A micro-mechanical analysis of the effect of particle clustering on the brittle-ductile transition in nuclear steels

The effect of the clustering of manganese sulfur precipitates in nuclear vessel steels on their brittle-ductile transition is analyzed through a micro-mechanical approach. Because of the early de-cohesion of the precipitates, these materials are described as isotropic porous elastoplastic media with, for simplicity, spherical voids. Their ductile response is analysed by means of homogenization models for nonlinear behaviours and the brittle fracture is described by the Beremin criterion which is computed from the local field predicted by these models. Microstructures with different morphologies are simulated and compared: random microstructure and microstructures with connected and disconnected clusters, with uniform or variable pore sizes. A clustering effect on the ductile fracture is revealed by two and three-dimensional numerical simulations based on the Fast Fourier Transform and through a semi-analytical model. The latter is based on a combination of the modified secant approach of Suquet and a representation of the microstructure by a generalized Hashin's multilayer composite spheres assemblage, which permits one to account for the fluctuations of the local porosity observed on real materials. This model leads to an upper bound for the macroscopic yield surface of porous media with a rigid-perfectly plastic matrix described by a Hashin's composite spheres assemblage. This bound improves on all existing bounds and converges towards the Gurson's bound for a purely hydrostatic load. The clustering effect on the brittle fracture is ambiguous in the two-dimensional case with an elastic-perfectly plastic matrix and is non-existent in the three-dimensional case with a hardening matrix. Finally, a morphological indicator for the detection of the presence of clusters and the characterization of their connectedness is proposed and applied on a sample of the studied steel. (author)