IRJET- Computation of Failure Index Strength of FML and FRB Composites

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 03 | Mar-2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 2313
COMPUTATION OF FAILURE INDEX STRENGTH OF FML AND FRB
COMPOSITES
M.RAJESH KANNAN1, DANISH AHMAD RESHI2, K.TAMILAN3, GIBREEL ABDULLAH HAMUD
MUQBEL4
1,3ASSISTANT PROFESSOR,DEPARTMENT OF MECHANICAL ENGINEERING,EXCEL COLLEGE OF
ENGINEERING AND TECHNOLOGY.KOMARPALAYAM
2,4 UG STUDENT,DEPARTMENT OF MECHANICAL ENGINEERING, EXCEL COLLEGE OF
ENGINEERING AND TECHNOLOGY.KOMARPALAYAM
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract –In this study computation of failure index of fml
and frb laminate at different orientations were prepared. To
examine the effect of fiber orientations, fml and frb at 0° and±
45° were consider. To study the failure index numerical
investigation using ANSYS static and linearanalysisreultsthat
FML at 0°possess high strength compared to ±45°, The
optimization is done by using ANSYS Composite Prep Post
(ACP).The strength behavior of FRP and FML under in-plane
load and out of-plane load is compared based on the results.
Results show that for in-plane load, due to the substituting of
metal alloy sheet for prepared layer, the strength behavior in
transverse direction is enhanced and FML has better
resistance to biaxial load. For out-of-plane point load, FML
offers strength performance superior to that of FRP and is
more stable for all the boundary conditions investigated.
Key Words: frb, fml, ansys, orientations
1. INTRODUCTION
A composite is a structural material that consists of two or
more combined constituents that are combined at a
macroscopic level and are not soluble in each other. One
constituent is called the reinforcing phase and the one in
which it is embedded is called the matrix. Composite
materials have successfully substituted the traditional
materials in several light weight and high strength
applications. The reasons why composites are selected for
such applications are mainly their high strength-to-weight
ratio, high tensile strength at elevated temperatures, high
creep resistance and high toughness. Typically, in a
composite, the reinforcing materials are strong with low
densities while the matrix is usually a ductile or tough
material. The strength of the composites depends primarily
on the amount, arrangement and type of fiber and particle
reinforcement in the resin.
1.1 FIBER REINFORCED POLYMER
Fiber-reinforced plastic (FRP) (also fiber-reinforced
polymer) is a composite material made of a polymer matrix
reinforced with fibers. The fibers are usually glass, carbon,
aramid, or basalt. Rarely, other fiberssuch aspaper or wood
or asbestos have been used.
The polymer is usually an epoxy, polyester , thermosetting
plastic, and phenol formaldehyde resins are still in use.
1.2FIBER METAL LAMINATE
Fiber Metal Laminate (FML) is a new class of composite
material for advanced aerospace/aeronautical structural
applications arisen in the recent years. It consists of thin
aluminum alloy sheets bonded together with fiber-
reinforced epoxy prepreg. These laminates demonstrate
advantagesover conventionalmonolithicaluminumalloysor
fiber reinforced plastic (FRP) composite materials, such as
excellent impact properties, fire and corrosion behaviorand
fatigue properties. In addition, FML retainsthe conventional
workshop practices of metals, namely, easy machining,
forming, and mechanical fastening abilities. These
advantagesfacilitate the use of FML forprimarystructuresin
aerospace industry.
1.3 SPECIAL CASES OF LAMINATES
Based on angle, material, and thickness of plies, the
symmetry or antisymmetry of a laminate may zerooutsome
elementsof the three stiffnessmatrices. Theseareimportant
to study because they may result in reducing or zeroing out
the coupling of forces and bending moments, normal and
shear forces, or bending and twisting moments
This not only simplifies the mechanical analysis of
composites, but also gives desired mechanical performance.
Symmetric Laminates:
A laminate is called symmetric if the material, angle, and
thickness of plies are the same above and below the
midplane. If it is subjected only to forces, it will have zero
midplane curvatures. Similarly, if it is subjected only to
moments, it will have zero midplane strains. It also prevents
a laminate from twisting due to thermal loads, such as
cooling down from processing temperatures and
temperature fluctuations during use such as in a space
shuttle, etc.

Cross-Ply Laminates:
A laminate is called a cross-ply laminate if only 00 and 900
plies were used to make a laminate. In these cases,
uncoupling occurs between the normal and shear forces, as
well as between the bending and twisting moments.
Angle Ply Laminates:
A laminate is called an angle ply laminate if it has pliesof the
same material and thickness and only oriented at +θ and –θ
directions. These angle ply laminates have higher shear
stiffness and shear strength properties than cross-ply
laminates.
Antisymmetric Laminates:
A laminate is called antisymmetric if the material and
thickness of the plies are the same above and below the
midplane, but the ply orientations at the same distance
above and below the midplane are negative of each other.
Balanced Laminate :
A laminate is balanced if layers at angles other than 0 and
90°occur only as plus and minuspairsof +θ and –θ. The plus
and minus pairs do not need to be adjacent to eachother,but
the thickness and material of the plus and minus pairs need
to be the same.
Quasi-Isotropic Laminates:
A laminate is called quasi-isotropic if itsextensionalstiffness
matrix[A] behaves like that of an isotropic material.
2. METHODLOGY
The aim of the project is to optimize the design of FMLbased
on strength. Here the FML is designed to meet specific
requirements by varying the fiber orientation. FML finds its
important application in aerospace industry. FML is
originally developed for their outstandingfatigueresistance;
other characteristics of fiber metal laminates include high
specific static properties, ease of manufacture, excellent
impact resistance, and good corrosion resistance. In aircraft
FML finds its application in cargo door and aircraft.
In this praperwork, the optimal strength design of FRP
laminates and FML under in-plane load and out-of-plane
load is to be conducted.
Step-1: By using Classical Lamination Theory (CLT), the
Stresses are predicted in FML Under In-planeTensileLoad.
Step-2: The failure indices are obtained through Tsai-Wu
criterion for FRP layers and Von-Mises criterion for metal
layers. The maximum and minimum failure index ofFRPand
FML has to be calculated respectively via altering the fiber
orientations of prepreg layers.
Step-3: ANSYS Composite PrepPost (ACP) an analysis
optimization tool in ANSYS is to be used for optimization.
Step-4: Based on the results, the strength behavior of FML
and FRP is to be discussed and compared andthesuperiority
of FML is to be demonstrated.
3. COMPUTATION OF FAILURE INDEX
This chapter presents the computation of failure index by
conventional classical lamination theory.
3.1 GENERALIZED HOOKE’S LAW
Generalized Hooke’slaw for orthotropic materialisgivenby,
{σ}=[Q]{ε} (1)
Assuming linear and elastic behaviour for a composite is
acceptable; however, assuming it to be isotropic is generally
unacceptable. Thus, the stress–strain relationships follow
Hooke’s law, but the constants relating stress and strain are
more in number. [Q] is called material stiffness matrix. For
plane stress conditions, we can write for each layer:
= (2)
The stiffness coefficients Qij are related to the engineering
constants as the follows.
= (3)
= (4)
= (5)
=G23; =G13; = G12
Where, E = Young’s Modulus, GPa
ν = Poisson’s ratio
G = Shear Modulus, GPa
Here, E1, E2, G12, G23, G13 and ν12 are engineering parameters
of the nth layer (lamina) in the laminate obtained from rule
of mixtures.

With respect to Figure 3.1 the [A], [B] and [D] are given by,
[A] = [ - ] (6)
[B] = [ - ] (7)
[D] = [ - ] (8)
Figure 3.1 Coordinate location of ply in Laminate
3.2 FAILURE STRENGTH PREDICTION
The Tsai-Wu criterion is used to predict the failure of
prepreg layer for it can account for interactions betweenthe
different stress components, and Von Mises criterionisused
for metal layer. The failure criterion of FML canbeexpressed
as follows:
max[f(θf), f(θm)] = 1,
where f(θf) denotes the FI of prepreg layer. A small value of
FI stands for a safer condition. In a uniaxial loadingsituation,
predicting failure obviously reduces itself to comparing the
internal stresses (σ) to the material’s strength (S) in the
loading direction. In this situation, the failure index (FI) is
defined as:
FI =
Due to the extremely FI =
3.2.1 Tsai–Wu Failure Theory
Failure index corresponding to Tsai-Wu criterion inprepreg
layer is,
F( ) = F11 σ1
2 + F22 σ2
2 + F33 σ3
2 + 2 F12 σ1 σ2 + 2 F23 σ2 σ3 +2
F13 σ1σ3 + F44 + F55 + F66 + F1 σ1+ F2 σ2+ F3
σ3
2 (9)
F11 = ; F22 = ; F33 =
F44 = ; F55 = ; F66 =
F1 = - ; F2 = - ; F3 = -
F12 = -0.5
F23 = -0.5
F13 = -0.5
XT and XC - tensile and compressive strengthsalong the fiber
direction,
YT and YC - tensile and compressive strengths along the
transverse direction,
R and T - out-of-plane shear strengths,
S - in-plane shear strength.
3.2.2 Von-Mises Failure criterion
Failure index corresponding to Von-Mises criterion in FML
is,
F( ) = (σx
2 + σy
2+ σz
2 – (σx σy+ σx σz+ σy σz) + 3(τ2
xy + τ2
xz
+ τ2
zy) (10)
where Y is the yield strength.
3.2.3 Calculation of Stresses in FML
The composite laminate considered for calculation is of
stacking sequence [Al/450/-450/Al/Al/450/-450/Al] under
uniaxial in-plane load Nx=10 N/mm, where ‘Al’ indicates
aluminium sheet, and 450 0r -450 represents the angle
between the fiber direction and the x-direction.Thematerial
of aluminium sheet is 2024-T3, E=76 GPa, ν=0.34.Eachlayer
is 0.125mm in thickness. The material of FRP layerisGLARE.
The material properties for FRP layer [19],
E1 = 135GPa
E2, E3 = 8GPa
G12, G13 = 4.5GPa
G23 = 3.97GPa
ν12, ν23, ν13 = 0.34
XT, XC = 1459,1400 (MPa)
YT, YC = 55,170 (MPa)
R= S= T = 90 (MPa)
Minor Poisson’s ratio,
Finding stiffness elements of FRP layer;

=
= = 135.924GPa
= = 2.738GPa
= = 8.054GPa
= G12 = 4.5GPa
For FRP the stiffness matrix is,
= GPa
The transformed stiffness matrix of FRP is,
45 = GPa
-45= GPa
The stiffness matrix of FML layer is, =
G = = 28.3582 GPa
The stiffness matrix of FML is,
= GPa
Finding [A], [B] and [D] matrices,
[A]= [ - ] (11)
= X 106 Pa-m
[B] = [ - ] (12)
[B] = 0 (Symmetric laminate)
[D]= [ - ] (13)
= Pa-m3
The laminate is subjected to an uniaxial in-plane load, Nx=
10N/mm
= N/m
The strain acting in the lamina is
, = [A-1] =
Stresses in the layers of FML,
In 450 Lamina, = 45
= x 10-3 GPa
In -450 Lamina, = -45
= x 10-3 GPa
In Al Lamina, =
= x 10-3 GPa

3.2.4 Calculation of Stresses in FRP:
The composite laminate considered for calculation is of
stacking sequence [00/450/-450/00/00/450/-450/00] under
uniaxial in-plane load Nx=10 N/mm, where 450 0r -450
represents the angle between the fiber direction and the x-
direction. Each layer is 0.125mm in thickness.
For FRP the stiffness matrix is,
0 = GPa
The transformed stiffness matrix of FRP is,
45= GPa
-45 = GPa
The [A], [B] and [D] matrices for the FRP laminate are,
= X 106 Pa-m
[B] = 0 (Symmetric laminate)
= Pa-m3
The laminate is subjected to an uniaxial in-plane load, Nx=
10N/mm
= N/m
The strain acting in the lamina is,
= [A-1] =
Stresses in the layers of FRP,
In 450 Lamina, = 45
= x 10-3 GPa
In -450 Lamina, = -45
= x 10-3 GPa
In 00 Lamina, =
= GPa
3.2.5 Calculation of failure index in FML layers
Failure index corresponding to Tsai-Wu criterion inprepreg
layer is,
F( ) = F11 σ1
2 + F22 σ2
2 + F33 σ3
2 + 2 F12 σ1 σ2 + 2 F23 σ2 σ3 +2
F13 σ1σ3 + F44 + F55 + F66 + F1 σ1+ F2 σ2+ F3
σ3
2 (14)
F11 = = 4.8957x10-4
F22 = = 1.0695x10-4
F33 = =
F44 = = 1.23456X10-4
F55 = = 1.23456X10-4
F66 = = 1.23456X10-4
F1 = - = -2.888X10-5
F2 = - = -0.0123

F12 = -0.5 = -3.618x 10-6
F23 = F13 = F3 = 0
Tthe failure index value of prepreg layer in FML is calculated
as,
F( ) = 0.0307
Failure index corresponding to Von- Misescriterioninmetal
layer is,
F( ) = (σx
2 + σy
2+ σz
2 – (σx σy+ σx σz+ σy σz) + 3(τ2
xy + τ2
xz
+ τ2
zy) (15)
σx = 14.533MPa
σY = 2.3477MPa
τxy = 0
Y = 381 MPa
The failure index value of metal layer in FML is calculatedas,
F( ) = 0.03546
3.2.6 Calculation of failure index in FRP layers
F11 = = 4.8957x10-4
F22 = = 1.0695x10-4
F33 = =
F44 = = 1.23456X10-4
F55 = = 1.23456X10-4
F66 = = 1.23456X10-4
F1 = - = -2.888X10-5
F2 = - = -0.0123
F3 = F23 = F13 = 0
The theoretically calculated failure index value of prepreg
layer corresponding to Tsai-Wu criterion in prepreg layer is
as follows.
In 00 laminate;
F( ) = 0.004744
In 450 laminate;
F( ) = 0.0045
In -450 laminate;
F( ) = 0.0045
3.2.7 Theoretical Results
In the laminate, stresses in each layer are predicted
theoretically by using Classical Lamination Theory. The
failure index values are calculated by using the suitable
failure criteria. Tsai-Wu criterion for prepreg layers and
Von- Mises criterion for metal layers.
In the FRP with a stacking sequence [00/450/-
450/00/00/450/-450/00] and subjected to uniaxial in-plane
load Nx=10 N/mm the predicted stress and failure index
values are listed in Table 1 Tsai-Wu criterion is used in the
calculation of failure index values in all the layers of FRP. In
00 prepreg lamina the failure index value for theappliedload
is -0.0047 and in 450 and -450 prepreg lamina the failure
index value is 0.0045.
Table 1: Theoretically calculated stress and failure
index values of FRP
Theoretically predicted
stress values
Theoretically
predicted failure
index value
00
Lamina
=
GPa
0.004744
450
Lamina
= x 10-3
GPa
0.0045
-450
Lamina = x
10-3 GPa
0.0045
In the FML with a stacking sequence [Al/450/-450/ Al / Al
/450/-450/ Al] and subjected to uniaxial in-planeloadNx=10
N/mm the predicted stress and failure index values are
listed in Table 2. For calculating failure index value in
prepreg layer Tsai-Wu criterion is used and for metal layers
Von- Misescriterion is used. In Aluminiumlaminathefailure

index value for the applied load is 0.03546 and in 450 and -
450 prepreg lamina the failure index value is 0.0307.
Table 2: Theoretically calculated stress and
failure index values of FML
Theoretically
predicted stress
values
Theoretically
predicted failure
index value
Al
Lamina
= x
10-3 GPa
0.03546
450
Lamina
= x
10-3 GPa
0.0307
-450
Lamina
= x
10-3 GPa
0.0307
4. RESULT AND DISSCUSSION
The predicted stresses obtained by Classical Lamination
Theory of FRP layer and Al layer in FML by ANSYS are listed
in Table 3. The predicted stresses obtained theoretically in
FRP and by ANSYS are listed in Table 4. Also comparison of
failure index values calculated theoretically and by ANSYS
listed in Table 3.
For in-plane uniaxial load, the optimum FI of FML and FRP
occurs when all the fiber angles are near 00 and the worst FI
occurs when the fiber angles are near 450. The fiber angles
are close to 00 or 450, but not exactly these values. This is
due to the characteristic of the evolution nature of the
optimization. The optimum FI of FRP is lower than FML, as
the longitudinal tensile strength of a lamina is greater than
the yielding strength of Al. The worst FI of FRP is greater
than FML, as the transverse tensile strength of a lamina is
much lower than the yielding strengthof Al. It demonstrates
that the substituting of aluminium alloy sheet for prepreg
layer enhances the strength behaviour of transverse
direction. The optimisations results of FML and FRP are
listed in Table 5
4.1 Comparison of predicted stress values in FML
For validation, the stress predicted by FEA in FML is
compared with theoretically predicted values and stress
values referred in the reference is shown in table 3
Table 3 Predicted stresses under uniaxial tensile load
in FML
Theoreticall
y predicted
stress values
(MPa)
FEA
predicte
d stress
values
(MPa)
Predicte
d stress
values in
the
reference
Journal
(MPa)
% of deviation
In
theoretica
l results
In
FEA
results
Al
Lamina σx = 14.553
σy = -2.347
τxy= 0
σx =
14.6948
σy = -
2.5661
τxy= 0
σx =
14.695
σy = -2.57
τxy= 0
0.966
8.6
0
0.001
3
0.155
0
450
Lamina
σx = 5.429
σy = 2.351
τxy= 3.388
σx =
5.305
σy =
2.566
τxy=
3.367
σx =
5.305
σy = 2.56
τxy= 3.37
-2.33
8.16
-0.29
0
0
-0.089
-450
Lamina σx = 5.429
σy = 2.351
τxy= 3.388
σx =
5.305
σy =
2.566
τxy= -3.36
σx =
5.305
σy = 2.56
τxy= -3.37
-2.33
8.16
-0.29
0
0
-0.089
The results obtained from ANSYS and CLT are compared to
Predicted values in the reference Journal for validation. It is
found that the results of this approach agree very closely
with the reference values and thus validated.
4.2 Comparison of predicted stress values in FRP
For validation, the stress predicted by FEA in FRP is
compared with theoretically predicted values as shown in
table 4
Table 4 Predicted stresses under uniaxial tensile load
in FRP
Theoretically
predicted stress
values (GPa)
FEA predicted stress
values (GPa)
00
Lamina = =
450
Lamina = x 10-3 = x 10-
3
-450
Lamina = x 10-3 = x 10-3
The results obtained from ANSYS and CLTarecompared.Itis
found that the results of this approach agree very closely
with each other. The results show that the FE analysis and
the CLT modelling can characterize the elastic or elastic
plastic properties of FRP at a good level

4.3 Comparison of predictedFailureindexvaluesin
FML
For validation, the failure index values predicted by FEA in
FML are compared with theoretically predictedfailureindex
values as shown in table 5. It is found that the results of this
theoretical approach agree very closely with the FEA results
and thus validated
Table 5 Predicted FI values under uniaxial tensile load
in FML
Theoretically
predicted
failure index
values
FEA predicted
failure index
values
Percentage
of deviation
(%)
Al
Lamina
0.03546 0.03857 -8.77
450
Lamina
0.0307 0.0299 2.6
-450
Lamina
0.0307 0.0299 2.6
4.4 Comparison of predictedFailureindexvaluesin
FRP
For validation, the failure index values predicted by FEA in
FRP are compared with theoretically predicted failure index
values as shown in table 5
Table 6 Predicted FI values under uniaxial tensile load
in FRP
Theoretically
predicted
failure index
values
FEA predicted
failure index
values
Percentage
of deviation
(%)
00
Lamina
0.004744 0.005142 -8.3
450
Lamina
0.0045 0.004495 0.11
-450
Lamina
0.0045 0.004495 0.11
It is found that the results of this theoretical approach agree
very closely with the FEA results and thus validated.
5. Conclusion
Using ANSYS, the induced stressesand failureindexvaluesof
the laminate under uniaxial tensile load were determined.
The comparison of results obtained using ANSYS and
theoretical results show good agreement. The results are
also compared with literature results for validation. Using
ANSYS Composite PrepPost (ACP) in the Workbench
simulation environment can be, it is believed that this
approach will provide designers a feasible and efficient
methodology with a great potential in developing the
tailoring applications in composite structural design and
other complex engineering designs.
Optimisation of composites done in ACP does not require
any other software’s to be integrated with it. ACP does not
require any coding such as used in MATLAB.
Nowadays, besides the existing products of FML, some new
types of FML consisting of other constituents are under
development. It is expected that the application of FML in
aerospace/aeronautical structureswill be furtherenhanced.
Optimisation of composites based on minimum number of
layers, minimum thickness, volume fraction, material and
price rate can also be done.
REFERENCES:
1. Andrei axinte, Liliana bejan1, Nicolaeţăranu(2013)
“Modern approaches on the optimization of
composite structures” Buletinul Institutului
politehnic din iasi November 27, 2013.
2. Akbulut, M. and Sonmez, F.O. (2008). Optimum
Design of Composite Laminates for Minimum
Thickness, Compos. Struct., 86(21_22):1974-1982.
3. Caprino, G., Spataro, G. and Del Luongo, S. (2004)
“Low-velocity Impact Behaviour of Fibreglass-
Aluminium Laminates, Composites” PartA,35:605-
616.
4. Chen, J.Q., Peng, W.J., Ge, R. and Wei, J.H. (2009).
Optimal Design of Composite Laminates for
Minimizing Delamination Stresses by Particle
Swarm Optimization Combined with FEM, Struct.
Eng. Mech., 31(4): 407-421.

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