Transformation toughening in ceramic with martensites or micro-cracks

Abstract

In certain ceramics, the high stress in the tip of a macroscopic crack induces martensitic type transformation of the second phase particles (e.g. Zirconia, ZrO 2). The transformation changes the near-tip stress by decreasing the net stress intensity factor and the toughness of the material is thereby enhanced. To evaluate the decrease of the stress intensity factor, one needs to know the distribution of the transformation strain around the crack tip. Therefore, an incremental analysis of plasticity, which takes into account the microstructural properties and mechanism of the particle transformation, is generally required. In this paper, we present a method of calculating the decrease of stress intensity factor without considering the microstructural details or performing an incremental analysis. Regardless of the history of loading and unloading, the current crack opening displacement is all the information needed for the calculation. It is proven that under a given distribution of crack opening displacement, there are infinite numbers of possible configurations of transformation zone with transformation strain inside. Identifying the actual transformation strain and transformation zone is impossible unless additional information is provided. However, all these transformation strains inside the corresponding transformation zones induce the same decrease of stress intensity factor. In this sense, they are all equivalent. If we can obtain any of these transformation strains with the corresponding transformation zone, the decrease of stress intensity factor is then determined. The problem is formulated as a system of integral equations of the first kind with transformation strain as unknown and crack opening displacement as input data. The regularization method is employed to obtain a stable solution of these ill-posed integral equations. The stress intensity factor is then computed by using Bueckner's weight function.