University of Illinois Urbana-Champaign

Necessary and sufficient conditions for onset of shear strain localization in thermal viscoplastic materials

Shawki, Tarek G.

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https://hdl.handle.net/2142/112231

Description

Title
Necessary and sufficient conditions for onset of shear strain localization in thermal viscoplastic materials
Author(s)
Shawki, Tarek G.
Issue Date
1988-12
Keyword(s)
  • Shear Strain Localization
  • Theoretical Viscoplastic Materials
Abstract
Shear strain localization in thermal viscoplastic materials is examined through the analysis of one-dimensional simple shearing deformation of a material slab with velocities prescribed at the insulated boundaries. An exact energy estimate is derived for the fully nonlinear problem. This estimate illustrates the weak effect of elasticity as regards the onset of localization. The existence, uniqueness and well-posedness properties of a homogeneous solution to the considered nonlinear initial boundary-value problem are examined. A unique homogeneous solution is shown to exist for simple shearing deformations with velocities prescribed at the insulated boundaries. This solution is also shown to be the unique static solution of the simple shear problem, with no elastic and heat conduction effects, consistent with the forgoing boundary conditions. A linear system of equations is derived for the perturbations superposed on the reference homogeneous solution. An alternative linear system is derived for the relative perturbations (as compared to the homogeneous solution). Exact energy estimates are derived in both cases for the linear system of equations. It is shown that energy estimates are insensitive to the use of absolute or relative perurbations. We further discuss the notions of stability and localization as well as the validity of the quasi-static approximation. A new localization criterion that takes full account of the time-variation of the homogeneous solution is introduced. Necessary and/or sufficient conditions for flow localization based on the behavior of the linear system for the absolute perturbations in the quasi-static limit are derived. This criterion associates the onset of shear localization with the positive rate of change of the total kinetic energy of the perturbations. The analysis is valid for a general material description which includes the effects of strain rate sensitivity, thermal softening and strain hardening. Effects of inertia and heat conduction are also discussed. A criterion for the assessment of the validity of conclusions based on a constant coefficient approximation is provided. Comparisons with available analytical, numerical and experimental results support the validity of our conclusions.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 489
  • 1988-6004
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112231
Sponsor(s)/Grant Number(s)
National Science Foundation 88/12 MSM 87 09299 88/12
Copyright and License Information
Copyright 1988 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.