Abstract
We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain tensors while operating with an infinite number of equivalent energy wells. The advantage of this approach is that it eliminates arbitrariness in dealing with topological transitions involved, for instance, in nucleation and annihilation of dislocations. We use discontinuous yielding of pristine micro-crystals as a benchmark problem for the new theory and show that the nature of the catastrophic instability, which in this setting inevitably follows the standard affine response, depends not only on lattice symmetry but also on the orientation of the crystal in the loading device. The ensuing dislocation avalanche involves cooperative dislocation nucleation, resulting in the formation of complex microstructures controlled by a nontrivial self-induced coupling between different plastic mechanisms.
Highlights
With the advance of nanotechnology and broad fabrication of nano-scale structures, the focus in the study of plastic deformation has shifted to atomic dimensions
We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global invariance of the energy in the space of strain tensors while operating with an infinite number of equivalent energy wells
We presented the first systematic demonstration of the effectiveness of the mesoscopic tensorial model (MTM) by showing that it can simulate complex plastic phenomena in crystals involving a large number of interacting dislocations
Summary
With the advance of nanotechnology and broad fabrication of nano-scale structures, the focus in the study of plastic deformation has shifted to atomic dimensions. The emerging science of nanomaterials deals, for instance, with machine parts printed by chemical vapor deposition or made of nano-grained metals At these manufacturing scales, external and internal (microstructural) lengths become comparable, and the dislocation-based description of plasticity comes to the forefront in providing design guidelines for miniaturized mechanical devices [1,2,3]. External and internal (microstructural) lengths become comparable, and the dislocation-based description of plasticity comes to the forefront in providing design guidelines for miniaturized mechanical devices [1,2,3] It was found, for instance, that sub-micron size objects, serving as components of such systems, are characterized by remarkably high strength.
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