Numerical modeling of the deformation and fracture of a porous alumina ceramics at mesoscale

The deformation and fracture of the mesovolumes of porous alumina ceramics during uniaxial tension were numerically simulated. The porous structure of the mesovolumes was obtained from the electron microscopy data and taken into account explicitly in the modeling process. The porosity of the mesovolumes was equal to 33, 26, and 17 %. Three different computer models of the mesovolumes of the same porosity were taken for each considered value of porosity. The modeling was implemented using the finite-difference method in a two-dimensional statement under plane-strain conditions. The constitutive equations accounting for damage accumulation which leads to a degradation of elastic properties were adopted. The equation defining damage accumulation kinetics was based on the calculation of effective stress of the Drucker–Prager material model with consideration for a stress state type (the Lode parameter). The mesoscopic fracture was described using the critical damage criterion. After meeting the fracture criterion, the stresses were set equal to zero, and the material ceased to resist tension but not compression. Based on the calculated results, the effect of the porous ceramic structure on the local fracture characteristics in the mesovolumes of material as well as on the macroscopic deformation diagram was analyzed. The presence of strong stress concentrators in the mesovolumes determined crack's nucleation cite and affected their propagation within the modeled mesovolumes. The calculated effective elastic and strength characteristics of materials are in a good agreement with experimental data.