Microscale modelling of the deformation of a martensitic steel using the Voronoi tessellation method

Abstract

The deformation of a martensitic steel (P91) at the microscale is investigated using the finite element method. The approach takes into account the hierarchical grain–packet–block microstructure of the steel as determined experimentally by electron backscatter diffraction (EBSD). The orientation relationship for P91 between the prior austenite grain (PAG) and the martensitic packet/block is determined and found to be consistent with the Kurdjumow–Sachs (K–S) relationship. This relationship is incorporated within a finite-element model to represent the material microstructure, using a representative volume element (RVE) generated by a modified centroidal Voronoi tesselation (VT) approach. A non-linear, rate dependent, finite strain crystal plasticity model is used to simulate the mechanical response of the material at the micro- and macro-level and the sensitivity of the results to the model assumptions is investigated. It is found that the global (macro) mechanical response predicted by the RVE generated using the modified VT model is in good agreement with that predicted by an RVE taken directly from the measured EBSD microstructure. The influence of block/packet/grain boundaries on the local (micro) deformation is examined and it is found that the microscale prediction obtained using the RVE based on the modified VT microstructure, with an appropriate choice of microstructural parameters, is consistent with that obtained using the measured EBSD map.