University of Illinois Urbana-Champaign

On shear flow localization with traction-controlled boundaries

Shawki, Tarek G.

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https://hdl.handle.net/2142/112453

Description

Title
On shear flow localization with traction-controlled boundaries
Author(s)
Shawki, Tarek G.
Issue Date
1994-07
Keyword(s)
  • Shear Flow Localization
  • Traction-controlled Boundaries
Abstract
The interactive roles of inertia and material viscosity as regards the evolution of inhomogeneous plastic flow are analyzed. The analysis is presented in the context of the dynamic, one-dimensional simple shear of a thermo-viscoplastic material subjected to traction-controlled boundaries. Existence and uniqueness questions of an exact homogeneous solution for this initial boundary-value problem are investigated. The breakdown of the so-called quasi-static homogeneous solution is related to the onset of localization. We introduce a dimensionless number, called the deformation number, and denoted by RD, as the ratio of inertial to viscous stresses. Characterization of a given deformation as being dynamic is shown to be related to large values of RD instead of simply high rates of applied loading. A model problem is formulated in order to illustrate the basic features of solutions for this class of deformations. An exact solution is derived for the model problem as well as a solution based on matched asymptotic expansions. It is shown, based on the model problem and fully nonlinear finite difference solutions, that plastic deformation localizes within narrow bands in the neighborhood of the boundaries. The shear band thickness is inversely proportional to the square root of the deformation number. The role of material viscosity concerning the introduction of a length scale to dynamic deformations of rate-dependent solids is illustrated.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 760
  • 1994-6016
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112453
Sponsor(s)/Grant Number(s)
National Science Foundation 94/07
Copyright and License Information
Copyright 1994 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.