Plasticity as a depinning phase transition

Crystalline materials deform in an intermittent way with slip-avalanches that are power-law distributed. In this work we study plasticity as a pinning-depinning phase transition employing a discrete dislocation dynamics (DDD) model and a phase eld crystal (PFC) model in two dimensions. Below a critical ( ow) stress, the dislocations are pinned/jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response. Above this critical stress the dislocations are mobile (the depinned/ unjammed phase) and the material constantly ows. We employ discrete dislocation dynamics to resolve the temporal pro les of slip-avalanches and extract the nite-size scaling properties of the slip-avalanche statistics, going beyond gross aggregate statistics of slip avalanche sizes. We provide a comprehensive set of scaling exponents, including the depinning exponent . Our work establishes that the dynamics of plasticity, in the absence of hardening, is consistent with the mean eld interface depinning universality class, even though there is no quenched disorder. We also use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density (Taylor's relation). Consequently, dislocations jam at any density, in contrast to granular materials, which only jam above a critical density. Finally, we utilize a phase eld crystal model to extract the size, energy and duration distributions of the avalanches and show that they exhibit power law behavior in agreement with the mean eld interface depinning universality class.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Tsekenis, Georgios

Contributors dc:contributor

• Dahmen, Karin A.
• Hubler, Alfred W.
• Weismann, Michael
• Ceperley, David M.

• critical phenomena
• phase transition
• dislocation
• plasticity
• simulation
• scaling
• deformation
• phase field crystal
• discrete dislocation dynamics

Statement dc:rights

• Copyright 2012 Georgios Tsekenis

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/35323

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/35323