 Open Access
 Total Downloads : 299
 Authors : Fazal Mohammed, Md Nasir Ali, S A Quadri
 Paper ID : IJERTV3IS090835
 Volume & Issue : Volume 03, Issue 09 (September 2014)
 Published (First Online): 29092014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Fracture Analysis of FRP Composites Subjected To Static and Dynamic Loading
Fazal Mohammed1, MD Nasir Ali2, S.A.Quadri 3
1M.Tech Student, Dept. of PG studies, VTU Regional office Gulbarga, Karnataka
2 Asst. Professor, Dept. of Mechanical Engineering, KBN College of engineering, Gulbarga, Karnataka
3 Asst. Professor, Dept. of Mechanical Engineering, KBN College of engineering, Gulbarga, Karnataka
Abstract The objective of this paper is to investigate the Stress Intensity Factor (SIF) for benchmark problems for static and dynamic loading in composite plates having center, edge. Further the analysis is extended to CT specimen, plate with 3point bend, vnotch. In the static analysis SIFs are found for an isotropic material using singular and jintegral approach and it is inferred that the deviation is minimal. For the orthotropic material SIF is found out for the above specimens with Carbon /Epoxy, R Glass /epoxy, S2 glass fabric/epoxy material properties. The Transient Dynamic analysis on the above specimens is carried out. Full method is employed to perform loading and the Jintegral approach is used to find the SIFs. The detail analysis using FEA is carried out for calculating SIF for the above specimens.
Keywords Crack tip, Jintegral, Stress Intensity Factor (SIF), Singularity, longitudinal and transverse modulus

INTRODUCTION
The fundamental goal in production and application of composite materials is to achieve performance from the composite that is not available from the separate constituents or from other materials. The need for high performance to weight ratio structure coming from the most advanced engineering fields is the main driver of the increasing usage of composite materials for crucial application. Recent developments in industries such as aerospace industry require lightweight and stiff materials fit the bill perfectly. The materials such as fibrereinforced plastics are widely being used as a replacement for steel in many industries.
Unlike conventional isotropic materials of steel and concrete there are no readily available design charts and guidelines to help the structural engineer when it comes to working with composites. Analytical solutions for cracked plates are very limited.
Among the available methods for calculating fracture parameters, the interaction energy integral method has emerged as a useful technique for the extraction of mixed mode stress intensity factors. The contour integrals where derived directly from the Jintegral by considering an additive composition of the existing fields with a judicious choice of known auxiliary fields. For the purpose of post processing finite element solutions, the contour integrals
were typically recast as equivalent domain integrals over a finite region surrounding the crack tip [1].
The work of B.K.Thakkar and P.C.Pandey [2] reviews the progressive failure analysis of fiberreinforced polymer composites. According to the work, various modes of failure of FRP laminae are fiber micro cracking, fiber kinking, fiber matrix debonding and matrix cracking. Matrix cracking: if the state of stress results in a pre dominant tensile stress in the direction perpendicular to the fibers, the matrix may separate out from the surface of the fibers and create a void. These voids nucleate to create a crack running parallel to the fibers. Matrix cracking affects the transfer of loads between fiber and matrix. Delamination is a mode of structural failure, which can be said to be material failure at laminate level. Delamination initiates a separation of layers in a localized manner and further propagation to peeling off of one ply from another. A continuum damage model describes mathematically the nucleation and evolution of a localized material failure zone
The need for testing such specimens is often dictated by the characteristic dimensions of the end product. A new methodology which combines experimentally determined loads and fracture time, together with a numerical model of the specimen is presented in paper [3]. Calculations are kept to a minimum by virtue of the linearity of the problem. The evolution of the stress intensity factor (SIF) is obtained by convolving the applied load with the calculated specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The numerical model is first tested by comparing numerical and analytical solutions of the impactloaded beam. One point impact experiments were carried out on of commercial tungsten base heavy alloy specimens.
Aim of this paper is to provide the structural engineer with data regarding SIF and variation of stress at the crack tip using Finite Element Analysis. FEA addressing plate problem fall under two categoriesone involving singularity formulations and other involving paths independent integrals approach [4].
ANSYS allows us to model orthotropic materials with specialize elements called Layered Elements. After building a model with a layered element structural analysis can be
carried out. Steel and glass polymer are taken as an orthotropic materials in our present study.

ELEMENT DESCRIPTION USED IN ANALYSIS

PLANE822D, 8node structural solid: It provides more accurate results for mixed (quadrilateraltriangular) meshes and can tolerate irregular shapes without as much loss of accuracy. The 8node elements id defined by eight nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a plane element or as an axisymmetry element. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.
Figure 1: PLANE82 Geometry

SHELL99Linear layered structural shell:
This is an 8node, 3D shell element can be used for layered applications of a structural shell model. It is designed to model thin to moderately thick plate and shell structures with asidetothickness ratio of roughly 10 or more . it allows up to 250 layers. The element has six degrees of freedom at each node; translations in the nodal x,y and z directions and rotations about the nodal x,y, and zaxes.
Figure 2: SHELL99 Geometry
LN= Layer number NL= Total number of layers


FRACTURE ANALYSIS OF CRACKS USING FEA
For case studyI, Plane 82 element is used for modelling of plate under plane stress conditions as per given dimensions. For case study II, SHELL 99 element is used varying the number of layers. The element near crack tip were meshed with crack tip elements by shifting mid side node to 1/4th distance. The meshed models are solved by applying tensile load and symmetric boundary conditions. Then the J integrals are completed.
Material properties
For isotropic plate E=48.3 GPa, =0.3. For orthotropic plates:
Table 1: Orthotropic Plates
Properties
Rglass
Sglass
Carbon/epoxy
Ex
48GPa
22.925GPa
70 GPa
Ey
12.4 GPa
22.925GPa
25 GPa
Ez
12.4 GPa
12.4 GPa
25 GPa
xy
0.32
0.12
0.32
yz
0.28
0.2
0.25
zx
0.28
0.2
0.25
Gxy
<>6.6 GPa 4.7 GPa
15 GPa
Gyz
4.14 GPa
4.2 GPa
12 GPa
Gzx
4.14 GPa
4.2 GPa
15 GPa
Density
2 gm/cm3
1.8gm/cm3
2 gm/cm3

CALCULATION OF FRACTURE PARAMETERS
For finding SIF first define a crack tip and crack path around the tip. The first node on the path should be the cracktip node. For a halfcrack model, two additional nodes are required, both along the crack face. For a fullcrack model, where both crack faces are included, four additional nodes are requires: two along one crack face and two along the other path along crack face.
Figure 3: path along the crack face
JIntegral is one of the most widely accepted parameters for elasticplastic fracture mechanics. The JIntegral is defined as follows:
Where W is the strain energy density, T is the kinematic energy density, represents the stresses, u is the displacement vector, and is the contour over which the integration is carried out. For a crack in a linear elastic material, the JIntegral represents the energyrelease rate

RESULTS & DISCUSSIONS Case1: Isotrophic Material
Static analysis:
Table 2: SIFs for isotropic plate under static loading
Table 4: SIFS for different layers by varying a/b ratios of Sglass material
Approach
J Integral
Singular
SIF
`26.29
37.528
Layers
a/b ratio
SIF, Nmm
0.2
0.4
0.6
0.8
2
7.0892
12.8333
20.1301
30.8745
4
4.8577
9.6751
14.5123
22.2153
6
5.12
10.1272
15.4309
23.4259
8
4.8577
9.6751
14.5123
22.2153
Case2 composite material: Static analysis:
SIF, Nmm3/2
Layers
a/b ratio
SIF , Nmm
0.2
0.4
0.6
0.8
2
4.4728
9.0672
13.6758
22.1776
4
4.4728
9.0672
13.6758
22.1776
6
4.4730
9.0675
13.6764
22.1785
8
4.4728
9.0672
13.6758
22.1776
25
20
15
10
5
0
0 5 10
No of layers
a/b ratio=0.2
a/b ratio=0.4
a/b ratio=0.6
a/b ratio=0.8
Evaluation of stress intensity factor (SIF) in composite plate with centre line crack.
Table 3: SIFS for different layers by varying a/b ratios of Rglass material
40
SIF, Nmm3/2
a/b
Figure 5: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table 4 it is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release is high as the crack grows. However the variation of SIF with respect to number of layers is almost constant because the transverse modulus
30
20
10
0
0 5 10
No of layers
ratio=0.2
a/b ratio=0.4
a/b ratio=0.6
a/b ratio=0.8
effect is neglected.
Table 5: SIFS for different layers by varying a/b ratios of carbon /epoxy material
Layers
a/b ratio
SIF , Nmm
0.2
0.4
0.6
0.8
2
6.6811
11.4237
17.5825
26.7372
4
5.38
9.4828
14.0852
22.1491
6
5.5616
9.8354
14.7751
23.016
8
5.38
9.4828
14.0852
22.1491
Figure 4: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table 3 it is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation; material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same and for plate with 2 layers SIF is very high as compared to all other layers. Due to symmetry lay up and when the crack is parallel to fibre direction the SIF is more and when it is in transverse direction the SIF is less.
Figure 6: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table 5 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation; material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same and for plate with 2 layers SIF is very high as compared to all other layers. Due to symmetry lay up and when the crack is parallel to fiber direction the SIF is more and when it is in transverse direction the SIF is less.
The SIF is high in Rglass as compared to Sglass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez , Hence its SIF is less than Rglass.
Evaluation of stress intensity factor (SIF) in composite plate with edge crack
Table 6: SIFS for different layers by varying a/b ratios of Rglass material
Layers a/b ratio
SIF , Nmm
0.2
0.4
0.6
0.8
2
12.9616
27.7766
62.9939
206.5355
4
10.3766
22.7027
53.4329
176.0265
6
10.8965
24.4534
56.889
187.9538
8
10.3766
22.7027
53.4329
176.0265
Figure 7: Variation of Stress Intensity Factor (SIF) with increasing number
From table 6 It is observed that by increasing the (a/b) ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same due to the symmetry lay up of even distribution. The SIF is higher at less number of layers and gradually decreases while increasing the number of layers symmetrically in odd numbers.
Table 7: SIFS for different layers by varying a/b ratios of Sglass material
Layers
a/b ratio
SIF , Nmm
0.2
0.4
0.6
0.8
/td>
2
9.7147
21.2567
50.6355
166.2591
4
9.7147
21.2567
50.6355
166.2591
6
9.7151
21.2576
50.6375
166.2658
8
9.7147
21.2567
50.6355
166.2591
Figure 8: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table7 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is almost constant because the transverse modulus effect is neglected.
Layers
a/b ratio
SIF , Nmm
0.2
0.4
0.6
0.8
2
13.1761
30.6753
66.0074
219.79
4
10.8237
23.5611
52.7597
174.364
6
11.2033
24.895
55.3584
183.4079
8
10.8237
23.5611
52.7597
174.364
Table 8: SIFS for different layers by varying a/b ratios of carbon /epoxy material
of layers
Figure 9: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table8 It is observed that by increasing the a/b ratio, the SIF is increasing. This is due to the crack propagation, material separation and energy release rate is high as the crack grows. However the variation of SIF with respect to number of layers is not linear. It is observed that the SIF for the plate with 4 and 8 layers is same due to the symmetry lay up of even distribution. The SIF is higher at less number of layers and gradually decreases while increasing the number of layers symmetrically in odd numbers.
From table9 it is observed that the variation of SIF with respect to number of layers is not linear for the plates with Rglass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the SGlass plate is almost minimal.
The SIF is high in Rglass as compared to Sglass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez ,hence its SIF is less than Rglass.
S.NO
SIF , Nmm
Layers
RGlass
SGlass
Carbon
1
2
14.3631
4.8929
12.6748
2
4
3.5936
4.8929
6.2458
3
6
5.8188
4.8893
7.663
4
8
3.5936
4.8929
6.2458
Evaluation of stress intensity factor (SIF) in CT specimen Table 10: SIF for different layers and different materials
SIF, Nmm3/2
The SIF is high in Rglass as compared to Sglass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez, hence its SIF is less than Rglass.
Evaluation of stress intensity factor (SIF) in composite plate with 3point bend.
Table 9: SIF for different layers and different materials
20
15
10
5
0
0 5 10
No of layers
RGlass SGlass Carbon
S.NO
SIF , Nmm
Layers
RGlass
SGlass
Carbon
1
2
196.7223
94.8953
153.4209
2
4
183.8553
94.8953
154.4226
3
6
170.1841
94.8983
143.1733
4
8
183.8553
94.8953
154.4226
Figure 10: Variation of Stress Intensity Factor (SIF) with increasing number of layers
Figure 11: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table10 it is observed that the variation of SIF with respect to number of layers is not linear for the plates with Rglass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the SGlass UD/Epoxy plate is almost minimal.
The SIF is high in Rglass as compared to Sglass and Carbon composite due to longitudinal and transverse modulus influence. In carbon composite, Ey=Ez ,hence its SIF is less than Rglass.
Evaluation of stress intensity factor (SIF) in composite plate with Vnotch
Table 11: SIF for different layers and different materials
S.NO
SIF , Nmm
Layers
RGlass
SGlass
Carbon
1
2
15.5864
8.7347
6.9341
2
4
16.5136
8.7347
4.8469
3
6
17.5849
8.7350
4.2871
4
8
16.5136
8.7347
4.8469
SIF, Nmm3/2
20
15

CONCLUSIONS
Singular finite element approach is used for calculating SIFs for plate made up of isotropic material and JIntegral approach is used for calculating SIF for both the plates made up of isotropic and orthotropic materials. Stress induced in the composite material plates are found to be much lesser than isotropic material plates due to fibre reinforcements at different angles. Further the crack growth is obstructed by the fibre orientation. The SIF in Rglass plates is high as compared to Sglass fabric/epoxy and Carbon /epoxy is due to longitudinal and transverse modulus influence. The SIF in Sglass is almost constant because the transverse modulus effect is being neglected. The SIF for all specimens subjected to dynamic loading is found to be nearly double when compared to static loading.
10
5
0
0 5 10
No of layers

lass SGlass Carbon
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Figure 12: Variation of Stress Intensity Factor (SIF) with increasing number of layers
From table11 It is observed that the variation of SIF with respect to number of layers is not linear for the plates with Rglass and Carbon /Epoxy materials. It is also observed that the SIF for these plates with 4 and 8 layers is same. The variation of SIF with respect to the number of layers for the SGlass plate is almost minimal.
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