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Interaction of a Screw Dislocation with Interfaces and Surfaces in Couple Stress Elasticity Theory Open Access


Other title
Image force
Screw Dislocation
Couple Stress Elasticity
Planar Interface
Type of item
Degree grantor
University of Alberta
Author or creator
Gharahi, Alireza
Supervisor and department
Dr. Peter Schiavone (Mechanical Engineering)
Examining committee member and department
Dr. Cagri Ayranci (Mechanical Engineering)
Dr. Chong-Qing Ru (Mechanical Engineering)
Department of Mechanical Engineering

Date accepted
Graduation date
2017-11:Fall 2017
Master of Science
Degree level
The fundamental problem of interaction of a screw dislocation with planar surfaces and interfaces is of great theoretical and practical interest from micro/nano mechanical point of view. In the present study, we aim to capture the micro/nano mechanical effects through the continuum based model of couple stress elasticity using an analytical approach for the problem. To do so, we establish the boundary value problem corresponding to a screw dislocation near planar interfaces and surfaces in couple stress materials. We evaluate four main cases: the presence of a screw dislocation near a bi-material interface; a screw dislocation in a substrate near a thin film interface; a screw dislocation inside a thin-film lying over a substrate; a screw dislocation in an unconfined thin-film. Using classical Fourier transform techniques, we solve the corresponding boundary value problem for antiplane deformations with appropriate boundary conditions. The interfaces are assumed to be perfectly bonded and we impose continuity of displacements and tractions. For the surfaces, the traction free condition is set up for the problem. We solve the antiplane problem for the displacement field and use the resulting displacement to calculate stresses and couple stresses in the entire media. We employ the displacement and stress distributions to calculate the force induced by the boundaries on the dislocation. The interaction force is important because it determines the state of mobility of dislocations in certain configurations which is highly influential on the plastic behavior of materials. We use conservative J-integral techniques with numerical integration over a path enclosing the dislocation to obtain the interaction force. The classical elasticity solutions of a screw dislocation near interfaces and surfaces of bi-materials, thin films and substrates are well-documented in the literature. We compare the resulting solutions with the reported solutions in the literature to verify our results, accordingly. The comparison also reveals the contribution of couple stresses to stress distributions and interaction forces. It is illustrated that, in general, couple stresses endow the structure with an extra stiffness which results in higher stress concentrations as well as higher values of interaction force.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
A. Gharahi, M. Dai, G. F. Wang and P. Schiavone, Interaction of a screw dislocation with bi-material interface in anti-plane couple stress elasticity, Mathematics and Mechanics of Solids, 2017, DOI: 10.1177/1081286516686824A.Gharahi, M. Dai, P. Schiavone, Screw dislocation in a thin-film substrate in couple stress elasticity, Journal of Applied Mathematics and Physics (ZAMP), 2017 68:37.

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