On the Mechanics of Stress-induced Phase Transformation in Zirconia

SOME CONWJWENCX~ of a simple theoretical model for the stress-induced, isothermal phase transformation of an isolated tetragnnal zirconia crystal are studied. The transformation to a monoclinic state is viewed as mechanical buckling from one homogeneous geometrical configuration to another. The model is used to predict the manner in which an applied shear stress should interact with hydrostatic stress in causing the transformation, and also the reverse monoclinic-to-tet~g(~nai phase change. An isolated tetragonal inclusion in an elastic matrix is also considered, and its response to a far-fieId combination of shear and hydrostatic stress is analysed. THE DISCOVERY by GARVIE et al. (1975) of the transformation-toughening effects of zirconia (Zr02) particles embedded in a brittle matrix has spawned a large literature on the subject [see Evans and HEUER (1980), EVAI% and CANNON (1986), GREEN et al. (I 989), R&KB and EVANS (1989) for reviews], and research continues apace. Early theoretical analyses of transformation toughening were based on the assumption that a ~etrago~l-ho-monoclinic fr m) phase transformation of zirconia incfusions is provoked by a critical hydrostatic tension ~~~~E~K~N~ and EVANS, t982 ; BUDIANSKY et al., 1983), and tbc same basis was used in several Iater studies (e.g. ROSE, 1986; AMAZXCO and BUDIAN~KY, 1988; STUMP and BUDIANSKY, I989a, b). But in several theoretical studies (e.g. EVANS and CANNON, 1986; LAMBROPOULOS, 1986: CHEN and REYES Monrz, 1987 ; SUN et cd., 1990 ; SRJMP, 1991) shear-stress effects on transformation toughening have been explored, and found to be substantial (and in Stump’s work, startling). Furthermore, experiments on composites (CHEN and REYE~ MOREL, 1986) have shown that shear and hydrostatic stress may interact significantly in triggering the m -+ t transformation. In this paper we explore some consequences of a simple Landau model for the stress-induced, isothermat phase ~ransforma~ian of an isofated tetragonal zirconia crystal. The transformation is viewed as mechanical buckling f’rom one homogeneous I445 I446 B. B~JDIANSKY and L. TKUSKIYOVSKY geometrical configuration to another. The analytical formulation is based on the most elementary polynomial strain-energy functional that is sufficiently rich to imply the t + m transformation at a critical pressure. A similar functional has been written for zirconia by CHAN (19X8), but we explore its implications in rather different directions here. The model is used to predict the manner in which an applied shear stress should interact with hydrostatic stress in causing the transformation, and also the reverse m + t transformation. The theory also implies constraints on the signs and ratios of some of the elastic constants in the monoclinic phase. These results will be confronted with those of recent acoustic experiments by NEVITT ct u/. (1988) and atomic N/J irzirio calculations by COHEN et d. (1988). On the basis of an idealized. approximate version of the model, we also look briefly at an isolated tetragonal inclusion in an elastic matrix, and study its response to a farfield combination of shear and hydrostatic stress vis-a-vis that of an unconstrained crystal.