www.ijaser.com 2012 by the authors Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Finite element modelling of infinitely wide Angle-ply FRP laminates B.Srinivasa Rao, Praveen Kumar, Balakrishna Murthy* Department of Mechanical Engineering, V. R. Siddhartha Engineering College, Vijayawada-520007, India. doi: 10.6088/ijaser.0020101048 Abstract: The objective of the present work is to determine the required width of the finite element model to represent an infinitely wide laminate for given load, crack length and boundary conditions for estimating its fracture behaviour. This exercise is useful for the prediction of fracture behaviour of angle-ply laminates having infinite width by developing finite element models of finite width as obtained from the present work without loss of generality. The three-dimensional model considered in the present work is a four-layered angle-ply FRP laminates of symmetric (Ө/-Ө/-Ө/Ө) and anti-symmetric (Ө/-Ө/Ө/-Ө) fibre orientations with an edge crack at its centre interface. The parameter Strain Energy Release Rate (SERR) is determined using Virtual Crack Closure Technique (VCCT) in association with finite element method. Keywords: Composites, FRP, Angle-ply, Strain energy release rate, VCCT, Delamination. 1. Introduction The use of composite materials has increased considerably in the fabrication of structural elements. They substitute the traditional materials due to their excellent stiffness to weight and strength to weight ratios. They found several applications in automobile, aeronautical and aerospace industries. Inter laminar delamination is a common and dangerous mode of failure in composite structures. This may develop during manufacturing or during operational life of the laminate. Delamination may grow due to opening mode (mode I), shear modes (mode II and mode III) and mixed-mode (mode I and mode II). Inter laminar tensile stresses give rise to mode I fracture while inter laminar shear stresses result in mode II fractures. The spontaneous growth of a delamination while the applied load is constant is called unstable growth. If the load has to be increased to promote further delamination, the growth is said to be stable growth. Interlaminar delamination results in the loss of stiffness and strength, which may lead to safety and reliability problems. Undetected subsurface delamination can lead to catastrophic failures without any external signs. The conventional design criteria are based on tensile strength, yield strength and buckling stress. These criteria are adequate for many engineering structures, but they are insufficient when the structures possess some cracks. Fracture mechanics compensates the inadequacies of conventional design concepts. Thus a better understanding of the fracture mechanics involved in interface delamination will enable to develop more effective damage tolerant and damage resistant structures. The delamination fracture of continuous carbon fibre/epoxy multidirectional-laminates under Mode I, Mode II and Mixed-Mode I/II loading conditions was characterized by Choi et al. (1999). The main type of laminate which was studied was a multidirectional fibre composite prepared from 24 ply lay-ups of (-45 /0 /+45 ) 2S (+45 /0 /-45 ) 2S. The initial delamination was located at the +45 /-45 mid-plane of the specimen. The results revealed that the values for the interlaminar fracture energy at crack initiation for the (-45 /0 /+45 ) 2S (+45 /0 /-45 ) 2S multidirectional laminates were always significantly greater than that for the corresponding unidirectional (i.e., 0 /0 ) laminates. The total strain energy release *Corresponding author (e-mail: vbkmpublications@yahoo.com) Received on May 16, 2012; Accepted on June 20, 2012; Published on July. 1, 2012 475
rate G T associated with delamination that initiate from a crack in a symmetric composite laminate is calculated by J. Zhang et al. (1994) using the potential energy approach in elastic fracture mechanics and a two-dimensional finite element analysis. Two laminate stacking sequences, [0 2 /90 4 ]s and [+25/90 4 ]s, are examined with a crack in the 90 plies and delamination growing uniformly from the matrix crack tip in the [0/90] and [25/90] interfaces respectively. The total strain energy release rate G T increases with increasing delamination length, but eventually approaches a constant asymptotic value, which is close to the G T result calculated from the analytical model was found. A study was conducted by Chengye et al. (2006) to investigate possibility of predicting delamination development in fibre-reinforced polymer specimens that have single off-axis insert layer and are subjected to 3-point bending. Finite Element method is used to facilitate the analysis of the energy release rate (G). Two analytical approaches are proposed to predict delamination size development in the beam test specimens. The prediction is then compared with experimental results. An experimental study on the mode I interlaminar fracture of carbon/epoxy multidirectional specimens with 0 /θ delaminating interfaces was done by Pereira and Morais (2004); A 3-D finite element analysis was first performed to determine the suitability of the double cantilever beam (DCB) specimen. An experimental study on the mode II interlaminar fracture of carbon/epoxy multidirectional laminates was done by Pereira et al. (2004). A 3-D finite element analysis was first performed to define appropriate stacking sequences for end-notched flexure (ENF) specimens with starter delamination on θ/ θ and 0 /θ interfaces. The interlaminar fracture behaviour of composite laminates under in-plane loading conditions has been investigated by (R. Rikards 2000). The delamination initiation at the interface of broken and continuous plies in case of [0/90/±Ө/0]s GR/E and GL/E laminates with broken central plies was studied by Chakraborty and B. Pradhan (1999) A full 3-D FE analysis has been performed with each layer of the laminate modelled as homogenous and orthotropic. Chakraborty and Pradhan (2002) studied the delamination growth behaviour of FRP composites having two embedded elliptical delaminations at the interface under uniaxial and transverse loading. A full 3-D FE analysis was performed to calculate the interlaminar stresses at the interface responsible for delamination. The concept of fracture mechanics was used to calculate the components of strain energy release rates at the interface. Mode I and Mode II delamination fractures in glass, carbon and kelvar fabric reinforced composites are investigated by Marom et al. (1988); The effects of the angle of reinforcement and of the fibre volume content are examined. The basic fracture mechanisms involved in matrix-dominated failures in fibrous composite laminates, specifically, interlaminar fracture in the form of free-edge ply delamination was investigated by A. S. D. Wang and F. W. Crossman (1980). A finite element technique incorporating the Virtual Crack-Closure procedure is developed to generate numerical results. Simultaneously, an experimental study is conducted using a series of graphite epoxy laminates in the form of (±25/90 n ) s, n = 1, 2, 3. Comparison is done between the analytical and experimental results. An experimental and analytical study was conducted by Ribicky et al. (1977) to examine the free edge delamination mode of failure in a [±30 /±30 /90 /90 ]s Boron/Epoxy laminate. Energy release rates were evaluated by a simple computational scheme that doesn t require special singular element or knowledge of the existence of a stress singularity in the solution. Jailai and Pizhong (2003) evaluated the shear-mode (Mode II) fracture toughness of wood-wood and wood-fibre reinforced plastic (FRP) bonded interfaces using unique linear tapered end-notched flexure (TENF) specimens. Delamination cracks originating from transverse cracking in two types of cross-ply laminates [90/0] s and [0/90] s are analysed for three types of loading: plane strain extension, plane strain bending and anti-plane shear by Kim (1993). The stability of crack growth and the effect of the relative ply thickness upon the crack growth stability are examined in terms of the energy release rate. Norbert Blanco V., (2004) has provided expressions for strain energy 476
release rate of structures subjected to individual and mixed mode fractures in his PhD Thesis. In the present Fracture analysis, the required width of the FE model to represent infinitely wide laminates is determined by using Virtual Crack Closure Technique (VCCT) in combination with three-dimensional Finite Element method. 2. Determining the width of laminate The geometric model considered for the present analysis has the dimensions of 100mm long, 10mm thick (each layer of thickness10/4=2.5mm) and its width is infinite. An edge crack of 15mm and a virtual crack of 0.11mm (Kranthi and Pranoy 2011); are considered. The required width of the finite element model to represent an infinitely wide laminate is determined by drawing a graph between strain energy release rates G and width b of laminates. Different models by varying width of laminates are created. The strain energy release rates for considered width are determined by varying the fibre angle from 15 0 to 90 0 for both symmetric and anti-symmetric fibre orientations. In this way strain energy release rates are calculated for different widths varying from 40mm to a width value beyond which the strain energy release rates remain constant in the graph drawn. 2.1 Finite Element Modelling For all the FE models created of different widths, the finite element mesh is generated using 8 node brick element SOLID 45 in (ANSYS Reference Manuals, 2012) software. This element is defined by 8 nodes having three degrees of freedom per node: translations in the nodal x, y and z directions. The element may have any spatial orientation. The element SOLID 45 has the capability to inherit orthotropic material properties and hence, best suited for analysing FRP composites. 2.2 Boundary and loading conditions The model is simply supported along the width of the laminates. Three different kinds of loadings, edge line loading of 1 N/mm in upward direction, centre line loading of 1 N/mm in downward direction and pressure loading of 1MPa are applied. Figures from 1 to 3 represent the models with different load conditions. Figure 1: Finite element model with edge line loading 477
Figure 2: Finite element model with centre line loading Figure 3: Finite element model with pressure loading 2.3 Material properties The following material properties of HTA/6376C carbon/epoxy prepreg composite are considered for the analysis. (Norbert Blanco V., 2004) i) Young s Modulus, E 1 = 120GPa, E 2 =10.5GPa, E 3 =10.5GPa ii) Poisson s Ratio, ν 12 = ν 13 = 0.3, ν 23 =0.51 iii) Rigidity Modulus, G 12 =G 13 =5.25GPa, G 23 =3.48GPa 3. Results and discussion The variation of strain energy release rates G with respect to width b for symmetric fibre orientation are depicted in figures 4 to 6 and for anti-symmetric fibre orientation are depicted in figures 7 to 9. From all the graphs it is shown that the required width of the laminates to represent an infinitely wide laminates is found to be 300mm for different loading conditions as well as for both symmetric and 478
anti-symmetric fibre orientations. The graphs for second and third load cases are only drawn for selected fibre angles (through an observation from edge line loading graph). The fibre angles corresponding to the curves, taking a large range of width to attain constant energy release rates are selected. Figure 4: Variation of G I with respect to width b for symmetric angle-ply laminates Figure 5: Variation of G II with respect to width b for symmetric angle-ply laminates 479
Figure 6: Variation of G II with respect to width b for symmetric angle-ply laminates Figure 7: Variation of G I with respect to width b for anti-symmetric angle-ply laminates 480
Figure 8: Variation of G II with respect to width b for anti-symmetric angle-ply laminates Figure 9: Variation of G II with respect to width b for anti-symmetric angle-ply laminates 4. Conclusion Under three different kinds of load conditions (i.e., edge line loading, centre line loading and pressure loading) for a crack length of 15mm and for simply supported boundary conditions, the required width of the laminates is found to be 300mm to represent an infinitely wide laminate for both symmetric and anti-symmetric fibre angle orientations. This analysis is useful in simplification of actual size of the laminate with finite model there by reducing the computational time and shows the way to develop simple finite element models to solve infinite plates of similar cases. 481
5. References 1. Choi, N. S., Kinloch, A. J., and Williams, J. G. 1999.Delamination fracture of multi-directional carbon/epoxy composites under Mode I, Mode II and Mixed-Mode Loading. Journal of Composite Materials, 33, 73-100. 2. Zhang, J., Soutis, C., and Fan, J. 1994. Strain Energy Release Rate associated with local delamination in cracked composite laminates. Journal of composite materials, 25(9), 851-862. 3. Chengye Fan., Ben Jar, P. Y., and Roger Cheng, J. J. 2006. Energy based analysis of delamination in fibre-reinforced polymers under 3-point bending.journal of composite materials, 66(13), 2143-2155. 4. Pereira, A. B., and de Morais, A. B. 2004. Mode I interlaminar fracture of carbon/epoxy multi-directional laminates.journal of composite materials, 64(13-14), 2261-2270. 5. Pereira, A. B., de Morais A. B., Marques, A. T., and de Castro, P. T. 2004. Mode II interlaminar fracture of carbon/epoxy multidirectional laminates.journal of composite materials, 64(10-11), 1653-1659. 6. Rikards, R. 2000. Interlaminar fracture behaviour of laminated composites. Journal of composites & structures, 76(1-3), 11-18. 7. Chakraborty, D., and Pradhan, B. 1999. Effect of ply thickness and fibre orientation on delamination initiation in broken ply composite laminates. Journal of reinforced plastics and composites, 18(8), 735-757. 8. Chakraborty, D., and Pradhan, B. 2002. Fracture behaviour of FRP composite laminates with two interacting embedded delaminations at the interface. Journal of reinforced plastics & composites, 19(13), 1004-1023. 9. Marom, G., Roman, I., Harel, H., Rosensaft, M., Kenig, S., and Moshonov, A. 1988. The strain energy release rate of delamination in fabric-reinforced composites. International Journal of Adhesion and Adhesives,8(2),85-91. 10. Wang, A. S. D., and Crossman, F. W. 1980.Initiation and growth of transverse cracks and edge delamination in composite laminates. Journal of composite materials, 14(1), 71-87. 11. Rybicki, E. F.,Schmueser, D. W., and Fox, J. 1977.An energy release rate approach for stable crack growth in free edge delamination problem. Journal of composite materials, 11(4), 470-487. 12. JailaiWang., and PizhongQiao. 2003. Fracture toughness of wood-wood and wood-frp bonded interfaces under Mode II loading.journal of composite materials, 37(10), 875-897. 13. Kim Yujun., andimseyoung. 1993. Delamination cracks originating from transverse cracking in cross-ply laminates under various loading. International journal of solids & structures, 30(16), 2143-2161. 14. Kranthi Chand, M., Pranoy, Y. 2011. Fracture behaviour of cross-ply laminates with interlaminar delamination. International journal of applied engineering research,6(20), 2373-2379. 15. ANSYS Reference Manuals, 2012. 16. Norbert Blanco V., 2004. Variable mixed mode delaminations in composite laminates under fatigue conditions; testing and analysis. Ph D thesis, Girona University. 482