Deformation patterning through non-convex strain gradient crystal plasticity

At the microscopic scale, deformed crystalline materials usually show heterogeneous plastic deformation, where the amount of plastic strain varies spatially. At moderate strain levels, regular cellular dislocation structures have been observed. Typical examples of dislocation microstructures are dislocation cells and dislocation walls. In addition to the cellular microstructures at meso-scale, clear band formation and related plastic flow localization in irradiated materials at lower scales and macroscopic plastic slip bands such as Luders bands are also commonly observed structures due to plastic deformation. These microstructures macroscopically manifest themselves through softening of the material or through plastic anisotropy under strain path changes. There have been various approaches to model the formation and evolution of such microstructures which involve coupled models. The difficulty in the modeling of these multi-field coupled problems is the localization of the corresponding field and strain hardening-softening elasto-plastic behavior which yields numerical instabilities. This paper presents a non-convex rate dependent strain gradient plasticity framework for the description of plastic slip patterning in metal crystals. The non-convexity is treated as an intrinsic property of the free energy of the material. Departing from explicit expressions for the free energy and the dissipation potential, the non-convex strain gradient crystal plasticity model is derived in a thermodynamically consistent manner, including the accompanying slip law. For the numerical solution of the problem, the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the resulting slip evolution equation. The slip law differs from classical ones in the sense that it naturally includes a contribution from the non-convex free energy term, which enables patterning of the deformation field. Different types of non-convex free energies are taken into account including both mathematical and physically based descriptions of the plastic slip patterning through 1D and 2D simulations.

BREKELMANS W.A.M.;  GEERS M.G.D.; 

YALCINKAYA Tuncay; 

2013-02-27

ESCOLA POLITECNICA - UNIVERSIDADE DE SAO PAULO

JRC77361

978-85-86686-69-6,   

https://publications.jrc.ec.europa.eu/repository/handle/JRC77361,