Dual boundary element analysis of rectangular-shaped cracks in graded materials

Abstract

This paper analyzes the rectangular-shaped crack in the graded materials by using the dual boundary element method. The method is based on the fundamental solutions for multilayered solids and uses a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. The former is collocated exclusively on the uncracked boundary, and the latter on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (i.e., displacement discontinuity) is treated as an unknown quantity on the crack surface. The layered technique is used to analyze the variation of parameters of the graded interlayer. Numerical examples of stress intensity factors (SIFs) calculation are given for the rectangular-shaped crack parallel to the graded interlayer. The results show that the SIFs obtained with the present formulation are in very good agreement with existing numerical results. The nonhomogeneous parameter and the distance of the crack from the interlayer exert an obvious influence on the SIFs of the rectangular-shaped crack in the graded material. Furthermore, it may be shown that the proposed method can be used to analyze different cracks subject to complex loads in graded materials and to model the non-homogeneous solids with multiple interacting cracks.

采用對偶邊界元方法分析了梯度材料中的矩形裂紋.該方法基于層狀材料基本解,以非裂紋邊界的位移和面力以及裂紋面的間斷位移作為未知量.位移邊界積分方程的源點配置在非裂紋邊界上,面力邊界積分方程的源點配置在裂紋面上.發展了邊界積分方程中不同類型奇異積分的數值方法.借助層狀材料基本解,采用分層方法逼近梯度材料夾層沿厚度方向力學參數的變化.與均勻介質中矩形裂紋的數值解對比,建議方法可以獲得高精度的計算結果.最后,分析了梯度材料中均勻張應力作用下矩形裂紋的應力強度因子,討論了梯度材料非均勻參數、夾層厚度和裂紋與夾層之間相對位置對應力強度因子的影響.