Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems

D. M. Parks, Said Ahzi

Research output: Contribution to journalArticle

138 Citations (Scopus)

Abstract

We clearly elucidate the kinematic constraints, and the corresponding kinematic indeterminacy of part of the deviatoric stress tensor, in a rigid-viscoplastic single crystal lacking five independent slip systems. The indeterminate stress component is a Lagrange multiplier enforcing the kinematic constraint, and it must be determined from equilibrium considerations. A simple polycrystalline model is constructed which precisely satisfies local kinematic constraints as well as global compatibility. Volume-average global stresses are obtained by approximating the local constraint stress as the corresponding projection of the (to-be-determined) global stress. Applications of the model to hexagonal crystals without pyramidal slip, and to large deformation and texturing of orthorhombic polycrystalline materials (olivine; HDPE) are made.

Original languageEnglish
Pages (from-to)701-724
Number of pages24
JournalJournal of the Mechanics and Physics of Solids
Volume38
Issue number5
DOIs
Publication statusPublished - 1990
Externally publishedYes

Fingerprint

plastic deformation
Plastic deformation
slip
kinematics
textures
Textures
Kinematics
Crystals
crystals
Lagrange multipliers
stress tensors
Olivine
Polycrystalline materials
olivine
compatibility
Texturing
High density polyethylenes
projection
Tensors
Single crystals

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

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T1 - Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems

AU - Parks, D. M.

AU - Ahzi, Said

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AB - We clearly elucidate the kinematic constraints, and the corresponding kinematic indeterminacy of part of the deviatoric stress tensor, in a rigid-viscoplastic single crystal lacking five independent slip systems. The indeterminate stress component is a Lagrange multiplier enforcing the kinematic constraint, and it must be determined from equilibrium considerations. A simple polycrystalline model is constructed which precisely satisfies local kinematic constraints as well as global compatibility. Volume-average global stresses are obtained by approximating the local constraint stress as the corresponding projection of the (to-be-determined) global stress. Applications of the model to hexagonal crystals without pyramidal slip, and to large deformation and texturing of orthorhombic polycrystalline materials (olivine; HDPE) are made.

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