3544 H Miyazaki et al. / Journal of the European Ceramic Sociery 26(2006)3539-3546 2 rial property data for alumina and zirconia ▲ alumina Alumina Zirconia oungs modulus, E(GPa) 210 杀 Poissons ratio, v Coeff. of thermal expansion, a(C-) g2=(af-am)△T where af and am are the coefficients of thermal expansion of ber and matrix, AT is the temperature difference over which Volume fraction of ZrO2 phase f (vol%) the residual thermal stress develops in the composites The average of residual thermal stress in fiber is given by Fig. 10. Full width at half maximum(FWHM)of XRD peaks of tetragonal zirconia(1 33)and alumina(1.0.10) reflections in the fibrous composites as a function of volume fraction of zirconia phase fz. Er Ile The thermal residual stresses in both the alumina and zirconia stress between the two phases is almost constant regardless of phases were calculated with the above equations by substituting the composition the physical properties data for the two materials(see Table 2) In order to confirm the above calculation of the residual and assuming AT=1000.C.,When fz is 47 vol % both the stresses in both the alumina and zirconia phases experimentally, alumina and zirconia phases were neither matrix nor fiber since FWHM of the XRD peak of both alumina(1.0.10)reflection they had nearly same volume content and were not covered by and zirconia(133) reflection was measured. The FWHM of each other(Fig. 2(b). Then the average residual stresses in both the alumina and zirconia is shown in Fig. 10 as a func both the alumina and zirconia phases were calculated for both tion of fz. The FWHM of the alumina peak increased with fi. the fiber and matrix cases. The result is shown in Fig9. It was suggesting that the residual stress in alumina increased,while found that the calculated residual stress in the alumina phase was the FWhm of the zirconia peak decreased with increasing fz, always compressive and proportional to the volume fraction of suggesting that the residual stress in zirconia decreased, which zirconia. It was also shown that the residual stress in the zirconia is consistent with the above calculation(Fig. 9). Then the above phase was always tensile and proportional to the volume fraction estimation of the difference in residual stress between the two of alumina. The discontinuity in both the residual stress curves phases is also reasonable. The effect of crack deflection per at fz=47 vol% is due to the switching of the zirconia fiber a fiber/matrix interface on the toughness is supposed to be the zirconia matrix. It is revealed that the difference in residual nearly constant in every composition. The volume fraction of the secondary zirconia phase is maximum at fz=47 vol% when fz <47 vol%. Similarly, when fz 247 vol%, the volume fraction of the secondary alumina phase is maximum at fz=47 vol%. Alumina Then the product of the volume fraction of the secondary phase Zirconia and the effect of crack deflection at a fiber/matrix interface has maximum at fz=47 vol%, which means the increment in frac- ture toughness due to the crack deflection mechanism should reach maximum at fz=47 vol%. Thus, the reason of the frac ture toughness having maximum value at fz=47 vol% was explained by the estimation of the residual stresses in the two 3.4. Bending strength Table 3 shows the bending strength and the Weibull modu lus of both the fibrous and powder-mixture composites, as well Volume fraction of zirconia f, (vol%) as the constituent monoliths The strength of the fibrous com- of residual thermal stress in both alumina and zirconia phases posites was almost the same as that of the monolithic alumina, volume fraction of zirconia, fz, calculated with the Eqs. (2)-(4 whereas the Weibull modulus of the fibrous composites was data in Table 2. Compressive stress is positive and tensile stress improved. The increase in Weibull modulus of these compos is negative in the figure. ites is attributable to the increment in the fracture toughness3544 H. Miyazaki et al. / Journal of the European Ceramic Society 26 (2006) 3539–3546 Table 2 Material property data for alumina and zirconia Alumina Zirconia Young’s modulus, E (GPa) 390 210 Poisson’s ratio, ν 0.25 0.3 Coeff. of thermal expansion, α ( ◦C−1) 8.3 × 10−6 10 × 10−6 given by Ω = (αf − αm)T (3) where αf and αm are the coefficients of thermal expansion of fiber and matrix, T is the temperature difference over which the residual thermal stress develops in the composites. The average of residual thermal stress in fiber is given by σf Ef = −λ2 λ1
Em E
cm 1 − νm Ω (4) The thermal residual stresses in both the alumina and zirconia phases were calculated with the above equations by substituting the physical properties data for the two materials (see Table 2) and assuming T = 1000 ◦C.3,7 When fZ is 47 vol%, both the alumina and zirconia phases were neither matrix nor fiber since they had nearly same volume content and were not covered by each other (Fig. 2 (b)). Then the average residual stresses in both the alumina and zirconia phases were calculated for both the fiber and matrix cases. The result is shown in Fig. 9. It was found that the calculated residual stress in the alumina phase was always compressive and proportional to the volume fraction of zirconia. It was also shown that the residual stress in the zirconia phase was always tensile and proportional to the volume fraction of alumina. The discontinuity in both the residual stress curves at fZ = 47 vol% is due to the switching of the zirconia fiber to the zirconia matrix. It is revealed that the difference in residual Fig. 9. Average of residual thermal stress in both alumina and zirconia phases as a function of volume fraction of zirconia, fZ, calculated with the Eqs. (2)–(4) and the physical data in Table 2. Compressive stress is positive and tensile stress is negative in the figure. Fig. 10. Full width at half maximum (FWHM) of XRD peaks of tetragonal zirconia (1 3 3) and alumina (1.0.10) reflections in the fibrous composites as a function of volume fraction of zirconia phase fZ. stress between the two phases is almost constant regardless of the composition. In order to confirm the above calculation of the residual stresses in both the alumina and zirconia phases experimentally, FWHM of the XRD peak of both alumina (1.0.10) reflection and zirconia (1 3 3) reflection was measured. The FWHM of both the alumina and zirconia is shown in Fig. 10 as a func￾tion of fZ. The FWHM of the alumina peak increased with fZ, suggesting that the residual stress in alumina increased, while the FWHM of the zirconia peak decreased with increasing fZ, suggesting that the residual stress in zirconia decreased, which is consistent with the above calculation (Fig. 9). Then the above estimation of the difference in residual stress between the two phases is also reasonable. The effect of crack deflection per a fiber/matrix interface on the toughness is supposed to be nearly constant in every composition. The volume fraction of the secondary zirconia phase is maximum at fZ = 47 vol% when fZ
47 vol%. Similarly, when fZ 47 vol%, the volume fraction of the secondary alumina phase is maximum at fZ = 47 vol%. Then the product of the volume fraction of the secondary phase and the effect of crack deflection at a fiber/matrix interface has maximum at fZ = 47 vol%, which means the increment in frac￾ture toughness due to the crack deflection mechanism should reach maximum at fZ = 47 vol%. Thus, the reason of the frac￾ture toughness having maximum value at fZ = 47 vol% was explained by the estimation of the residual stresses in the two phases. 3.4. Bending strength Table 3 shows the bending strength and the Weibull modu￾lus of both the fibrous and powder-mixture composites, as well as the constituent monoliths. The strength of the fibrous com￾posites was almost the same as that of the monolithic alumina, whereas the Weibull modulus of the fibrous composites was improved. The increase in Weibull modulus of these compos￾ites is attributable to the increment in the fracture toughness,