Trapped cracks at indentations - Part II Fracture mechanics model

Abstract

A fracture-mechanics model for indentation cracking in phase-transforming materials is developed, based on the competing interaction of the tensile residual-mismatch field and the compressive contact-induced transformation field. In addition to the usual subthreshold and well-developed cracking ranges, the model predicts the trapping of cracks at indentations, within the transformation zone. As an example, the model is used to describe the dependence of radial crack length on indentation load in a range of yttria-tetragonal zirconia polycrystals (Y-TZP), explicitly addressing the trapping behaviour observed in Part I. The crucial parameters of the model obtained from the experimental fits, the size of the transformation zone relative to the contact impression, b/a, and the magnitude of the transformation stress relative to the hardness, σT/H, agree with independent measurements. Although applied to phase-transforming materials here, the principles of the model are generally applicable to systems with short-range, compensating stress fields competing with longer-ranged, dominant fields, leading to two discrete crack populations. © 1994 Chapman & Hall.