Atomistic modelling of near-crack-tip plasticity

Abstract

An atomistic model of near-crack-tip plasticity on a square lattice under anti-plane shear kinematics is formulated and studied. The model is based upon a new geometric and functional framework of a lattice manifold complex, which ensures that the crack surface is fully taken into account, while preserving the crucial notion of duality. As a result, existence of locally stable equilibrium configurations containing both a crack opening and dislocations is established. Notably, with the boundary in the form of a crack surface accounted for, no minimum separation between a dislocation core and the crack surface or the crack tip is required. The work presented here constitutes a foundation for several further studies aiming to put the phenomenon of near-crack-tip plasticity on a rigorous footing.

arXiv comment35 pages, 6 figures

References in corpus (4)

• Existence and stability of a screw dislocation under anti-plane deformation
• Analysis of stable screw dislocation configurations in an anti--plane lattice model
• Convergence and non-convergence of many-particle evolutions with multiple signs
• Upscaling a model for the thermally-driven motion of screw dislocations