Analysis of a family of unstable lattice orientations in (110) channel die compression
type: Item
instance of: scholarly article
title: Analysis of a family of unstable lattice orientations in (110) channel die compression
zbMATH Open document ID: 0629.73032
DOI: 10.1007/BF01175724
author: D. Chidambarrao
author: Kerry S. Havner
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: The family of f.c.c. crystal orientations defined by loading direction (110) and any channel die constraint direction between \((00\bar 1)\) and \((1\overline{12})\) is kinematically unstable. We establish that the experimentally observed finite rotation of the lattice about the loading axis, for initial orientations in this range, is uniquely predicted by the constraints and critical slip-system inequalities without regard to particular hardening theory. We further establish that experimental information on the changing constraint stress would serve to distinguish among theories. Predictions of three specific hardening rules, including classical Taylor hardening and the ``simple theory'', are illustrated for initial constraint directions \((1\;\bar 1 \overline{16})\) and \((3\overline{37})\). For the first of these orientations the predictions include constraint stress, lattice rotation, active and latent hardening, and overall crystal shearing to a logarithmic compressive strain of 1.0.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 4024891
zbMATH Keywords: finite strain
zbMATH Keywords: f.c.c. crystal orientations
zbMATH Keywords: loading direction
zbMATH Keywords: channel die constraint direction
zbMATH Keywords: kinematically unstable
zbMATH Keywords: finite rotation of the lattice
zbMATH Keywords: critical slip-system inequalities
zbMATH Keywords: hardening rules
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024891