Model of Transformation Toughening in Brittle Materials

Assuming that the energy dissipation decreases inversely with distance from the crack tip, the increase in steady-state toughness of a transformation-toughened ceramic is estimated to be δ J = (δ J ₀/ω) In (1 +ω), where (i) δ J ₀ denotes the toughness increment which would be expected for a given zone height h ₀ assuming full transformation throughout the zone, and (ii) ω is a nondimensional parameter giving the ratio of the inelastic transformation strain (for full transformation) to the initial elastic strain at the onset of transformation. This estimate extends the earlier result of McMeeking and Evans (1982) in two significant respects: (i) the transformation strain may include a shear component, instead of being purely dilatational, and (ii) the range of ω is now unrestricted, whereas the McMeeking and Evans approach strictly applies only in the weak transformation limit, ω« 1. The height of the inner zone h _i within which transformation has proceeded to completion (or saturation) is estimated to be h _i= h ₀/(1 +ω). Experimental data of Mg-PSZ and Ce-TZP can be quantitatively accounted for using this approximate model, which is also in very good agreement with the rigorous finite-element results of Budiansky, Hutchinson, and Lambropoulos in the special case of subcritical dilatational transformation.