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Interaction of multiple straight cracks and elliptical inclusions in a finite plate due to mismatched thermal expansion
Engineering Fracture Mechanics ( IF 5.4 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.engfracmech.2020.107267
Jiong Zhang , Yunhai Huang , Weidong Liu , Liankun Wang

Abstract The purpose of this paper is to study the interaction between multiple elliptical inclusions and straight cracks in a finite plate due to a uniform temperature change. In this solution, Eshelby’s equivalent inclusion method involving both interior Eshelby’s tensor and exterior Eshelby’s tensor is applied to calculate the thermal stress fields of an infinite plate containing multiple elliptical inclusions under a uniform temperature change first. Then the multiple cracks and the boundary are modeled by continuous distributions of dislocation densities in an infinite plate. Based on the stress boundary conditions of the cracks and boundary, a system of singular integral equations with Cauchy kernels are obtained. After solving the singular integral equations with Gauss–Chebyshev numerical quadrature, the stress intensity factor of each crack can be calculated. Besides, the finite element method is employed to examine the accuracy and efficiency of the presented method. Finally, the effects of the material and geometric parameters on the normalized stress intensity factors of the cracks are studied.

中文翻译:

由于热膨胀不匹配导致有限板中多个直线裂纹和椭圆夹杂物的相互作用

摘要 本文的目的是研究有限板内由于均匀温度变化引起的多个椭圆夹杂物与直线裂纹之间的相互作用。在该解决方案中,首先应用包含内部 Eshelby 张量和外部 Eshelby 张量的 Eshelby 等效包裹体方法来计算均匀温度变化下包含多个椭圆形包裹体的无限板的热应力场。然后通过无限板中位错密度的连续分布来模拟多裂纹和边界。基于裂纹和边界的应力边界条件,得到了具有柯西核的奇异积分方程组。用高斯-切比雪夫数值求积求解奇异积分方程后,可以计算出每个裂纹的应力强度因子。此外,采用有限元方法来检验所提出方法的准确性和效率。最后,研究了材料和几何参数对裂纹归一化应力强度因子的影响。
更新日期:2020-10-01
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