A computational investigation of a model of single-crystal gradient thermoplasticity that accounts for the stored energy of cold work and thermal annealing
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A theory of single-crystal gradient thermoplasticity that accounts for the stored energy of cold work and thermal annealing has recently been proposed by Anand et al. (Int J Plasticity 64:1–25, 2015). Aspects of the numerical implementation of the aforementioned theory using the finite element method are detailed in this presentation. To facilitate the implementation, a viscoplastic regularization of the plastic evolution equations is performed. The weak form of the governing equations and their time-discrete counterparts are derived. The theory is then elucidated via a series of three-dimensional numerical examples where particular emphasis is placed on the role of the defect-flow relations. These relations govern the evolution of a measure of the glide and geometrically necessary dislocation densities which is associated with the stored energy of cold work.
KeywordsGradient single crystal plasticity Thermoplasticity Finite element method Cold work Annealing
A.M. and B.D.R. acknowledge the support provided by the National Research Foundation through the South African Research Chair in Computational Mechanics. A part of this work was undertaken while A.M. was visiting the Hamburg University of Technology. A.M. also acknowledges the support provided by the University Research Committee of the University of Cape Town.
- 2.Armero F, Simo JC (1992) A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems. Int J Numer Methods Eng 35(4):737–766. ISSN 0029-5981Google Scholar
- 26.Gurtin ME, Anand L (2005) A theory of strain-gradient plasticity for isotropic, plastically irrotational materials, Part I: small deformations. J Mech Phys Solids 53(7):1624–1649Google Scholar
- 29.Intel. Math Kernel Library (2014) http://developer.intel.com/software/products/mkl/