A hybrid method for the thermo-mechanical analysis of elastic cracks in two-dimensional heterogeneous materials

The present paper describes a numerical method for the thermo-mechanical analysis of two-dimensional heterogeneous materials which combines the finite-element method (FEM) and the Voronoi cell finite-element method (VCFEM). The method was used for evaluating the stress intensity factor (SIF) in heterogeneous materials. In particular, alumina–zirconia composite ceramics were investigated, by considering the effects of zirconia tetragonal-monoclinic transformation (t->m) and of thermal stresses which arise during the cooling stage of the sintering process. In the numerical model the isoparametric elements were used to model the crack tip, while the Voronoi cells were used to represent the second phase heterogeneities. Furthermore, the VCFEM was used to calculate the effective Young's modulus and the coefficient of thermal expansion (CTE) of alumina–zirconia composites, for different volume fractions of the constituent materials. A systematic comparison between the results of the proposed method with some analytical solutions and experimental data was carried out. In particular, the effective Young's modulus was compared with the predictions of a periodic microstructure model and with experimental data found in literature; the results of the CTE were verified by a comparison with an analytical solution; finally, the SIF was initially compared with an analytical solution for an edge crack in a homogeneous plate, and successively alumina–zirconia composites were analysed. The results show a high capability and efficiency of the method in simulating the effective properties of heterogeneous materials, as well as the toughening effects due to phase transformations and thermal stresses.