Analytical and numerical prediction of mechanical properties of heterogeneous materials with expansive inclusions: Application to waste cementation

Abstract

In this paper, we are concerned with the analytical and numerical study of the effective properties of heterogeneous microstructures resulting from nuclear waste cementation processes. In certain cases, the presence of free-water in the cement matrix pores causes corrosion of metal inclusions that are immobilized, and which transform progressively into an expansive metal oxide layer. Such expansions may lead to high stress/strain levels able to generate micro-cracks in the cement matrix, and to affect the integrity of the waste containers. A homogenization model is then developed to estimate the effective properties of a composite material including spherical inclusions surrounded by a corrosion product layer seen as an expansive phase. The differential scheme is applied, allowing to extend the model to different types of inclusions with high volume fraction, and an interaction coefficient is introduced that relates macroscopic behavior and expansions at microscale. Finally, numerical 3D simulations are performed to determine the effective properties of representative elementary volumes generated with different shapes and volume fractions of inclusions, some of them exhibiting a layer of expansive phase. A comparison between numerical and analytical results shows a good agreement, which confirms the relevance of the model.