The influence of finite element meshes on the results of a spatial polycrystalline aggregate model

The influence of the microstructural inhomogenities in materials on the life-time of safety significant components of nuclear power plants is still not fully characterized. One of the most important sources of inhomogenities in metals is their grain structure. Differences in crystallographic orientations of grains lead to different responses under the applied loads and increased stresses at the grain boundaries. Engineering tools which are used to assess a response of a structural component to the applied loads are typically based upon the mechanics of continuum and are not able to account for these effects. Dedicated polycrystalline aggregate models are therefore being developed to study the effects of the microstructure on the load carrying capabilities of materials. However, a limited number of finite element types can be used due to the geometrical complexity of such models. A procedure for testing the behaviour of different finite elements in simulations involving explicit models of randomly shaped and oriented grains described by crystalline elasticity and crystal plasticity is therefore proposed. Cumulative distributions of the stress/strain tensors in all integration points in the model are compared, enabling comparison of the “average” (macroscopic) as well as “extreme” (local) behaviour of different meshes. Such an approach provides an easy to use probabilistic measure of the quality of results obtained using different element types, formulations and mesh densities.