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An analysis of cracks in ductile single crystals—I. Anti-plane shear

Mohan, R. and Ortiz, M. and Shih, C. F. (1992) An analysis of cracks in ductile single crystals—I. Anti-plane shear. Journal of the Mechanics and Physics of Solids, 40 (2). pp. 291-313. ISSN 0022-5096. doi:10.1016/S0022-5096(05)80014-6.

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The problem of a stationary mathematically sharp semi-infinite crack in an FCC crystal is considered. We adopt a geometrically rigorous formulation of crystalline plasticity accounting for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. A comparison of results with earlier small-strain solutions reveals some notable differences. These include the expected development of finite deformations and rotations near the crack tip, but also discrepancies such as a considerable spread of the plastic zones. In addition, nearly self-similar, square-root singular fields are obtained within the portion of the plastic zone where the crystal is in a state of high positive hardening. The results suggest that both finite-deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.

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Ortiz, M.0000-0001-5877-4824
Additional Information:© 1992 Elsevier. (Received 23 July 1990; in revised form 7 February, 1991) The support of the National Science Foundation through the Materials Research Group at Brown University, Grant DMR-8714665, is gratefully acknowledged. The authors are indebted to J. R. Rice for helpful discussions.
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Official Citation:R. Mohan, M. Ortiz, C.F. Shih, An analysis of cracks in ductile single crystals—I. Anti-plane shear, In Journal of the Mechanics and Physics of Solids, Volume 40, Issue 2, 1992, Pages 291-313, ISSN 0022-5096, (
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ID Code:83909
Deposited By: Lydia Suarez
Deposited On:14 Dec 2017 18:47
Last Modified:15 Nov 2021 20:15

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