New Literature Review - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8544/9/09... · 2015....
Transcript of New Literature Review - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8544/9/09... · 2015....
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Literature Review
2.1. Introduction
Literature review is made on the characterization of FMLs to know
the information on the basic characterization of Fiber Metal Laminated
composites. The characterization reported in the literature covers
behavior of the laminates under static, fatigue and impact loads and
shows the wide range of applications and the flexibility in design of
FMLs. The basic survey related to identification of the area and broad
definition of the problem is presented here and detailed discussion on
specific points is presented in subsequent chapters along with the
evolution of the solution. The reviewed papers herewith-presented in
order of the publishing year.
2.2. Review
An experimental study is conducted on a laminate consisting of
monolithic thin aluminum plates alternating with unidirectional
carbon/epoxy (Fiberite) prepeg tapes (Dov Sherman et al. [19]). Enhanced
strain energy dissipation caused by multiple fracture mechanisms led
the FML to exhibit pseudo ductile behavior. It is also observed that a
minimum volume fraction of the reinforcing layers is required to exhibit
this behavior. The mechanical behavior of the laminate is explored. The
influence of number of layers, volume fraction on transverse properties
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are also investigated. The loss of stiffness with increase of the
applied strain is estimated using a simple shear lag theory.
Static indentation and low and high velocity impact tests are
conducted on specimens with a circular clamped test area (Vlot [20]).
Monolithic Al 2024-T3 and 7075-T6, various grades of FMLs and
composites are tested. Fiber critical behavior is observed in ARALL and
CARE laminates, due to low strain to failure. It is observed that GLARE
laminates will show a fiber critical or aluminum critical failure mode
depending on the lay up of the laminate. The dent depth after impact on
FML is approximately equal to that of the monolithic aluminum alloy.
The results from impact tests also showed that the damage zone in the
FMLs is smaller than observed for fiber reinforced composite materials.
Statistical analysis, stress analysis and failure characteristics
analysis of two types of tension specimens (ARALL) are made in (Wu et
al. [21]). The specimen geometries considered are straight sided and dog
bone specimens. It was found that the tensile yield strength, tensile
modulus and tensile ultimate strength are independent of specimen type.
Results from both experimental and analytical studies are compared.
Analysis is made (Johnson et al. [22]) on a material system
consisting of thin sheets of titanium bonded together with a polymer
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composite prepeg consisting of a high temperature resin reinforced
with high or intermediate modulus fibers useful for aerospace
applications. It is observed to have beneficial performance for this FML,
the polymer composite layers should have a higher modulus than that of
titanium. More isotropic behavior is observed in HTCL than a
unidirectional composite and this behavior is attributed to transverse
property contribution of titanium layers. This work includes analytical
studies as well as experimental results. Many combinations of
constituents in various proportions were analytically studied by
predicting the complete tensile stress-strain curve up to failure. Effect of
fiber volume fraction, orientation, titanium percentage on stress strain
behavior is studied.
Features of spliced laminates are discussed in (Asundi et al. [6]).
Spliced concept is used to manufacture much wider panels (> 4mts) and
to retain the benefits of smaller panels of FMLs used in the construction.
The increased width capability can results in a significant reduction in
manufacturing cost. The author in his discussion concluded that spliced
laminates are promising candidates for fuselage and lower wing materials
for the next generation of very large civil transport aircraft and the ultra
high capacity aircraft for 600 to 800 passengers.
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Inelastic behavior and strength of fiber metal hybrid composite,
GLARE 2 is studied under static loading conditions in (Kawai et al. [23]).
The classical lamination plate theory is applied for describing the off-axis
inelastic behavior of GLARE 2 laminate. It has been shown that the
anisotropy for the tensile fracture strength of the GLARE 2 laminate can
be predicted using Tsai-Hill theory. A CLT based model, which takes into
account the transverse failure in the GFRP layer to cause an
instantaneous degradation of transverse and shear elastic module is
used to describe the characteristic deformation behavior of the GLARE 2
laminate. Influence of degradation methods on modeling of the GFRP
failure is investigated by adopting three different methods (i) no-ply
fracture method, (ii) complete-ply fracture method and (iii) incomplete ply
fracture method. Stress-strain diagrams till the ultimate failure of the
laminate are drawn and compared with experimental results. The no-ply
fracture method predicted much larger tangent moduli and higher
strengths than those of the experimental results after yielding of the
aluminum layers. The complete-ply fracture method overestimated the
stiffness reduction and reported less strengths. The incomplete-ply
fracture method that retains the stiffness in the fiber direction after
GFRP layers have satisfied the Tsai–Hill criterion, yielded good
approximations when compared with experimental results. The off-axis
influence of young’s modulus and poisons ratios is also discussed.
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Numerical models for delamination in FMLs are discussed in
(Hashagen et al. [24]). Intensive experimental analyses have been carried
out to assess the possible application of new design methods that make
use of the layered structure of FMLs. To support the experimental
analyses, numerical models have been developed to describe
delamination in FMLs. To achieve this goal, a special continuum element
and corresponding interface elements are introduced. Loading functions
have been derived to account for delamination. Using this methodology
the impact of delamination on spliced FMLs has been studied
numerically and has been compared to experimental results.
Results from the investigations carried out on a material consisting
of carbon-epoxy prepreg and aluminum alloy layers are reported in
(Klement et al. [25]). Mechanical properties like tensile strength, tensile
modulus, shear strength, bending strength and modulus are determined.
The results of formability testing are described. It is observed under
fatigue loading the crack propagation rate is greatest immediately after
crack initiation and decreases with the number of loading cycles. The
material formability results showed that forming techniques can be used
to limited extent for manufacture of parts by using this material.
Analytical formulations to predict energy absorption and the
ballistic limit of fully clamped GLARE panels subjected to impact by a
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blunt cylinder were formulated (Fatt et al. [26]). The ballistic limit was
found through an iterative process such that the initial kinetic energy of
the projectile would equal the total energy dissipated by panel
deformation, delamination/debonding and fracture. The transient
deformation of the panel as shear waves propagate from the point of
impact was obtained from an equivalent mass–spring system, whereby
the inertia and stiffness depend on the shear wave speed and time. The
formulation results are within 13% margin of the results reported by
experimentation.
The tensile and fatigue properties of carbon fiber reinforced PEEK-
titanium FMLs are investigated in (Cortes et al. [27]). It has been
observed during the in-plane on-axis tensile tests on unidirectional un-
notched laminates, that their mechanical properties follow the
predictions offered by a simple law of mixtures approach. Tension-
tension fatigue tests on notched unidirectional FMLs has shown that
these laminates offer fatigue lives up to fifty times greater than those
preferred by a notched monolithic titanium alloy. The variation of
modulus, un-notched tensile strength and notched tensile strength with
volume fraction of composite is studied. The presence of small quantities
of titanium has shown a lot of improvement in the notched tensile
strength. It has also been shown that delamination is more widespread
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in FMLs based on thick composite layers than in laminates containing
thin composite layers.
The high velocity impact response of a range of novel aluminum
foam sandwich structures has been investigated (Reyes et al, [28]) using
a nitrogen gas gun. Tests were undertaken on sandwich structures based
on plain composite and FML skins. High velocity impact tests on the
sandwich structures resulted in a number of different failure modes.
Delamination and longitudinal splitting of the composite skins were
observed in the unidirectional glass fiber/polypropylene-based systems.
In contrast, the woven glass fiber/polypropylene-based sandwich
structures exhibited smaller amounts of delamination after high velocity
impact testing. In addition, the aluminum foam in both systems
exhibited a localized indentation failure followed by progressive collapse
at higher impact energies. The ballistic limit of all of the sandwich
structures was predicted using a simple analytical model. It has been
shown that the predictions of the model are in good agreement with the
experimental data.
Analytical modeling and numerical simulation of the nonlinear
deformation of FMLs, GLARE 4 and GLARE 5 are made in (Wu et al.
[16]). Non-linear tensile response and fracture behavior of these
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laminates under in-plane loading is investigated. Both an
analytical constitutive model based on a modified Classical Lamination
Theory, which incorporate the elasto-plastic behavior of the aluminum
alloy, and a numerical simulation based on finite element modeling are
used to predict the stress-strain response and deformation behavior of
GLARE laminates. Fracture modes are also discussed. The developed
model predictions deviate from experimental results at high stress levels.
Maximum strain criterion is used to decide the failure of GFRP layers. It
was opined by the author that further studies are necessary to predict
the progressive failure. The author also opined that the future models
should also focus on damage progression and degradation.
A study of the mechanical properties of steel/aluminum/GFRP
laminate is made in (Khalili et al. [29]). The presence of steel layers in
FML sample helped in increasing the energy absorption, stiffness and
displacement with respect to other FML samples. For some
configurations it is reported that the stiffness of the composite with steel
layer in bending shows an increase of 16 times and the displacement
under the point of loading shows an increase of nearly 4 times as
compared to the corresponding GFRP sample.
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A range of FMLs based on a lightweight magnesium alloy have
been manufactured and tested (Cortes et al. [17]). Two types of composite
reinforcement have been investigated, a woven fiber reinforced epoxy and
a unidirectional glass fiber reinforced polypropylene. Tests on both types
of laminates indicated that increasing the volume fraction of the
composite in the FML resulted in a significant increase in its tensile
strength. The effect of volume fraction of composite on Young’s Modulus
and on fatigue strength is also analyzed. Results from low velocity impact
tests are also presented.
A review on the development and properties of continuous
fiber/epoxy/aluminum hybrid composites for aircraft structures is made
in (Botelho et al. [11]). Behavior of FMLs under tensile, compressive and
shear loads are discussed. Environmental effects and damping behavior
are also studied to limited extent. It is highlighted that the moisture
absorption in FML composite is slower when compared with polymer
composites, even under relatively harsh conditions. This is due to the
barrier effect of metal layers.
The tensile properties of titanium based FMLs have been
investigated (Cortes et al. [14]) at quasi-static rate of strain. Initial
attention is focused on investigating the effect of variation of the fiber
orientation; on the tensile modulus and strength of a range of carbon
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fiber peek FMLs. Here as expected, increasing the off-set angle, resulted
a decrease in the tensile properties of the FML. Micro level nature of the
failure at on-axis and off-axis angles is discussed. The significance of
residual stress is estimated along off-axis loading angles. The results
showed that the residual stress plays a major role in estimating the
failure strength. Ignoring the residual stress in formulations leads to
increased strength predictions at off-axis angles. At the same time the
influence of residual stress shows a different behavior on FPF strengths.
The failure mechanisms in the hybrid laminates were investigated
through a series of cyclic tensile tests on a number of edge-polished
samples. An examination of the specimen edges indicated that failure in
laminates whose fibers were oriented at angles between 00 and 150
occurred as a result of fracture of individual carbon fibers. At offset
angles greater than 150, initial failure took the form of localized
debonding at the fiber–matrix interface. In addition to this debonding,
laminates with fiber angles between 150 and 450 exhibited delamination
between the composite plies. First Ply Failure as well as the tensile
strength of the FMLs was predicted using a number of simple failure
criteria. Here, it was shown that the onset of damage under tensile
loading conditions could be successfully predicted over a wide range of
off-set angles.
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The high velocity impact response of a range of polypropylene-
based FML structures has been investigated in (Abdulla et al. [30]). The
perforation resistances of the various laminates investigated here were
compared by determining the specific perforation energy of each system.
Here, the sandwich FMLs based on the low density PP/PP core out-
performed the multi-layer systems, offering specific perforation energies
roughly double that exhibited by a similar kevlar-based laminate. A
closer examination of the panels highlighted a number of failure
mechanisms such as ductile tearing, delamination and fiber failure in
the composite plies as well as permanent plastic deformation, thinning
and shear fracture in the metal layers. Finally, the perforation threshold
of all of the FML structures was predicted using the Reid–Wen
perforation model. Here, it was found that the predictions offered by this
simple model were in good agreement with the experimental data.
Experiments were conducted [Cantwell et al. [31]) to examine the
contact behavior of FMLs when subjected to localized explosive blast
loading. Experiments are conducted on samples of varying thickness and
material distribution. Plastic deformation, debonding, delamination, fiber
fracture and matrix cracking have all been identified as energy
absorption mechanisms. Widespread debonding is particularly evident
between layers. As the number layers in a laminate increases, no
significant improvement is noticed in blast impact performance. This
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suggests that debonding does not absorb a significant proportion of the
blast energy.
The aerospace industry is currently focusing on the development of
the next supersonic transportation aircraft, in which structures will be
subjected to relatively high temperatures for long periods of time. In this
regard, FMLs based on high-temperature thermoplastic composite
material properties are studied (Cortes et al. [32]). The author opined
that titanium (Ti)-FMLs based on poly-ether-ether-ketone (CF/PEEK) or
poly-ether-imide (GF/PEI) composites are the suitable candidates for
such applications. The low and high velocity impact properties of two
high temperature FMLs have been investigated. The results have also
shown that interlaminar and interfacial delaminations appear to be the
primary mechanisms for absorbing and dissipating energy during the
impact event in these laminates. A number of analytical studies have
also been undertaken to predict the mechanical properties of Ti-FMLs,
where it has been shown that the resulting predictions agree well with
the experimental data.
A simplified model to predict the tensile and shear stress – strain
behavior of fiber glass/ aluminum laminates is developed (Iaccarino et al.
[15]) and analyzed. Mechanical tests were carried out on a fiber glass/
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aluminum hybrid laminate, made of 0/90 S2 glass/epoxy lamina
and Al 2024 T3 sheets in order to find its tensile stress-tensile strain
curve. To theoretically predict the laminate response, Classical
Lamination Theory was modified to account for the inelastic behavior of
the aluminum, which was substituted by the equivalent material
governed by a simple constitutive law. Final failure conditions were
calculated by assuming the maximum strain criterion and Tsai-Hill
criterion for aluminum and fiberglass respectively. Theoretical
predictions are compared with experimental results. The author
substantiated the deviations by citing the complex failure mechanisms
leading to final failure. The need for the more sophisticated models than
proposed in this work is highlighted by the author to model the damage
development and to more accurate predictions of the final failure
strength.
The onset and propagation of interlaminar defects is one of the
main damage mechanisms in composite materials. This is even more the
case when considering layered materials comprising metallic layers
(typically aluminum) and FRP laminas. Propagation of delamination
mainly depends on the initial crack extension and its loading mode. The
work reported in (Marannano et al. [33]) presents some results of a
combined analytical–numerical–experimental study on the onset and
propagation mechanisms regarding interlaminar defects. Two cases have
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been analyzed in this regard, the first consisting of a glass-fiber
reinforced epoxy resin laminate, and the second consisting of a hybrid
laminate where a lamina of aluminum is layered between FRP laminas.
The tensile and fatigue properties of FMLs employing lightweight
self-reinforced polypropylene and glass fiber reinforced polypropylene
laminas have been studied and established in (Reyes et al. [34]). Initial
tensile testing results showed self-reinforced polypropylene based hybrid
materials exhibited a ductile type of behavior, where the ultimate tensile
strength and strain at fracture was mainly dominated by the aluminum
alloy. In contrast, the glass fiber reinforced polypropylene based systems
exhibited a more brittle behavior associated with the composite material.
The tensile properties of both systems were determined by the
mechanical properties of the constituent materials. Stress-strain
behavior of aluminum, FMLs are compared and fatigue testing results
along with the failure features are discussed.
Results from blast loading tests for clamped boundary conditions
are reported by (Langdon et al. [35]). The FMLs were constructed from
aluminum alloy, a polypropylene interlayer and co-mingled glass
fiber/polypropylene woven cloth. The spatial loading distribution is
approximated as uniform and was generated by detonating annuli of
explosive. Observations from blast experiments performed on panels with
different stacking configurations are reported and the response compared
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to similar locally blast loaded FML panels. Multiple debonding, plastic
deformation, internal buckling and metal tearing were all observed.
An initial evaluation of FMLs based on magnesium alloy is
presented in (Rene et al. [18]). Experiments are conducted to determine
various static properties and fatigue properties. These values are
evaluated for aircraft structural applications and advantages and
disadvantages are presented.
2.3. Review of literature for Degradation Models
The ultimate failure of the FRPs or FMLs is preceded by a sequence
of complex failures like longitudinal/transverse cracking, interface
debonding, failure of metal layers and fiber failure etc. Each failure will
reduce the stiffness parameters of the laminate to a certain extent. These
effects are to be built into the analytical model either by selecting an
existing stiffness degradation model or by developing a new one. The
improper selection/development of degradation model results in the
change of the final output of the analytical model considerably.
Degradation models reported in the recent literature and their features
are discussed below.
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A degradation model, employing different degradation factors is
proposed in (Ihirane et al. [36]) for FRPs. In case of fiber failure, the total
stiffness discount method is adopted whereas for matrix failures the
stiffness is reduced by three successive values i.e. 0%, 50% and 100%.
The numerical simulations carried out in this analysis shows significant
improvement than the previously published results.
Many Material Property/stiffness Degradation Methods (MPDM) are
compiled in (Tay et al. [37]) for FRPs. A very conservative version of the
progressive degradation is the ply discount method, (Chu et al.[38], Pal
et al. [39], Prusty et al. [40]), where by entire set of stiffness properties of
a ply is removed from consideration if the ply is deemed to have failed. A
comparison of the theoretical and experimental results shows that the
predicted failure occurs at a substantially lower load than the
experimentally failure load. It is generally observed that the ply discount
method underestimates laminate strength and stiffness because it does
not recognize that the damage is localized and that a failed ply may have
residual load carrying capacity. In order to use Tsai-Wu in progressive
failure modeling, some researchers regarded failure to be fiber dominated
if the fiber direction stress is the main contributor to the failure index
(Kuraishi et al. [41]). Otherwise failure is assumed matrix dominated.
The author (Tay et al. [37]) felt this is some what arbitrary. In some of
these models the Poisson’s ratios are not degraded and only Young’s
Modulus and Shear Modulus are modified for a failed lamina (Tan et al.
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[42, 43, 44]) as E11 = D1011E , E22 = D2
022E , G12 = D6
012G where E11, E22 and
G12 are the effective material properties of the damaged lamina and 011E ,
022E and 0
22G are the material properties of the undamaged lamina. But
the parametric studies have shown that the predicted values of ultimate
strength are very sensitive to the selected values of the internal state
variables D1, D2 and D6. So the values of D1, D2, and D6 are fixed based
on comparison made with experimental values on a base line laminate
( 45/90/0 )s. Employing constant degradation factors is popular
because of the simplicity and the easiness to adopt them into computer
models. The gradual stiffness reduction scheme (Reddy et al. [45])
proposing the reduction of stiffness properties to a minimum level at
which the failure criterion is no longer satisfied, is resulting good
approximations. This allows repeated failures of the same elements and
used with finite element techniques. The degraded elastic properties are
constant multiples of the elastic properties before current failure setup.
The values of coefficients of stiffness reduction used in this method are
adjusted between zero and one. More sophisticated material stiffness
degradation schemes have been formulated with continuum damage
mechanics (CDM). (Schuecker et al. [46]) CDM approaches are proposed
with second order damage tensors whose eigen-values represent the
density of distributed micro-cracks. The damage parameters are to be
calibrated from experiments in order to determine the damage evolution
laws.
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Many recognized failure theories; along with the degradation
models are compiled (Kaddour et al. [47], Soden et al. [48]) thru the
World Wide Failure Exercise. The wide variations in the prediction by
various theories can be attributed to different methods of modeling the
progressive failure process, the nonlinear behavior of matrix dominated
laminates (angle plies), the inclusion or exclusion of curing residual
stresses in the analysis, and the definition of ultimate laminate failure.
The ultimate failure is defined in at least three different ways: the
maximum load attained; the occurrence of first fiber failure; and the
occurrence of last fiber failure.
Now if the failure models available for FMLs are considered,
(Iaccarino et al. [15]) used the Tsai-Hill criterion theory as the fracture
criterion to identify the failure in GFRP. Whether fracture involves
matrix or fiber failure is decided on the basis of the relative amplitude of
the quadratic terms appearing in the fracture criterion. If matrix failure
occurs in a layer, its matrix dependent properties are zeroed. The
hypothesis of pseudo plasticity, implying that the broken lamina
continues to carry the portion of load shared at failure, is made. The
equivalent material approach based on volume change is used to bring
the plasticity of aluminum layers into the formulation. It is assumed that
final failure of the laminate is precipitated when at least one of the
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following phenomena occurs; (a) the aluminum sheets fail, according to
the maximum strain theory; (b) the reinforcing fibers in at least one of
the GFRP layers are broken, according to the Tsai-Hill strength criterion.
Maximum strain failure criterion was used by (Guocai et al. [16]) to
predict the failure load in this study, and fracture is expected to occur
when the strain in glass/epoxy layer reach the ultimate failure strain
because aluminum has a much higher ductility than the fiber/epoxy
composite layer. The aluminum layer was modeled as an elasto-plastic
orthotropic solid and the elasto-plastic behavior of aluminum alloy was
described by the flow theory of von-Mises type. The plastic potential
function introduced by (Chen et al. [49], Kenaga et al. [50]) is used by
the author to model the elasto plastic behavior of aluminum alloy.
Two degradation models were considered by (Cortes et al. [14]). The
first was applied to those FMLs with fiber orientation angles of 00 and
150 and assumes that after failure of the ply or groups of plies, the
properties change as follows; 012121 GE ; and 22 EE . For those
FMLs with fibers oriented between 300 and 900, the properties of the
failed ply or groups of plies are assumed to degrade as 012122 GE ;
and 11 EE . In addition it was assumed that once the stress in the metal
layer reached its ultimate stress, these plies yielded rather than failed.
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This procedure was not employed when the last remaining ply is of that
of the metal layer.
Prediction of the strength of a FML consisting of unidirectional
glass/epoxy layers and aluminum sheets is reported (Kawai et al. [23]) by
using an incomplete lamina failure mode. In this model, stiffness of
GFRP layers are altered to 11 EE , 012122 GE , after the GFRP layers
has failed according to a failure criterion. As a fracture criterion for the
GFRP layers, the Tsai-Hill theory is used. To model the elastic plastic
behavior of the aluminum different tangent modulus are used one in
elastic range and two in plastic range. The condition for final failure of
the laminate is not discussed.
(Hart Smith et al. [51,52]) opined matrix cracking under transverse
tension loads is a fracture mechanics problem, involving possible
interactions not only with other stresses in the same lamina, but
definitely with the stiffness of adjacent plies. He suggested using of some
factor in the analytical formulations to consider this.
(Sun et al. [53]) opined that although it has not been reported in
the literature the strength of the lamina in a laminate is dependent on
lamina thickness and on the constraints from adjacent layers. The
authors concluded that the constraining layers have some effect on the
effective stiffness of the failed lamina and that shall be considered in the
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formulation. (Rotem [54]) has expressed that even a partially failed
lamina has an effect on adjacent lamina because of some residual matrix
material along the fibers.
2.4. Summary
The literature survey shows a continuous development in the area
of FMLs with the introduction of new materials and also divergence in
the analytical models and degradation methods. There is extensive
characterization of FMLs that are designed in earlier days of FML design
like ARALL and GLARE. The characterization includes the estimation of
tensile strength, estimation of tensile strength variation with off-axis
angles, estimation of off-axis stiffness and the study of the nature of
failures. Many new FMLs using titanium layers, magnesium layers and
new variants of GLARE with cross-ply GFRP configurations are designed
during the last 5 years and the analytical characterization of some of
these FMLs is offering the problems as noted in (Iaccarino et al. [15],
Guocai et al. [16]). At the same time different authors are proposed
different characterization techniques for analytical predictions of the
strengths and behavior. In brief the literature survey shows (1) Classical
Lamination Theory is not sufficient to represent inelastic responses,
since its basic hypothesis involve linear elasticity (2) Bringing in the
elasticity and plasticity of metal sheets into the analytical formulation is
modified over the years. From using the limited number of elastic moduli
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to replacing the material stiffness with the stiffness of an equivalent
material at any desired state of strain. This is very much essential since
the behavior of metal layers plays a vital role in the failure at off-axis
angles. Most of the ultimate failures at off-axis depend on the failure
and properties of metal layers. (3) Different analytical formulations based
on the nature of composite and nature of the metal layers are employed
to design analytical models whose outputs are in tune with the
experimental results. But, as explained in the next sections these models
cannot be interchanged. (4) Recent investigations are focused on the
production and development of FMLs with cross-ply stacking of FRP
layers. The study of off-axis behavior is of recent attention and essential
to fully understand the behavior of the FML and evaluating their
usefulness both in-plane and transverse loadings. It is noticed that the
strength estimates of the analytical models developed by earlier workers
are deviating from experimental results (Guocai et al. [16], Iaccarino et
al.[15] ) (5) Magnesium based FMLs are relatively new and the light
weight of the magnesium layers is making it attractive for aircraft
components. Estimation of off-axis strength variation of magnesium
based FMLs is not attempted. (6) The literature survey also highlighted
the need for reliable analytical procedures and damage propagation
methodologies that will closely and sufficiently represent the complex
failure mechanism in FMLs. Predictive tools are very important in the
design to avoid the extensive and expensive tests. Developing an
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analytical model to estimate the off-axis strength of FMLs is a very
important step in this regard. (7) Literature survey has also established
that once the occurrence of certain type of failure is predicted by the
analytical models, the stiffness values of the laminas are reduced by
some constant terms called as degradation coefficients / stiffness
degradation factors. The values for these coefficients are selected such
that, they bring the analytical predictions closer to experimental values
[14, 36, 37, 48]. Once selected these values can be used for analytical
strength predictions of other laminates [42, 43, 44, 46]. This procedure is
used as basis for the analytical formulations in the present thesis.
2.5. Scope and objectives
From the above described status of the field, the scope and
objectives of the thesis are as follows:
(1) An analytical procedure is to be developed to estimate the
Ultimate Tensile Strength of FML. This procedure should be capable of
estimating the ultimate tensile strength of FML with cross-ply GFRP
laminas and aluminum layers. The predictions should be closer to the
experimental values than predicted by the existing procedures.
(2) The strength estimation of magnesium based FMLs is to be
made and its variation with off-axis loading, that is not reported earlier,
is to be investigated. To facilitate this an analytical procedure that is
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capable of predicting the strength values for different types of FMLs is to
be developed.
(3) The effect of increasing the thickness of magnesium layers on
tensile strength of the FML is to be investigated.
(4) CLT is quite popularly used together with failure criteria, and
property degradation schemes to calculate the strength of FRP composite
laminates. In such studies the sequence of failure events are tracked
when the composite is stressed and the degradation of failed lamina’s
properties are decremented progressively. In calculating the stresses and
strains of FMLs also, it is anticipated this procedure works with respect
to events related to FRP layers.
(5) CLT theory formulated with assumed linear elastic behavior of
laminate is not suitable for computing the ultimate strength, if behavior
of a lamina is the inelastic. The plastic behavior metal layers, is required
to be incorporated in modeling the progressive failure behavior of FMLs.
In the present work the plastic behavior of metal layers is accounted for
by defining an equivalent modulus from uni-axial stress-strain curve of
aluminum alloy and using it in the computation. This procedure was
suggested by Iaccarino et al. [15].
(6) This analysis is based on the macroscopic lamina properties of
metal and FRP lamina and the individual fiber and matrix properties do
not enter into the computation.
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(7) Material systems investigated in this study are laminates
produced by stacking metal layers with GFRP layers. The aluminum
layers are made from Al 2024 T3 and S2/FM94 GFRP laminas are used
as composite layers. The magnesium layers are made from AZ31BH24.
(8) All results reported in this work are related to uni-axial quasi-
static in-plane loading of FML. The orientation of the fiber is varied
systematically by different angles and the aluminum layers are treated
parallel to the loading direction.
(9) Manufacture of FMLs involve a step wherein very thin metal
sheet (foils) are sandwiched with glassy or semi-crystalline FRP in a
mold and heated to a hot curing temperature and subsequently cooled
under some compressive load on the composite laminate. Differential
thermal contraction of FRP and metal layers on cooling from this
temperature induce residual stresses in the thickness direction. The sign
and distribution of these residual stresses is such that the strength
properties are lowered. In this work the influence of residual stresses on
the off-axis strength of laminate is studied. The importance of
considering residual stresses in the accurate calculation of failure
strengths has been emphasized by Cortes et al. [14].
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