Distributed non-singular dislocation technique for cracks in strain gradient elasticity

Abstract

AbstractThe mode III fracture analysis of a cracked graded plane in the framework of classical, first strain gradient, and second strain gradient elasticity is presented in this paper. Solutions to the problem of screw dislocation in graded materials are available in the literature. These solutions include various frameworks such as classical elasticity, and the first strain and second strain gradient elasticity theories. One of the applications of dislocations is the analysis of a cracked medium through distributed dislocation technique. In this article, this technique is used for the mode III fracture analysis of a graded medium in classical elasticity, which results in a system of Cauchy singular integral equations for multiple interacting cracks. Furthermore, the technique is modified for gradient elasticity. Owing to the regularization of the classical singularity, a system of non-singular integral equations is obtained in gradient elasticity. A plane with one crack is studied, and the stress distribution in classical elasticity is compared with those in gradient elasticity theories. The effects of the internal lengths, introduced in gradient elasticity theories, are investigated. Additionally, a plane with two cracks is studied to elaborate the interactions of multiple cracks in both the classical and gradient theories.