S. Mahmoud Mousavi

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

Abstract The 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.

A note on dislocation-based mode III gradient elastic fracture mechanics

*Corresponding author: S. Mahmoud Mousavi, Department of Civil and Structural Engineering, Aalto University, Aalto 12100, Finland; and Laboratory of Mechanics and Materials, Aristotle University, Thessaloniki 24124, Greece, e-mail: mahmoud.mousavi@aalto.fi E.C. Aifantis: Laboratory of Mechanics and Materials, Aristotle University, Thessaloniki 24124, Greece; International Laboratory for Modern Functional Materials, ITMO University, St. Petersburg 191002, Russia; School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China; and College of Engineering, Michigan Technological University, Houghton, MI 49931, USA S. Mahmoud Mousavi* and E.C. Aifantis A note on dislocation-based mode III gradient elastic fracture mechanics

Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks

The in-plane classical dislocation-based linear elastic fracture mechanics analysis is extended to the case of strain gradient elasticity. Nonsingular stress and smooth-closure crack profiles are derived. As in the classical treatment, the crack is represented by a distribution of climb edge dislocations (for Mode I) or glide edge dislocations (for mode II). These distributions are determined through the solution of corresponding integral equations based on variationally consistent boundary conditions. An incompatible framework is used and the nonsingular full-field plastic distortion tensor components are calculated. Numerical results and related graphs are provided illustrating the nonsingular behaviour of the stress/strain components and the smooth cusp-like closure of the crack faces at the crack tip. The work provides an alternative approach to celebrated “Barenblatt’s treatment” of cracks, without the introduction of a cohesive zone and related to intermolecular forces ahead of the physical crack tip. It also supplements a recent paper by the authors in which the mode III crack, represented by an array of screw dislocations, was solved within the present gradient elasticity framework.

Analytic solutions of multiple moving cracks in an orthotropic layer bonded to an orthotropic FGM coating

In this paper, the dynamic behavior of an orthotropic substrate weakened by moving cracks and reinforced by a non-homogenous coating is studied. First, the solution to the screw dislocation in an orthotropic strip with imperfect orthotropic functionally graded coating is obtained. Then, for the anti-plane analysis of cracks, the screw dislocations are distributed along the crack lines and the dislocation solution is used to derive integral equations for dislocation density functions on the surface of cracks. The effects of non-homogeneity parameters, geometrical parameters and bonding coefficient on the stress intensity factors are investigated.