Strain gradient crystal plasticity modelling of size effects in a hierarchical martensitic steel using the Voronoi tessellation method

Inelastic deformation of a high-strength martensitic steel (P91) is investigated using a strain gradient crystal plasticity model implemented using the finite element method. Voronoi tessellation is used to model the hierarchical structure, prior austenite grain (PAG)/packet/block, of the martensitic steel and the effect of PAG/packet/block size on the macro- and micro-scale mechanical response is analysed numerically. The role of lath interaction and the influence of dislocation type (statistically stored and geometrically necessary dislocations) are investigated. It is found that block size determines the overall mechanical response, consistent with the Hall-Petch relation, while packet and block diameters influence the microplastic strain distribution. A modified Hall-Petch relation is examined which provides a relationship between material flow strength and block diameter (size) which holds for a wide range of initial dislocation densities and block diameters