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The Reissner-Sagoci problem for an interfacial crack in an elastic bilayer medium under torsion of an embedded rigid circular disc
Theoretical and Applied Fracture Mechanics ( IF 5.3 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.tafmec.2020.102825
B. Kebli , F. Madani

Abstract This paper studies an axisymmetric problem of a penny-shaped crack at the interface of a bi-material under a static torsion by an embedded circular rigid disc. By using the Hankel integral transformation method, the angular displacements and the shear stresses are formulated. The faces of the crack are supposed stress free, and the displacement is continuous outside in the crack plane while the rigid circular disc inclusion rotates about the axis passing through their centers and the stress is continuous outside in the rigid disc plane. Considering these mixed conditions associated with the embedded rigid disc and the interfacial crack, the mixed boundary values are taken into account, that are transformed, to a system of dual integral equations. By appropriate transform, the dual integral equations are converted into a regular system of Fredholm integral equations of the second kind with two unknown functions which is then solved by quadrature rule. Numerical results for displacements and stresses in the interaction zone, the stress intensity factor at the edges of the crack and the rigid disc and the applied torque are obtained and discussed according to certain relevant parameters. The torsional effects of the disc on the elastic bilayer are evaluated by the analysis of the Mode III stress intensity factor in the crack vicinity depending on the degree of nonhomogeneity at the interfacial plane, crack size and the depth of embedment of the rigid disc. The efficiency of the method and of the mathematical formulation are checked by comparison with the results available for a relevant analysis in homogeneous solids.

中文翻译:

嵌入式刚性圆盘扭转下弹性双层介质界面裂纹的 Reissner-Sagoci 问题

摘要 本文研究了内嵌圆形刚性盘在静扭作用下双材料界面处的硬币状裂纹轴对称问题。通过使用 Hankel 积分变换方法,可以公式化角位移和剪应力。裂纹面假设无应力,在裂纹平面外侧位移是连续的,而刚性圆盘夹杂物绕通过其中心的轴旋转,应力在刚性圆盘平面外侧连续。考虑到这些与嵌入式刚性盘和界面裂纹相关的混合条件,混合边界值被考虑在内,并被转换为对偶积分方程组。通过适当的变换,对偶积分方程转换为具有两个未知函数的第二类 Fredholm 积分方程的正则系统,然后通过求积法则求解。根据一定的相关参数,得到并讨论了相互作用区的位移和应力、裂纹和刚性盘边缘的应力强度因子以及施加的扭矩的数值结果。盘对弹性双层的扭转效应通过分析裂纹附近的模式 III 应力强度因子来评估,这取决于界面处的非均匀程度、裂纹尺寸和刚性盘的嵌入深度。该方法和数学公式的效率通过与可用于均质固体的相关分析的结果进行比较来检查。
更新日期:2020-12-01
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