延伸有限元素法模擬雙層材料界面裂縫

XFEM Simulation of an Interface Crack in a Bi-Material Subjected to Bending

簡婉芸(Wan-Yun Chien)

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)

https://doi.org/10.6838/YZU.2012.00045

摘要

延伸有限元素法 (Extended Finite Element Method; XFEM) 改善了傳統的有限元素法，它擁有傳統有限元素法的優點，但是在處理裂縫成長時所產生的不連續(discontinuity)或奇異(singularity)問題時，不需再重新網格化及重新定義裂縫軌跡，且在裂縫成長時，不需要定義明確的裂縫表面。利用這種方法，可以更快速且有效的求得準確的數值解。
本論文利用延伸有限元素法模擬在一個基材/薄膜系統下，一存在於基材靠近介面處之裂縫。探討整個薄膜受平均應力時，裂縫是否會穩態成長；以及薄膜與基材系統在不同的材料的情況下，對於裂縫穩態成長時深度的影響。
接著探討在四點彎矩試片模型下，使用不同材料系數以及不同裂縫長度比時的應力強度因子與能量釋放率，並與理論值比較其誤差。

關鍵字

裂縫 ； 材料界面 ； 延伸有限元素

並列摘要

The extended finite element method (XFEM) keeps the merit of classical finite element method (FEM) and can be used to solve discontinuity and singularity problems without re-meshing
The case of a substrate crack in a thin film/substrate system subjected to a uniform stress applied to the film is firstly considered. The effect of material properties on the steady-state crack location is studied.
The interface crack in a bi-material system subjected to symmetric or asymmetric four-point bending is considered next. The computed stress intensity factors and energy release rates are benchmarked against analytic solutions. In addition, the effects of material property and crack length on mixed-mode stress intensity factor are discussed.

並列關鍵字

XFEM ； crack ； interface

參考文獻

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. and Gracie, R. (2007), “On XFEM applications to dislocations and interfaces,” International Journal of Plasticity, 23, pp. 1721-1738.

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