P.A Gourgiotis
Distributed dislocation approach for cracks in couple-stress elasticity: shear modes
Gourgiotis, P.A; Georgiadis, H.G.
Authors
H.G. Georgiadis
Abstract
The distributed dislocation technique proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work aims at extending this technique in studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. As a first step, the technique is introduced to study finite-length cracks under remotely applied shear loadings (mode II and mode III cases). The mode II and mode III cracks are modeled by a continuous distribution of glide and screw dislocations, respectively, that create both standard stresses and couple stresses in the body. In particular, it is shown that the mode II case is governed by a singular integral equation with a more complicated kernel than that in classical elasticity. The numerical solution of this equation shows that a cracked material governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a material governed by classical elasticity. Also, the stress level at the crack-tip region is appreciably higher than the one predicted by classical elasticity. Finally, in the mode III case the corresponding governing integral equation is hypersingular with a cubic singularity. A new mechanical quadrature is introduced here for the numerical solution of this equation. The results in the mode III case for the crack-face displacement and the near-tip stress show significant departure from the predictions of classical fracture mechanics.
Citation
Gourgiotis, P., & Georgiadis, H. (2007). Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. International Journal of Fracture, 147(1), 83-102. https://doi.org/10.1007/s10704-007-9139-5
Journal Article Type | Article |
---|---|
Publication Date | Sep 1, 2007 |
Deposit Date | Sep 22, 2016 |
Publicly Available Date | Oct 3, 2016 |
Journal | International Journal of Fracture |
Print ISSN | 0376-9429 |
Electronic ISSN | 1573-2673 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 147 |
Issue | 1 |
Pages | 83-102 |
DOI | https://doi.org/10.1007/s10704-007-9139-5 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s10704-007-9139-5
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