Prediction of crack-tip toughness of alumina for given residual stresses with parallel-bonded-particle model

Distinct element method (DEM) is a powerful method to simulate the behavior of the heterogeneous materials. In this article the effect of average grain size on the crack-tip toughness of alumina ceramics is investigated by using a commercial computer program PFC2D with the inclusion of residual stresses caused by thermal expansion anisotropy (TEA) of alumina grains into a DEM model. This is the first time that the residual stresses are included into DEM model and the residual stresses will be included as deviation to the strength of parallel bonds. Since the sintering technology and modeling of sintering is not the main subject of this article, the experimentally measured microlevel residual stress values will be used in order to predict a macrolevel behavior (fracture) of alumina. Comparison of the numerical results with the experimental ones showed that the default parallel-bonded-particle model in program PFC2D gives particle-size dependent results when the fracture of alumina is simulated. With the help of the introduced normalization procedure, the crack-tip toughness of alumina with any average grain size can be predicted if the residual stresses are known and vice versa.