Dislocation-based fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type—Part II: Inplane analysis

This paper is the sequel of a companion Part I paper devoted to dislocation-based antiplane fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type. In the present paper, the inplane analysis is carried out to study cracks of Modes I and II. Generalized continua including non...

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Bibliographic Details
Published in:International journal of solids and structures 2016-08, Vol.92-93, p.105-120
Main Author: Mahmoud Mousavi, S.
Format: Article
Language:English
Subjects:
Crack
Dislocation
Dislocation density
Dislocations
Elasticity
Fracture mechanics
Glide
Gradient elasticity of bi-Helmholtz type
Inplane
Materials Engineering
Materialteknik
Mathematical models
Nonlocal elasticity of bi-Helmholtz type
Nonsingular
Strain
Stresses
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Summary:This paper is the sequel of a companion Part I paper devoted to dislocation-based antiplane fracture mechanics within nonlocal and gradient elasticity of bi-Helmholtz type. In the present paper, the inplane analysis is carried out to study cracks of Modes I and II. Generalized continua including nonlocal elasticity of bi-Helmholtz type and gradient elasticity of bi-Helmholtz type (second strain gradient elasticity) offer nonsingular frameworks for the discrete dislocations. Consequently, the dislocation-based fracture mechanics within these frameworks is expected to result in a regularized fracture theory. By distributing the (climb and glide) edge dislocations, (Modes I and II) cracks are modeled. Distinctive features are captured for crack solutions within second-grade theories (nonlocal and gradient elasticity of bi-Helmholtz type) comparing with solutions within first-grade theories (nonlocal and gradient elasticity of Helmholtz type) as well as classical elasticity. Other than the total stress tensor, all of the field quantities are regularized within second-grade theories, while first-grade theories give singular double stress and dislocation density and classical elasticity leads to singularity in the stress field and dislocation density. Similar to gradient elasticity of Helmholtz type (first strain gradient elasticity), crack tip plasticity is captured in gradient elasticity of bi-Helmholtz type without any assumption of the cohesive zone.
ISSN:0020-7683
1879-2146
1879-2146
DOI:10.1016/j.ijsolstr.2016.03.025