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The Role of First Order Surface Effects in Linear Elastic Fracture Mechanics Open Access

Descriptions

Other title
Subject/Keyword
size-dependent stress distributions
interface cracks
First Order Surface Effects
linear elastic fracture mechanics
plane deformations
anti-plane deformations
Cauchy singular integro-differential equations
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
KIM, CHUN IL
Supervisor and department
Peter Schiavone (Mechanical Engineering)
Chong-Qing Ru (Mechanical Engineering)
Examining committee member and department
Walied Moussa (Mechanical Engineering)
David Steigmann (Mechanical Engineering, University of California_Berkeley)
Peter Schiavone (Mechanical Engineering)
Chongqing Ru (Mechanical Engineering)
Jozef Szymanski (civil and environmental engineering)
Tian Tang (Mechanical Engineering)
Department
Department of Mechanical Engineering
Specialization
Solid Mechanics-Nano Mechanics
Date accepted
2012-04-30T09:34:17Z
Graduation date
2012-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Structures at relatively small scales (e.g. nano/micro scale) behave differently in comparison to those examined at the macro scale. This is mainly because a high surface area to volume ratio is present at this scale making physical factors such as surface stress/energy and electromagnetic forces much more significant. In particular, ‘surface effects’ induced by a local environmental change of the region near the surface of solids, greatly influence the general behavior of the corresponding bulk material especially when the scale of materials become compatible with the nano/micro scale. This in turn, suggest that a more accurate and comprehensive description of the general behavior of an elastic solid with one or more surfaces can be achieved by incorporating a description of the separate surface mechanics near each surface of the solid. In the dissertation, we examine the effects of first-order surface elasticity in linear elastic fracture mechanics. A complete analysis has been performed for both plane and anti-plane deformations and for cases in which cracks are present in a homogeneous material and subsequently in the interface between two dissimilar elastic materials. It is shown that the introduction of the effects of first-order surface elasticity results in, in most cases, the reduction of the stress singularity at the crack tip from the classical strong square root singularity to a weaker logarithmic singularity. In particular, the refined model (with first-order surface effects integrated) predicts a more realistic description of size-dependent stress distributions commonly existing at the small scale structures. In the case of an interface crack arising in the interfacial region between two dissimilar materials, the refined model removes the classical oscillatory behaviors of the corresponding stress distributions leading again to size-dependent and stable stresses in the vicinity of the crack.
Language
English
DOI
doi:10.7939/R3XH1S
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Structures at relatively small scales (e.g. nano/micro scale) behave differently in comparison to those examined at the macro scale. This is mainly because a high surface area to volume ratio is present at this scale making physical factors such as surface stress/energy and electromagnetic forces much more significant. In particular, ‘surface effects’ induced by a local environmental change of the region near the surface of solids, greatly influence the general behavior of the corresponding bulk material especially when the scale of materials become compatible with the nano/micro scale. This in turn, suggest that a more accurate and comprehensive description of the general behavior of an elastic solid with one or more surfaces can be achieved by incorporating a description of the separate surface mechanics near each surface of the solid. In the dissertation, we examine the effects of first-order surface elasticity in linear elastic fracture mechanics. A complete analysis has been performed for both plane and anti-plane deformations and for cases in which cracks are present in a homogeneous material and subsequently in the interface between two dissimilar elastic materials. It is shown that the introduction of the effects of first-order surface elasticity results in, in most cases, the reduction of the stress singularity at the crack tip from the classical strong square root singularity to a weaker logarithmic singularity. In particular, the refined model (with first-order surface effects integrated) predicts a more realistic description of size-dependent stress distributions commonly existing at the small scale structures. In the case of an interface crack arising in the interfacial region between two dissimilar materials, the refined model removes the classical oscillatory behaviors of the corresponding stress distributions leading again to size-dependent and stable stresses in the vicinity of the crack.Kim, C. I., Schiavone, P. and Ru, C-Q. (2011). “Effect of Surface Elasticity on an Interface Crack in Plane Deformations.” Proc. Roy. Soc. London A. 467: 3530–3549.Kim, C. I. (2011). “An Analysis of an Elastic Solid Incorporating a Crack Under the Influences of Surface Effects in Plane & Anti-plane Deformations.” Invited Paper – Special Issue on Interaction and Multiscale Mechanics. 4(2): 123-137.Kim, C. I., Schiavone, P. and Ru, C-Q. (2011). “The Effect of Surface Elasticity on a Mode-III Interface Crack.” Arch. Mech. 63(3): 267–286.Kim, C. I., Schiavone, P. and Ru, C-Q. (2011). “Analysis of Plane-Strain Crack Problems (Mode I and Mode II) in the Presence of Surface Elasticity.” J. Elasticity. 104(1): 397–420.Kim, C. I., Schiavone, P. and Ru, C-Q. (2010). “The Effects of Surface Elasticity on an Elastic Solid with Mode-III Crack: Complete Solution.” ASME J. Appl. Mech. 77: 021011-1-021011-7.Kim, C. I., Schiavone, P. and Ru, C-Q. (2010). “Analysis of a Mode-III Crack in the Presence of Surface Elasticity and a Prescribed Non-Uniform Surface Traction.” Z. angew. Math. Phys. 61(3): 555–564.

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