Two-scale Modelling of material degradation and failure

Abstract

It is widely recognized that macroscopic material properties depend on the features of the microstructure. The understanding of the links between microscopic and macroscopic material properties, main topic of Micromechanics, is of relevant technological interest, as it may enable deep understanding of the mechanisms governing materials degradation and failure. Polycrystalline materials are used in many engineering applications. Their microstructure is determined by distribution, size, morphology, anisotropy and orientation of the crystals [1]. At temperature below 0.3-0.5 Tmelting there are no ductile or creep mechanisms and two are the main failure patterns: intergranular, where the damage follows the grain boundaries and transgranular where instead the damage goes through the grain by splitting it into two parts.In this talk a two-scale approach to degradation and failure in polycrystalline materials will be presented. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using two- and three-dimensional boundary element formulation in which the presence of damage is formulated through an initial stress approach to account for the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighbourhood of the selected points. A grainboundary formulation is used to simulate intergranular/transgranular degradation and failure in the microstructure, whose morphology is generated using the Voronoi tessellations. Intergranular/transgranular degradation and failure are modeled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVEs as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macroscale, integral non-local counterparts of the strains are employed. A multiscale processing algorithm is described. Two multiscale simulations are performed to demonstrate the capability of the method.Finally numerical simulations have been performed in order to demonstrate the validity of the model in comparison with experimental observations and literature results.