Numerical Analysis of an Edge Crack Isotropic Plate with Void/Inclusions under Different Loading by Implementing XFEM

Document Type : Research Paper


Department of Mechanical Engineering, S. V. National Institute of Technology, Surat-395007, India


In the present work, the effect of various discontinuities like voids, soft inclusions and hard inclusions of the mixed-mode stress intensity factor (MMSIF), crack growth and energy release rate (ERR) of an edge crack isotropic plate under different loading like tensile, shear, combine and exponential by various numerical examples is investigated. The basic formulation is based on the extended finite element method (XFEM) through the M interaction approach using the level set method. The effect of single and multi voids and inclusions with position variation on MMSIF and crack growth are also investigated. The presented results would be applicable to enhancing the better fracture resistance of cracked structures and various loading conditions.


[1] G. C. Sih, Energy-density concept in fracture mechanics, Engineering Fracture Mechanics, 5 (1973) 1037-1040.
[2] J. S. Ke and H. W. Liu, The measurements of fracture toughness of ductile materials, Engineering Fracture Mechanics, 5 (1973) 187-202.
[3] W. Z. Chien, Z. C. Xie, Q. L. Gu, Z. F. Yang and C. T. Zhou, The superposition of the finite element method on the singularity terms in determining the stress intensity factor, Engineering Fracture Mechanics, 16 (1982) 95-103.
[4] T. Belytschko, H. Chen, J. Xu, and G. Zi, Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal of Numerical Methods in Engineering, 58 (2003) 1873–1905.
[5] N. Sukumar and J.H. Prevost, Modelling quasi-static crack growth with the extended finite element method, Part –I, computer implementation, International Journal of Solids and Structures, 40 (2003) 7513-7537.
[6] J. Bellec andJ.E. Dolbow, A note on enrichment functions for modeling crack nucleation, Communications in Numerical Methods in Engineering, 19 (2003) 921–932.
[7] T. Belytschko, R. Gracie and G.A. Ventura, A review of extended/generalized finite element methods for material modeling, International Journal of Fracture, 131 (2005) 124–129.
[8] A. Asadpoure, S.  Mohammadi and A. Vafaia, Modelling crack in orthotropic media using a coupled finite element and partition of unity methods, Finite Elements in Analysis and Design, 42 (2006) 1165 – 1175.
[9] Z. LI and Q. Chen, Crack- inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method, International Journal of Fracture, 118 (2002) 29–40.
[10] S.E. Mousavi and N. Sukumar, Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 3237-3249.
[11] S. Kumar, I.V. Singh, B.K. Mishra and A. Singh, New enrichments in XFEM to model dynamic crack response of 2-D elastic solids, International Journal of Impact Engineering, 87 (C ) (2016) 198-211.
[12] T. Belytschko and R. Gracie, XFEM applications to dislocations and interfaces, International Journal of Plasticity, 23 (10–11) ( 2007) 1721-1738.
[13] N. Sukumar, D.L. Chop, N. Moes and T. Belytscko, Modelling holes and inclusions by level set in the extended finite element method, Comp. Methods Apll. Mech., 190 (2001) 6183-6200.
[14] W. Limtrakarn and P. Dechaumphai, Adaptive finite element method to determine KI and KII of crack plate with different EINCLUSION/EPLATE ratio, Transactions of the Canadian Society for Mechanical Engineering, 35 (3) (2011) 355-368.
[15] S. Jiang, C. Du, and C. Gu, An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM, Structural Engineering and Mechanics, 49 (5) (2014) 597-618.
[16] S. Natarajan, P. Kerfriden, D. R. Mahapatra and S. P. A. Bordas, Numerical analysis of the inclusion-crack interaction by the Extended Finite Element Method, International Journal for Computational Methods in Engineering Science and Mechanics, 15 (2014) 26–32.
[17] K. Sharma, Crack Interaction Studies Using XFEM Technique, Journal of Solid Mechanics, 6 (4) (2014) 410-421.
[18] A. S. Shedbale, I. V. Singh and B. K. Mishra, Nonlinear Simulation of an Embedded Crack in the Presence of Holes and Inclusions by XFEM, Procedia Engineering, 64 (2013) 642 – 651.
[19] J. Grasa, J. A. Bea, J. F. Rodriguez, and M. Doblare, The perturbation method, and the extended finite element method. An application to fracture mechanics problems, Fatigue Fract. Engng. Mater. Struct., 29 (2006) 581–587.
[20] K. Khatri and A. Lal, Stochastic XFEM fracture and crack propagation behavior of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings, Mechanics of Advanced Materials and Structures, 25 (9) (2018) 732-755.
[21] K. Khatri and A. Lal, Stochastic XFEM based fracture behavior and crack growth analysis of a plate with a hole emanating cracks under biaxial loading, Theoretical and Applied Fracture Mechanics, 96 (2018) 1–22.
[22] M.T. Ebrahimi, D. Dini, D.S. Balint, A.P. Sutton, and S. Ozbayraktar, Discrete crack dynamics: A planar model of crack propagation and crack-inclusion interactions in brittle materials, International Journal of Solids and Structures, 152 (2018) 12-27.
[23] K. Huang, L. Guo and H. Yu, Investigation of mixed-mode dynamic stress intensity factors of an interface crack in bi-materials with an inclusion, Composite Structures, 202 (2018) 491-499.
[24] T. Yu and T.Q Bui, Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement, Composite Structures, 196 (2018) 112-133.
[25] J. Zhang, Z. Qu, Q. Huang, L. Xie, and C. Xiong, Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method, Arch. Appl. Mech., 83 (2013) 861–873.
[26] I.V. Singh, B.K. Mishra, S. Bhattacharya, and R.U. Patil, The numerical simulation of fatigue crack growth using extended finite element method, International Journal of Fatigue, 36 (2012) 109–119.
[27] A. Lal, S.P. Palekar, S.B. Mulani and R.K. Kapania, Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack, Aerospace Science and Technology, 60 (2017) 131-151.
[28] S. Kumar, I.V. Singh, B.K. Mishra, and T. Rabczuk, Modeling, and simulation of kinked cracks by virtual node XFEM, Computer Methods in Applied Mechanics and Engineering, 283 (2015) 1425-1466.
[29] T.Q. Bui and C. Zhang, Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading, Computational Materials Science, 62 (2012) 243-257.
[30] Z.H. Teng, D.M. Liaoa, S.C. Wu, F. Sun, T. Chen and Z.B. Zhang, An adaptively refined XFEM for the dynamic fracture problems with micro defects, Theoretical and Applied Fracture Mechanics, 103 (2019) 102255.
[31] Z. Han, D. Weatherley and R. Puscasu, A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model, Int. J. Numer. Anal. Meth. Geomech., 10 (2017) 1–13.
[32] J. Zhao, Modeling of Crack Growth Using a New Fracture Criteria Based Peridynamics, J. Appl. Comput. Mech., 5(3) (2019) 498-516.
[33] X. Sun, G. Chaia and Y. Bao, Nonlinear numerical study of crack initiation and propagation in a reactor pressure vessel under pressurized thermal shock using XFEM, Fatigue Fract. Eng. Mater. Struct., 10 (2017) 1–13.
[34] J.M. Sim and Y.S. Chang, Crack growth evaluation by XFEM for nuclear pipes considering thermal aging embrittlement effect, Fatigue Fract. Eng. Mater. Struct., 11 (2018) 1–17.
[35] D. Wilson, Z. Zheng and F.P.E. Dunne, A microstructure-sensitive driving force for crack growth, Journal of the Mechanics and Physics of Solids, 121 (2018) 1–41.
[36] M. Surendran, A.L.N. Pramod and S. Natarajan, Evaluation of Fracture Parameters by Coupling the Edge-Based Smoothed Finite Element Method and the Scaled Boundary Finite Element Method, J. Appl. Comput. Mech., 5(3) (2019) 540-551.
[37] Z. Sun, X. Zhuang and Y. Zhang, Cracking Elements Method for Simulating Complex Crack Growth, J. Appl. Comput. Mech., 5(3) (2019) 552-562.
[38] M. Francesco Funari, P. Lonetti and S. Spadea, A crack growth strategy based on moving mesh method and fracture mechanics, Theoretical and Applied Fracture Mechanics, 102(2019) 1-39.
[39] J.L. Curiel-Sosa, B. Tafazzolimoghaddam, and C. Zhang, Modelling fracture and delamination in composite laminates energy release rate and interfacial stress, Composite Structures, 189(2018) 641-647.
[40] D. Roberto and L. Ma, Energy Release Rate of Moving Circular-Cracks, Engineering Fracture Mechanics, 213 (2019) 118-130.
[41] A.M. Aguirre-Mesa, D. Ramirez-Tamayo, M.J. Garcia, A. Montoya, and H. Millwater, A stiffness derivative local hypercomplex-variable finite element method for computing the energy release rate, Engineering Fracture Mechanics, 218(2019) 106581.
[42] R.U. Patil, B.K. Mishra, and I.V. Singh, A new multiscale XFEM for the elastic properties evaluation of heterogeneous materials, International Journal of Mechanical Sciences, 122 (2017) 277-287.
[43] S.Z. Feng and W. Li, An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations, Applied Mathematical Modelling, 55 (2018) 600-615.
[44] S.Z. Feng and X. Han, A novel multi-grid based reanalysis approach for efficient prediction of fatigue crack propagation, Computer Methods in Applied Mechanics and Engineering, 353 (2019) 107-122.
[45] T.Q. Bui and C. Zhang, Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM, Finite Elements in Analysis and Design, 69(2013) 19-36.
[46] X. Zhang and T.Q. Bui, A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures, International Journal for Computer Aided Engineering and Software, 32 (2015) 473-497.
[47] Z. Kang, T. Quoc Bui, D. Dinh Nguyen, T. Saitoh, and S. Hirose, An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics, Acta Mechanica, 226 (2015) 3991-4015.
[48] Z. Wang, T. Yu, T. Quoc Bui, N. Anh Trinh, N.T. Hien Luong, N. Dinh Duc, and D. Hong Doan, Numerical modeling of 3-D inclusions and voids by a novel adaptive XFEM, Advances in Engineering Software, 102 (2016) 105-122.
[49] Z. Kang, T. Quoc Bui, D. Dinh Nguyen and S. Hirose, Dynamic stationary crack analysis of isotropic solids and anisotropic composites by enhanced local enriched consecutive-interpolation elements, Composite Structures, 180 (2017) 221-233.
[50] Z. Kang, T. Quoc Bui, T. Saitoh, and S. Hirose, Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments, Composite Structures, 180 (2017) 221-233.
[51] Z. Wang, T. Yu, T. Quoc Bui, S. Tanaka, C. Zhang, S. Hirose, and J.L. Curiel-Sosa, 3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks, Computer Methods in Applied Mechanics and Engineering, 313 (2017) 375-405.
[52] Z. Kang, T. Quoc Bui, T. Saitoh and S. Hirose, Multi-inclusions modeling by adaptive XIGA based on LR B-splines and multiple level sets, Finite Elements in Analysis and Design, 148 (2018) 48-66.
[53] N. Sukumar, D.L. Chopp, N. Moës and T. Belytschko, Modelling holes and inclusions by level sets in the extended finite-element method, Comput. Methods Appl. Mech. Eng., 190 (2001) 6183–6200.
[54] M. Stolarska, D.L. Chopp, N. Moës and T. Belytschko, Modelling crack growth by level sets in the extended finite element method, Int. J. Numer. Methods Eng., 51 (2001) 943–960.
[55] S. Mohammadi, Extended Finite Element Method for Fracture Analysis of Structures, Wiley/Blackwell, 2008.