Computer simulation of transformation induced plasticity using finite element method

Some important aspects associated with the transformation induced plasticity in Al₂O₃ZrO₂ are analyzed using a computer simulation based on Finite Element Method (FEM). These aspects include (i) an estimation of the residual stress in the second phase, arising during post fabrication cooling, which affects the critical stress for transformation, (ii) the constitutive behavior of the material during the dilatational transformation of ZrO₂ and (iii) the crack deflection due to the transformation. This simulation study was conducted for angular as well as spherical shapes of second phase particles and also for varying volume fractions of the second phase, using a master finite element mesh. Apart from this numerical experiment, analytical expressions were derived for the residual stress and the constitutive behavior, assuming spherical shape for the second phase particles. The analysis of the constitutive behavior mainly consists of an estimation of the composite modulus and of the irreversible strain due to the transformation. The comparison of the analytical solutions with the results obtained through the simulation shows a very good agreement. Using the simulation of crack deflection, the increase in crack surface area due to the transformation was computed, to approximately estimate the improvement in fracture toughness due to the crack deflection mechanism.