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Gradient crystal plasticity as part of the computational modelling of polycrystals
Author(s) -
Ekh M.,
Grymer M.,
Runesson K.,
Svedberg T.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2015
Subject(s) - hardening (computing) , crystal plasticity , finite element method , plasticity , slip (aerodynamics) , materials science , strain hardening exponent , representative elementary volume , mechanics , geometry , mathematics , physics , thermodynamics , metallurgy , composite material , layer (electronics)
This paper describes how gradient hardening can, in a thermodynamically consistent fashion, be included into a crystal plasticity model. By assuming that the inelastic part of the free energy includes contributions from the gradient of hardening along each slip direction, a hardening stress due to the second derivative of the hardening along each slip direction can be derived. For a finite element model of the grain structure a coupled problem with displacements and gradient hardening variables as degrees of freedom is thereby obtained. This problem is solved using a dual mixed approach. In particular, an algorithm suitable for parallelization is presented, where each grain is treated as a subproblem. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening. Finally, the results of different prolongation assumptions, i.e. how to impose the macroscopic deformation gradient on a representative volume element, are compared. Copyright © 2007 John Wiley & Sons, Ltd.