3D Nonlinear XFEM Simulation of Delamination in Unidirectional Composite Laminates: A Sensitivity Analysis of Modeling Parameters
Damoon Motamedi, Abbas S. Milani
DOI: 10.4236/ojcm.2013.34012   PDF    HTML     6,371 Downloads   11,208 Views   Citations

Abstract

This article presents a three-dimensional extended finite element (XFEM) approach for numerical simulation of delamination in unidirectional composites under fracture mode I. A cohesive zone model in front of the crack tip is used to include interface material nonlinearities. To avoid instability during simulations, a critical cohesive zone length is defined such that user-defined XFEM elements are only activated along the crack tip inside this zone. To demonstrate the accuracy of the new approach, XFEM results are compared to a set of benchmark experimental data from the literature as well as conventional FEM, mesh free, and interface element approaches. To evaluate the effect of modeling parameters, a set of sensitivity analyses have also been performed on the penalty stiffness factor, critical cohesive zone length, and mesh size. It has been discussed how the same model can be used for other fracture modes when both opening and contact mechanisms are active.

Share and Cite:

Motamedi, D. and Milani, A. (2013) 3D Nonlinear XFEM Simulation of Delamination in Unidirectional Composite Laminates: A Sensitivity Analysis of Modeling Parameters. Open Journal of Composite Materials, 3, 113-126. doi: 10.4236/ojcm.2013.34012.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Hillerborg, M. Modeer and P. E. Petersson, “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, Vol. 6, No. 3, 1976, pp. 773-781.
http://dx.doi.org/10.1016/0008-8846(76)90007-7
[2] X. P. Xu and A. Needleman, “Numerical Simulations of Fast Crack Growth in Brittle Solids,” Journal of the Mechanics and Physics of Solids, Vol. 42, No. 9, 1994, pp. 1397-1434.
http://dx.doi.org/10.1016/0022-5096(94)90003-5
[3] G. T. Camacho and M. Ortiz, “Computational Modelling of Impact Damage in Brittle Materials,” International Journal of Solids and Structures, Vol. 33, No. 20-22, 1996, pp. 2899-2938.
http://dx.doi.org/10.1016/0020-7683(95)00255-3
[4] P. P. Camanho, C. G. Dávila and M. F. De Moura, “Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials,” Journal of Composite Materials, Vol. 37, No. 16, 2003, pp. 1415-1424.
http://dx.doi.org/10.1177/0021998303034505
[5] B. R. K. Blackman, H. Hadavinia, A. J. Kinloch and J. G. Williams, “The Use of a Cohesive Zone Model to Study the Fracture of Fiber Composites and Adhesively-Bonded Joints,” International Journal of Fracture, Vol. 119, No. 1, 2003, pp. 25-46.
[6] Y. F. Gao and A. F. Bower, “A Simple Technique for Avoiding Convergence Problems in Finite Element Simulations of Crack Nucleation and Growth on Cohesive Interfaces,” Modelling and Simulation in Materials Science and Engineering, Vol. 12, No. 3, 2004, pp. 453-463.
http://dx.doi.org/10.1088/0965-0393/12/3/007
[7] T. M. J. Segurado and C. T. J. Llorca, “A New Three-Dimensional Interface Finite Element to Simulate Fracture in Composites,” International Journal of Solids and Structures, Vol. 41, No. 11-12, 2004, pp. 2977-2993.
http://dx.doi.org/10.1016/j.ijsolstr.2004.01.007
[8] Q. Yang and B. Cox, “Cohesive Models for Damage Evolution in Laminated Composites,” International Journal of Fracture, Vol. 133, No. 2, 2005, pp. 107-137.
http://dx.doi.org/10.1007/s10704-005-4729-6
[9] M. Nishikawa, T. Okabe and N. Takeda, “Numerical Simulation of Interlaminar Damage Propagation in CFRP CrossPly Laminates Under Transverse Loading,” International Journal of Solids and Structures, Vol. 44, No. 10, 2007, pp. 3101-3113.
http://dx.doi.org/10.1016/j.ijsolstr.2006.09.007
[10] A. Turon, C. G. Dávila, P. P. Camanho and J. Costa, “An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models,” Engineering Fracture Mechanics, Vol. 74, No. 10, 2007, pp. 1665-1682.
http://dx.doi.org/10.1016/j.engfracmech.2006.08.025
[11] T. Belytschko and T. Black, “Elastic Crack Growth in Finite Elements with Minimal Remeshing,” International Journal for Numerical Methods in Engineering, Vol. 45, No. 5, 1999, pp. 601-620.
http://dx.doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
[12] N. Moes, J. Dolbow and T. Belytschko, “A Finite Element Method for Crack Growth without Remeshing,” International Journal for Numerical Methods in Engineering, Vol. 46, No. 1, 1999, pp. 131-150.
http://dx.doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[13] J. M. Melenk and I. Babuska, “The Partition of Unity Finite Element Method: Basic Theory and Applications,” Computer Methods in Applied Mechanics and Engineering, Vol. 139, No. 1-4, 1996, pp. 289-314.
http://dx.doi.org/10.1016/S0045-7825(96)01087-0
[14] N. Sukumar, N. Moёs, B. Moran and T. Belytschko, “Extended Finite Element Method for Three-Dimensional Crack Modeling,” International Journal for Numerical Methods in Engineering, Vol. 48, No. 11, 2000, pp. 1549-1570. http://dx.doi.org/10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A
[15] J. Dolbow, N. Moёs and T. Belytschko, “An Extended Finite Element Method for Modeling Crack Growth with Frictional Contact,” Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 51-52, 2001, pp. 6825-6846. http://dx.doi.org/10.1016/S0045-7825(01)00260-2
[16] T. Belytschko, H. Chen, J. Xu and G. Zi, “Dynamic Crack Propagation Based on Loss of Hyperbolicity and a New Discontinuous Enrichment,” International Journal for Numerical Methods in Engineering, Vol. 58, No. 12, 2003, pp. 1873-1905. http://dx.doi.org/10.1002/nme.941
[17] T. Belytschko and H. Chen, “Singular Enrichment Finite Element Method for Elastodynamic Crack Propagation,” International Journal of Computational Methods, Vol. 1, No. 1, 2004, pp. 1-15.
http://dx.doi.org/10.1142/S0219876204000095
[18] P. M. A. Areias and T. Belytschko, “Analysis of Three-Dimensional Crack Initiation and Propagation Using the Extended Finite Element Method,” International Journal for Numerical Methods in Engineering, Vol. 63, No. 1, 2005, pp. 760-788. http://dx.doi.org/10.1002/nme.1305
[19] A. Asadpoure, S. Mohammadi and A. Vafai, “Crack Analysis in Orthotropic Media Using the Extended Finite Element Method,” Thin-Walled Structures, Vol. 44, No. 9, 2006, pp. 1031-1038.
http://dx.doi.org/10.1016/j.tws.2006.07.007
[20] D. Motamedi and S. Mohammadi, “Dynamic Analysis of Fixed Cracks in Composites by the Extended Finite Element Method,” Engineering Fracture Mechanics, Vol. 77, No. 17, 2010, pp. 3373-3393.
http://dx.doi.org/10.1016/j.engfracmech.2010.08.011
[21] D. Motamedi and S. Mohammadi, “Dynamic Crack Propagation Analysis of Orthotropic Media by the Extended Finite Element Method,” International Journal of Fracture, Vol. 161, No. 1, 2010, pp. 21-39.
http://dx.doi.org/10.1007/s10704-009-9423-7
[22] N. Moes and T. Belytschko, “Extended Finite Element Method for Cohesive Crack Growth,” Engineering Fracture Mechanics, Vol. 69, No. 1, 2002, pp. 813-833.
http://dx.doi.org/10.1016/S0013-7944(01)00128-X
[23] J. F. Unger, S. Eckardt and C. Konke, “Modelling of Co-Hesive Crack Growth in Concrete Structures with the Extended Finite Element Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 41-44, 2007, pp. 4087-4100.
http://dx.doi.org/10.1016/j.cma.2007.03.023
[24] E. Benvenuti, “A Regularized XFEM Framework for Embedded Cohesive Interfaces,” Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 1, 2008, pp. 4367-4378.
http://dx.doi.org/10.1016/j.cma.2008.05.012
[25] A. R. Khoei, S. O. R. Biabanaki and M. Anahid, “A Lagrangian Extended Finite Element Method in Modeling Large Plasticity Deformations and Contact Problems,” International Journal of Mechanical Sciences, Vol. 51, No. 5, 2009, pp. 384-401.
http://dx.doi.org/10.1016/j.ijmecsci.2009.03.012
[26] A. Needleman, “A Continuum Model for Void Nucleation by Inclusion Debonding,” Journal of Applied Mechanics, Vol. 54, No. 3, 1987, pp. 525-531.
http://dx.doi.org/10.1115/1.3173064
[27] H. Yuan, G. Lin and A. Cornec, “Applications of Cohesive Zone Model for Assessment of Ductile Fracture Processes,” Journal of Engineering Materials and Technology, Vol. 118, No. 1, 1996, pp. 192-200.
[28] P. Harper and S. R. Hallett, “Cohesive Zone Length in Numerical Simulations of Composite Delamination,” Engineering Fracture Mechanics, Vol. 75, No. 16, 2008, pp. 4774-4792. http://dx.doi.org/10.1016/j.engfracmech.2008.06.004
[29] C. Fan, J. P. Y. Ben and J. J. R. Cheng, “Cohesive Zone with Continuum Damage Properties for Simulation of Delamination Development in Fiber Composites and Failure of Adhesive Joints,” Engineering Fracture Mechanics, Vol. 75, No. 13, 2008, pp. 3866-3880.
http://dx.doi.org/10.1016/j.engfracmech.2008.02.010
[30] E. Barbieri and M. Meo, “A Meshfree Penalty-Based Approach to Delamination in Composites,” Composites Science and Technology, Vol. 69, No. 13, 2009, pp. 2169-2177.
http://dx.doi.org/10.1016/j.compscitech.2009.05.015
[31] J. Planas and M. Elices, “Nonlinear Fracture of Cohesive Materials,” International Journal of Fracture, Vol. 51, No. 2, 1991, pp. 139-157.
http://dx.doi.org/10.1007/978-94-011-3638-9_10
[32] Q. D. Yang, B. N. Cox, R. K. Nalla and R. O. Ritchie, “Fracture Length Scales in Human Cortical Bone: The Necessity of Nonlinear Fracture Models,” Biomater, Vol. 27, No. 9, 2006, pp. 2095-2113.
http://dx.doi.org/10.1016/j.biomaterials.2005.09.040
[33] P. P. Camanho and C. G. Dávila, “Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials,” NASA/TM, No. 211737, 2002.
[34] A. Carpinteri, P. Cornetti, F. Barpi and S. Valente, “Cohesive Crack Model Description of Ductile to Brittle Size-Scale Transition: Dimensional Analysis vs. Renormalization Group Theory,” Engineering Fracture Mechanics, Vol. 70, No. 14, 2003, pp. 1809-1839.
http://dx.doi.org/10.1016/S0013-7944(03)00126-7
[35] J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” Journal of Applied Mechanics, Vol. 35, No. 1, 1968, pp. 379-386.
http://dx.doi.org/10.1115/1.3601206
[36] J. H. Kim and G. H. Paulino, “The Interaction Integral for Fracture of Orthotropic Functionally Graded Materials: Evaluation of Stress Intensity Factors,” International Journal of Solids and Structures, Vol. 40, No. 15, 2003, pp. 3967-4001. http://dx.doi.org/10.1016/S0020-7683(03)00176-8
[37] E. M. Wu and R. C. Reuter Jr., “Crack Extension in Fiberglass Reinforced Plastics,” University of Illinois, Champaign, 1965.
[38] M. L. Falk, A. Needleman and J. R. Rice, “A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture,” Journal de Physique IV, Vol. 11, No. 5, 2001, pp. 543-550. http://dx.doi.org/10.1051/jp4:2001506
[39] D. Motamedi, A. S. Milani, M. Komeili, M. N. Bureau, F. Thibault and D. Boucher, “A Stochastic XFEM Model to Study Delamination in PPS/Glass UD Composites: Effect of Uncertain Fracture Properties,” Applied Composite Materials, in Press.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.