In this article, the strain gradient elasticity (SGE) theory is used to investigate the mechanical behaviour of a functionally graded material (FGM) weakened by two unequal collinear mode-III cracks. The SGE theory uses two material characteristic lengths, and , to account for volumetric and surface strain-gradient factors, respectively. The directions of both cracks coincide with the material gradation, which is oriented parallel to the -axis. The numerical outcomes of the problem are obtained by constructing the system of equations using the hyper-singular integral-differential equation technique. The influence of the material gradation parameter on various fracture parameters, including the stress intensity factor (SIF), strain and crack surface displacement (CSD), is numerically shown. In addition, different loads are considered while analysing CSD profiles in connection to the gradation parameter . Furthermore, the effect of inter-crack distance on CSD profiles is comprehensively explored, showing information between crack geometry and material gradation.

中文翻译：

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通过应变梯度弹性理论研究功能梯度材料中平行于两个不等III型裂纹的材料梯度的影响


在本文中，应变梯度弹性 (SGE) 理论用于研究被两个不等共线 III 型裂纹弱化的功能梯度材料 (FGM) 的力学行为。 SGE 理论使用两个材料特征长度 和 来分别考虑体积和表面应变梯度因子。两个裂纹的方向与材料级配一致，材料级配的方向平行于 - 轴。该问题的数值结果是通过使用超奇异积分微分方程技术构造方程组来获得的。数值显示了材料级配参数对各种断裂参数的影响，包括应力强度因子 (SIF)、应变和裂纹表面位移 (CSD)。此外，在分析与级配参数相关的 CSD 配置文件时，还考虑了不同的负载。此外，还全面探讨了裂纹间距对 CSD 剖面的影响，显示裂纹几何形状和材料级配之间的信息。