XFEM based thermo-elastic numerical analysis of FGMs with various discontinuities

References

• Amit, H. K, and Jeong, K. C. 2008. Interaction integrals for thermal fracture of functionally graded materials. Engineering Fracture Mechanics 75:2542–65. doi:10.1016/j.engfracmech.2007.07.011.
   Web of Science ®Google Scholar
• Belytschko, T., and T. Black. 1999. crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45 (5):601–20. doi:10.1002/(sici)1097-0207(19990620)45:5<601::aid-nme598>3.0.co;2-s.
   Web of Science ®Google Scholar
• Bhardwaj, G., and I. V. Singh. 2015. Fatigue crack growth analysis of a homogeneous plate in the presence of multiple defects using extended isogeometric analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering 37 (4):1065–82. doi:10.1007/s40430-014-0232-1.
   Web of Science ®Google Scholar
• Bhattacharya, S., K. Sharma, and V. Sonkar. 2018. Fatigue fracture of functionally graded materials under elastic-plastic loading conditions using extended finite element method. IntechOpen Chapter 9:169–94. doi:10.5772/intechopen.72778.
   Google Scholar
• Bouhala, L., A. Makradi, and S. Belouettar. 2012. Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method. Engineering Fracture Mechanics 88:35–48. doi:10.1016/j.engfracmech.2012.04.001.
   Web of Science ®Google Scholar
• Duflot, M. 2008. The extended finite element method in thermo-elastic fracture mechanics. International Journal for Numerical Methods in Engineering 74 (5):827–47. doi:10.1002/nme.2197.
   Web of Science ®Google Scholar
• Ebrahimi, M. T., D. Dini, D. S. Balint, A. P. Sutton, and S. Ozbayraktar. 2018. Discrete crack dynamics: A planar model of crack propagation and crack-inclusion interactions in brittle materials. International Journal of Solids and Structures 152-153:12–27. doi:10.1016/j.ijsolstr.2018.02.036.
   Web of Science ®Google Scholar
• Gayen, D., R. Tiwari, and D. Chakraborty. 2019. Static and dynamic analyses of cracked on functionally graded 2 structural components: A review. Composites Part B.173:106982. doi:10.1016/j.compositesb.2019.106982.
   Web of Science ®Google Scholar
• Ghatage, P., S. V. R. Kar, P, and E. Sudhagar. 2020. On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review. Composite Structures 236:111837. doi:10.1016/j.compstruct.2019.111837.
   Web of Science ®Google Scholar
• Hosseini, S. S., H. Bayesteh, and S. Mohammadi. 2013. Thermo-mechanical XFEM crack propagation analysis of functionally graded material. Materials Science and Engineering: A 561:285–302. doi:10.1016/j.msea.2012.10.043.
   Web of Science ®Google Scholar
• Huang, K., L. Guo, and H. Yu. 2018. Investigation of mixed-mode dynamic stress intensity factors of an interface crack in bi-materials with an inclusion. Composite Structures 202:491–9. doi:10.1016/j.compstruct.2018.02.078.
   Web of Science ®Google Scholar
• Jiang, S., C. Du, and C. Gu. 2014. An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM. Structural Engineering and Mechanics 49 (5):597–618. doi:10.12989/sem.2014.49.5.597.
   Web of Science ®Google Scholar
• Khatri, K., and A. Lal. 2018. Stochastic XFEM based fracture behaviour and crack growth analysis of a plate with hole emanating cracks under biaxial loading. Theoretical and Applied Fracture Mechanics 96:1–22. doi:10.1016/j.tafmec.2018.03.009.
   Web of Science ®Google Scholar
• Khatri, K., and A. Lal. 2018. Stochastic XFEM fracture and crack propagation behaviour of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings. Mechanics of Advanced Materials and Structures 25 (9):732–55. doi:10.1080/15376494.2017.1308599.
   Web of Science ®Google Scholar
• Kim, J. H., and G. H. Paulino. 2002. Finite element evaluation of mixed-mode stress intensity factors in functionally graded materials. International Journal for Numerical Methods in Engineering 53 (8):1903–35. doi:10.1002/nme.364.
   Web of Science ®Google Scholar
• Kitey, R., A. V. Phan, H. Tippur, and T. Kaplan. 2006. Modeling of crack growth through particle clusters in brittle matrix by symmetric-Galerkin boundary element method. International Journal of Fracture 141 (1–2):11–25. doi:10.1007/s10704-006-0047-x.
   Web of Science ®Google Scholar
• Lal, A., and K. Markad. 2019. Stochastic mixed mode stress intensity factor of center cracks FGM plates using XFEM. International Journal of Computational Materials Science and Engineering 08 (03):1950009. doi:10.1142/S204768411950009X.
   Google Scholar
• Lal, A., S. B. Mulani, and R. K. Kapania. 2017. Stochastic fracture response and crack growth analysis of laminated composite edge crack beams using extended finite element method. International Journal of Applied Mechanics 09 (04):1750061–94. doi:10.1142/S1758825117500612.
   Google Scholar
• Lal, A., S. P. Palekar, S. B. Mulani, and R. K. Kapania. 2017. Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack. Aerospace Science and Technology 60:131–51. doi:10.1016/j.ast.2016.10.028.
   Web of Science ®Google Scholar
• Li, Z., and Q. Chen. 2002. Crack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method. 118:29–40. International Journal of Fracture doi:10.1023/a:1022652725943.
   Web of Science ®Google Scholar
• Li, Z., Q. Sheng, and J. Sun. 2006. A generally applicable approximate solution for mixed-mode crack-inclusion interaction. Acta Mechanica 187 (1–4):1–9. doi:10.1007/s00707-006-0375-y.
   Web of Science ®Google Scholar
• Liu, X. Y., Q. Z. Xiao, and B. L. Karihaloo. 2004. XFEM for direct evaluation of mixed-mode SIFs in homogenous and bi-materials. 59:1103–18. International Journal for Numerical Methods in Engineering. doi:10.1002/nme.906.
   Web of Science ®Google Scholar
• Natarajan, S., P. Kerfriden, D. R. Mahapatra, and S. P. A. Bordas. 2014. Numerical analysis of the inclusion-crack interaction by the extended finite element method. International Journal for Computational Methods in Engineering Science and Mechanics 15 (1):26–32. doi:10.1080/15502287.2013.833999.
   Google Scholar
• Nojumi, M. M., and X. Wang. 2020. Analysis of crack problems in functionally graded materials under thermo-mechanical loading using graded finite elements. Mechanics Research Communications 106:103534. doi:10.1016/j.mechrescom.2020.103534.
   Web of Science ®Google Scholar
• Pant, M., I. V. Singh, and B. K. Mishra. 2011. A numerical study of crack interactions under thermo-mechanical load using EFGM. Journal of Mechanical Science and Technology 25 (2):403–13. doi:10.1007/s12206-010-1217-3.
   Web of Science ®Google Scholar
• Pathak, H. 2020. Crack interaction study in functionally graded materials (FGMs) using XFEM under thermal and mechanical loading environment. Mechanics of Advanced Materials and Structures 27 (11):903–26. doi:10.1080/15376494.2018.1501834.
   Web of Science ®Google Scholar
• Pathak, H., and A. Singh. 2012. Crack Interactions Study under thermal load using EFGM and XFEM. International Journal on Theoretical and Applied Research in Mechanical Engineering 1 (1):2319–3182.
   Google Scholar
• Peng, B., Z. Li, and M. Feng. 2015. The mode I crack-inclusion interaction in orthotropic medium. Engineering Fracture Mechanics 136:185–94. doi:10.1016/j.engfracmech.2015.01.028.
   Web of Science ®Google Scholar
• Petrova, V., and S. Schmauder. 2014. FGM/homogeneous bi-materials with systems of cracks under thermo-mechanical loading: Analysis by fracture criteria. Engineering Fracture Mechanics 130:12–20. doi:10.1016/j.engfracmech.2014.01.014.
   Web of Science ®Google Scholar
• Reddy, J. N., and C. D. Chin. 1998. Thermo-mechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses 21 (6):593–626. doi:10.1080/01495739808956165.
   Web of Science ®Google Scholar
• Sajith, S., K. S. R. K. Murthy, and P. S. Robi. 2018. A simple technique for estimation of mixed mode (i/ii) stress intensity factors. Journal of Mechanics of Materials and Structures 31 (2):141–54. doi:10.2140/jomms.2018.13.141.
   Google Scholar
• Sajith, S., K. S. R. K. Murthy, and P. S. Robi. 2020. Estimation of stress intensity factors from crack flank displacements. Materials Today: Proceedings 24:887–94. doi:10.1016/j.matpr.2020.04.399.
   Google Scholar
• Saleh, B., J. Jiang, R. Fathi, T. Al- hababi, Q. Xu, L. Wang, D. Song, and A. Ma. 2020. 30 Years of functionally graded materials: An overview of manufacturing methods. Applications and Future Challenges. Composites Part B.201:108376. doi:10.1016/j.compositesb.2020.108376.
   Web of Science ®Google Scholar
• Sharma, K. 2014. Crack interaction studies using XFEM technique. Journal of Solid Mechanics 6 (4):410–21.
   Google Scholar
• Shedbale, A. S., I. V. Singh, and B. K. Mishra. 2013. Nonlinear simulation of an embedded crack in the presence of holes and inclusions by XFEM. Procedia Engineering 64:642–51. doi:10.1016/j.proeng.2013.09.139.
   Google Scholar
• Shi, M., H. Wu, L. Li, and G. Chai. 2014. Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique. International Journal of Mechanics and Materials in Design10 (1):65–77. doi:10.1007/s10999-013-9231-0.
   Web of Science ®Google Scholar
• Singh, I. V., B. K. Mishra, S. Bhattacharya, and R. U. Patil. 2012. The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue 36 (1):109–19. doi:10.1016/j.ijfatigue.2011.08.010.
   Web of Science ®Google Scholar
• Stolarska, M., D. L. Chopp, N. Moës, and N. T. Belytschko. 2001. Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering 51 (8):943–60. doi:10.1002/nme.201.
   Web of Science ®Google Scholar
• Sukumar, N., D. L. Chopp, N. Moës, and T. Belytschko. 2001. Modelling holes and inclusions by level set in the extended finite element method. Computer Methods in Applied Mechanics and Engineering 190 (46-47):6183–200. doi:10.1016/S0045-7825(01)00215-8.
   Web of Science ®Google Scholar
• Sun, Z., X. Zhuang, and Y. Zhang. 2019. Cracking elements method for simulating complex crack growth. 5 (3):552–62. Journal of Applied and Computational Mechanics doi:10.22055/JACM.2018.27589.1418.
   Web of Science ®Google Scholar
• Surendran, M., A. L. N. Pramod, and S. Natarajan. 2019. Evaluation of fracture parameters by coupling the edge-based smoothed finite element method and the scaled boundary finite element method. 5 (3):540–51. Journal of Applied and Computational Mechanics doi:10.22055/JACM.2018.24125.1172.
   Web of Science ®Google Scholar
• Teng, Z. H., D. M. Liao, S. C. Wu, F. Sun, T. Chen, and Z. B. Zhang. 2019. An adaptively refined XFEM for the dynamic fracture problems with micro defects. Theoretical and Applied Fracture Mechanics 103:102255. doi:10.1016/j.tafmec.2019.102255.
   Web of Science ®Google Scholar
• Tsang, D. K. L., S. O. Oyadiji, and A. Y. T. Leung. 2007. Two-dimensional fractal-like finite element method for thermo-elastic crack analysis. International Journal of Solids and Structures 44 (24):7862–76. doi:10.1016/j.ijsolstr.2007.05.008.
   Web of Science ®Google Scholar
• Walters, M. C., G. H. Paulino, and R. H. Dodds. 2004. Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermo-mechanical loading. International Journal of Solids and Structures 41 (3-4):1081–118. doi:10.1016/j.ijsolstr.2003.09.050.
   Web of Science ®Google Scholar
• Wang, Y. B., and K. T. Chau. 2001. A new boundary element method for mixed boundary value problems involving cracks and holes: Interactions between rigid inclusions and cracks. International Journal of Fracture. 110:387–406. doi:10.1023/a:1010853804657.
   Web of Science ®Google Scholar
• Yu, H., L. Wu, L. Guo, S. Du, and Q. He. 2009. Investigation of mixed-mode stress intensity factors for non-homogeneous materials using an interaction integral method. International Journal of Solids and Structures 46 (20):3710–24. doi:10.1016/j.ijsolstr.2009.06.019.
   Web of Science ®Google Scholar
• Yu, H., L. Wu, L. Guo, Q. He, and S. Du. 2010. Interaction integral method for the interfacial fracture problems of two non-homogeneous materials. Mechanics of Materials 42 (4):435–50. doi:10.1016/j.mechmat.2010.01.001.
   Web of Science ®Google Scholar
• Yu, T., and T. Q. Bui. 2018. Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement. Computers & Structures 196:112–33. doi:10.1016/j.compstruc.2017.11.007.
   Web of Science ®Google Scholar
• Zhang, J., Z. Qu, Q. Huang, L. Xie, and C. Xiong. 2013. Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method. Archive of Applied Mechanics 83 (6):861–73. doi:10.1007/s00419-012-0722-5.
   Web of Science ®Google Scholar
• Zhao, J. 2019. Modeling of crack growth using a new fracture criteria based peridynamics. 5 (3):498–516. Journal of Applied and Computational Mechanics doi:10.22055/jacm.2017.23515.1160.
   Web of Science ®Google Scholar
• Zheng, H., J. Sladek, V. Sladek, S. K. Wang, and P. H. Wen. 2021. Fracture analysis of functionally graded material by hybrid meshless displacement discontinuity method. Engineering Fracture Mechanics 247:107591. doi:10.1016/j.engfracmech.2021.107591.
   Web of Science ®Google Scholar