Journalof the American Ceramic Society-Marshall et al. No. 7 The fracture behavior of the ZrO, /LaPO layered composites grow from LapO, to ZrO2, a=0. 2(E,= 133 GPa(Ref 9). ly similar to that of Al, o,/LaPo composites E2= 200 GPa)and T/T2=0.05; and (2)for a crack about to investigated previously. Specifically, normally incident cracks grow from LapO4 to Al2O3/ZrO2, a=0.35(E2=300 GPa) in a ZrO, layer appear to penetrate the ZrO2-LaPO. interface and T/T-0. 1. These values fall below the critical condition and to debond either at the lapo4- zro2 interface or within the in Fig 10 so that debonding is expected, as observed LapO. layer. The specific location of debonding and dam within the Lapo, layers is influenced by the morphology of the LaPO,, a different response is predicted. In that case, T,is the of the grain size(see Fig. 1). Although debonding rs near changed, corresponding to interchanging the two materials the interface, the crack path lies both at the interface and in corresponding value of r/T,(-1)falls above the critical con- the LapO. This observation is consistent with the measure terlaminar toughness being approximately equal to the tough dition, where the crack is predicted to gro w into the Lapo. as observed ness of LaPO4. Despite this complication, useful insight may be ained by comparing the measured toughnesses with the analy The debonding criterion in Fig. 10 is also infuenced by sis of interfacial debonding by he and Hutchinson, 20 residual stresses parallel and normal to the interface. In these Whether a crack approaching an interface between two mate composites there are two sources of residual stresses (i) Transformation Stresses: If the ZrO, layers were to the second material depends on the ratio I/Ti of the fracture either during cooling or in the tensile stress field ahead of the elastic mismatch parameter,a, given by effect of these stresses can be estimated using the analysis of a=(E2-E1)(E2+E) (1) He et aL., 4 who define a normalized residual stress parameter where e is the plane strain Young,s modulus. The critical alues of T/T, calculated by He and Hutchinson are shown in m= orva/K where o is the residual stress either normal to the interface or parallel to the interface in material 2, a is a characteristic fiaw 5 Fig. 9. Vickers indentations in composite of Y-Zro2/Al,O, and LaPO4.(a)and(b)SEM micrographs showing damage within LaPO. layers (c)Comparison of interlaminar crack length and crack length in Y-ZrO2/Al2O, matri1682 Journal of the American Ceramic Society-Marshall et al. Vol. 80, No. 7 The fracture behavior of the ZrO,/LaPO, layered composites is qualitatively similar to that of Al,O,/LaPO, composites investigated previou~ly.~~ Specifically, normally incident cracks in a ZrO, layer appear to penetrate the zrO2-LaPo4 interface and to debond either at the LaP0,-ZrO, interface or within the LaPO, layer. The specific location of debonding and damage within the LaPO, layers is influenced by the morphology of the interface, which in these composites has roughness on the scale of the grain size (see Fig. 1). Although debonding occurs near the interface, the crack path lies both at the interface and in the LaPO,. This observation is consistent with the measured interlaminar toughness being approximately equal to the tough￾ness of LaPO,. Despite this complication, useful insight may be gained by comparing the measured toughnesses with the analy￾sis of interfacial debonding by He and Hutchinson?o Whether a crack approaching an interface between two mate￾rials will debond along the interface rather than penetrate into the second material depends on the ratio &/r2 of the fracture energies of the interface and the second material, as well as the elastic mismatch parameter,m a, given by (1) where E‘ is the plane strain Young’s modulus. The critical values of r/r2 calculated by He and Hutchinson” are shown in Fig. 10. With the toughnesses measured in the previous section, the following parameters are obtained. (1) for a crack about to a = (E; - E;)/(E; + E:) grow from LaPO, to ZrO,, a = 0.2 (El = 133 GPa (Ref. 9), E, = 200 GPa) and rl/r2 = 0.05; and (2) for a crack about to grow from LaPO, to Al2O3/ZrO2, a = 0.35 (E, = 300 GPa) and &/r2 - 0.1. These values fall below the critical condition in Fig. 10 so that debonding is expected, as observed. For a crack growing in the reverse direction, from zirconia to LaPo,, a different response is predicted. In that case, r, is the fracture energy of LaPO, (-7 J/m2) and the sign of a is changed, corresponding to interchanging the two materials. The corresponding value of &/I-, (-1) falls above the critical con￾dition, where the crack is predicted to grow into the LaPO,, as observed. The debonding criterion in Fig. 10 is also influenced by residual stresses parallel and normal to the interface. In these composites there are two sources of residual stresses. (i) Transformation Stresses: If the Zro, layers were to undergo the tetragonal-to-monoclinic phase transformation, either during cooling or in the tensile stress field ahead of the incident crack, large residual stresses would be generated. The effect of these stresses can be estimated using the analysis of He et ~l.,~ who define a normalized residual stress parameter q = u,&K (2) where u, is the residual stress, either normal to the interface or parallel to the interface in material 2, a is a characteristic flaw Fig. 9. Vickers indentations in composite of Y-Zr0,/AI2O3 and LaPO,. (a) and (b) SEM micrographs showing damage within LaPo, layers. (c) Comparison of interlaminar crack length and crack length in Y-ZrO,/AI,O, matrix