Numerical simulation of bi-material interfacial cracks using EFGM and XFEM
Tóm tắt
In this paper, bi-material interfacial cracks have been simulated using element free Galerkin method (EFGM) and extended finite element method (XFEM) under mode-I and mixed mode loading conditions. Few crack interaction problems of dissimilar layered materials are also simulated using extrinsic partition of unity enriched approach. Material discontinuity has been modeled by a signed distance function whereas strong discontinuity has been modeled by two functions i.e. Heaviside and asymptotic crack tip enrichment functions. The stress intensity factors for bi-material interface cracks are numerically evaluated using the modified domain form of interaction integral. The results obtained by EFGM and XFEM for bi-material edge and center cracks are compared with those available in literature. In order to check the validity of simulations, the results have been obtained for two different ratio of Young’s modulus.
Tài liệu tham khảo
Anderson, T.L.: Fracture mechanics fundamentals and applications. CRC Press, Florida, ISBN 0-8493-4260-0 (1995)
Belytschko, T., Loehnert, S.: Crack shielding and amplification due to multiple micro-cracks interacting with a macrocrack. Int. J. Fract. 145, 1–8 (2007)
Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng. 37, 229–256 (1994)
Gosz, M., Moran, B.: An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Eng. Fract. Mech. 69, 299–319 (2002)
Hutchinson, J.W., Suo, Z.: Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191 (1991)
Kim, J.H., Paulino, G.H.: An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models. Int. J. Numer. Methods Eng. 58, 1457–1497 (2003)
Liu, G.R., Gu, Y.T.: An Introduction to Meshfree Methods and Their Programming. Springer, Berlin (2005)
Matos, P.P.L., Mc Meeking, R.M., Charalambides, P.G., Drory, M.D.: A method for calculating stress intensities in bimetal fracture. Int. J. Fract. 40, 235–254 (1989)
Meguid, S.A., Tan, M., Zhu, Z.H.: Analysis of cracks perpendicular to bimaterial interfaces using a novel finite element. Int. J. Fract. 73, 1–23 (1995)
Melenk, J.M., Babuska, I.: The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 139, 289–314 (1996)
Miyakazi, N., Ikeda, T., Soda, T., Munakata, T.: Stress intensity factor analysis of interface crack using boundary element method (application of virtual crack extension method). JSME Int. J. Ser. A 36, 36–42 (1993)
Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 135–150 (1999)
Mohammadi, S.: Extended finite element method for fracture analysis of structures. Blackwell Publishing, Singapore, ISBN-978-1-4051-7060-4 (2008)
Nagashima, T., Omoto, Y., Tani, S.: Stress intensity factor analysis of interface cracks using X-FEM. Int. J. Numer. Methods Eng. 56, 1151–1173 (2003)
Pant, M., Singh, I.V., Mishra, B.K.: Evaluation of mixed mode stress intensity factors for interface cracks using EFGM. Appl. Math. Model. 35, 3443–3459 (2011)
Sukumar, N., Moran, B., Black, T., Belytschko, T.: An element-free Galerkin method for three-dimensional fracture mechanics. Comput. Mech. 20, 170–175 (1997)
Sukumar, N., Chopp, D.L., Moes, N., Belytschko, T.: Modeling holes and inclusions by level sets in the Extended Finite Element Method. Comput. Methods Appl. Mech. Eng. 190, 6183–6200 (2001)
Sukumar, N., Huang, Z.Y., Prevost, J.H., Suo, Z.: Partition of unity enrichment for bimaterial interface cracks. Int. J. Numer. Methods Eng. 59, 1075–1102 (2004)
Tan, M., Meguid, S.A.: Dynamic analysis of cracks perpendicular to bimaterial interfaces using a new singular finite element. Finite Elem Anal. Des. 22, 69–83 (1996)
Tan, M., Meguid, S.A.: Analysis of bimaterial wedges using a new singular finite element. Int. J. Fract. 88, 373–391 (1998)
Wang, X.D., Meguid, S.A.: On the general treatment of an oblique crack near bimaterial interface under antiplane loading. Int. J. Solids Struct. 33, 2485–2500 (1996a)
Wang, X.D., Meguid, S.A.: On the general treatment of interacting cracks near an interfacial crack. Int. J. Eng. Sci. 34, 1397–1408 (1996b)
Yu, H., Wu, L., Guo, L., Du, S., He, Q.: Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method. Int. J. Solids Struct. 46, 3710–3724 (2009)
Yu, H., Wu, L., Guo, L., He, Q., Du, S.: Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials. Mech. Mater. 42, 435–450 (2010)