An extended crystal plasticity model for latent hardening in polycrystals
Journal article, 2011

In this contribution, a computational approach to modeling size-dependent self- and latent hardening in polycrystals is presented. Latent hardening is the hardening of inactive slip systems due to active slip systems. We focus attention on the investigation of glide system interaction, latent hardening and excess dislocation development. In particular, latent hardening results in a transition to patchy slip as a first indication and expression of the development of dislocation microstructures. To this end, following Nye (Acta Metall 1:153-162, 1953), Kondo (in Proceedings of the second Japan national congress for applied mechanics. Science Council of Japan, Tokyo, pp. 41-47, 1953), and many others, local deformation incompatibility in the material is adopted as a measure of the density of geometrically necessary dislocations. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening effects. A large-deformation model for latent hardening is introduced. This approach is based on direct exploitation of the dissipation principle to derive all field relations and (sufficient) forms of the constitutive relations as based on the free energy density and dissipation potential. The numerical implementation is done via a dual-mixed finite element method. A numerical example for polycrystals is presented.



Dual mixed finite

Strain gradient plasticity



element method


dislocation density

Dislocation density

variational formulation


strain-gradient plasticity

Size-dependent hardening



Swantje Bargmann

Technische Universität Dortmund

B. Svendsen

RWTH Aachen University

Magnus Ekh

Chalmers, Applied Mechanics, Material and Computational Mechanics

Computational Mechanics

0178-7675 (ISSN) 1432-0924 (eISSN)

Vol. 48 6 631-645

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Sustainable development

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Materials Science

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Applied Mechanics


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