Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface
Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface
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DOI：
10.1016/j.euromechsol.2007.11.006
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发表时间：
2008-09
影响因子：
4.1
通讯作者：
Yong-Dong Li;K. Lee;Yao Dai
中科院分区：
文献类型：
--
作者：
Yong-Dong Li;K. Lee;Yao Dai
建立了弹性性能光滑梯度材料与弹性性能不连续的尖锐界面两侧垂直的两条共线裂纹的反平面动态断裂问题的力学模型。通过拉普拉斯积分变换和傅立叶积分变换，将问题归结为第一类柯西奇异积分方程组。采用Erdogan配点法求解积分方程组，由Miller和Guy提出的拉普拉斯数值反演法求解动态应力强度因子。讨论了几何参数和物理参数对动应力强度因子的影响，并在此基础上得出以下结论：(A)增加界面两侧的FGM条厚度有利于减小垂直于双FGM界面且嵌入其中一个FGM条中心的裂纹的动态应力强度因子；(B)增加裂纹所在的FGM条的刚度将增加动态应力强度因子。然而，当界面一侧的材料较刚性时，另一侧界面垂直埋入裂纹的应力强度因子将减小；(C)与界面裂纹不同，减小双功能梯度材料界面的弱不连续性并不一定会降低垂直于其的裂纹的应力强度因子；(D)对于两个半长相等的共线裂纹，当两个内端之间的距离小于半长的约3倍时，它们之间的相互作用增强，但当距离大于时，相互作用变弱。
The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak.