Theoretical analysis of the channel die compression test. I. General considerations and finite deformation of f.c.c. crystals in stable lattice orientations
type: Item
instance of: scholarly article
title: Theoretical analysis of the channel die compression test. I. General considerations and finite deformation of f.c.c. crystals in stable lattice orientations
zbMATH Open document ID: 0574.73054
DOI: 10.1016/0022-5096(84)90029-2
author: P. L. Sue
author: Kerry S. Havner
published in: Journal of the Mechanics and Physics of Solids
publication date: 1984-01-01T00:00:00Z
review text: An extensive theoretical investigation of f.c.c. crystals under [110] loading in the channel die compression test is presented. Two lattice orientations known from experiment to be stable relative to the channel axes, through large deformations, are investigated for each of four hardening laws. These are Taylor's classical isotropic hardening rule, a 2-parameter empirical rule from the metallurgical literature, the ''simple theory'' of anisotropic latent hardening [the second author and \textit{A. H. Shalaby}, Proc. R. Soc. London, Ser. A 358, 47-70 (1977; Zbl 0366.73042)], and a modification of the simple theory proposed by \textit{D. Peirce}, \textit{R. J. Asaro} and \textit{A. Needleman} [Acta Met. 30, 1087 ff. (1982)]. Predictions of active systems, equal multiple-slip and consequent lattice stability, finite shape change, and lateral constraint stress are the same for all theories, corresponding to minimum rate of plastic work, and are in general agreement with experiments on copper crystals. The predictions of latent hardening differ among the theories, however, depending upon whether there is relative rotation of material and lattice. The potential significance of experimental studies of latent hardening in these particular stable lattice orientations is emphasized.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
zbMATH DE Number: 3917839
zbMATH Keywords: kinematic relations
zbMATH Keywords: rate inequalities
zbMATH Keywords: lattice rotation
zbMATH Keywords: conflict between (ideal) frictionless walls and free end conditions
zbMATH Keywords: uniform deformation
zbMATH Keywords: stress state
zbMATH Keywords: critical systems
zbMATH Keywords: f.c.c. crystals
zbMATH Keywords: [110] loading
zbMATH Keywords: channel die compression test
zbMATH Keywords: Two lattice orientations
zbMATH Keywords: large deformations
zbMATH Keywords: four hardening laws
zbMATH Keywords: Taylor's classical isotropic hardening rule
zbMATH Keywords: 2-parameter empirical rule
zbMATH Keywords: ''simple theory'' of anisotropic latent hardening
zbMATH Keywords: modification of the simple theory
zbMATH Keywords: equal multiple-slip
zbMATH Keywords: consequent lattice stability
zbMATH Keywords: finite shape change
zbMATH Keywords: lateral constraint stress
zbMATH Keywords: minimum rate of plastic work
zbMATH Keywords: copper crystals
MaRDI profile type: Publication
full work available at URL: 0022-5096(84)90029-2
OpenAlex ID: W2075474745
cites work: A theoretical analysis of finitely deforming f.c.c. crystals in the sixfold symmetry position
cites work: First- and second- order analysis of axially loaded crystals in n-fold symmetry
cites work: Theoretical latent hardening in crystals. - II. bcc crystals in tension and compression
cites work: Theoretical latent hardening of crystals in double slip. I. F. C. C. crystals with a common slip plane
cites work: Theoretical latent hardening of crystals in double-slip. II. f.c.c. crystals slipping on distinct planes
cites work: A simple mathematical theory of finite distortional latent hardening in single crystals
cites work: Further Investigation of a New Hardening Law in Crystal Plasticity
cites work: Theoretical latent hardening in crystals - I. General equations for tension and compression with application to F. C. C. Crystals in tension
cites work: Q3243972
cites work: Theoretical latent hardening in crystals. III. f.c.c. crystals in compression
description: scientific article; zbMATH DE number 3917839