Dr Tuncay Yalcinkaya, Department of Engineering Science, Oxford University

Deformation patterning and grain boundary modelling through strain gradient crystal plasticity
When Oct 28, 2013
from 02:00 PM to 03:00 PM
Where LR8
Contact Name
Contact Phone 01865-283302
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Plastic deformation and its possible combination with other loadings (thermal, irradiation etc.) induce various types of dislocation microstructure evolution, which eventually result in a spatially heterogeneous deformation field. Different type of dislocation structures exist in metallic materials at different length scales. Typical examples at macro scale are Lüders bands, Portevin-Le Chatelier (PLC) bands, while dislocation cell structures, labyrinth, mosaic, fence or carpet structures develop at meso scale, which are mainly due to self-organization of dislocations.


The plastic localization induces macroscopic softening-hardening and stress-plateau type of responses, arising numerical issues in the solution procedure. The application of standard finite element methods yields mesh-dependent post-critical results due to loss of ellipticity of the incremental boundary value problem.  In order to remedy these problems during the formation of microstructures several models have been proposed however a complete understanding of models which can simulate the patterning of dislocation slip or formation of dislocation substructures is not at hand. In order to contribute to this, inspired by the success of phase field models, an approach is proposed to illustrate the ability of non-convex field models to predict the emergence and evolution of dislocation slip microstructures in a rate dependent strain gradient crystal plasticity framework.


The framework studies the plastic slip patterning in a system with energetic hardening. Both the displacement and the plastic slip are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and slip evolution equation which is derived from thermodynamical considerations. The slip law used in this context differs from the classical ones in the sense that it includes the non-convex free energy term leading to the patterning of this field. The non- convexity is treated as an intrinsic property of the free energy of the material. The framework is enriched by incorporating a non-dissipative dislocation-grain boundary interaction potential in terms of grain boundary Burgers tensor. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated. The proposed formulation is capable of capturing the effect of misorientation of neighbouring grains and the orientation of the grain boundaries on slip evolution in a natural way. The numerical examples illustrate the patterning of deformation field in grains and plastic slip accumulation at the grain boundaries.