PHILOSOPHICAL MAGAZINE, I I DECEMBER 2004 VoL.84,NO.35,3741-3754 Taylor Francis Effect of internal stress disturbance on the stress-induced transformation toughening of an alumina/zirconia dual-phase composite TAKASHI AKATSUT, SHIN NAKANISHI, YASUHIRO TANABE FUMIHIRO WAK AI and EIICHI YASUD Nagatsuta 4259, Midori, Yokohama 226-8503. Japul nology Materials and Structures Laboratory, Tokyo Institute of Tecl I Received 5 February 2004 and accepted in revised form / July 200-n1 BSTRAC CI The toughening and strengthening of a dual-phase composite, consisting of alpha-alumina (a-Al-O3)and tetragonal-zirconia(I-ZrO2), were investigated. The toughness of the composite was evaluated through the precise measurement of work-of-fracture (WOF), which is a measure of total fracture resistance involving he rising R-curve eflect. It was found that both the WOF and flexural strength of the composite were maximized at a I-ZrO, volume fraction z of about 0.7. The thermal degradation of the mechanical properties was also observed. The effect of the internal stresses arising from the thermoelastic mismatch between a-Al, and I-ZrO, on the critical stresses of the reversible phase transformation of I-ZrO, was numerically examined to describe the /z- and temperature- dependencies of woF quantitatively §1. INTRODUCTION Since Garvie et al.(1975)revealed an increase in fracture toughness due to the stress-induced martensitic transformation of zirconia from metastable tetragonal ( -ZrO2) into monoclinic phase (m-ZrO2), a large number of studies have been carried out in the hope of improving the mechanical properties of ceramics by utilizing I-ZrO2 particles. A dual-phase composite that consists of alpha-alumina (a-Al2O3) and 1-ZrO2 is designed to have superior mechanical properties, e.g. extre mely high flexural strength(over I GPa) and high toughness at room temperature ( Claussen et al. 1977, Lange 1982. McMeeking and Evans 1982. Tsukuma et al. 1985a, b, Rose and Swain 1986, Ruhle et al. 1986. Heuer 1987, Nettleship and Stevens 1987, Pezzotti et al. 1999). It is well known that the mechanical properties of this composite depend strongly on the volume fraction /z of ZrO. The nature of the /z-dependence is, however, still not clear for several reasons. First, an A where the designed properties are maximized is not specified in previous studies Lange 1982, Tsukuma et al. 1985a, b, Pezzotti et al. 1999). Also, the dual-phase composite with maximized fracture toughness does not always have the maximized flexural strength. Second, the maximized toughness has been often explained through the combination of the stress-induced transformation and tAuthor for correspo Email: Takashi Akatsu(a msl titech ac jp. hiasophical Magazine ISsN 1478-6435 print ISSN 1478-6443 online I 2004 Taylor Francis Ltd http:/www,tandf.couk/journa Ol:10.108014786430412331293478
PHILOSOPHICAL MAGAZINE. II DLCLMBER 2004 VOL. 84, NO. 35, 3741 - 3754 Effect of internal stress distnrbance on the stress-induced transformation toughening of an aluniina/zirconia dual-phase composite TAKASH! AKATSut, SHIN NAKANISHI, YASUHIROTANABH, FUMIHIROWARAI and EIICHIYASUDA Materials and Struciures Labortitory. Tokyo Insliliiti: of Technology, Nagatsiita 4259. Midori, Yokohama 226-8503, Japim [Recfivect 5 Fchruarv 2004 and accepted in revised t'orm I .fitly 2004] ABSTRACT The toughening and strengthening of a dual-phase composite, consistitig of alpha-altiniina (cy-AUOi) and tctragonal-zirconia (/-ZrO:). were invesligalcd. The toughness of the composite was evaluated through Ihe precise measurement of work-of-fracture (WOF). which is a measure of total IViiclure resistance involving the rising /^-curve eflect. It was found that both Ihc WOF and Hexiiral strength of the composite were maximized at a z-ZrOi volume fraction // of about 0.7. The thermal degradation of the mechanical properties was also observed. The elTect of the intertial stresses arising from the thermoelastic mismatch between a-AliO, and /-ZrOi on the critical stresses ofthe reversible phase transformation of /-ZrO2 was numerically examined lo describe the f^- and temperaturedependencies of WOF quantitatively, § 1. INTRODUCTION Since Garvic el at. (1975) revealed ati increase in Iracture toughness due to the stress-induced martensitic tratislortTiation of zirconia from nietastable tetragonal (^ZrOi) into monoclinic phase (m-ZrOi), a large number of studies have been carried mit in lhe hope of improving the tnechanical properties of ceramics by utilizing /-ZrO^ particles. A dual-phase composite that consists oi' alpha-alumina (a-AljOi) and /-ZrOj is designed to have superior mechanical properties, e.g. extremely high flexiiral strength (over 1 GPa) and high toughness at room temperature (Claussen et al. 1977, Lange 1982, McMceking atid Evans 1982. Tsukumu cf al. 1985a,b, Rose and Swain 19H6. Ruhle et al. 1986. Heuer 1987. Nettleship and Stevens 1987, Pezzotti ('/ al. 1999). It is well known that the mechanical properties of this composite depend strongly on the volutiie fractioti/z of ZrO?. The nature of the/z-dependenee is, however, still not clear for several reasons. First, an/z-value where the designed properties are maximized is not specified in previous studies (Lange 1982. Tsukuma et ai. I985a,b. Pezzotti et al. 1999). Also, the dual-phase composite with maximized fracture toughness does not always have the maximized flexural strength. Second, the maximized toughness hiis been often explained thtoueh lhe combination of the slress-induced transformation and tAulhor for correspondence. Email: Takashi_Akiitsu(fl:msl.titech.ac.jp. ritihsoplmat Mu^iizine ISSN 1478-6435 pnnl,iSSN 1478 6443 online 'C. 2004 Ta.vlor & Francis Ltd ht[pi//w ww.tarjdf.co.uk/journals DOI: 10.1080/14786430412331293478
3742 T. Akatsu et al microcracking(Lange 1982, Tsukuma et al. 1985a.. Evans and Cannon 1986) although microcracking usually leads to the degradation of flexural strength Finally, there exists an experimental problem associated with fracture toughness evaluation, in which the rising R-curve behaviour due to the stress-induced trans formation( Evans and Cannon 1986, Rose and Swain 1986) is ignored. According to Evans and Cannon(1986). the toughening of I-ZrO, strongly depends on the critical stress ac of the transformation from I- into m-ZrO, In the case of the dual-phase composite, the value of oc must vary due to the internal stress disturbance caused by the thermoelastic mismatch between a-AlO3 and I-ZrO. However, no quantitative examination has been reported in the literature regarding the eflect of this change in ac on the mechanical properties of the composite. Therefore, in this study, the work of-fracture(WOF). a measure of total fracture resistance involving the R-curve effect (Akatsu ef al. 1996), and flexural strength of the dual-phase composite with various values of fz were measured over a range of temperatures. A stress-induced reversible transformation between f-ZrO, and -ZrO, was reported by Marshall and James (1986). Based on the possibility of such a reversible transformation, the stress dis- turbance in the dual-phase Al O3-ZrO, composite was numerically derived.These numerical data were then utilized to examine whether the /z- and temperature- dependences of the mechanical properties could be accounted for entirely by the change in the ac-value S2. THEORETICAL CONSIDERATION The efTect of the stress-induced phase transformation on the relationship between tensile stress and strain in ZrO, is shown schematically in figure 1: I-ZrO, transforms into m-ZrO, at ac on loading, while m-ZrO, changes into /-ZrO, at oR on unload ing. In addition, the Young,s modulus of m-ZrO, is considered to be the same as that of I-ZrO for simplicity. Thus Aw, the increase of woF due to the transformation toughening, is given as follows(see appendix A) zeroca I(+u)< 54(-) 1(+)K loadin Figure 1. Schematic illustration of the relationship between the tensile stress and strain of ZrO, affected by the stress-induced phase transformation
3742 T. Akatsu et al. microcracking (Lange 1982, Tsukuma ct al. 1985a.b, Evans and Cannon 1986) allhough mierocracking usually leads to the degradation of flexural strength. Finally, there exists an experimental problem associated with fracture toughness evaluation, in which the rising /?-curve behaviour due lo the stress-indueed transformation (Evans and Cannon 1986, Rose and Swain 1986) is ignored. According to Evans and Cannon (1986), the toughening of ;-ZrO:^ strongly depends on the critical stress Oc of the transformation from /- inio m-ZrOi. In the case of the dual-phase composite, the value of (TC must vary due to the internal stress disturbatice eaused by the thermoelaslic mismatch between ff-AhOi and i-ZxO^. However, tio quantitative examination has been reported in the literature regarding the effect of lhis change in (Tf on the mechanical properties of the composite. Therefore, in this study, the workof-fraeture (WOF), a measure of totai fracture resistanee in\ olving the /^-curve eflect (Akatsu et at. 1996). and flexural strength of the dual-phase composite with various values of/? were measured over a range of temperatures. A stress-induced reversible transformation between f-ZrOi and m-ZvO^ was reported by Marshall and James (1986). Based on lhe possibility of sueh a reversible transformation, the stress disturbance in the dual-phase ANO^-ZrOi cotnposite was numerically derived. These numerical data were then utiH/ed to examine whether the fz- and temperaluredependences of lhe mechanical properties could be accounted for entirely by the change in the CTC-value. §2. THEORETICAL CONSIDERATION The effect ofthe stress-induced phase transformation on the relationship between tensile stress and strain in ZrO2 is shown schematically in figure I: /-ZrO^ transforms into tn-ZrOi at CTC- O" loading, while tn-ZxO^ ehanges into /-ZrO;> at an on unloading. In addition, the Young's rnodulus of m-ZrOi is considered to be the same as that of /-ZrOi for simplicity. Thus AW. lhe increase of WOF due to the transformation toughening, is given as follows (see appendix A) AW =^ lor for 0 Strain Figure 1. Schemalic illustration of lhe relalionship beuveen llic tensile stress and strain of ZrOi alVecletl by the stress-induced phase transformaiion
Transformation toughening of an 4l0/Z,O where Er is the bulk strain due to the transformation(0.04), v the Poissons ratio, Ko the critical value of the local stress intensity factor at a crack tip, 5 and s are constants, and other terms have the meanings defined earlier. ch.3 oc varies as a result of the internal stress disturbance caused by the thermoelastic mogeneity in the dual-phase composite to give a value ac, calculated as follows dix B) o={1-(1-f)Bz{oc-(1-/z)B2Q2(a2z-aA)AT for Al,Ox-particles/ZrO,-matrix ac= Ba ac-(1-2)BAOA( )△7 for ZrOy-particles/Al,O-matrix B2={+12Q2(CA-C2) BA=/+(1-20A(CZ-CAI Qz=cz(-Sz (4) where a represents the thermal expansion coefficient, AT the difference between ambient temperature and a characteristic temperature where residual stresses arising from the thermal expansion mismatch are eliminated. I the unit tensor, C the elastic stiffness tensor, and S the Eshelby tensor (Eshelby 1957, 1959). The variables attached with subscripts A and Z are calculated from the properties of Al, and ZrO2, respectively. The value of oR also changes to or due to the internal stress disturbance, as follows: OR-(1-T)BAZ OAZ(az-aAZAT- with BAZ=[/+(1-T)OAZICZ-CAZ) Q AZ(-SAZ) where / r is the volume fraction of ZrO, transformed from tetragonal phase to monoclinic The subscript AZ denotes that a part of the dual-phase composite excluding transformed ZrO, and the tensors CAz and SAz are given as a function of/T, CA, vA Cz and vz. The value of A W for the dual-phase composite is then equal to the change in the solution to equation(1) when oc from equation (2)and OR from equation (5)are substituted for ae and oR S3. EXPERIMENTAL PROCEDURE A mixture of Al-O, and Y,O(3 mol%)-doped ZrO, powders was processed by tumbling mixing in n-butyl alcohol followed by quick-drying in a rotary evaporator. The fz-value in the mixture was selected to be from zero to unity. For the prepara tion of the a-Al,O3/1-ZrO, dual-phase composite, the mixture was hot-pressed with graphite dies at 1500 C under a uni-axial pressure of 33 MPa for I hour in a flowing argon gas atmosphere. The density of each composite was determined by fluid
Transforniaiion toughening of au AljOj/Z^O: 3743 where ei is the bulk strain due to the transformation (0.04), v the Poisson's ratio, A^o the critical value of the ioeal stress intensity faetor at a crack tip, ^ and <• are constiints, and other terms have the tneanings defined earlier. fTc varies as a result of the internal stress disturbance caused by the thermoelastic inhomogeneity in the dual-phase composite to give a value CT^;., calculated as follows (see appendix B): { } for AUOi-particles/ZrOi-matrix or " (2) for ZrOi-particles/AUOj-tnatrix with Qz = where a represents the thermal expansion eoeffieient. AT the ditiercnce between ambient temperature and a characteristic temperature where residual stresses arising from the thermal expansion mismatch are eliminated, /the unit tensor. C the elastic .stillness tensor, and S the Eshelby tensor (Eshclby 1957. 1959). The variables attached with subscripts A and Z are calculated from the properties of AI2O3 and ZrOi. respectively. The value of (TR also changes to a'^ due to the intemal stress disturbance, as follows; [ j ^)] (5) with | {J J)!" ' (6) CMa-SA^) (7) where f-y is the volume fraction of ZrOj transformed from tetragonal phase to monoelinic The subseript AZ denotes that a part of the dual-phase composite excluding translormed ZrO? and the tensors CA/ and SAZ ^''^^ given as a function of/r, CA, I'A, CZ and vz- The value of A Wfor the dual-phase composite is then equal to the change in the solution to equation (I) when a'^- from equation (2) and O-R from equation (5) are substituted for a^. and aR. §3. ExpERiMtNTAL PROCEDURE A mixture of ANOi and Y:Oi(3mol%)-doped ZrO2 powders was processed by tumbling mixing in n-butyl alcohol followed by quick-drying in a rotary evaporator. The //-value in the mixture was selected to be from zero to unity. For the preparation of the a'-AUOi/z-ZrOi dual-phase composite, the mixture was hot-pressed with graphite dies at 1500 C under a uni-axial pressure of 33 MPa for I hour in a flowing argon gas atmosphere. The density of eaeh composite was determined by fluid
3744 T. Akatsu et al displacement (using n-butyl alcohol), and was confirmed to be more than 99%o of the heoretical value Rectangular beams 3 mm x 4 mm x 36 mm were cut from the hot-pressed billet. The surface of the beams used for flexural strength measurement was polished to a mirror finish with 3 um-diamond paste. For WOF measurement, a symmetrical chevron notch with an apex angle of 90 was machined at the center of the beams using a diamond wheel with a thickness of 0.2 mm. The flexural strength was mea- sured using a graphite four-point bending apparatus with inner and outer spans of 10 mm and 30 mm, respectively, and a crosshead speed of 0.5 mm/min. Experiments were conducted at a range of temperatures from ambient up to 1400 C in a flowing argon gas atmosphere For WOF measurement, a three-point bending of the chevron notched beam with a span of 30 mm was carried out using a silicon carbide appa ratus. A crosshead speed of 0.005 mm/ min was used and tests were conducted in a vacuum at intervals from room temperature to 1000 C. The deflection of the chev ron-notched beam needed to be accurately measured even at elevated temperatures in order to evaluate external work required for the separation of the beam into two pieces. The external work, which corresponds to an area surrounded by a load deflection curve, is divided by the double of the ligament area to derive WoF The crosshead displacement of a test machine during bending of the beam is con- ventionally taken as being equal to the deflection of the beam. However, this gives an inaccurate measurement of the external work as it fails to take account of the deformation and thermal expansion of the apparatus and the test machine at ele- vated temperatures. Therefore, in this study, the deflection was directly obtained through an optical observation using a no contact displacement meter with a CCD camera and an infrared-lines cut filter. In order to avoid the overestimation of WOF, it was evaluated only for the chevron notched specimen, in which quasi- stable fracture was observed continuously during crack propagation Anti-stokes Raman-scattering spectroscopy was carried out with an ultraviolet laser on a surface fractured at elevated temperatures to confirm the stress-induced phase transformation from /- into m-ZrO, S4. RESULT The WOF and flexural strength of the dual-phase composite at room tempera ture are shown as a function of / z in figure 2(a). The maxima in both properties are observed in the composite with/z of about 0. 7(3A7Z). A theoretical calculation of the z-dependence of WoF was obtained by (see appendix C) combining equations (1).(2)and(5) with the constants and parameters listed in table 1. The results obtained are shown as solid lines in figure 2(b). Considering the plastic deformation of the dual-phase composite at elevated temperatures, AT was estimated to be 1000C (although the sintering temperature was 1500 C). Values of the constants 5. 4. oc and og were calculated to give the best fit between the experimental and theoretical data for the /z-dependence of wol The WOF and flexural strength of unmixed a-Al-O3(MA), unmixed I-ZrO2 (MZ) and 3A7Z were measured as a function of temperature and are shown in figures 3 and 4. As expected, continuous thermal degradation of these properties was observed from room temperature to 1000 C for MZ and 3A7Z while the prop- erties of MA remain largely unchanged over this temperature range. A thick solid line shown in figure 3 is the thermal degradation of the WOF-value of 3A7Z as predicted theoretically. The prediction was carried out simply by decreasing AT
3744 T. AkalsLi et al. displacement (using n-butyl alcohol), and wiis conlirmed lo be more than 99'^ of the theoretical value. Rectangular beams 3mm x 4mm x 36 mm were cul from the hot-pressed billet. The surface of the beams used for flexural strength measurement was polished to a mirror finish with 3|im-diamond paste. For WOF measurement, a symmetrical chevron notch with an apex angle of 90 was machined at the center of the beams using a diamond wheel with a thickness of 0.2mm. The flexural strength was measured using a graphite four-point bending apparatus with inner and outer spans of lOmm and 30mm. respectively, and a crosshead speed of 0.5 mm min. Experiments were conducted at a range of tempera lures from ambient up to 1400 C in a flowing argon gas atmosphere. For WOF measurement, a three-point bending of the chevron notched beam with a span of 30mm was carried out using a silicon carbide apparatus. A erosshead speed of 0.005 mm/min was used und tests were conducted in a vacuum at intervals from room temperature to lOOC'C. The deflection of the ehevron-nolched bcLim needed to be accurately measured even at elevated temperatures in order to evaluate external work required for the separation of the beani into two pieces. The external work, which corresponds to an area surrounded by a ioaddeflection curve, is divided by the double of the ligament area to derive WOF. The crosshead displacement of a test machine during bending of the beam is conventionally taken as being equal to the deflection of the beam. However, this gives an inaccurate measuiemeni of the external work as it fails to take account of the deformation and thermal expansion of the apparatus and the test machine at elevated temperatures. Therefore, in this study, the deflection was directly obtained through an optical observation using a no contact dispkicement meter with a CCD camera and an infrared-lines cul filter. In order to avoid the overestimation of WOF, it was evaluated only for the chevron notched specimen, in which quasistable fracture was observed coniinuously during crack propagation. Anti-stokes Raman-scattering spectroscopy was carried out with an ultraviolet laser on a surface fractured at elevated temperatures to confirm the stress-induced phase transformation from /- into /;7-ZrO2. §4. RESULT.S The WOF and flexural strength of the dual-phase composite at room temperature are shown as a function olf/_ in figure 2{a). The maxima in both properties are observed in the eomposite with /z of about 0.7 (3A7Z). A theoretical calculation of the /^-dependence of WOF was obtained by (see appendix C) combining equations (1), (2) and (5) with the constants and parameters listed in table I. The results obtained are shown as solid lines in figure 2(h). Considering the plastic deformation of the dual-phase composite ut elevated temperatures. AT* was estimated to be 1000 C (although the sintering temperature was 1500 C). Values of the constants $. <•. ac und CTR were calculated to give the best tit between the experimental and theoretical data for the /^-dependence of WOF. The WOF and flexural strength of unmixed a-AUO^ (MA), unmixed /-ZrO^ (MZ) and 3A7Z were measured as a function of temperature and are shown in figures 3 and 4. As expected, continuous thermal degradation of these properties was observed from room temperature to 1000 C for MZ and 3A7Z, while the properties of MA remain largely unchanged over this temperature range. A thick solid line shown in figure 3 is the thermal degradation of the WOF-value of 3A7Z as predicted theoretically. The prediction was carried out simply by decreasing A 7
Transformation toughening of an Al203/Z,O 1200 1000 402 20名 00.20.40.60.8 Volume fraction of I-ZrO,fz 40 ZrOzmatrix 10 Al-Or-matrix 00.20.40.60.81 (b) Volume fraction of t-ZrO2 fz Figure 2. (a) Flexural strength(open circles) and work-of-fracture WOF(filled circles) of an a-Al2O3/t-ZrO, dual-phase composite as a function of I-ZrO, volume fraction (b) Experimental and theoretical woF as a function of ZrO,. Broken lines with open triangle and squares are based on equations (1)(7). The solid line indicates the the oretical zdependence of the wOF and filled circles are experimental results from 1000 to 0C in the WOF calculation described previously, and the theoretical values show good agreement with those obtained experimentally The Raman-scattering spectra for surfaces in the original polished condition and after fracture at various temperatures are shown in figures 5 and 6 for MZ and 3A7Z. respectively. In both the materials and on each surface, the spectrum assigned to I-ZrO2(marked by open circles) is clearly observable §5. DISCUSSION In earlier studies, the strengthening of a dual-phase composite that consists of a-Al2O, and (-ZrO, is conventionally described through the decrease of flaw size due to the fine grain structure of the composite(Tsukuma et al. 1985a, b). the
Transformation toughening of an Alj 3745 I ' I ' T 1200 1000 800 600 400 200 (a) 0 0.2 0.4 0.6 0.8 1 Volume fraction of r-ZrO, fz 80 60 40 20 0 IN 6 O i G 0 > ur e \ ~0f-1 o 50 40 30 20 10 n 1 ' 1 • 1 - _ ZrO2-matrix ^; / J AI:O,-r 1,1. 1 1 • 1 • 1 Al-Oi-niairix" I.I. I 0 0.2 0.4 0.6 0.8 1 (/» Volume fraction of t-ZrOj fz Figure 2. (a) Flexural strength (open circles) and work-or-IVaclure WOF (filled circles) of an a-AliOi/z-ZrO^ dual-phase composite as a rutiction of /-ZrOi volume fraclion (^) Experimental and llicorclical WOF as a function of ZrO;. Broken lines with open triangle and squares are based on equations (l)-(7). The solid line indicates the theoretical/;^dcpeiidencc of the WOF and filled circles are experimental results. from 1000 to 0 C in the WOF calculation described previously, und lhe theoretical values show good agreement with those obtained experimentally. The Raman-scattering spectra for surfaces in the original polished condition and alter fracture at various temperatures are shown in ligures 5 and 6 for MZ and 3A7Z. respectively. In both the materials and on each surface, the spectrum assigned to /-ZrOi (marked by open circles) Is clearly observable. §5. DISCUSSION In earlier studies, the strengthening of a dual-phase composite that consists of u-AUOi and /-ZrOi is conventionally described through the decrease of flaw size due to the fine grain structure of the composite (Tsukuma ei al. 1985a, b), the
3746 T Akatsu et al Table 1. Constants and parameters used for the theoretical calculation of the work-of-fracture of an AlO,/ZrOz 2-phase Parameters related to Alumina EA 390GPa K. 3.mPAm/ 2 3.3×10-K K, 2.0 MPam E0.32 1.88 OR 0.63 GP E=9=2÷ 3A7Z 30 10 02004006008001000 Temperature/C Figure 3. Work-of-fracture WOF of unmixed a-Al-O,(MA. filled triangles). I-ZrOz(MZ. tilled squares) and 3A7Z (filled circles)as a function of temperature. The woF-value of 3A7Z is theoretically predicted as a thick solid line stress-induced transformation (Lange 1982, Tsukuma et al. 1985a. b, Heuer 1987) stress-induced microcracking( Claussen et al. 1977. Ruhle et al. 1986. and so on Pezzotti et al.(1999)also found that the strength of the dual-phase composite was maximized at an fz-value of about 0.7. They described the /z-dependence of the strength through the combination of strength limitations(Swain and Rose 1986) and local residual microstresses due to thermoelastic inhomogeneity in the compo- site. However, the effect of the residual stresses on the transformation of -ZrO, was disregarded, as no significant toughening was observed in their composite. In this study, the /z-dependence and remarkable thermal degradation of the flexural strength of the dual-phase composite(see figures 2(a) and 4) are found to be very similar to those of WOF(see figures 2(a) and 3). This similarity suggests that the changes in strength and toughness of the composite are controlled by the same
3746 T. Akatsu ('/ al. Table I. Constants and parameters used for the theoretical calculation of Ihc work-oi-tVacture ofan Al2O.i/ZrO2 2-phase composite. Parameicrs related lo material properties Constants B IL. O^ork-of-i s? sn 40 30 \ - 20 ^ Alumina L,\ "ft Zirconia Ei Vy Kz C CTc J • J ' 1 ' 1 A: fl : \ » "•••1 fl 1 . 1 . I . 1 3yOGP;i 0.25 8.0 X IO-"K-' 210GPa 0.30 13.3 X IO-''K-' 2.0 MPa m''^ 0.32 1 .X8 )4m 1.60 GPa 0.63 GPa ' 1 MA MZ 3A7Z — - — • 0 200 400 600 SOO 1000 TemperaturerC Figure 3. WorkHil-fraclure WOF of unmixed of-AbO* (MA. filled triangles). /-ZrO^ (MZ, filled squares) and 3A7Z (filled circles) as a (unction of temperature. The WOF-viilue of 3A7Z is theoreiically predicted as a thick solid tine. stress-induced transformation (Lange 1982. Tsukuma ct al. 1985a. b, Heuer 1987). stress-induced microcracking (Chuissen ct al. 1977. Ruhle ct al. 1986.) and so on. Pezzotti et al. (1999) also found that the strength of (he dual-phase composite was niLixiniized at an /z-value of about 0.7. They described the //-dependence of the strength through the combination of strength limitations {Swain and Rose 1986) and local residual microstrcsscs due to thermoelastic inhomogeneity in the composite. However, the effect of the residual stresses on the transformation of /-ZrO^ was disregarded, as no significant toughening was observed in their composite, ln this study, the /^-dependence and remarkable thermal degradation of the flexural strength of the dual-phase composite (see figures 2((/) and 4) are found to be very similar to those of WOF' (sec figures 2((/) and 3). This similarity suggests that the changes in strength and toughness of the composite are controlled by the same
Transformation toughening of an Al2O /Z,O 3747 1200 MA 100 司 200 Temperature/C Figure 4. Flexural strength of a-Al O,(MA filled triangles). I-ZrO,(MZ, filled squares)and 3A7Z(filled circles)as a function of temperature. Fractured at 100C 800C 100200300400500600700 Raman shift/cm-l Figure 5. Raman-scattering spectra in I-Zro,(MZ) on the polished surface and those frac- tured at elevated temperatures. Open circles indicate (-ZrO2 spectra mechanism. If this is so, then the strengthening cannot be explained by the conven tional mechanism, (the combination of the stress-induced transformation and micro- cracking) because the microcracking conventionally degrades flexural strength but improves fracture toughness. The good agreement between the experimental and calculated fz-dependences of WOF and successful prediction of the thermal degra dation of woF by considering the increase in ac and or due to the relaxation of inelastic strain mismatch in the composite would seem to indicate that the toughen- ing as well as strengthening of the dual-phase composite is controlled by the rever- sible transformation of I-ZrO, and is well described through the effect of internal
Transformation toughening ofan 3747 CO c onural Fle x 1200" 1000 800, 600 400' 200 1 f r ^ r T\ L -^\ -\ ^ r \ I '1:;::; - V -i • :MA • ;MZ # : .^A7Z - • - • - _ 1 , . , . 500 1000 1500 Temperalure/^C Figure 4. Flexural strength of or-AliOi (MA, filled triangles), ^-ZrOi (MZ. filled squares) and 3A7Z (filled circles) as a function of temperature. MZ Fractured al UHHt'C 100 200 300 400 500 600 700 Raman shitt/cm-' Figure 5. Raman-scattering spectra in t-ZrOj (MZ) on the polished surface and those fractured al elevated temperatures. Open circles indicate t-ZrOi spectra. mechanism. If this is so. then the strengthening cannot be explained by the conventional mechanism, (the combination ofthe stress-indueed transformaiion and mierocracking) because the microcraeking conventionally degrades flexural strength but improves fraeture lotighness. The good agreement between the experimental and calculated /^-dependences of WOF and successful prediction ofthe thermal degradation of WOF by considering the increase in ^^ and a^ dtte to the relaxation of inelastic strain mismatch in the composite would seem to indicate that the toughening as well as strengthening ofthe dual-phase cotnposite is controlled by the reversible transformation of t-ZrOj and is well described through the effect of internal
3748 T. Akatsu et a 3A7Z O rZro Fractured at 8OOC RT Polished 100200300400500600700 Raman shift/cm-I Figure 6. Raman-scattering spectra in 3A7Z on the surfaces polished and fractured at ele vated temperatures. Open circles indicate the I-ZrO, spectra stress disturbance on oc and oR. A rather small discrepancy between theoretical and experimental values of WOF observed at higher temperatures (figure 3)seems to be attributable to the increase in the chemical stability of 1-ZrO,, which also increases According to linear fracture mechanics, flexural strength increases with an increase in fracture toughness. However, the strength of the composite is limited up to oc(Swain and Rose 1986). This seems to be one of the reasons why (in previous studies)the composite with fracture toughness maximized at a certain / z did not always have the maximized strength. In this study, both toughening and strengthen- ing were maximized at a specific z because the strength of the present composite was less than the calculated value of oc( 1. 6 GPa). The validity of ac= 1.6 GP seems to be supported by the results for the limited strength of the composite up to about the ac-value in previous studies Next, we examine each parameter which seems to have a significant influence WOF (see equation(A-1)in appendix A). The values of r, Ao and h are plotted as a function of /z in figures 7, 8 and 9, respectively. The maximum values of fr and Ao are observed at an /z of about 0. 7 while h decreases with increasing z. The /r-value is maximized at the transition from /T=/z to r=h/sz, and the condition for the transition is given by loc(1 +v)Kol=E/s(see figure 7). The maximized Ao appears due to the obvious change in the positive fz-dependence of og from initiall gradual variation to rather steep one at a /z of 0.7(see figure 8), which is also related to the transition in /r. Therefore, the maximization of the strength and WOF of the dual-phase composite consequently corresponds to the maximization of fr and Ao at loc/(1+v)Kol=5/S, which gives a specific z-value of 0.7. fr, Ao and h are plotted as a function of temperature in figures 10. I I and 12. respectively. The steady decrease in h with an increase in temperature(see figure 12) which leads to the negative temperature dependence of /r (see equation(A-3)in appendix A) shown in figure 10, is due to the increase in oc(see equation(A-2)in appendix A). The value of Ao also decreases with an increase in temperature
3748 T. Akatsu ct al. 3A7Z Fratiuretl al Figure 6. RT. Pill i shed 100 200 300 400 500 600 700 Raman shift/cm-' Raman-scutiering spectra in 3A7Z on Ihc surfaces polished and fractured at elevaied temperaiures. Open circles indleale the /-ZrO2 spectra. stress disturbance on CTC and a^. A rather small discrepancy between theoretical and experimental values of WOF observed at higher temperatures (figure 3) seems to be attributable lo the increase in the chemical stability of/-ZrOi. which also increases According to linear fraclure mechanics. Rexural strength increases wilh an increase in fracture toughness. However, the strength of the composite is limited up to (T( (Swain and Rose 1986). This seems lo be one ofthe reasons why (in previous studies) lhe composite with fracture toughness tnaximized at a certain // did not alway.s have the maximized strength. In Ihis study, both toughening and strengthening were maximized al a specific //. because the strength of the presenl composite was less than the calculated value of ad l.6GPa). The validity of (T^ — l-6GPa seems to be supported by the results for the limited strength of the composite up to about the o-c-value in previous studies. Next, we examine each parameter which seems to have a significant influence on WOF (see equation (A-1) in appendix A). The values o^fy. ACT and h are plotted as a function o(f/ in figures 7. 8 and 9. respectively. The maximum values of/f and ACT are observed at an /^ of about 0.7 while // decreases with increasing /;^. The/i-value is maximized at the transition from/r=/ z to./V = h/i^fz-, and the condition for the transition is given by {CT{/(1 + i')A',,}" — $/;; (see figure 7). The ma.\imi/.ed ACT appears due to lhe obvious change in the positive /z-dependence of CT^ from initially gradual variation to rather steep one at a,/z of 0.7 (see figure 8). which is also related lo the transition in /y. Therefore, the maximization of the strength and WOF ofthe dual-phase composite consequently corresponds to the maximization ofyj and ACT at {a'cf{\ + v)Ao}^ = §/?, which gives a specific /z-value of 0.7. / j . ACT and /; are plotted as a function of temperature in figures 10. 11 and 12, respectively. The steady decrease in h with an increase in temperature (see figure 12), which leads to the negative temperature dependence of/V (see equation (A-3) in appendix A) shown in figure 10. is due to the increase in CT(- (see equation (A-2) in appendix A). The value of ACT also decreases with an increase in temperature
Transformation toughening of an A1203/Z,0 3749 0.4 00.20.40.60.81 Volume fraction of t-ZrO,fz Figure 7. Volume fraction of ZrO, transformed from tetragonal to monoclinic, /r, as a function of f-ZrO, volume fraction /z of the composite, 0.5 0.20.40.60.81 Volume fraction of t-ZrO2 fz Figure 8. Critical of the reversible transformation between t- and m-ZrO2, dc broken line ed triangles) and or (broken line with filled squares). as a function of z. The between them. Aa, is also plotted (solid line/with filled circles) (figure 11). because the positive temperature dependence of or is significantly higher than that of oc. The positive temperature dependence of og and ac is caused by the relaxation of inelastic strain mismatch in the composite with an increase in tempera ture. Therefore the thermal degradation of the WOF and strength of the composite (see figures 3 and 4) can be ascribed to the negative temperature dependence of/T, Aa, and h which, in turn are caused by the decrease in the internal stress disturbance with an Increase in temperature
Transformation tou^henitig ofan 0.8 3749 o c _o a 4 - D SVoi r i oN *.- Pans 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 Volume fraction of /-ZrO2 /z Figure 7. Volume fraction of ZrOi transformed from tetragonal to monoclinic, /V- ss i* of /-ZrOi volume fraction /? of the composite. ^ 0 0 0.2 0.4 0.6 0.8 1 Volume fraction of t-ZrOj fz Figure S. Critical stresses of the reversible transformation between t- and (broken line with Hllcd triangles) and a\i (broken line with filled squares), as a funciion •^'./z' The ditlerence between them. Aff, is also plotted (solid line/with lilled circles). (figure 11), because the positive temperature dependence of a^ is significantly higher than that of o"c- T^^e positive temperature dependence of CTR and OQ is caused by the relaxation of inelastic strain mismatch in the composite with an increase in temperature. Therefore the thermal degradation of the WOF and strength of the composite (see figures 3 and 4) can be ascribed to the negative temperature dependence of/V, A(T. and h which, in turn, are caused by the decrease in the internal stress disturbance with an increase in temperature
3750 T. Akatsu et al 日25 号≥EEv一 0.20.40.60.8 Volume fraction of I-ZrO2 fz Figure 9. Transformation zone width h derived from equation (A-2) in appendix A as a function of f, 0.8 0.6 E≌与 02004006008001000 Temperature/C Figure 10. Volume fraction of ZrO, transformed from tetragonal to monoclinic, /r. as a function of temperature The fact that Raman-spectra assigned to -ZrO, were scarcely observed on fractured surfaces(see figures 5 and 6) seems to conflict with the strengthening and toughening of the dual-phase composite due to the stress-induced transforma tion of I-ZrO2. However, the reason why only the Raman-spectra assigned to l-ZrO was observed on the fractured surfaces can be explained through the inverse phase transformation from m-into [,(Marshall and James 1986) behind a crack tip where concentrated stresses at the tip are relaxed. The inverse phase transformation, which proves the validity of the positive oR-value, indicates the relatively higl hemical stability of I-ZrO, containing 3 mol% Y20, at room temperature
3750 T. Akatsu (7 al. E 25 20 15 10 5 0 1 ' 11 • 1 ' X . , . , . 1 • 1 ' 1 - - - 1 . I T • H 0 0.2 0.4 0.6 0.8 1 Volume fraction of t-ZrOz fy Figure 9. Transfomiation zone widih h derived from equation (A-2) in appendix A as a function of/z. 200 400 600 800 1000 Temperature/°C Figure 10. Volume fraction of ZrO;; transformed Prom lelragonal lo monoclinic. function of temperature. . as a The fact that Raman-spectra assigned to Ajf-ZrOi were scarcely observed on fractured surfaces (see figures 5 and 6) seems to conllict with the strengthening and toughening of the dual-phase composite due to lhe slress-induced transformation of ^ZrOi. However., the reason why only the Raman-spectra assigned to /-ZrOi was observed on the fractured surfaces can be explained through the inverse phase transformation from m- into /-ZrO? (Marshall and James 1986) behind a crack tip where concentrated stresses at the tip are relaxed. The inverse phase transformation, whieh proves the validity of lhe positive CTR-value, indicates lhe relatively high chemical stabihty of /-ZrO2 containing 3mo!% Y2O3 al room temperature