Dynamics of texture evolution in face-centered cubic polycrystals
type: Item
instance of: scholarly article
title: Dynamics of texture evolution in face-centered cubic polycrystals
zbMATH Open document ID: 1196.74023
author: Ashish Kumar
author: Paul R. Dawson
published in: Journal of the Mechanics and Physics of Solids
publication date: 2009-08-31T00:00:00Z
review text: The paper considers the texturing of face-centered polycrystals as the flow of an orientation density over a fundamental region of orientation space. First, the polycrystal model is discussed based on an orientation distribution function. The single crystal model is employed, and properties of Rodrigues' space relevant to the analysis are discussed. Then, the authors investigate the dynamics of the velocity fields arising from imposed deformation modes looking for the presence or absence of equilibriums in the field to identify critical points. It is shown that the equilibria are connected with crystallographic fibers by associating the slip systems with crystal symmetries. In order to simplify the analysis, two tools are introduced, namely standardized linearized stability analysis to assess the behavior of equilibrium interactions, and a parametrization of lattice spin that enables collapse of reorientation velocities under arbitrary deformation to a one-parameter family superposed by the macroscopic spin. The macroscopic spin is shown to affect the positions of equilibria. The continuous flows are examined relative to the stability of equilibria of flows starting with the same normalized spin. Under sufficiently high spin, the annihilation of equilibria implies that stable texture components do not persist under continued monotonic deformation. The parametrization of the lattice spins facilitates the connection of the evolving texture to related flows having equilibria. As examples, three deformation modes are examined: plane strain compression, pure shear and simple shear under Taylor hypothesis for partitioning the straining among crystals within an aggregate. As pure shear is related to plane strain compression by a rotation of the deformation rate and does not involve a macroscopic spin, the existing equilibria and their stabilities are identical to the equilibria within the rotation. On the other hand, simple shear possesses sufficient macroscopic spin to an…
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74E25
zbMATH DE Number: 5600184
zbMATH Keywords: crystal plasticity
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: macroscopic spin
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
full work available at URL: j.jmps.2008.11.013
OpenAlex ID: W1993080784
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DOI: 10.1016/J.JMPS.2008.11.013
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description: scientific article; zbMATH DE number 5600184