The influence of material gradation parallel to two unequal mode-III cracks in functionally graded materials via strain gradient elasticity theory

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-08-22 DOI:10.1016/j.apm.2024.115647

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Abstract

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, ℓ and $ℓ^{'}$ , 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 x-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 β. Furthermore, the effect of inter-crack distance on CSD profiles is comprehensively explored, showing information between crack geometry and material gradation.

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通过应变梯度弹性理论研究平行于功能分级材料中两条不等模 III 裂纹的材料分级的影响

本文采用应变梯度弹性（SGE）理论来研究功能梯度材料（FGM）在两条不等长的共线模态 III 裂纹作用下的力学行为。SGE 理论使用两个材料特征长度 ℓ 和 ℓ′，分别表示体积应变梯度因子和表面应变梯度因子。两条裂缝的方向与平行于 x 轴的材料分级相一致。利用超奇异积分微分方程技术构建方程组，得出问题的数值结果。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 CSD 剖面时，还考虑了不同载荷与梯度参数 β 的关系。此外，还全面探讨了裂纹间距对 CSD 剖面的影响，显示了裂纹几何形状与材料梯度之间的信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.

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