New Literature Review - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/8544/9/09... · 2015. 12. 4. · Literature Review 2.1. Introduction Literature review is made on the

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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

39

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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