Microstructural aspects of crack propagation

This mechanism has been analyzed theoretically and various calculations have shown that crack bowing should lead to an increase in fracture toughness. For 

The stresses near a crack tip in a linear elastic material are related to the applied stress intensity factor K. In some materials, non-linear deformation behavior may occur in the high-stress zone at the crack tip. The effect of this process zone will be to change the stresses at the crack tip. These stresses can often described by a local stress intensity factor K. If the stresses are reduced and the 

Several approaches have been taken to calculating the toughening associated with a stress-induced phase transformation and there is agreement between these various analyses. The simplest calculations assume the phase transformation is purely dilatational and that it is nucleated by a critical value of the mean stress at a crack tip. In a material that contains a crack, the transformation will occur in a frontal zone at the crack tip, as shown schematically in Fig. 8.60. For this case, the transformation is found not to increase toughness. Toughening only 

The size of the zirconia particles is very important in controlling the extent of the stress-induced transformation and the effect is shown schematically in Fig. 8.61. At small particle sizes compared to the critical size d, a very high critical stress is needed to induce the transformation and thus h and the toughening are 

Net strain coupling Zone shape Toughness constant, C 

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