A numerical method is presented for obtaining the stress intensity factors of cracks terminating at a bimaterial interface based on extended finite element method (XFEM). A new 6-term crack tip displacement enrichment function is derived. Based on the analytical solution of the stress and displacement fields around the crack tip, the expression of the path independent integral Jkε and the stress intensity factors KⅠ and KⅡ, is established. The XFEM numerical solution is used to calculate the integral Jkε, and the stress intensity factors are obtained by using the above expression. Finally, the maximum circumferential stress criterion is used to request the crack propagation angle θp. Results of the numerical simulations show that propagation problems of vertical crack at the bimaterial interface can be solved efficiently by the combination of the integral Jkε method and the XFEM. The crack propagation angle θp is smaller when the crack propagates from a softer material into a harder material, but θp is larger when the crack propagates from a harder material into a softer material. In the case of the four-point bending test, the crack propagation angle θp is independent of the ratio of the Poisson's ratios (v1/v2) of materials on both sides of the interface, but θp and the logarithm of the ratio of elasticity modulus lg(E1/E2) meet an exponential relation.
SHI Fang
,
GAO Feng
,
GAO Yanan
. Crack Propagation Terminating at a Bimaterial Interface Studied Using Extended Finite Element Method[J]. Science & Technology Review, 2014
, 32(23)
: 15
-21
.
DOI: 10.3981/j.issn.1000-7857.2014.23.001
[1] 姚战军, 倪新华, 郑坚, 等. 陶瓷颗粒增强金属基复合材料的细观强度 分析[J]. 应用力学学报, 2007, 24(3): 443-446. Yao Zhanjun, Ni Xinhua, Zheng Jian, et al. Micro-strength of particle reinforced metal matrix composites[J]. Chinese Journal of Applied Mechanics, 2007, 24(3): 443-446.
[2] 王扬卫, 王富耻, 于晓东, 等. 梯度陶瓷金属装甲复合材料研究进展[J]. 兵工学报, 2007, 28(2): 209-214. Wang Yangwei, Wang Fuchi, Yu Xiaodong, et al. Research advancement on graded ceramic-metal armor composites[J]. Acta Armamentarii, 2007, 28(2): 209-214.
[3] 杨福树, 孙志刚, 李龙彪, 等. 正交铺设陶瓷基复合材料基体裂纹演化 研究[J]. 南京航空航天大学学报: 英文版, 2011, 28(1): 111-119. Yang Fushu, Sun Zhigang, Li Longbiao, et al. Research on matrix crack evolution of cross-ply ceramicmatrix composite[J]. Transactions of Nanjing University of Aeronautics & Astronautics, 2011, 28(1): 111-119.
[4] Abdelaziz Y, Hamouine A. A survey of the extended finite element[J]. Computers and Structures, 2008, 86(11): 1141-1151.
[5] Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601-620.
[6] Belytschko T, Moës N, Usui S, et al. Arbitrary discontinuities in finite elements[J]. International Journal for Numerical Methods in Engineering, 2001, 50(4): 993-1013.
[7] Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131-150.
[8] Moës N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets part I: Mechanical model[J]. International Journal for Numerical Methods in Engineering, 2002, 53 (11): 2549-2568.
[9] Sukumar N, Prévost J H. Modeling quasi static crack growth with the extended finite element method part I: Computer implementation[J]. International Journal of Solids and Structures, 2003, 40(26): 7513-7537.
[10] Huang R, Prévost J H, Huang Z Y, et al. Channel cracking of thin films with the extended finite element method[J]. Engineering Fracture Mechanics, 2003, 70(18): 513-2526.
[11] Sukumar N, Huang Z Y, Prévost J H, et al. Partition of unity enrichment for bimaterial interface cracks[J]. International Journal for Numerical Methods in Engineering, 2004, 59(8): 1075-1102.
[12] Bouhala L, Shao Q, Koutsawa Y, et al. An XFEM crack-tip enrichment for a crack terminating at a bi-material interface[J]. Engineering Fracture Mechanics, 2013, 102: 51-64.
[13] Chen D H. A crack normal to and terminating at a bimaterial interface[J]. Engineering Fracture Mechanics, 1994, 49(4): 517-532.
[14] Chen D H, Nisitani H. Body force method[J]. International Journal of Fracture, 1997, 86(1): 161-189.
[15] CookTS,ErdoganF.Stressinboundedmaterialwithacrack perpendicular to the interface[J]. International Journal of Engineering Science, 1972, 10: 677-697.
[16] Wang T C. Stress state in front of a crack perpendicular to bi-material interface[J]. Engineering Fracture Mechanics, 1998, 59(4): 471-485.
[17] Lim W, Lee C. Evaluation of stress intensity factors for a crack normal to bi-material interface using isoparametric finite elements[J]. Engineering Fracture Mechanics, 1995, 52(1): 65-70.
[18] Chang J H, Wu D J. Calculation of mixed-mode stress intensity factors for a crack normal to a bimaterial interface using contour integrals[J]. Engineering Fracture Mechanics, 2003, 70(13): 1675-1695.
[19] Erdogan F, Sih G C. On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963, 85 (4): 519-527.
[20] Chang J, Xu J Q. The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface[J]. International Journal of Mechanical Science, 2007, 49(7): 888-897.
[21] Lin K Y, Mar J W. Finite element analysis of stress intensity factors for cracks at a bi-material interface[J]. International Journal of Fracture, 1976, 12(4): 521-531.