.

This trend is consistent with the analysis of the -ess of the models. Figure 3.2.3.9

illustmtes a plot of tensile stifnless of the five models against the area fiaction. The graph shows

that the area fiaction is directly proportional to the tensile stifniess. Table 3.2.3.1 summarizes the

modeling results.

Table 3.2.3.1 Summary of modeling results in comparing effect of area fraction of SIC.

I II 111 N V radius (mm) 0.2 0.2885 0.3 0.325 0.35 Area fraction 3.0% 6.3% 6.8% 8.0% 9.3% E 30.21 32.43 32.81 33.66 34.59

The stif35ess and the area fraction of particles are estimated by linear regression and it

can be expressed as:


Due to the spatial restriction, which limts the size and the number of partides that can be

incorporated on the surface of a foam cell, the area hction cannot exceed 10% under the current

modeling configuration. However, the stifThess of the foam at a higher area fiaction could be

estimated by linear extrapolation using equation 3.1. As mentioned in Chapter 1 , the operatïng

range of Al foam production is between 5% to 15% volume fiaction. Based on equation (3.1),

the stifiess of foam with a Sic volume fiaction of 15% is about 22% higher than that of foam

with 5% Sic volume hction.

Comparison of Stress Distribution of foams with different Area Fraction (L-L direction)

O 2 4 6 8 10 12 14 16

Bottorn Specimen Height TOP

Figure 3.2.3.6 Comparison of Von Mises Stress distribution of FEM rnodels under different area fiaction in L-L direction


Comparison of Stress Distribution of foam with different Area Fraction (T-T direction)

J.WE.OO I.OMIQO s.w~*m LWEIQI T~OEIOO O.OOLIQO r.ai~-oa t OMIOI I.lOE41 1 1 < ~ 4 t

Bottom Specimen Helght

Figure 3.2.3.7 Comparison of Von Mises Stress distribution of FEM models under different area fraction in T-T direction

Cornparison of statistics on average relative Von Mises Stress under different

area fraction

Figure 3.2.3.8 Cornparison of the statistics of Von Mises Stress of FEM models under different area fraction in L-L direction.


Effect of area fraction on Modulus of Elasticity

0.0% 2.0% 4.0% 6.0% 8.0% 10.0%

Area fraction of Sic particle

Figure 3.2.3.9 A plot of stiffness against particle area fraction.

3.2.4 Effecf of foam ceil size on tensile pmperties

This purpose of this section is to study the effect of foam ce11 size on the tende stiffbess.

As discussed in Chapter 1, the strength of the foam is directly related to its density. Ce11 size and

ce11 thichess are two of the important parameters determinhg foam density. The smaller the ce11

size, the higher the density of the foam.

Four FEM models with foam celI size varying from 5mm to 5.8 mm were developed.

Figures 3.2.4.1 to 3.2.4.4 (Iocated at the end of this chapter) show the stress distribution under

different foam ce11 size. The modeling results of the stifhess are surnmarized in table 3.2.4.1.


Table 3.2.4.1 Summary of eEect of ceil size on stiffbess and stiffiiess-to-weight ratio

I II 111 N V Size of void (mm) O 4.5 5 5.5 5.8

RpIRv 0.00 0.06 0.06 0.05 0.05 E Gpa 73.00 32.43 20.56 9.91 4.93

Uweight 1 18735.54 841 34.35 63979.87 40058.55 24908.75

Figures 3.2.4.5 and 3.2.4.6 depict the relative Von Mises Stress in L-L and T-T directions

of the FEM model. Both figures show that the smaller foam ce11 size has a lower Von Mises

stress distribution. Therefore, foam with s d e r ce11 size is less liable to plastic defornation and

hence is stronger.

The tende stifniess of the four models is plotted against the relative foarn density in

figure 3.2.4.7. The relative foam density is the ratio of the foam density with respect to the

density of solid duminum. The data point at the right hand side of the figure represents pure

alurninurn while the N o data points at the left bottom corner represeot two experimental stiffness

values. In general, the stiffneos of foam increases with decrease in foam ce11 size.

In the previous two sections, the area fiaction of the solid was keep constant. However, it

varies for al1 the models in this section and hence the weight as well as the foam density are

different. Therefore, the stifhess-to-weight ratio is another indicator to study because it is

desirable to make a stiff but light material. Figure 3.2.4.8 illustrates a plot of stifiess-to-weight

ratio as a fiinetion of particle radius to ce11 radius ratio (Rp/Rc). As the radius of the particles is

kept constant, the higher the RpRc ratio, the smaller the foam ce11 size. h is indicated from the

figure that the stiffness-to-weight ratio increases with increase in RpRc ratio, which means that

it increases with decrease in ce11 size. Therefore, Al foam materials with smaller ce11 sizes are

more preferable than foams with larger ceil sizes.

3. ResuIts and Discussion 67

Comparison of Stress Distribution of foams with different Cell Size (L-L direction)

Bottom Specimen Heig ht

Figure 3.2.4.5 Comparison of Von Mises Stress distribution on FEM models with different ce11 size in L-L direction.

Comparison of Stress Distribution of foam with different Cell Size (T-T direction)

4.OOt3m 6.-

Specimen Height

Figure 3.2.4.6 Comparison of Von Mises Stress distribution of FEM mode15 with different ce11 size in T-T direction.

3. Results and Discussion 6 8

Effect o f Cel l Size o n Elastic Modulus

20% 40% 6 0 % 80%

Relative foam Density

Figure 3.2.4.7 A plot of tende stifiess against relative foam density.

E f f e c t o f Ce I I Size on Sti f fness to we igh t ratio

Figure 3.2.4.8 A plot of stiffhess-to-weight ratio against Rpmc ratio.


3.2.5 Effect of foam ce11 wall thickness on tensile properfies

The effect of foam ce11 wall thickness on tensile sriffness was studied by varying the ce11

size under constant ce11 configuration. Six rnodels were developed and the results are

summarized in table 3.2.5.1.

Table 3.2.5.1 Sumrniuy of modeling results on effect of ce11 wall thickness on stiffhess and stifikess-to- weight ratio

I II 111 N v VI Thickness (mm) 4.0 3.4 2.8 2.2 1.8 1 -4 E Gpa 28.04 24.85 20.88 16.10 12.31 8.72 ENV 25.25 26.62 27.30 26.65 24.53 21 -61

Figures 3.2.5.1 to 3.2.5.6 (located at the end of this chapter) show the results for the six

FEM models. The maximum Von Mises Stress level, shown on the colour bar at the right hand

side of the figures, increases with decrease in ce11 wall thickness. Thus, foams with thicker ce11

wall is less Iiable to plastic deformation than that of with thinner ce11 wall. This result is furùier

supported by cornparing the Von Mises stress distribution dong L-L and T-T direction, which

are plotted in figures 3.2.5.7 and 3.2.5.8. Both figures demonstrate that foam rnodels with thicker

ce11 walls have lower relative Von Mises stress.

The tensile stifniess of the six models is plotted in figure 3.2.5.9. The stiffness of the

thickest ce11 wall has the highest tensiie stifiess. This result agrees with the Von Mises stress

results that are under predicted because the foam with a thicker ce11 wall contains more material

and is also denser. The density is directly related to the stifiess as discussed in Chapter 2.

Although the stiff'hess increases with ce11 wall thickness, it is also trading off the weight

of the material because the weight of material increases with ce11 wdl thickness. Therefore, the

stiffhess-to-weight ratio is another indicator for selecting the modeling parameter. A mode1 with


a higher value of this ratio implies that it weights less and M e r . Figure 3.2.510 depicts a plot of

stifiess-to-weight against the ceU wall thickness. It is found that the stiffhess-to-weight ratio

increases and then has a dùninisbing retum. The maximum value occurs at a ce11 walI thickness

of 2.7 mm which means that the model under this thickness has a good balance between the

stifiess and the weight. Hence in terms of the design aspect, if the s-ess fulfills the

specification, one would intend to choose a material with a lower weight and therefore the model

with 2.7 mm thickness is preferable to other models.

3. Results and Discussion 7 1

Comparison of Stress Distribution of foams with different Cell Wall Thickness (1-L direction)

a m ~ a a- aca.a, 1.00~loc 1 Q E M ~

Boitorn Specimen Height TOP

Figure 3.2.5.7 Comparison of Von Mises Stress distribution on FEM modeIs with different ce11 size in - L-L direction.

Comparison of Stress Distribution of foarn with different Cell Wall Thickness (T-T direction)

Bottom Specimen Height

Figure 3.2.5.8 Comparison of Von Mises Stress distribution of FEM models with different cell wall thickness in T-T direction.


Effect of Cell Thickness on Tensile Stiffness

0.0 1 .O 2.0 3.0 4.0 5.0

Cell Wall Thickness (mm)

Figure 3 -2.5.9 A plot of tensile stifiess against ceIl wall thickness.

Effect of Cell Thickness on Tensile Stiffness to Weight ratio

1 .O 2.0 3.0 4.0

Cell Wal l Thickness (mm)

Figure 3.2.5.10 A cornparison of stiffhess-to-weight ratio arnong six models with different ce11 wall thickness

3. ResuIts and Discussion

3.2.6 VemScation of Modeling results

Figure 3.2.6.1 exhibits the compressive properties of Al foam from Alcan [4]. The

stifniess (or Young's Modulus) is directly related to the foam density. Since the FEM modeling

range of this study is beyond that shown in figure 3.2.6.1, the best curve is determined in figure

3.2.6.2 to obtain the data by extrapolation for comparison.

Figure 3.2.6.1 Experirnental result fiom Alcan

ûetermination of best fit cunre

Figure 3.2.6.2 Determination of best fit of figure 3.2.6.1

Figure 3 -2.6.3 shows a comparison of the modeling data, extrapolation of best-fit curve

and experimentd data of this work. In generd, the tensile stimess of the FE.M models and the

experimental data are higher than that of the compressive data from Alcan. The stifiess data of

the FEM models are comparable to the compression data. However, the stiffhess of experimental

data is relatively higher.


Verification of Modefing Results

1 .O0 Density (glcc)

Figure 3.2.6.3 Verification of rnodeling and experimenta1 data with available data from Alcan.


EMRC - DI SPLAV 1 1 POST- PROCESSOR UER 91.13 Oc 1 / 7 / 9 7 STRESS CONTOUR

WON-MI SES STRE

UIE14 : 4.08E+

RANGE: 5.91E+

(Band ff 1 .@El

Figure 3.2.1.3 Fi111 view of figure 3.2.1.1

EMRC - DISPLAY I I POST-PROCESSOR UER 9 2 . 0 O O ~ / 7/97 STRESS CONTOURS

WON- MI SES STRESS

UIEW : 3.83E+0Q

RANGE: 7 . 9 3 E 7 0 3

(Band * l l O E 1 )

Figiirc 3.2.1.4 Full view of figiire 3.2.1.2

EMRC - DISPLAY I I POST-PROCESSOR UER 91 . Q Aus/18/97 STRESS COI\ITOURS

WON- MI SES STRESS

VIEN : 2.64E4Ql

RANCE: 6.3LE+@3

(Band ++ 1 . 0 E l )

.-

Figim 3.2.2.1 The Voti Mises stress distribiitioii a 12 pariicles iiiodel witli pnrticle ratliiis = 0.500 iniii

EMRC - DI SPLAY 1 1 POST- PROCESSOR UER 91.0 Aus/l8/9? STRESS CONTOURS

UON- M I SES STRESS

VI EN : 1.99E+01

RANGE: 7.2SE+03

(Band M 1.0El)

Figiire 3.2.2.2 'rtie Voii Mises stress disiribiitioii a 20 pariiclcs ttiodel witli particle r a d' iiis = 0.387 r i i i i i

EMRC - Dl SPLAY 1 I POST- PROCESSOR UER 91.0 00 1 / 8 /97

Figiire 3.2.2.4 Tlie Von Mises stress distribiitioii n 64 particles iiiodel witli particle nidiiis = 0.2 17 iiitn

STRESS CONTOURS

UON- MI SES STRESS

VIEN : 4.15E-01

RANCE: 9.21E703

EMRÇ - DI SPLAY 1 1 POST- PROCESSOR VER 91 . Q Au3/l6/98

Figiire 3.2.3.1 Tlie Voii Mises stress distribiitioii a 36 particles model witli area fractioii = 3.0%

STRESS CONTOURS

VON- MI SES STRESS

UIEW : 3.Q9E+00

RANGE: 8.32E+El3

RY: 0 RZ= 0

EMRC - DI SPLAV 1 1 POST- PROCESSOR UER 91.0 Aus/l8/97 STRESS CONTOURS

WON- MI SES STRESS

UIEW : 5,15E+00

RANGE: 7.6lE+Q3

Figiire 3.2.3.4 The Von Mises stress distribiitiori n 36 particles iiiodel witli area fraction = 9.3%

EMRC - Dl SPLA V 1 1 PQST- PROCESSOR VER 91.0 Sep/ 2/98 STRESS CONTOURS

UON-MI SES STRESS

U I E W : 3.09E-t-00

RANGE: l .88E+04

(Band % 1.QE2)

Figiire 3.2.4.3 The Von Miscs stress distribiitiori a 36 particles inodel witli f m m cell radins = 5.5 riiiii

L'Y a V) .- 2

EMRC - Dl SPLAY I I POST-PROCESSOR VER 91.0 O O ~ / 7/97 STRESS CONTOURS

UON-MI SES STRESS

UIEW : 3.24E+00

RANGE: 8.86€+03

(Band * 1.0E1)

Figiire 3.2.5.2 The Voii Mises stress tlistribiitioii n 36 particles iiio(lcl witli foaiii cell wall tliickiiess = 3.4 1111

EMRC - DI SPLAY

EMRC - DISPLAY 1 1 POST- PROCESSOR UER 41 . Q 00 f / 8 / 9 7 STRESS CONTOURS

UON-MISES STRESS

V I E N : 2.?&E+0Q

RANGE: 1.56E+Q4

RX= 0

Figure 3.2.5.5 The Von Mises stress distribution a 36 particles mode1 with foam ce11 wall thickness = 1.8 m m

Based on the above results and discussion, the following conclusions are reached:

A complete procedure and methodology for testing aluminum foam in a tensile test were

developed. Together with the digital image analyzïng techniques, this testing method is

able to produce an Image Stress-Strain curve, which relates the shape of the foam ce11 to

its stress and strain level.

Tensile stress-strain response of Al foam possesses the same charactenstics of a normal

metal stress-strain curve, except the failure process beyond the UTS point occurs in under

a unique stepwise manner due to the ce11 wall rupture.

Based on the stiffness of the two foam samples, Al foam fiom Alcan is found be

structurdly similar to circular ce11 rather than hexagonal.

Crack propagation via foam ce11 can be transcellular and intercellular.

Based on the FEM anaiysis, it found that Al foarn with larger Sic particles has a Iower

Von Mises stress and higher stiflhess.

Higher SIC volume fiaction leads to lower Von Mises stress and higher stifiess.

Foams with smaller foam ce11 size have a lower Von Mises Stress, higher stiflhess and

higher stiffhess-to-weight ratio.

Foams with thicker ceU wails induce a lower Von Mises stress state and have a higher

sti&ess but the stiffiiess-to-weight ratio is maximized at a ce11 wall thickness of 2.ïmm.

From the FEM analysis, larger Sic particles and higher particle volume fiactions leads to

stronger foams. Therefore, it is recommended to produce Al foam at the top right hand

corner (as circled) of the following diagram which at 15% volume fiaction and 2 0 ~ .

4. Conclusion 1 O0

References

Chapter 1

L. Gibson and M. Ashby, Cellular Soli&, structure andproperties, Cambridge

University Press 7 997.

A Sosnik, US Patent 2434 775 (1948).

G.J. Davies and S. Zhen, J o d of Materiais Science 18 1899 (1983).

1 Jin, L.D. Kemy, and H. Sang, US Patent No. 5, 1 12,697 (1 992).

L. Gibson, A.E. Simone, Alurninum Foams: Structure and Properties, Intemet

address h t t p : / / d a s - w w w . h a r v a r d . e d u ~ u s e r s / f a c u l t y c I e 3

/Article3 .htrnl

L.D. Kenny, Materials Science Form Vols. 2 17-222 (1 996) pp. 1883- 1890.

Y. Sugimara, J. Meyer, M.Y. He, H. Bart-Smith, J. Grenestedt and A.G. Evans, On

the Mechanical Performance of Closed Ce12 Al AlIoy Foam, htemet address

J.C. Elliott, US Patent 275 1 289 (1956)

H.A. Kuchek, US patent 398 1 720 (1976)

J.K. Gibson, US Patent 3055 763 (1962)

References 101

1. i 1 Jpn. Ind.Tech. Bull. 8 (1980) 29

1.12 L.A. Cohen, W.A. Power and D.A. Fabel, Master. Eng. 67 (1 986) 44

1.13 J.P. Drolet, Int. Powder Met. Powder Tech. 13 (1 977) 222

1.14 F.V. Lenel, Powder Metallurgy Principles and Application, Metal Powder Industries

Federation, London, 1 980

1.15 1. M. Fedorchenko, Sov. Powder Metall. Met. Ceram. 18 625 (1 979)

1.16 J. W. Patten, US Patent 4099 967 (1 978)

1.1 7 0. Prakash, H. Sang and J.D. Embury, Structure and Properties of &Sic Foam,

AJcan R&D Centre.

1.18 L.J. Gibson, Alurninurn Foam: Structure and Properties, hm>:/idas-

~ww.liarvai.d.edu~usrs~facuIt~~Anthonv EvansTechnicaI articles/Article3.htinl

1.19 J.L. Grenestedt, J. Mech. Phys. Solids 46,29-50(I 998)

1.20 A.E. Sirnone and L. J. Gibson, Acta Mater. 46, #6,2139

1.2 1 A.E. Simone and L. J. Gibson, Acta Mater. 46, #9,3 1 09

1.22 Y. Sugimara, J. Meyer, M.Y. He, H. Bart-Smith, J. Grenestedt, On the mechanical

performance of clcised ceIl al dloy foams, http://das-

w~w.harvard.ed~~usrs;tacul~~AntIiony Evans.Technical article~Article2.html

1.23 R.J. Arsenault and R. M. Fisher: Scr. Medl., 1983, 17,67-7 1.

1.24 R.J. Arsenault and N. Shi: Mater. Scr. Eng., 1986, 8 1, 175- 187.

References 102

1.25 2. Wang and R. J. Bang: Metall. Trans. A, 1991,22A 1585-1 593

1.26 Z. Wang, T. Chen, and D. J. Lloyd: Metall. Trans. A 1993,24A, 197-2-7.

1.27 T. H. Yip and 2. Wang: Materials Science and Technology, Feb. 1997 vol. 13.

C h a m 2

2.1 Standmd Test Methuds for Semi-Flexible Cellular Urethanes for Autumotive and

Similar Energv Absorption Applicafiom, ASTM Deignation: D5308-92,289-30 1

2.2 J Lloyd, International Matends Reviews, 1994 vol. 39 No. l

2.3 Metal Handbook, 9" Edition, Volume 2.

2.4 L.D. Kemy, dcan htemationd Limited, 945 Princess Street, Kingston, Ontario,

Canada.

References 1 03

INFORMATION TO - University of Toronto T-Space Response of Sic@) ReinfOrced Al Based Foam Material...

Documents

Transcript of INFORMATION TO - University of Toronto T-Space Response of Sic@) ReinfOrced Al Based Foam Material...