H Miyazaki et al Journal of the European Ceramic Society 26(2006)3539-3546 3543 By contrast, the fracture toughness of the fibrous ites was increased even by introducing a small amount of fine zirconia filaments into alumina matrix(Fig. 5), and was further increased with fz and reached a maximum(6.2 MPam")where fz was 47 vol%. Then the fracture toughness decreased slightly with fz but still maintained higher value than that of the mono- lithic zirconia. The volume fractions of transformed zirconia in the fibrous composites are shown in Fig. 6(solid square). The volume fraction of transformed zirconia in the fibrous compos- ites increased with fz, which was almost the same rising curve behavior as that of the powder- mixture composites. It is rea- sonable to suppose that contribution from the"stress-induced transformation to the toughness of the fibrous composites was 100m almost the same level as that of the powder-mixture composites Consequently, the higher fracture toughness of the fibrous com- posites over that of powder-mixture composites is attributed Fig. 8. SEM image of fracture surface of the 47/53 vol% zirconia/alumina co. extruded composite. No trace of the pullout of fibers was observed. another toughening mechanism. 3.3.2. Effect of crack deflection mechanism on the fracture deflection. and the effect of a crack deflection at an interface between the fiber and the matrix. The frequency of interaction Fig 7 shows crack propagation of an indenter-induced crack between the crack and the second phase is represented by the on both the 47/53 vol% zirconia/alumina fibrous composite and volume fraction of the second phase providing the width of the the 50/50 vol% zirconia/alumina powder-mixture composite. second phase filaments is constant. Adachi et al. reported that in the fibrous composite, whereas crack deflection was not phase lamer composite increased with increasing the difterence posite. The same result was also obtained at the 10/90 vol% assume that the effect of a crack deflection on the toughness is zirconia/alumina composite 10 It is clear that the residual stress almost proportional to the variation in the residual stress across produced by mismatch of thermal expansion between alumina and zirconia affected the crack propagation more effectively in due to the crack-deflecting mechanism on fz can be analyzed the case of fibrous microstructure further increasing the fracture by the product of the volume fraction of the secondary phase toughness. Although the composites have the fibrous microstru ture, pullout of the fine fibrous second phase was not observed the matrix. The residual thermal stress in the fiber-reinforced (Fig8). The lack of pullout of the fibrous phase is due to a tough composites was analyzed by Budiansky et al., by using the com- bonding at the interface between the two phases posite cylinder model. The average of residual stress of matrix fz over 47 vol%(Fig. 5), despite the increased rot osites with is given by the following equation The decrease in toughness of the fibrous com olume fraction 入2「Er from the"crack-deflection"mechanism caused by residual stress Em-X EJLI-Vml of transformed zirconia(Fig. 6), implies that the contribution decreased. The contribution of the crack-deflection mechanism where g is axial stress. e the youngs modulus. c the volume to the increment in fracture toughness of the fibrous composite fraction, v Poisson's ratio and subscripts m and f refer to matrix an be estimated by the product of the frequency of interaction and fiber, respectively. A1 and A2 are functions of cm, Em/Er, between the crack and the second phase, which causes crack vm and vf shown explicitly in appendix. S2 is the thermal strain 50um 50m Fig. 7. Propagation of crack generated by indentation in(a)47/53 vol% zirconia/alumina co-extruded composite and( b)50/50 vol o zirconia/alumina powder- composite. The indentation load was 196N for(a) and 98N for(b)H. Miyazaki et al. / Journal of the European Ceramic Society 26 (2006) 3539–3546 3543 By contrast, the fracture toughness of the fibrous compos￾ites was increased even by introducing a small amount of fine zirconia filaments into alumina matrix (Fig. 5), and was further increased with fZ and reached a maximum (6.2 MPa m1/2) where fZ was 47 vol%. Then the fracture toughness decreased slightly with fZ but still maintained higher value than that of the mono￾lithic zirconia. The volume fractions of transformed zirconia in the fibrous composites are shown in Fig. 6 (solid square). The volume fraction of transformed zirconia in the fibrous compos￾ites increased with fZ, which was almost the same rising curve behavior as that of the powder-mixture composites. It is rea￾sonable to suppose that contribution from the “stress-induced” transformation to the toughness of the fibrous composites was almost the same level as that of the powder-mixture composites. Consequently, the higher fracture toughness of the fibrous com￾posites over that of powder-mixture composites is attributed to another toughening mechanism. 3.3.2. Effect of crack deflection mechanism on the fracture toughness Fig. 7 shows crack propagation of an indenter-induced crack on both the 47/53 vol% zirconia/alumina fibrous composite and the 50/50 vol% zirconia/alumina powder-mixture composite. Crack deflection at the zirconia/alumina interface was observed in the fibrous composite, whereas crack deflection was not observed by an optical microscope in the powder-mixture com￾posite. The same result was also obtained at the 10/90 vol% zirconia/alumina composite.10 It is clear that the residual stress produced by mismatch of thermal expansion between alumina and zirconia affected the crack propagation more effectively in the case of fibrous microstructure further increasing the fracture toughness. Although the composites have the fibrous microstruc￾ture, pullout of the fine fibrous second phase was not observed (Fig. 8). The lack of pullout of the fibrous phase is due to a tough bonding at the interface between the two phases. The decrease in toughness of the fibrous composites with fZ over 47 vol% (Fig. 5), despite the increased volume fraction of transformed zirconia (Fig. 6), implies that the contribution from the “crack-deflection” mechanism caused by residual stress decreased. The contribution of the crack-deflection mechanism to the increment in fracture toughness of the fibrous composite can be estimated by the product of the frequency of interaction between the crack and the second phase, which causes crack Fig. 8. SEM image of fracture surface of the 47/53 vol% zirconia/alumina co￾extruded composite. No trace of the pullout of fibers was observed. deflection, and the effect of a crack deflection at an interface between the fiber and the matrix. The frequency of interaction between the crack and the second phase is represented by the volume fraction of the second phase providing the width of the second phase filaments is constant. Adachi et al. reported that the degree of the crack deflection in the alumina/zirconia bi￾phase lamer composite increased with increasing the difference of residual stress between the two phases.7 It is reasonable to assume that the effect of a crack deflection on the toughness is almost proportional to the variation in the residual stress across the interface. Then the dependence of the increment in toughness due to the crack-deflecting mechanism on fZ can be analyzed by the product of the volume fraction of the secondary phase and the difference of the residual stress between the fiber and the matrix. The residual thermal stress in the fiber-reinforced composites was analyzed by Budiansky et al., by using the com￾posite cylinder model.22 The average of residual stress of matrix is given by the following equation. σm Em = λ2 λ1
Ef E
cf 1 − νm Ω (2) where σ is axial stress, E the Young’s modulus, c the volume fraction, ν Poisson’s ratio and subscripts m and f refer to matrix and fiber, respectively. λ1 and λ2 are functions of cm, Em/Ef, νm and νf shown explicitly in appendix.  is the thermal strain Fig. 7. Propagation of crack generated by indentation in (a) 47/53 vol% zirconia/alumina co-extruded composite and (b) 50/50 vol% zirconia/alumina powder-mixture composite. The indentation load was 196 N for (a) and 98 N for (b).