Mines Paritech + Safran (FRANCE)
The PhD student will work on a finite deformation crystal plasticity model implemented in the implicit finite element code Zset (common code for MAT-SAF). She/he will identify the material parameters for the titanium alloy for which experimental results are available within the project, using simulations of representative volume elements of polycrystals. The model will be also implemented in an explicit code for comparison. Finite element simulations will be performed at large strains in order to investigate the possibility of remeshing and field transfer in the context of crystal plasticity.
In a second step, the crystal plasticity framework will be extended to incorporate the effect of Geometrically Necessary Dislocations (GND) that arise in the presence of strong strain gradients. Two types of strain gradient crystal plasticity models will be considered. The first one is an available strain gradient crystal plasticity model incorporating the gradient of cumulative slip in the formulation. The corresponding implicit code is already available at finite strains. This first approach will be extended to incorporate the full dislocation density tensor (GND tensor) defined as the curl of the plastic deformation field. Again, implicit and explicit formulations will be proposed. Size effects associated with grain size and strong strain gradients induced by the loading will be investigated and compared to experimental results obtained within the project.
The last stage will be devoted to the identification of a homogenized polycrystal model at large strains from the simulations of the polycrystalline aggregates. This reduced model will be used to determine the effect of the crystallographic texture and its evolution during straining. A first version of the model is available and will be extended to incorporate suitable constitutive laws including dislocation densities and characteristic lengths deduced from the full field simulations. The results of the homogenization model will serve for the calibration of more macroscopic models not based on crystal plasticity.
Available codes : Implicit finite deformation crystal plasticity, Implicit gradient of cumulative slip crystal plasticity model at finite deformation. Implicit homogenized polycrystal model at finite deformations (Zset).
Codes to be produced : Explicit finite deformation crystal plasticity, Implicit and explicit Curl-based strain gradient crystal plasticity model. Explicit homogenized polycrystal model at finite deformations.