Constitutive models based on dislocation density formulation and implementation into finite element codes

Abstract: Correct description of the material behaviour is an extra challenge in simulation of the materials processing and manufacturing processes such as metal forming. Material models must account for varying strain, strain rate and temperature, and changing microstructure. This study is devoted to the physically based models of metal plasticity - dislocation density models, their numerical implementation and parameter identification. The basic concepts of dislocation density modelling are introduced including the effects of static and dynamic recovery, influence of strain path and modelling of the back-stress. Possible mechanisms controlling athermal and thermally activated processes involving dislocations, vacancies and solute atoms are also discussed. Mobile and immobile dislocation densities, vacancy concentrations and other variables are treated as internal state variables. The dislocation models are incorporated in a classical continuum plasticity or viscoplasticity framework by means of the evolution equations for these internal variables which effectively control the hardening behaviour. Implementation of these models into finite element codes is straightforward and numerically efficient. Dislocation models are implemented in user material subroutines and used in simulations of sheet metal forming and extrusion. The models are also implemented in a custom toolbox for parameter optimisation in Matlab. A special extended version of a return-map stress update algorithm and its consistent tangent are derived to accommodate the complex coupling effects in a material model, in which all thermo-elastic and hardening properties may depend on the plastic strain. Numerical difficulties of parameter optimisation such as non-uniqueness of the solution, high sensitivity to the starting guess-value and to the choice of the error function appear to be a common problem with advanced material models. Simultaneous curve-fitting of multiple experimental curves of different mechanical testing types is advised to achieve more robust optimisation results. Parameters of dislocation density models usually have clear physical interpretation, and it is possible to obtain values of some of them from sources other than mechanical testing. The accuracy of physically based models is totally dependent on finding the adequate equations to describe the physical processes dominating the material behaviour during deformation. These equations may be more or less accurate than standard engineering models or data interpolation approaches. However, the use of physically significant parameters related to the microstructure properties such as grain size etc gives a natural way to couple them to the models for microstructure evolution, which is important in simulations of manufacturing processes.