以延伸有限元素法模擬薄膜/基材系統在均勻應力下的基材裂縫成長

XFEM Simulation of Channeling Crack Propagation in a Thin Film/Substrate System

呂學俊(Hsueh-Chun Lu)

指導教授 ： 余念一

元智大學/工程學院/機械工程學系/碩士(2012年)

摘要

延伸有限元素法(Extended Finite Element Method；XFEM)是由傳統有限元素法延伸而來，它延續了傳統有限元素法的優點，在模擬裂縫成長等不連續問題時，不需要明確定義裂縫表面且無須重新網格化，利用這種方法可以快速及精確的求得解析解。

本論文利用延伸有限元素法程式，模擬薄膜基材系統受到單軸拉伸後裂縫的應力分佈，並求得應力強度因子(stress intensity factor)，將其結果與斷裂力學之解析解比較，並與其他例子驗證，確保程式的可信度；接著探討薄膜與基材受平均應力時裂縫是否會穩態的成長，與改變基材與薄膜材料的情況之下，對基材裂縫深度的影響，並用模擬方法計算出能量釋放率與理論值做比較。

關鍵字

有限元素分析 ； XFEM ； 裂縫成長

並列摘要

The extended finite element method (XFEM)is extended from the conventional finite element method. In the simulation of crack growth, it does not need a clear definition of the fracture surface and does not have to be remeshed.

In the present work, the extended finite element method is employed to simulate the propagation of a matrix crack in a thin film/substrate system subjected to uniaxial tensile stresses. The stress intensity factors are computed and compared with the results obtained by fracture mechanics. In addition, the crack propagation is simulated.

並列關鍵字

Finite element ； XFEM ； Crack propagation

參考文獻

Akisanya A. R. and Fleck N. A. (1994), “The edge cracking and decohesion of thin films.” International Journal of Solids Structures. 31, 23, pp. 3175-3199.

Asadpoure, A., Mohammadi, S., and Vafai, A. (2006a), “Crack analysis in orthotropic media using the extended finite element method,” Thin-Walled Structures, 44, pp. 1031-1038.

Asadpoure, A., Mohammadi, S., and Vafai, A. (2006b), “Modeling crack in orthotropic media using a coupled finite element and partition of unity methods,” Finite Elements in Analysis and Design, 42, pp. 1165-1175.

Belytschko, T., and Black, T. (1999), “Elastic crack growth in finite elements with minimal remeshing,” International Journal for Numerical Methods in Engineering, 45, pp. 601-620.

Belytschko, T., Chen, H., Xu, J., and Zi, G. (2003), “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment,” International Journal for Numerical Methods In Engineering, 58, pp. 1873-1905.