 Open Access
 Total Downloads : 1612
 Authors : Prof. Yogananda. A, Mr. R. Vijayakumar
 Paper ID : IJERTV2IS80324
 Volume & Issue : Volume 02, Issue 08 (August 2013)
 Published (First Online): 19082013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Strength Prediction Of Composite Laminate
Prof. Yogananda. A 1, Mr. R. Vijayakumar 2
Assistant Professor, Department of Mechanical Engineering, East West Institute of Technology, Bangalore.
Research Scholar, VTU RRC, Bangalore & Assistant Professor, Aeronautical Department, Adhiyamaan College of Engineering, Hosur.
Abstract
The use of composites in modern structures is steadily increased. The use of these materials was encountered in first place in the aerospace applications. In order to predict failure load, requires information about stresses and strains in a structure. In the present investigation, the stress analyses of CFRP composite laminates with and without cutouts have been carried out by using both analytical and finite element approaches. In analytical approach, a matlab code has been developed for a flat panel using Classical Laminated Plate Theory (CLPT) and different composite failure theories. MSC.NASTRAN finite element analysis code is used for carrying out finite element analysis. Comparison of stress and strain values obtained from both analytical and finite element methods shows that they are in good agreement for flat panel. Failure load of the flat composite laminate (without cutout) is determined using four different failure criteria such as maximum stress, maximum strain, TsaiHill and TsaiWu criteria. The predicted values are compared with experimental results. It is found that the most appropriate theory is TsaiWu failure criterion, since the predicted value based on this theory is very closure to experimental failure loads. The results are compared with experimental failure loads available in the literature. The comparison shows that they are in very good agreement. TsaiWu failure criterion best predicts the failure load of a composite laminate with and without cutouts.
Key words: Composite laminate, CFRP, Static Analysis of laminate, Analytical calculation, Numerical calculation

Introduction
Composite materials occupy an important place in every important field such as aerospace, defence, automobiles, civil infrastructure, biomaterials as well as sports and leisure. These materials originally developed for the use in aerospace applications have now become a part of daily life. The scope of application of composites being unlimited, these materials will dominate the materials field for a long period in the years to come.
Fibre Reinforced Polymer (FRP) composites are extensively used for primary structural components such as wing, empennage and fuselage; and sub structures such as wing ribs and intermediate spars in new generation aircraft as they give rise to high stiffness and strength to weight ratio. In this present investigation the failure load predictions of composites are extremely important in order to ascertain the flight safety during its service periods. The stress analysis is a part of failure prediction process.
Composite panels of size 35mmÃ—100mmÃ—2.4 mm, under uniform static tensile loading with and without cutouts are considered for study. Cutouts considered in this study are respectively of circular and elliptical shape. The panel consists of 16 layers of carbon fiber and epoxy matrix, each layer has 0.15mm thickness with a stacking sequence of [45/45/0/45/0/45/0/90]s. Stress analyses of those panels will be carried out and failure loads will be predicted using failure theories. The results will be correlated with experimentally obtained failure loads.

Literature
Improvement in flight performance is one of the most important criteria in the design of aerospace structures. Weight reduction measures, combined with compliance to strength, stiffness and stability requirements are important.
Y.X. Zhang and C.H. Yang [2] presented a review of the recent development of the finite element analysis for laminated composite plates. The first ply failure analysis and the failure were presented clearly.
T.Y Kam and F.M Lai [3] studied the Experimental and theoretical methods for the first ply failure strength of laminated composite plates under different loading conditions.
D. Bruno, G. Spadea and R. Zinno [5] adopts the firstply failure criterion by application of a polynomial function and the finite element procedure.
M Yasar Kaltake [8] investigated the tensile and compression stress concentration and failure
criteria for anisotropic composite plates with circular cut outs.
X W Xu and H C. Man [12] presented a strength prediction technique for the composite plate with elliptical holes.

Stress Analysis of Composite Laminate
An engineering problem can be solved by Analytical, Numerical & Experimental method.
3.1 Nomenclature Used in Laminates
Firstly the coordinate system must be defined through the thickness, length and width of the laminate for the purpose of analysis.
Composite Laminate Properties, Composite laminate is made up of 16 layers of CFRP T300/914C, lamina of thickness 0.15mm following stacking sequence [+45/ 45/0/+45/0/45/0/90]S. The properties are obtained from the literature [16] is tabulated in the table 1.
Material
Engineering constants for lamina and laminate
E1
(MPa)
E2
(MPa)
E3
(MPa)
G12
(MPa)
G23
(MPa)
G31
(MPa)
12
23
21
Lamina[16]
130
10
10
5.0
3.27
5.0
0.35
0.5
0.027
Table 1 Material Constants for Lamina and Laminate
The Matlab codes are developed using Classical Lamination Plate Theory and local stressstrains are determined.

Finite Element Analysis of Composite Laminate
In the present work MSC NASTRAN is used for carrying out the stress analysis of composite laminate. The finite element model i.e. finite element mesh, boundary conditions and material properties is generated using preprocessor PATRAN. The postprocessing is done in PATRAN. Finite element mesh for 560 numbers of
elements has been shown in Figure. 1. The mesh details have been tabulated in Table 2.
Finite Element Meshes
Element types
Number of Elements
No. of nodes
Mesh1
Quad4
40
55
Mesh2
Quad4
140
168
Mesh3
Quad4
225
260
Mesh4
Quad4
396
442
Mesh5
Quad4
560
615
Mesh6
Quad4
900
969
Table 2 Convergence Study Mesh Details for flat panel
Ply orient ation
1 (MPa)
o 2
(MPa)
12 (MPa)
1
2
12
+45
199.8
20.2
37.3
0.001
0.001
0.003
45
199.8
20.2
37.3
0.001
0.001
0.003
0
677.3
4.32
0.00
0.005
0.002
0
90
277.6
44.7
0.00
0.002
0.005
0
Figure 1 Finite Element Model of the Flat Panel

Results and Discussion

Stress Analysis of a Flat Panel
Tabulation of Analytical Results
Global strains for all laminas are found to be same because midplane curvature terms are zero. Since only extension force is and not moment.
The laminate is the combination of +45,45, 0 and
90 degree orientation laminas, values of same laminas are tabulated.
Global stresses are calculated by using global strains and stiffness matrix of each lamina. These values are shown in Table 3.
Ply orientation
x(MPa)
y(MPa)
xy(MPa)
+45
147.4358
72.6528
89.8321
45
147.4358
72.6528
89.8321
0
677.3916
4.3241
0
90
44.7486
277.6388
0
Table 3 Global Stresses in Flat Panel by Analytical Method
The global stresses i.e. Stresses in laminate coordinate system is transformed to the principal material coordinate system. These values are tabulated in Table 4.
Table 4 Local StressStrains in Flat Panel by Analytical

Mesh details of Flat panel
The finite element model with boundary condition is shown in Figure 1. Local coordinate is created with x axis along length, yaxis along width and zaxis along the thickness of laminate. All laminas are oriented with respect to the xaxis i.e. 00 lamina along xaxis. Uniformly distributed load of 800N/mm is applied at the top edge
The mesh is converged and the stress values are varied based on number of elements, finally where the stress value is constant, that mesh is considered for further analysis and noted in below table 5.
Sl NO
Mesh details
Mesh
1
Element type
CQuad 4
2
No. of elements
560
3
No. nodes
615
Table 5 Converged Mesh Details for Flat Panel
Tabulation of FEA Results
Ply orient ation
1 (MPa)
o 2
(MPa)
12 (MPa)
1
2
12
+45
205.42
20.36
36.68
0.0015
0.0015
– 0.0036
45
205.42
20.36
36.68
0.0015
0.0015
0.0036
0
674.3
4.78
0
0.0051
– 0.0021
0
90
– 263.45
45.50
0
0.0021
0.0051
0
Table 6 Local StressStrain in Flat Panel by FEA

Stress Analysis of Panel with Circular Hole Composite panel of dimensions 352.4 mm with a circular hole of 3mm diameter is modelled using MSC.PATRAN. The bottom edge is constrained with Ux, Uy, Uz, Rx, Ry, and Rz values zeros. Uniformly

distributed load of 550N/mm is applied at the top edge and details of mesh are shown in Table 7.
Sl NO 
Mesh details 
Mesh 
1 
Element type 
Quad 4 
2 
No. of elements 
2016 
3 
No. nodes 
2100 
Table 7 Mesh Details for Flat Panel with Circular Hole
The mesh refinement around hole is performed by taking 1/10th of the element length of mesh of flat panel (same as element sizes located far from hole). Figure 2 shows the finite element model with boundary conditions for panel with circular hole.
Figure 2 Finite Element Model of Panel with Circular Hole
The Average Local StressStrains values in Panel with Circular Hole for Different Lamina Orientations are shown in below Table 8.
Ply orient ation 
1 (MPa) 
o 2 (MPa) 
12 (MPa) 
1 
2 
12 
+45 
137.62 
13.92 
26.35 
0.0010 
0.0010 
0.00264 
45 
137.62 
13.92 
26.35 
0.0010 
0.0010 
0.002635 
0 
474.14 
3.37 
0 
0.0036 
0.001 
0 
90 
198.90 
31.21 
0 
0.001 
0.0036 
0 
Table 8 The average local stress and strain values for panel with circular hole
The below figure 3 shows the average stress variations across laminate thickness along fiber direction and perpendicular to fiber direction. The average value has been obtained by taking the average value of all respective stresses developed in the elements.
Figure 3 Stress variations along Thickness of Panel with circular hole

Comparison of Analytical and FEA Results for the Flat Panel
The below tables gives the comparison of analytical and FEA results for flat panel.
Ply Orientation
1 (MPa)
%
Error
Analytical
FEA
+45
199.88
205.42
2.698
45
199.88
205.42
2.698
0
677.39
674.29
0.4579
90
277.63
– 263.45
5.11
Table 9 Comparison of Principal Fiber Direction Stresses for Flat Panel
Ply Orientation
1 (MPa)
% Error
Analytical
FEA
+45
20.21
20.36
0.710913
45
20.21
20.36
0.710913
0
4.32
4.79
9.679373
90
44.75
45.50
1.654325
Table 10 Comparison of Stresses Perpendicular to Fiber Direction for Flat Panel
Ply orientation
12(MPa)
% Error
Analytical
FEA
+45
37.39
– 36.69
1.92363
45
37.39
36.69
1.92363
0
0
0
0
90
0
0
0
Table 11 Comparison of Shear Stress for Flat Panel
Ply orientation
1
% Error
Analytical
FEA
+45
0.0015
0.00153
1.960784
45
0.0015
0.00153
1.960784
0
0.0052
0.005199
0.01923
90
0.0023
0.00214
7.47664
Table 12 Comparison of Principal Fiber Direction Strain for Flat Panel
Ply orientation
2
% Error
Analytical
FEA
+45
0.0015
0.00153
1.960784
45
0.0015
0.00153
1.960784
0
0.0023
0.00214
6.9565
90
0.0052
0.005199
0.01923
Table 13 Comparison of in Plane Strain for Flat Panel
Ply orientation
12
% Error
Analytical
FEA
+45
0.0037
– 0.00367
0.81744
45
0.0037
0.00367
0.81744
0
0
0
0
90
0
0
0
Table 14 Comparison of shear strain for Flat Panel
The percentage of error is very much less for the comparison of FEA v/s Analytical, so the comparison graph is almost same. Comparison of stress and strain values obtained by analytical and finite element
methods are in good agreement for flat panel. Local stresses and strains developed along fiber direction is maximum in 00 lamina and that of the 900 lamina is minimum for all the three panels (Flat, with circular and elliptical cutouts). Local stress and strain developed perpendicular to fiber direction is maximum in 900 lamina and that of 00 lamina is minimum. The shear stress and strain in 00 and 900 lamina is zero and
+45 and 450 laminas is maximum. The stress analysis results are used for strength prediction of different
laminates.

Strength Prediction of Composite Laminate
Failure criteria for composite materials are significantly more complex than yield criteria for metals because composite materials can be strongly anisotropic and tend to fail in a number of different modes depending on their loading state.
First Analytical method is used to predict the strength of panel Using Maximum Stress, Maximum Strain, TsaiHill and TsaiWu with Hoffmans coefficient and compared with Experimental data. Most suitable failure theory is selected and used for Finite Element Analysis of panel with and without cutout.

Strength Prediction of Flat Panel by Analytical Method
Stress values obtained in chapter 4 for flat panel are used in different failure theories and Failure Index (FI) and strength ratio (SR) is determined. The values are tabulated in Table 15.
Lamina orientation
Max. stress Theory
Max. strain Theory
Tsai Hill Theory
TsaiWu Theory
FI
SR
FI
SR
FI
SR
FI
SR
45
0.5753
1.738
0.3707
2.6971
0.6112
1.2791
0.7534
1.3272
45
0.5753
1.738
0.3707
2.6971
0.6112
1.2791
0.7534
1.3272
0
0.5644
1.772
0.5657
1.7676
0.3218
1.7626
0.211
4.731
90
1.1187
0.894
1.3056
0.7659
1.341
0.8635
1.308
0.7245
Table 15 FI and SR for Flat Panel from Analytical Method
From the above values it is observe that 900 lamina as got minimum strength ratio compare to +45,45and 00 lamina. So we can conclude that 900 lamina will fail first under axial tensile load.
Now neglect the 900 lamina and following the same procedure to calculate the local stress strain and tabulated in Table 16. It shows that 900 lamina will not play any role in caring load.
Lamina orientation
o 1
(MPa)
o 2
(MPa)
12
(MPa)
1
2
12
+45
116
11.7
48.7
8.62E04
8.62E04
4.87E03
45
116
11.7
48.7
8.62E04
8.62E04
4.87E03
0
739
20.2
0
5.74E03
4.01E03
0
90
–
–
–
–
–
–
Table 16 Local StressStrains for Flat Panel after First Ply Failure by Analytical Method
Further using the above Local StressStrains, Failure index and Strength ratio is calculated. Table 19 shows the Failure index and strength ratio from different failure theories after first ply failure from analytical method. From the Table 17 it is observe that+45 and – 450 lamina as got minimum strength ratio compare to 00 lamina. So we can conclude that +45 and 450 laminas will fail leaving only 00 Lamina.
Now neglect the +45 and 450 laminas and follow the same procedure to calculate the stress strain values after calculating the stress strain values, it shows that 900 lamina and 45/450 lamina will not play any role in carrying load. FI & SR for Second ply failure for flat panel also predicted.
Lamina orientation
Max. stress Theory
Max. strain Theory
Tsai Hill Theory
TsaiWu Theory
FI
SR
FI
SR
FI
SR
FI
SR
45
0.7518
1.33
0.2154
4.6424
0.6570
1.2337
0.8
1.25
45
0.7518
1.33
0.2154
4.6424
0.6570
1.2337
0.8
1.25
0
0.6155
1.625
0.6214
1.6092
0.4006
1.5799
.0181
9.5
90
–
–
–
–
–
–
–
–
Table 17 FI and R after First Ply Failure for Flat Panel by Analytical Method
The strength ratio obtained from different failure theory is multiplied with corresponding applied load gives the
Failure load and is tabulated in Table 18.
Failure load KN
Max. stress Theory
Max. strain Theory
Tsai Hill Theory
TsaiWu Theory
First ply
25
21.44
24.179
21.392
Second ply
45.5
45.05
34.54
34.6584
Last ply
37.8
37.8
37.8
54.8716
Table 18 : Failure Load for Flat Panel by Analytical Method

Strength Prediction of flat Panel by FEA
From analytical method, most suitable failure theory is found i.e. TsaiWu theory with Hoffmans coefficient which predicts the failure load closure to experimental data. So in Finite element analysis only TsaiWu criterion is used to predict the strength. In order to get the failure index (FI) of lamina, average FI (sum of all elements FI/NO. of elements) is tabulated and shown in Table 19.This results are good agreement with analytical results shows in Table 15.Further for
calculation of FI same procedure is adopted for panel with cutout.
Lamina orientation
TsaiWu Theory
FI
SR
45
0.7691
1.3002
45
0.7691
1.3002
0
0.188
5.3186
90
1.317
0.7593
Table 19 Failure Index and Strength Ratio by FEA
Figure 3 FI Plot for Flat Panel +450 Lamina
Figure 4 FI Plot for Flat Panel 450 Lamina
Figure 5 FI Plot for Flat Panel 00 Lamina
Figure 6 FI Plot for Flat Panel 900 Lamina

FI and SR for Flat Panel after First Ply Failure by FEA
Lamina orientation
TsaiWu Theory
FI
SR
45
0.7887
1.2679
45
0.78887
1.2679
0
0.00463
215.9
90
–
–
Table 20 Failure Index and Strength Ratio by FEA

FI and SR for Flat Panel after Second Ply Failure by FEA
Lamina orientation
TsaiWu Theory
FI
SR
45
–
–
45
–
–
0
0.5448
1.84
90
–
–
Table 21 Failure Index and Strength Ratio by FEA

Failure Load for Flat Panel by FEA
Flat Panel
Failure load (KN)
First ply
21.26
Second ply
35.5
Last ply
51.394
Table 22 Failure Load for Flat Panel by FEA


Strength Prediction of Panel with Circular Hole by FEA
TsaiWu theory predicted failure load is closely match with the experimental data for the flat panel. Therefore for further analysis only TsaiWu with Hoffmans coefficient failure theory is used. Table 23 shows the failure index and strength ratio for panel with circular hole before any lamina fails.
Lamina orientation
TsaiWu
FI
SR
45
0.7854
1.27
45
0.7854
1.27
0
0.0763
13.1
90
0.8549
1.17
Table 23 FI and SR for Panel with Circular Hole by FEA
Figure 7 FI Plot for Panel with Circular Hole +450 Lamina
Figure 8 FI Plot for Panel with Circular Hole 450 Lamina
Figure 9 FI Plot for Panel with Circular Hole 00 Lamina
Figure 10 FI Plot for Panel with Circular Hole 900 Lamina

FI and SR for Panel with Circular Hole after First Ply Failure by FEA
Lamina orientation
TsaiWu
FI
SR
45
0.7936
1.25
45
0.7936
1.25
0
0.0975322
10.25
90
–
–
Table 24 FI and SR for Panel with Circular Hole after First Ply Failure by FEA

FI and SR for Panel with Circular Hole after Second Ply Failure by FEA
Lamina orientation
TsaiWu
FI
SR
45
–
–
45
–
–
0
0.70319
1.422
90
–
–
Table 25 FI and SR for Panel with Circular Hole after Second Ply Failure by FEA

Failure Load of a Panel with circular hole by FEA

Flat Panel 
Failure load (KN) 
First ply 
20.1 
Second ply 
24.0625 
Last ply 
27.37 
Table 26 Failure Load for Flat Panel by FEA
The strength ratio obtained from first ply, second ply and last ply failure is multiplied with the applied load gives the corresponding failure load and tabulated in Table 26.

Validation Study
Analytical and finite element method results are validated by experimental method. The experimental data is shown in Table 27 for flat panel and panel with circular hole. The universal test machines are used for testing CFC panels.
Specimen number
Failure Load for
Flat panel(KN)
Failure Load for FP with circular hole(KN)
1
56.98
28.5
2
54.93
29.66
3
50.45
28.72
4
58.50
–
Average
55.22
28.97
Table 27 Experimental Failure Load for Panel and Panel with Circular Hole
Last ply Failure load (KN)
Percentage error between Analytical and FEA
Percentage error between Analytical and Experimental method
Percentage error between FEA and Experimental method
Flat panel
4.37
0.6338
4.96
FP with circular hole
–
–
5.52
Table 28 Comparison of Failure Loads between Analytical, FEA and Experimental Method
Comparison of failure loads between analytical, finite element method and experimental method istabulated in Table 28 in terms of percentage error. Results show good agreement with each other. Allowable stress stains are calculated for each case and tabulated in Table 29.
Flat Panel
Panel with circular Hole
allow (MPa)
allow 103
allow (MPa
)
allow 103
First ply failure
253.1
3.947
239.2
3.795
Second ply failure
422.6
7.172
275
5.031
Third ply failure
611.8
12.545
325.8
33
6.779
Table 29 Allowable StressStrain Curve for Flat Panel, with Circular Hole and Elliptical Hole by FEA

Conclusions and Scope of Future Work
Stress analysis of a flat composite panel is carried out using both analytical and finite element methods. Convergence study has been carried out for this composite panel considering 6 different meshes. Local stresses and strains developed along fiber direction is maximum in 00 lamina and that of the 900 lamina is minimum for both cases. Local stress and strain developed perpendicular to fiber direction is maximum in 900 lamina and that of 00 lamina is minimum. The shear stress and strain in 00 and 900 lamina is zero and
+45 and 450 laminas is maximum. The stress analysis
results are used for strength prediction of different laminates. Failure load for flat composite panel has been predicted by both analytical method and finite element methods. These values are in good agreement. The failure loads are obtained using different failure theories such as maximum stress, maximum strain, TsaiHill and TsaiWu failure criteria. On comparison of these values with experimental failure loads, it is observed that failure load obtained using TsaiWu failure criterion is in very good agreement with experimental failure load. This observation concludes that TsaiWu failure criterion is appropriate criterion for predicting the failure of laminated composite panels. For further analysis of composite panel with a circular cutout in order to predict failure load, TsaiWu criterion is used. This failure criterion predicts the failure loads of composite panels with circular cutout very closely with experimental failure loads. It is concluded that TsaiWu failure criterion predicts the failure loads of composite panels with and without cut outs more accurately.

Scope of Future Work


In the present work composite laminate is modeled using 2D quad4 elements. 3D finite element analysis may be carried out to obtain more realistic results. The curved composite panels have not been covered in the present study. The same can be taken up in future investigation. The nonlinearity aspect has not been considered in the present study. The same may be considered in future.

References
2395.
[4]. Y.V. Satish Kumar and Anand Srivastava, First ply failure analysis of Laminated stiffened plates Composite Structures 60 (2003) 307315. [5]. D. Bruno, G. Spadea and R. Zinno, Firstply failure of laminated composite plates. Theoretical and applied fracture mechanics 19 (1993) 2948. [6]. Y.S.N. Reddy & J. N. Reddy, Linear and non linear failure analysis of composite laminates with transverse shear. Composites Science and technology 44 (1992) 227225.[7]. M.H.R. Jen and C.H. Lee Strength and life in thermoplastic composite laminates under static and fatigue loads. Part I: Experimental, International Journal of Fatigue. 20 (1998) 605
615.
[8]. M. Yasar Kaltaker, Stress concentrations and failure criteria in anisotropic plates with circular holes subjected to tension or compression Computers and structures 61 (1996) 6778. [9]. S. Tolson and N. Zabaras, Finite element analysis of progressive failure in laminated composite plates. Computers and structures 38 (1991) 361376. [10]. J.N. Reddy and A. K. Pandey, A firstply failure Analysis of composite laminates. Computers and structure 25 (1987) 371393. [11]. T.Y. Kam & T.B. Jan, Firstply failure analysis of laminated composite plates based on the layerwise linear displacement theory. Composite structures 32 (1995) 583591. [12]. X W. Xu and H.C. Man, Strength prediction of composite laminates with multiple elliptical holes. International journal of solids and structures 37 (2000) 28872900. [13]. WWW.Google search.org/ composite material. [14]. Robert. M. Jones, Mechanics of Composite Materials, Second Edition 1998 [15]. Autar. K. Kaw, Mechanics of composite Materials Second Edition Published in 2006 by CRC Press Taylor & Francis