Bending Crystals: Emergence of Fractal Dislocation Structures

Abstract

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar structures strikingly similar to those seen experimentally-reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. Our model provides a framework for understanding emergent dislocation structures on the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modeling program, and a new example of self-similar structure formation in nonequilibrium systems.

The effect of prior cold work on the chloride stress corrosion cracking of 304L austenitic stainless steel under atmospheric conditions

“…As more deformation is induced, the stacking faults form a cell structure. Cell walls differ from grain boundaries as they exhibit lower misorientation and a different morphology [50]. At low strain, these cell structures are rather heterogeneous, but as further deformation is introduced into the material, a much more uniform distribution of dislocations is observed [6,[47][48][49].…”

Graph states as ground states of two-body frustration-free Hamiltonians

“…If one can show that an N × N cluster state (a graph state on a square lattice) can be obtained by applying LOCC to an entangled state ψ | 〉 of N poly ( ) particles, then we have a proof that ψ | 〉 is a universal resource for MBQC. This conversion, called quantum state reduction [29], can be used to show that the following states are universal resources for MBQC: the tricluster state [2], spin-3/2 AKLT quasi-chains [30,31], spin-3/2 AKLT states on a variety of 2D lattices [4,28] spin-3/2 and spin-2 AKLT states with a commuting structure [6] and certain mixtures of spin-2 and lower spin AKLT states [32]. The resource states described in [33], whose universality was proven using tensor network methods, are universal state preparators [30] and thus can also be used to efficiently prepare cluster states.…”

“…One simple way of showing this is using the tabular form of an MPS described in [29]. Following section 2.2, we can then define a one-parameter family of frustration-free Hamiltonians by δ δ We remark that a similar type of deformation to the AKLT model, which preserves frustration freeness and   × 2 2 symmetry, has been studied previously [44].…”

Dislocation pattern formation in finite deformation crystal plasticity

“…Different approaches have been used in the literature to model the development of dislocation microstructures such as [OR99,LS06,CCPS10,XEA15], and other references mentioned therein. In the work of Ortiz and Repetto [OR99], dislocation structures at finite deformation have been shown to be compatible with deformation fields that are minimizers of a pseudoelastic energy functional for a discrete time step of a rate independent crystal plasticity formulation.…”