On the formation and stability of dislocation patterns. I. One- dimensional considerations
type: Item
instance of: scholarly article
title: On the formation and stability of dislocation patterns. I. One- dimensional considerations
zbMATH Open document ID: 0586.73183
DOI: 10.1016/0020-7225(85)90113-2
author: D. Walgraef
author: E. C. Aifantis
published in: International Journal of Engineering Science
publication date: 1985-01-01T00:00:00Z
review text: By distinguishing among mobile and immobile dislocations and operating within the framework of continuum mechanics it is possible to derive a set of partial differential equations of the diffusion-reaction type for the evolution of dislocation species. On examining the competition between gradient dependent terms modelling the motion of dislocations and nonlinear terms modelling their interactions, it is shown that stable solutions are possible. The wavelength turns out to be a material property in agreement with observations. The discussion is limited to one dimension, that is to glide of straight dislocations in the slip direction, and the model corresponds physically to the ladder-like structure of persistent slip bands.
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
zbMATH DE Number: 3940973
zbMATH Keywords: mobile and immobile dislocations
zbMATH Keywords: set of partial differential equations
zbMATH Keywords: diffusion-reaction type
zbMATH Keywords: gradient dependent terms
zbMATH Keywords: stable solutions
zbMATH Keywords: one dimension
zbMATH Keywords: ladder-like structure of persistent slip bands
MaRDI profile type: Publication
full work available at URL: 0020-7225(85)90113-2
OpenAlex ID: W4238288431
cites work: Q4138569
cites work: Q3893028
cites work: On a proposal for a continuum with microstructure
cites work: Q3688157
description: scientific article; zbMATH DE number 3940973