Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear

IF 2.3 3区 工程技术 Q2 MECHANICS
Evgeny Lomakin, Olesia Korolkova
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Abstract

Deformation fields near the tip of a crack in a material with properties depending on the type of stress state are presented for conditions of longitudinal shear. These properties are revealed in rocks, concretes, refractory ceramics, cast iron, structural graphite, some composites, and many other microheterogeneous materials. The behavior of heterogeneity depends on the loading conditions, and as a result, the deformation properties of these materials are stress state-dependent. Moreover, shear and volume deformation processes are interrelated in these materials. Therefore, it is impossible to distinguish between the fields corresponding to shear strain and bulk strain in solids. For the study of stress, strain, and displacement fields at a crack tip, corresponding constitutive equations are used to simulate the dependence of equivalent elastic properties on the type of stress state and to describe the relationship between shear strains and volumetric deformations. The traditional approach based on anti-plane strain hypothesis cannot be used for solving problems under longitudinal shear conditions because shear strains are not independent of bulk strains. Therefore, the corresponding representations for displacements have been proposed. Nonlinear constitutive relations are used, and conditions for a unique solution to the boundary value problem have been shown. The obtained solutions are compared with the known solutions for a linear elastic solid. The opening of crack faces is observed under conditions of out-of-plane shear, and the dependence of the crack opening on the sensitivity of material properties to the stress state is studied.

Abstract Image

Abstract Image

反平面剪切条件下具有应力状态弹性特性的固体裂缝附近的应力场和应变场
介绍了在纵向剪切条件下,材料裂缝尖端附近的变形场,其特性取决于应力状态的类型。岩石、混凝土、耐火陶瓷、铸铁、结构石墨、某些复合材料以及许多其他微异质材料都具有这些特性。异质性的行为取决于加载条件,因此,这些材料的变形特性与应力状态有关。此外,在这些材料中,剪切和体积变形过程是相互关联的。因此,无法区分固体中的剪切应变和体积应变。为了研究裂纹尖端的应力、应变和位移场,需要使用相应的构成方程来模拟等效弹性特性对应力状态类型的依赖性,并描述剪切应变和体积变形之间的关系。基于反平面应变假设的传统方法不能用于解决纵向剪切条件下的问题,因为剪切应变与体积应变无关。因此,我们提出了相应的位移表示法。使用了非线性构成关系,并给出了边界值问题唯一解的条件。获得的解与线性弹性固体的已知解进行了比较。在平面外剪切条件下观察了裂纹面的开裂,并研究了裂纹开裂与材料特性对应力状态敏感性的关系。
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
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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