Crack front trapping in transformation-toughened ceramics

A theoretical study is made of the trapping of a crack front in brittle matrix ceramic reinforced by dispersed transformable zirconia particles. The trapped discontinuous crack front is modelled by a collinear array of microcracks interspersed by transformable particles. The effect of trapping of the macrocrack front is approximated by a closing pressure on a bridged zone. The maximum closing pressure and the critical opening of the macrocrack are related to the volume (area) fraction and size of the transformable particles. It is found that the maximum toughening due to trapping occurs at moderate volume (area) fractions of large particles. This is in agreement with available theoretical and experimental results.