《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_FRACTURE-A-Z

doi:10.111460·2695.2006.00962X fracture behaviour of an Al203-ZrO2 multi-layered ceramic with residual stresses due to phase transformations' R BERMEJo, Y TORRES, A.J. SANCHEZ-HERENCIA2, C. BAUDIN2, M. ANGLADA' and L. LLANES' Departamento de Ciencia de los Materiales e Ingenieria Metalirgica, ETSEI.B, Universitat Palitecnica de Catalunya, Auda. Diagonal 647, 08028 Barcelona, Spain,Instituto de Ceramica y Vidrio(CSIC), Camino de valdelatas s/n, 28049 Madrid, Spain Received in final form 19 September 2005 ABSTRACT The fracture behaviour of a ceramic multi-layer designed with thin internal com- ressive layers and obtained by slip casting is studied. It consists of nine alternated 12O3-5vol%tZrO2 and Al2O3-30vol%mZrO2 layers of 530 um and 100 um thick- ness, respectively. Mechanical characterization includes evaluation of Vickers Hardnes Young's modulus and fracture strength under four-point bending. In addition, the resid ual stress magnitude and distribution in the laminate is determined both analytically from calculations using the differential strain between layers and the elastic properties, mechanical strength and fractography show ques. The experimental findings in terms of ing indentatio a subcritical growth of the natural flaws in the laminate before catastrophic failure occurs, owing to the relevant role of the thin Al2O3-30vol%mZrO2 layers with compressive stresses inherent to the zirconia phase transformation. These layers are also responsible for the increase in toughness to levels of at least three times that of the reference Al,O3-5vol %tZro, monolith Keywords alumina; mechanical strength; multi-layer; phase transformation; residual stresses: zircona NOMENCLATURE a= crack length into the material B=specimen width c=crack length at the surface co initial crack length at the surface (c/a)= crack eco E= Youngs modul El= flexural rigidity of the multi-lay F=applied load fecc= eccentricity correction factor Fres= eccentricity correction factor Ke=critical stress intensity factor 1= distance betwee and or M= moment in four-point bendin P= indentation load e layer Correspondence: R. Bermejo. E-mail: raul bermejo@upc.edu This paper is based on a presentation made at the Spanish Fracture Group meeting in Punta Umbria, 24-26 March 2004. @2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71-78

doi: 10.1111/j.1460-2695.2006.00962.x Fracture behaviour of an Al2O3–ZrO2 multi-layered ceramic with residual stresses due to phase transformations∗ R. BERMEJO1, Y. TORRES 1, A. J. SANCHEZ-HERENCIA ´ 2, C. BAUD´ IN2, M. ANGLADA1 and L. LLANES 1 1Departamento de Ciencia de los Materiales e Ingenier´ıa Metal´urgica, E.T.S.E.I.B., Universitat Polit`ecnica de Catalunya, Avda. Diagonal 647, 08028 Barcelona, Spain, 2Instituto de Cer´amica y Vidrio (CSIC), Camino de Valdelatas s/n, 28049 Madrid, Spain Received in final form 19 September 2005 ABSTRACT The fracture behaviour of a ceramic multi-layer designed with thin internal com￾pressive layers and obtained by slip casting is studied. It consists of nine alternated Al2O3–5vol%tZrO2 and Al2O3–30vol%mZrO2 layers of 530 µm and 100 µm thick￾ness, respectively. Mechanical characterization includes evaluation of Vickers Hardness, Young’s modulus and fracture strength under four-point bending. In addition, the resid￾ual stress magnitude and distribution in the laminate is determined both analytically, from calculations using the differential strain between layers and the elastic properties, and experimentally, using indentation techniques. The experimental findings in terms of mechanical strength and fractography show a subcritical growth of the natural flaws in the laminate before catastrophic failure occurs, owing to the relevant role of the thin Al2O3–30vol%mZrO2 layers with compressive stresses inherent to the zirconia phase transformation. These layers are also responsible for the increase in toughness to levels of at least three times that of the reference Al2O3–5vol%tZrO2 monolith. Keywords alumina; mechanical strength; multi-layer; phase transformation; residual stresses; zirconia. NOMENCLATURE a = crack length into the material ac = critical flaw size B = specimen width c = crack length at the surface c0 = initial crack length at the surface (c/a) = crack eccentricity E = Young’s modulus EI = flexural rigidity of the multi-layer F = applied load f ecc = eccentricity correction factor Fres = eccentricity correction factor Kc = critical stress intensity factor KIc = fracture toughness l = distance between inner and outer spans M = moment in four-point bending n = number of layers P = indentation load t = thickness of the layer Correspondence: R. Bermejo. E-mail: raul.bermejo@upc.edu ∗ This paper is based on a presentation made at the Spanish Fracture Group meeting in Punta Umbria, 24–26 March 2004. c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78 71

72 R BERMEJo et al Y=flaw shape factor y= position coordinate normal to the layer plar na= position of neutral axis in the material under flexural loading x =residual-stress factor Xo= dimensionless constant dependent on the modulus-to-hardness ratio ER=residual strain in the laminate OR rupture stress res residual stress u= Poisson's ratio y= crack-shape factor vo= geometric constant for an embedded circular crack c subscript used to indicate compressive layers subscript used to indicate tensile layers INTRODUCTION processing flaw at surface layers, independent of origi nal size and location, such that failure tends to take place The interest in the mechanical behaviour of ceramic ma- under conditions of maximum crack growth resistance; rials is ed by their possible application as struc- and, consequently, strength becomes flaw-size indepen tural components, especially in the cases where properties dent, and reliability gets significantly enhanced. Within such as high hardness, chemical stability, low density and this framework, anextreme 'case is the possibility of de high strength, among others, may be exploited. In fact, veloping materials exhibiting athreshold eramics have been used for a long time as structural el- is, a stress below which failure would not occur despite the ements, but always under effective compressive loading presence of very large cracks, as reported by Rao et al.on onditions. However, most of the new engineering de- an alumina-alumina mullite multi-layered system when a signs need to withstand tensile stresses, which imply a tensile stress was applied parallel to the layers limitation for these inherently brittle ceramics In the last Two main mechanisms have been proposed as residual three decades, remarkable advances have been achieved to stress developers. One is the difference in thermal expan overcome the lack of toughness of these materials. Several sion coefficients, which forces residual stresses inside lay processing routes have been approached for improving ered ceramics during cooling from the sintering tempera toughness, from which doping, fibre and/or particle re- ture. The other comes from the incorporation of a second inforcement, functional grading and layered architectural phase that transforms during cooling with an associated design may be highlighted. Particularly, ceramic compos- expansion. This is the case of pure zirconia on alumina or tes with a layered structure such as alumina-zirconia.2 stabilized zirconia matrices. 2.7-In these systems,residual and mullite-alumina among others, have been reported stresses develop in association with the martensitic trans- o exhibit increased apparent fracture toughness, energy formation of zirconia. As the expansion occurs inside the bsorption and/or non-catastrophic failure behaviour. layers that are fixed to other layers that do not expand, One of the most used multi-layer designs that assures the material does not degrade but residual stresses arise higher apparent toughness is that which combines layers with magnitude enough to modify the fracture behaviour ent volume changes during cooling f compared with a monolithic or a laminate without resid- sintering temperature. Under these conditions, an alter- ual stresses. nate tensile-compressive residual stress state develops It is the purpose of this investigation to evaluate ith specific location of the compressive layers, either at the mechanical behaviour of a multi-layered Al2O the surface or internally, depending on the attempted de- 5vol%ZrO2/Al2O3-30vol%mZrOz ceramic designed to sign approach, based on mechanical resistance or damage improve damage tolerance, that tolerance, respectively. In the former case, superposition residual compressive stresses, and compare it with that of the compressive residual and nominally applied stresses exhibited for a monolithic material of the same compo- result in a higher, but single-value, apparent fracture sition as that of the external layers, Al2O3-5vol%tzrO2 toughness together with enhanced strength(the main The composition of the external layers has been chosen to goal)and some improved reliability. 4. On the other achieve the desirable properties of alumina while control- hand, in the latter one, the internal compressive layer is ling its grain growth. Vickers Hardness, Young's modulus microstructurally designed to rather act as stopper of any and modulus of rupture (MOR)under four-point bending @2006 Blackwell Publishing Ltd. Fatigue Fact Engng Mater Struct 29, 71-78

72 R. BERMEJO et al. W = specimen height Y = flaw shape factor y = position coordinate normal to the layer plane yna = position of neutral axis in the material under flexural loading χ = residual-stress factor χ0 = dimensionless constant dependent on the modulus-to-hardness ratio εR = residual strain in the laminate σ = stress σR = rupture stress σres = residual stress υ = Poisson’s ratio ψ = crack-shape factor ψ0 = geometric constant for an embedded circular crack c = subscript used to indicate compressive layers t = subscript used to indicate tensile layers INTRODUCTION The interest in the mechanical behaviour of ceramic ma￾terials is motivated by their possible application as struc￾tural components, especially in the cases where properties such as high hardness, chemical stability, low density and high strength, among others, may be exploited. In fact, ceramics have been used for a long time as structural el￾ements, but always under effective compressive loading conditions. However, most of the new engineering de￾signs need to withstand tensile stresses, which imply a limitation for these inherently brittle ceramics. In the last three decades, remarkable advances have been achieved to overcome the lack of toughness of these materials. Several processing routes have been approached for improving toughness, from which doping, fibre and/or particle re￾inforcement, functional grading and layered architectural design may be highlighted. Particularly, ceramic compos￾ites with a layered structure such as alumina–zirconia1,2 and mullite–alumina3 among others, have been reported to exhibit increased apparent fracture toughness, energy absorption and/or non-catastrophic failure behaviour. One of the most used multi-layer designs that assures higher apparent toughness is that which combines layers with different volume changes during cooling from the sintering temperature. Under these conditions, an alter￾nate tensile–compressive residual stress state develops with specific location of the compressive layers, either at the surface or internally, depending on the attempted de￾sign approach, based on mechanical resistance or damage tolerance, respectively. In the former case, superposition of the compressive residual and nominally applied stresses result in a higher, but single-value, apparent fracture toughness together with enhanced strength (the main goal) and some improved reliability.4,5 On the other hand, in the latter one, the internal compressive layer is microstructurally designed to rather act as stopper of any processing flaw at surface layers, independent of origi￾nal size and location, such that failure tends to take place under conditions of maximum crack growth resistance; and, consequently, strength becomes flaw-size indepen￾dent, and reliability gets significantly enhanced. Within this framework, an ‘extreme’ case is the possibility of de￾veloping materials exhibiting a ‘threshold strength’, that is, a stress below which failure would not occur despite the presence of very large cracks, as reported by Rao et al. 6 on an alumina–alumina mullite multi-layered system when a tensile stress was applied parallel to the layers. Two main mechanisms have been proposed as residual stress developers. One is the difference in thermal expan￾sion coefficients, which forces residual stresses inside lay￾ered ceramics during cooling from the sintering tempera￾ture. The other comes from the incorporation of a second phase that transforms during cooling with an associated expansion. This is the case of pure zirconia on alumina or stabilized zirconia matrices.2,7–9 In these systems, residual stresses develop in association with the martensitic trans￾formation of zirconia. As the expansion occurs inside the layers that are fixed to other layers that do not expand, the material does not degrade but residual stresses arise with magnitude enough to modify the fracture behaviour if compared with a monolithic or a laminate without resid￾ual stresses. It is the purpose of this investigation to evaluate the mechanical behaviour of a multi-layered Al2O3– 5vol%tZrO2/Al2O3–30vol%mZrO2 ceramic designed to improve damage tolerance, that is, exhibiting internal residual compressive stresses, and compare it with that exhibited for a monolithic material of the same compo￾sition as that of the external layers, Al2O3–5vol%tZrO2. The composition of the external layers has been chosen to achieve the desirable properties of alumina while control￾ling its grain growth. Vickers Hardness, Young’s modulus and modulus of rupture (MOR) under four-point bending c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

FRACTURE BEHAVIOUR OF AN Al20 3-ZrO2 MULTI-LAYERED CERAMIC 73 for natural flaws are determined in this work. In addition, the total strain change during cooling for each mate- indentation techniques are used to evaluate the residual rial. Transformation strains of the thin layers contain- stress profile in the multi-layer. ing monoclinic ZrO2 were estimated by measuring with a dilatometer DIL 402 E/7, Netzsch, Germany)the trans- EXPERIMENTAL WORK formation strains of monolithic bar specimens(with the same compositions as the thin compressive layers). These cessing and characterization data were recorded during cooling from densification The following starting powders were used: (a-alumina temperature. In addition, relative volume fractions ofeach ( Condea, HPAOS, USA) with 0.29 um average particle ZrOz phase within the AMZ were determined from the ze and 8.5 m'g specific surface area(N2 adsorp- X-ray diffraction spectra(D-5000, Siemens, Germany) tion; BET method), (i) Y2O3-free and Y2O3-stabilized and using the Garvie-Nicholson equation. The mag- zirconia(TZ-0& TZ-3YS Tosoh, Japan)with 0.60 um nitude of the residual stresses was calculated analytically and 0.37 um average particle size and 14.0 m2g-1 and in the bulk material considering an equally biaxial stress 6.7m2g'specific surface area, respectively. A slurry com- distribution on the layer plane assuming an infinite body, posed of Al2O3/5vo1% Y2O3-stabilized ZrO2(t-ZrO2), as given by referred to as atz. was used to form the thicker lavers. The t-ZrO2 was employed to control the grain size of Oc=ER Ec.[1+ E the Al2O3 during densification. To form the thin layers, a slurry composed of Al2O3 /30vo1% Y2O3-free ZrO2(m- and ZrO2), named AMZ, was employed. The content of pure 0=-cLnt-t nc·te zirconia was selected to promote a hig of phase transformation during cooling, which will induce where ER=EATZ-EAMz is the difference in deformation high residual compressive stresses in these layers, as re- between adjacent layers, t; and n; are the thickness and ported in previous works where a maximum in compres- sive stresses was approached near 0.35 volume fraction number of layers, respectively, Ei=E /(1-vi), and the m-ZrO,10-12 subscripts c and t indicate one layer or the other aqueous suspensions with a sol content of Vickers indentation technique was employed to evalu ate experimentally the residual stress field in the laminate 70 wt% were stabilized adding a 0.8% of a polyelectrolyte Several indentations with a load of 30N were applied in sant. Powders were dispersed by an ultrasonic device(IKa the laminate at different distances from the free surface as U400S)during 2 min and then stirred for 4h for stabiliza- well as at an internal ATZ layer, as shown schematically tion. Then, they were slip cast on a plaster of Paris mould. In Fig. 1. The cracks normal to the ATZ/AMZ interface Wall thickness versus time curves were experimentally cal emanating iro om these indentations were measured using culated on monolithic samples for both slurries and used interference contrast. To determine the crack tip posi to calculate the time for sequential slip casting of lami- tion for each indentation crack, the light beam was re- natesI3 Cast specimens were carefully removed from the duced so that the crack tip was in the dark field next to the moulds and dried at room temperature for 48 h. Green beam area. The magnitude of the residual stresses in the densities were measured by the Archimedes technique in mercury. Cast specimens were fired at 1550C for 2 h us ng heating and cooling rates of 5C/min Rectangular lates of approximately 60 mm x 60 mm x 4 mm were obtained after sintering. The outer ATZ layers were cast 500 um thicker than the inner ones to allow grinding and olishing of them to reach a final symmetrical archite ATZ AMZ ture Microstructures were observed by scanning electron microscopy(SEM)on polished and thermally etched(at 1400C during 20 min)surfaces and grain sizes measured by the intercept line method from the SEM micrographs Theoretical and experimental evaluation of residual stresses in the laminates Fig. 1 Scheme of the indentation profile in the(a)ATZ inner Dynamic sintering was carried out on the monoliths to layers and (b) ATZ outer layers of the laminate, using a Vickers determine shrinkage evolution during heating as well as indenter with an applied load of 30N @2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71-78

FRACTURE BEHAVIOUR OF AN Al 2O 3–ZrO 2 MULTI-LAYERED CERAMIC 73 for natural flaws are determined in this work. In addition, indentation techniques are used to evaluate the residual stress profile in the multi-layer. EXPERIMENTAL WORK Processing and characterization The following starting powders were used: (i) α-alumina (Condea, HPA05, USA) with 0.29 µm average particle size and 8.5 m2 g–1 specific surface area (N2 adsorp￾tion; BET method), (ii) Y2O3-free and Y2O3-stabilized zirconia (TZ-0 & TZ-3YS, Tosoh, Japan) with 0.60 µm and 0.37 µm average particle size and 14.0 m2 g–1 and 6.7 m2 g–1 specific surface area, respectively. A slurry com￾posed of Al2O3/5vol% Y2O3-stabilized ZrO2 (t-ZrO2), referred to as ATZ, was used to form the thicker layers. The t-ZrO2 was employed to control the grain size of the Al2O3 during densification. To form the thin layers, a slurry composed of Al2O3/30vol% Y2O3-free ZrO2 (m￾ZrO2), named AMZ, was employed. The content of pure zirconia was selected to promote a high percentage of phase transformation during cooling, which will induce high residual compressive stresses in these layers, as re￾ported in previous works where a maximum in compres￾sive stresses was approached near 0.35 volume fraction m-ZrO2. 10–12 Both aqueous suspensions with a solid content of 70 wt% were stabilized adding a 0.8% of a polyelectrolyte (Duramax-3021, Rhom and Haas, Germany) as disper￾sant. Powders were dispersed by an ultrasonic device (IKA U400S) during 2 min and then stirred for 4 h for stabiliza￾tion. Then, they were slip cast on a plaster of Paris mould. Wall thickness versus time curves were experimentally cal￾culated on monolithic samples for both slurries and used to calculate the time for sequential slip casting of lami￾nates.13 Cast specimens were carefully removed from the moulds and dried at room temperature for 48 h. Green densities were measured by the Archimedes technique in mercury. Cast specimens were fired at 1550◦C for 2 h us￾ing heating and cooling rates of 5 ◦C/min. Rectangular plates of approximately 60 mm × 60 mm × 4 mm were obtained after sintering. The outer ATZ layers were cast 500 µm thicker than the inner ones to allow grinding and polishing of them to reach a final symmetrical architec￾ture. Microstructures were observed by scanning electron microscopy (SEM) on polished and thermally etched (at 1400 ◦C during 20 min) surfaces and grain sizes measured by the intercept line method from the SEM micrographs. Theoretical and experimental evaluation of residual stresses in the laminates Dynamic sintering was carried out on the monoliths to determine shrinkage evolution during heating as well as the total strain change during cooling for each mate￾rial. Transformation strains of the thin layers contain￾ing monoclinic ZrO2 were estimated by measuring with a dilatometer (DIL 402 E/7, Netzsch, Germany) the trans￾formation strains of monolithic bar specimens (with the same compositions as the thin compressive layers). These data were recorded during cooling from densification temperature. In addition, relative volume fractions of each ZrO2 phase within the AMZ were determined from the X-ray diffraction spectra (D-5000, Siemens, Germany) and using the Garvie–Nicholson equation.14 The mag￾nitude of the residual stresses was calculated analytically in the bulk material considering an equally biaxial stress distribution on the layer plane assuming an infinite body, as given by15 σc = εR · E c ·
1 + nc · tc · E c nt · tt · E t −1 (1) and σt = −σc ·
nc · tc nt · tt , (2) where εR = εATZ – εAMZ is the difference in deformation between adjacent layers, ti and ni are the thickness and number of layers, respectively, Ei’ = Ei/(1 – υi), and the subscripts c and t indicate one layer or the other. Vickers indentation technique was employed to evalu￾ate experimentally the residual stress field in the laminate. Several indentations with a load of 30 N were applied in the laminate at different distances from the free surface as well as at an internal ATZ layer, as shown schematically in Fig. 1. The cracks normal to the ATZ/AMZ interface emanating from these indentations were measured using interference contrast. To determine the crack tip posi￾tion for each indentation crack, the light beam was re￾duced so that the crack tip was in the dark field next to the beam area. The magnitude of the residual stresses in the ATZ AMZ a) b) 200 µm Fig. 1 Scheme of the indentation profile in the (a) ATZ inner layers and (b) ATZ outer layers of the laminate, using a Vickers indenter with an applied load of 30 N. c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

74 R. BERMEJo et a/ inner and outer ATZ layers of the laminate was deter- Mechanical properties mined using Eqs. (3)and (4), wh Vickers hardness. Young's modulus and mor of mono- of the critical stress intensity factor, Klc, for indentation liths and laminates were evaluated. Vickers hardness of cracks in a stress-free ceramic16 and in a ceramic within a both aTZ and AMZ monoliths was determined measur- residual stress field, 7 respectively, ing the imprint made with a Vickers indenter at an applied oung s m (3) ples was obtained by the impulse excitation technique19 (ET), following the guidelines provided by asTM E 1876-99 and ENV-843-2 On the other hand. for the lam inates it was assessed using the lower-bound estimate of K=x·+ψv Ravichandran Four-point bending tests were accomplished on mono- where p is the indentation load. c is the initial crack size liths and laminates to compare the mechanical behaviour for the stress-free ceramic and c is the crack length on a of both materials in terms of strength and fracture tough ceramic under residual stresses. x is a residual-stress fac- ness. In doing so, a fully articulated test jig with inner and torand y a crack-shape factor, which can be calculated for outer spans of 10 and 20 mm, respectively, was used. Tests a given geometry. Both factors depend on the indentation were made under load control at a testing rate of 100Ns-I crack eccentricity,(c/a), which is an important parameter The stress distribution under four-point bending on a for describing the shape ofindentation cracks. This eccen- prismatic bar formed by different lay hay be predicted tricity was measured by recourse to subsequent grinding following the expression given by21 and polishing of cracks induced using indentation loads of E:M 150 N applied at the surface of the specimens. Half- (-yna) cracks were observed for the monoliths, thus(c/a) results in a value of l, being x=Xo, where xo is a dimensionless where Ei is the Young's modulus of the corresponding constant that depends on the modulus-to-hardness ratio layer, M is the moment for the case of four-point bending as given by tests(M=F-1, where Fis the applied load and l the distance between inner and outer spans), yna is the position of the ng to ∑1E1xt×B×(2×∑ y1 ith e as the Youngs modulus and h the material hard- 2×∑=1E1×txB ness. 5 is a material-independent constant with an aver- and EI the flexural rigidity of the multi-layer calculated aged value of 0.016 calibrated by Anstis et al. for certain for bending perpendicular to the interfaces between the reference materials. On the other hand, eccentricity for layers as given by: 22 1. 25 in the ATZ layers, where a is the crack length into the material and c is half the crack length at the surface. (ED=3 2E.B.2t-yoa Thus, two correction factors, fece and Fres, as given by Smith and Scattergood, 8 were implemented to account for this effect, leading to a geometric factor v yofe with yo= 1. 29 for an embedded circular crack, and residual-stress factor x Xo Fres From Eqs. 3)and (4), and introducing the corresponding where t; is the corresponding layer thickness and b the correction factors, Eq (6)was obtained and then used to Decimen width. The commonly used expression to de- calculate the stresses through the layers of the laminate termine the stress on the surface of a monolithic material OR=(1.5. Fy/(BW), where W is the specimen height, is a particular case for Eq. (7) (6 In addition, fractured specimens were inspected by both reflected light optical microscopy and SEM EOL JMS 6400) to determine type and size of the failure-controlling The critical stress intensity factor value used in Eq.(6), natural flaws. The effect of the multi-layer architecture on graphs observation. Moreover, the mechanical respo- Kle, was obtained by the indentation method (IM)in the the growth of these critical flaws was assessed by mic monolithic material utilizing Eq. 3)for an applied inder tation load of 50 N of the laminate compared to the monolithic was base @2006 Blackwell Publishing Ltd. Fatigue Fact Engng Mater Struct 29, 71-78

74 R. BERMEJO et al. inner and outer ATZ layers of the laminate was deter￾mined using Eqs. (3) and (4), which represent the value of the critical stress intensity factor, KIc, for indentation cracks in a stress-free ceramic16 and in a ceramic within a residual stress field,17 respectively, KIc = χ · P c 3/2 o (3) and KIc = χ · P c 3/2 + ψ · σres · √c, (4) where P is the indentation load, co is the initial crack size for the stress-free ceramic and c is the crack length on a ceramic under residual stresses. χ is a residual-stress fac￾tor and ψ a crack-shape factor, which can be calculated for a given geometry. Both factors depend on the indentation crack eccentricity, (c/a), which is an important parameter for describing the shape of indentation cracks. This eccen￾tricity was measured by recourse to subsequent grinding and polishing of cracks induced using indentation loads of 150 N applied at the surface of the specimens. Half-penny cracks were observed for the monoliths, thus (c/a) results in a value of 1, being χ = χ0, where χ0 is a dimensionless constant that depends on the modulus-to-hardness ratio as given by: χ0 = ξ · E H 1/2 , (5) with E as the Young’s modulus and H the material hard￾ness. ξ is a material-independent constant with an aver￾aged value of 0.016 calibrated by Anstis et al.16 for certain reference materials. On the other hand, eccentricity for the laminates with residual stresses was found to be about 1.25 in the ATZ layers, where a is the crack length into the material and c is half the crack length at the surface. Thus, two correction factors, f ecc and Fres, as given by Smith and Scattergood,18 were implemented to account for this effect, leading to a geometric factor ψ = ψ0·f ecc, with ψ0 = 1.29 for an embedded circular crack, and to a residual-stress factor χ = χ0·Fres. From Eqs. (3) and (4), and introducing the corresponding correction factors, Eq. (6) was obtained and then used to calculate the stresses through the layers of the laminate. σres = 1 ψ · √c · KIc ·  1 − Fres · c 0 c 3/2  . (6) The critical stress intensity factor value used in Eq. (6), KIc, was obtained by the indentation method (IM) in the monolithic material utilizing Eq. (3) for an applied inden￾tation load of 50 N. Mechanical properties Vickers Hardness, Young’s modulus and MOR of mono￾liths and laminates were evaluated. Vickers hardness of both ATZ and AMZ monoliths was determined measur￾ing the imprint made with a Vickers indenter at an applied load of 9.8 N. Young’s modulus for the monolithic sam￾ples was obtained by the impulse excitation technique19 (IET), following the guidelines provided by ASTM E 1876–99 and ENV-843–2. On the other hand, for the lam￾inates it was assessed using the lower-bound estimate of Ravichandran.20 Four-point bending tests were accomplished on mono￾liths and laminates to compare the mechanical behaviour of both materials in terms of strength and fracture tough￾ness. In doing so, a fully articulated test jig with inner and outer spans of 10 and 20 mm, respectively, was used. Tests were made under load control at a testing rate of 100 N s–1. The stress distribution under four-point bending on a prismatic bar formed by different layers may be predicted following the expression given by21 σi,y = EiM (E I) · (y − yna) , (7) where Ei is the Young’s modulus of the corresponding layer, M is the moment for the case of four-point bending tests (M=F·l, where F is the applied load and l the distance between inner and outer spans), yna is the position of the neutral axis according to yna = n i=1 Ei × ti × B ×  2 × i−1 j=1 tj + ti 2 × n i=1 Ei × ti × B (8) and EI the flexural rigidity of the multi-layer calculated for bending perpendicular to the interfaces between the layers as given by:22 (EI) = 1 3 · n i=1 Ei · B ·   i j=1 tj − yna3 + yna − i−1 j=1 tj 3   , (9) where ti is the corresponding layer thickness and B the specimen width. The commonly used expression to de￾termine the stress on the surface of a monolithic material, σ R = (1.5·Fl)/(BW2), where W is the specimen height, is a particular case for Eq. (7). In addition, fractured specimens were inspected by both reflected light optical microscopy and SEM (JEOL JMS 6400) to determine type and size of the failure-controlling natural flaws. The effect of the multi-layer architecture on the growth of these critical flaws was assessed by micro￾graphs observation. Moreover, the mechanical response of the laminate compared to the monolithic was based on c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

FRACTURE BEHAVIOUR OF AN Al20 3-ZrO2 MULTI-LAYERED CERAMIC 75 the evaluation of the residual stress distribution within the Table 1 Thermal expansion coefficients and grain size for the multi-layered structure AMZ and ATZ monolithic specimens CTEs(×10-6C-1) RESULTS AND DISCUSSION Material 20-700 800-1200 Processing and physical characterization AMZ Laminates composed of nine alternated 530+ 10umATZ ATZ 2.0-3.00.3-0.6 and 100+ 10 um AMZ layers were obtained by control ling the casting time for each layer according to the wall thickness versus time curves. Green densities for the atz and AMZ monoliths resulted in 69% and 62% of the the oretical density, respectively. Regardin Table 2 Vickers hardness, Young,s modulus and modulus of spec- rupture(MOR)of the AMZ and ATZ monoliths and laminate, imens, relative density was above 99% calculated at the surface The dilatometries showed the thermal strain variation from the reference temperature, that is, 1200C, above MOR (MPa)at which residual stresses between lavers are neglected, and Material HVI (GPa) E(GPa) the surface the room temperature. In Fig. 2, the expansion associated with the martensitic transformation of zirconia(Y,O, AMZ 10.2 280±30 90士20 725 oC and generates residual compressive stresses in the LAMINATE163 free)can be observed. This transformation occurs at ATZ 390±10 422±30 373士10431±8 AMZ layers(Eq. ( 1). ) and tensile stresses in the aTZ lay ers (Eq (2).), yielding as a result to a characteristic biaxial stress field in each laver of the laminate. Out of this trans- formation zone, both samples shrink in a linear way. Both coefficients of thermal expansion(CTEs) and grain size measurements of the ATZ and AMZ monolithic speci mens are presented in Table 1 Residual stresses in the laminate The residual stresses originated in the multi-layeredarchi- 90 tecture were estimated both analytical and experimentally. 2 Using Eqs. (1)and (2)and considering the thermal expan- 80 sion coefficients and Young's moduli given in Tables I and 0100200300400500 Distance(um) Fig 3 Measured values of the indentation crack lengths vs the distance to the(a)internal ATZ/AMZ inter-face(O), (b ) free surface of the outer most ATZ layer(O) and (c)centre of the ATZ monolith surface(■) 2, respectively, for the ATZ and aMz layers, the analytical biaxial residual stress values in the bulk material resulted AMZ n 74 MPa for the ATZ tensile layers and -695 MPa for the AMz compressive layers Experimentally, the length of the indentation cracks, 2 c. measured as a function of the distance to the inter mperature℃) layer is presented in Fig 3. The two correction factors, f ecc and Fres, describing the shape of these indentation 200°C, and room are, of the ATz and AMZ monolithic cracks were found to be 0.70 and 1.11, respectively. 8 materials that form of the lamin slope on The critical stress intensity factor used in Eq.(6), Klc, the AMZ is due to the zirconia phase transformation obtained by the indentation method resulted in a value of @2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71-78

FRACTURE BEHAVIOUR OF AN Al 2O 3–ZrO 2 MULTI-LAYERED CERAMIC 75 the evaluation of the residual stress distribution within the multi-layered structure. RESULTS AND DISCUSSION Processing and physical characterization Laminates composed of nine alternated 530 ± 10µm ATZ and 100 ± 10 µm AMZ layers were obtained by control￾ling the casting time for each layer according to the wall thickness versus time curves. Green densities for the ATZ and AMZ monoliths resulted in 69% and 62% of the the￾oretical density, respectively. Regarding the sintered spec￾imens, relative density was above 99%. The dilatometries showed the thermal strain variation from the reference temperature, that is, 1200 ◦C, above which residual stresses between layers are neglected, and the room temperature. In Fig. 2, the expansion associated with the martensitic transformation of zirconia (Y2O3 free) can be observed. This transformation occurs at 725 ◦C and generates residual compressive stresses in the AMZ layers (Eq. (1).), and tensile stresses in the ATZ lay￾ers (Eq. (2).), yielding as a result to a characteristic biaxial stress field in each layer of the laminate. Out of this trans￾formation zone, both samples shrink in a linear way. Both coefficients of thermal expansion (CTEs) and grain size measurements of the ATZ and AMZ monolithic speci￾mens are presented in Table 1. Residual stresses in the laminates The residual stresses originated in the multi-layered archi￾tecture were estimated both analytical and experimentally. Using Eqs. (1) and (2) and considering the thermal expan￾sion coefficients and Young’s moduli given in Tables 1 and 0 300 600 900 1200 -8 -6 -4 -2 0 ∆L/L0 ( ×103 ) Temperature (°C) ATZ AMZ εR Fig. 2 Dilatometry curves, between a reference temperature, 1200 ◦C, and room temperature, of the ATZ and AMZ monolithic materials that form the layers of the laminate. Change in slope on the AMZ is due to the zirconia phase transformation. Table 1 Thermal expansion coefficients and grain size for the AMZ and ATZ monolithic specimens CTEs (×10−6C−1) Grain size (µm) Material 20–700 800–1200 Al2O3 ZrO2 AMZ 8.4 10.5 1.2–2.0 0.4–1.5 ATZ 9.82 9.82 2.0–3.0 0.3–0.6 Table 2 Vickers hardness, Young’s modulus and modulus of rupture (MOR) of the AMZ and ATZ monoliths and laminate, calculated at the surface MOR (MPa) at Material HV1 (GPa) E (GPa) the surface AMZ 10.2 280 ± 30 90 ± 20 ATZ 16.3 390 ± 10 422 ± 30 LAMINATE – 373 ± 10 431 ± 8 0 100 200 300 400 500 80 90 100 110 Crack length, 2c ( µm) Distance (µm) Fig. 3 Measured values of the indentation crack lengths vs. the distance to the (a) internal ATZ/AMZ inter-face ( ✉), (b) free surface of the outer most ATZ layer ( ❡) and (c) centre of the ATZ monolith surface (
). 2, respectively, for the ATZ and AMZ layers, the analytical biaxial residual stress values in the bulk material resulted in 74 MPa for the ATZ tensile layers and −695 MPa for the AMZ compressive layers. Experimentally, the length of the indentation cracks, 2c, measured as a function of the distance to the inter￾layer is presented in Fig. 3. The two correction factors, f ecc and Fres, describing the shape of these indentation cracks were found to be 0.70 and 1.11, respectively.18 The critical stress intensity factor used in Eq. (6), KIc, obtained by the indentation method resulted in a value of c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

R. BERMEJO et al. 3.5 MPa. m/. Thus, the magnitude and distribution of limitations due to the small AMz layer dimensions hin- the residual stresses within the inner and outer layers of dered the study of the empiric residual stress profile de- the laminate, calculated using Eq (6), are shown in Fig 4. termination in these thin compressive layer For the internal ATZ layers, a symmetrical parabolic dis tribution is obtained reaching a maximum value close the atz/aMz interfaces. On the other hand. for the Mechanical re outer layers, residual stresses decrease near the free sur- Vickers Hardness, Young's modulus and fracture strength face. These observations are in accordance with the trends of monoliths and laminates are reported in Table 2. The reported by other authors using finite element calcula- lower-hardness value of the AMZ monolith may be ex- tions' and the indentation technique. 3 The mean value plained by the higher content of monoclinic ZrO2 phase of the tensile residual stresses evaluated experimentally As expected, AMZ strength(90+ 20 MPa)is much lower at an internal ATZ laver, that is 876+ 10 MPa, is in than the value for the atz monolith(422+ 30 MPa) good agreement with the value obtained analytically, de- On the other hand, the fracture strength of the laminate spite the uncertainty in crack length measurements and (431 +8 MPa)is similar to that of the ATZ monolith the edge stress effects.24 In this direction, experimental This result along with the fractographic observations of the fracture surfaces(see Fig. 5)reveal several aspects: (i) Distance to the atZ/amz interlayer [um] the scatter on the laminates is much lower than on the ATZ monoliths, (i) monoliths show a surface flaw popu 0 100 200 300 400 500 lation most likely originated at a time when the grinding process and laminates present a natural flaw population inherent to the processing, that is agglomerates formed in the casting step, (iii) the dominating flaws in both ma- terials are located at or near the surface where maximum stress is developed under flexural loading and (iv)the crit- ical flaws that origin fracture are different in monoliths 切 up to n the multi-layers(see white arrows in Fig 5b) To rationalize the obtained al results and sidering monoliths and laminates as brittle materials and their fracture occurring from pre-existing natural flaws, the linear elastic fracture mechanics approach is imple mented in this work Distance to the free surface (um) Kc=Y·∝R·√r:a Fig.4 Plot of the residual stress profile calculated experimentally where, on the inner(O and outer(O aTZ layers of the laminate vs the where Y represents a flaw shape factor, ac is the critical size distance to the aTz/AMZ inter-layer and to the free surface, of the natural flaw and or is the failure stress, which in the case of the laminate accounts for the residual stresses 100pm 100μm g electron microscope micrographs of fracture sites (a)in the ATZ monolith and (b) in the laminate. In the latter, the natural flaw propagates stably under flexural loading from the surface up to the first ATZ/AMZ inter-face(white arrows on the outer ATZ layer) before catastrophic failure occurs. It is also observed another possible stable growth of the natural flaw up to the second AMZ layer(white arrows on the internal ATZ layer) @2006 Blackwell Publishing Ltd. Fatigue Fact Engng Mater Struct 29, 71-78

76 R. BERMEJO et al. 3.5 MPa.m1/2. Thus, the magnitude and distribution of the residual stresses within the inner and outer layers of the laminate, calculated using Eq. (6), are shown in Fig. 4. For the internal ATZ layers, a symmetrical parabolic dis￾tribution is obtained reaching a maximum value close to the ATZ/AMZ interfaces. On the other hand, for the outer layers, residual stresses decrease near the free sur￾face. These observations are in accordance with the trends reported by other authors using finite element calcula￾tions5 and the indentation technique.23 The mean value of the tensile residual stresses evaluated experimentally at an internal ATZ layer, that is, ≈76 ± 10 MPa, is in good agreement with the value obtained analytically, de￾spite the uncertainty in crack length measurements and the edge stress effects.24 In this direction, experimental 0 100 200 300 400 500 0 20 40 60 80 100 0 100 200 300 400 500 Distance to the ATZ/AMZ interlayer [µm] Residual stresses (MPa) Distance to the free surface (µm) Fig. 4 Plot of the residual stress profile calculated experimentally on the inner ( ✉) and outer ( ❡) ATZ layers of the laminate vs. the distance to the ATZ/AMZ inter-layer and to the free surface, respectively. a) 100 µm b) 100 µm f i Fig. 5 Scanning electron microscope micrographs of fracture sites (a) in the ATZ monolith and (b) in the laminate. In the latter, the natural flaw propagates stably under flexural loading from the surface up to the first ATZ/AMZ inter-face (white arrows on the outer ATZ layer) before catastrophic failure occurs. It is also observed another possible stable growth of the natural flaw up to the second AMZ layer (white arrows on the internal ATZ layer). limitations due to the small AMZ layer dimensions hin￾dered the study of the empiric residual stress profile de￾termination in these thin compressive layers. Mechanical response Vickers Hardness, Young’s modulus and fracture strength of monoliths and laminates are reported in Table 2. The lower-hardness value of the AMZ monolith may be ex￾plained by the higher content of monoclinic ZrO2 phase. As expected, AMZ strength (90 ± 20 MPa) is much lower than the value for the ATZ monolith (422 ± 30 MPa). On the other hand, the fracture strength of the laminate (431 ± 8 MPa) is similar to that of the ATZ monolith. This result along with the fractographic observations of the fracture surfaces (see Fig. 5) reveal several aspects: (i) the scatter on the laminates is much lower than on the ATZ monoliths, (ii) monoliths show a surface flaw popu￾lation most likely originated at a time when the grinding process and laminates present a natural flaw population inherent to the processing, that is agglomerates formed in the casting step, (iii) the dominating flaws in both ma￾terials are located at or near the surface where maximum stress is developed under flexural loading and (iv) the crit￾ical flaws that origin fracture are different in monoliths and laminates, being up to five times larger in the case of the multi-layers (see white arrows in Fig. 5b). To rationalize the obtained experimental results and con￾sidering monoliths and laminates as brittle materials and their fracture occurring from pre-existing natural flaws, the linear elastic fracture mechanics approach is imple￾mented in this work: Kc = Y · σR · √π · ac, (10) where Y represents a flaw shape factor, ac is the critical size of the natural flaw and σR is the failure stress, which in the case of the laminate accounts for the residual stresses. c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

FRACTURE BEHAVIOUR OF AN Al20 3-ZrO2 MULTI-LAYERED CERAMIC 77 Table 3 Critical stress intensity factor values, Ke, for the ATZ monolithic and laminate considering the critical natural flaw, ae, (a)located at the surface of the monolith, (b)near the surface of the laminate and(c) growing stably up to the first AMZ layer in the laminate Material Natural flaw site OR(MPa) Ke(MPa m/2) surface 422士30 45 3.2±0.2 LAMINATE Near surface 402±8 3.4±0.2 Near surface up to the first AMZ layer 402±8 f 94±0 natural flaw near the surface of the laminate f= critical natural flaw extended up to the first AMZ layer(see Fig. 5). In this framework, using the experimental results of flex- layered system, the following main results and conclusions ural strength, aR, the measured flaw sizes, ac, and the fac- may be inferred: tor y being chosen as that corresponding to the solution () The residual stresses developed in the multi-layer of a simple circular crack, that is, 2/T, the critical stress in- during sintering, evaluated using the indentation tech tensity factor is estimated using Eq (9)for both monoliths nique, reveal a difference in both magnitude and distri and laminates(see Table 3) bution between external and internal ATZ layers. For the Fracture toughness of3. 2 MPa.m/was calculated con- former, residual stresses decrease near the free surface. For dering natural flaws located at the surface of the atz the latter a symmetrical parabolic distribution is observed, monoliths. This value is similar to that obtained using the reaching a maximum value close to the ATZ/amz inter- IM method (3.5 MPa. m). For the laminates two cases faces. The mean value of these tensile residual stresses must be considered: (i) the initial natural flaw located near that is 76+ 10 MPa, is in good agreement with the re the surface of the outer most ATZ layer, that is, agglom- sults obtained with analytical calculations(74 MPa). Fol- erate in Fig. 5b, that with the corresponding stress at the lowing a similar approach, a value of -695 MPa is found aw site, that is, 402 MPa, (value calculated using Eq (7) for the thin AMZ compressive layers. at 100 um beneath the surface) gives a fracture tough -( i) Flexural strength in the laminates(431+ 8 MPa) ness of 3. 4 MPa. m/ and (i) the critical flaw as a result similar to that of the atz monoliths(422+ 30 MPa) of a stable growth of the initial natural flaw up to the first However, the scatter in the former is much lower. This ATZ/AMZ inter-layer(see white arrows on the outer ATz along with the observation of the step-wise fracture sur layer in Fig 5b)that for the given stress at the initial flaw face is explained by the subcritical growth experienced by site,that is, 402 MPa, would lead to a toughness value the natural flaws, independently of their initial size, up of9.4 MPa. m /. This value might be even higher if we to the first AMZ layer, which acts as a barrier due to its considered the step-wise behaviour at the fracture surface high compressive residual stresses inherent to the zirco- f the laminate where it is observed another subcritical nia phase transformation during sintering. This behaviour growth of the natural flaw up to the second AMZ layer proposes the presence of a threshold strength, in this type (see white arrows on the internal aTZ layer in Fig 5b), of laminated, below which catastrophic failure will not as compared with the flat character exhibited by the ATz occur monolith(see Fig. 5a), leading to a toughness value of (ii) The increase in the fracture toughness of the multi 14.7 MPa.m/ and indicating the relevant effect of the layered material is found to be at least three times thin compressive layers impeding unstable propagation of that of the reference Al2O3-5vol %tZrO2 monolith. The tural flaws within the multi-layered structure. ep-like fracture observed in the multi-layered structure As commented above, the scatter in the laminates is much shows the complex mode of loading to which this ma lower than in the ATZ monoliths. This might also be ex- terial is subjected during fracture and thus the difficulty plained by the subcritical growth experienced by the nat- in the evaluation of the real fracture toughness of the ural flaws up to the first ATZ/AMZ inter-layer, regardless multi-layer. their initial size. This allows us to speculate on the exis tence of a threshold strength in this multi-layered system, as seen in other laminar structures reported in literature, Acknowledge below which catastrophic failure will not occu Financial support by the Ministerio de Ciencia y CONCLUSIONS Tecnologia(MAT2002-00368 and MAT2003-00836) Spain, is acknowledged. Work supported in part by the Based on the analysis of the mechanical behaviour European Communitys Human Potential Program un- of an Al2O3-5vol%t ZrO2/Al2O3-30vol%mZrO2 multi- der contract HPRN-CT-2002-00203, [SICMAC]. The @2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71-78

FRACTURE BEHAVIOUR OF AN Al 2O 3–ZrO 2 MULTI-LAYERED CERAMIC 77 Table 3 Critical stress intensity factor values, Kc, for the ATZ monolithic and laminate considering the critical natural flaw, ac, (a) located at the surface of the monolith, (b) near the surface of the laminate and (c) growing stably up to the first AMZ layer in the laminate Material Natural flaw site σ R (MPa) ac (µm) Kc (MPa·m1/2) ATZ At surface 422 ± 30 45 3.2 ± 0.2 LAMINATE Near surface 402 ± 8 55 i 3.4 ± 0.2 Near surface up to the first AMZ layer 402 ± 8 430 f 9.4 ± 0.2 i = initial natural flaw near the surface of the laminate. f = critical natural flaw extended up to the first AMZ layer (see Fig. 5). In this framework, using the experimental results of flex￾ural strength, σ R, the measured flaw sizes, ac, and the fac￾tor Y being chosen as that corresponding to the solution of a simple circular crack, that is, 2/π, the critical stress in￾tensity factor is estimated using Eq. (9) for both monoliths and laminates (see Table 3). A fracture toughness of 3.2 MPa.m1/2 was calculated con￾sidering natural flaws located at the surface of the ATZ monoliths. This value is similar to that obtained using the IM method (3.5 MPa.m1/2). For the laminates two cases must be considered: (i) the initial natural flaw located near the surface of the outer most ATZ layer, that is, agglom￾erate in Fig. 5b, that with the corresponding stress at the flaw site, that is, 402 MPa, (value calculated using Eq. (7) at 100 µm beneath the surface) gives a fracture tough￾ness of 3.4 MPa.m1/2 and (ii) the critical flaw as a result of a stable growth of the initial natural flaw up to the first ATZ/AMZ inter-layer (see white arrows on the outer ATZ layer in Fig. 5b) that for the given stress at the initial flaw site, that is, 402 MPa, would lead to a toughness value of 9.4 MPa.m1/2. This value might be even higher if we considered the step-wise behaviour at the fracture surface of the laminate where it is observed another subcritical growth of the natural flaw up to the second AMZ layer (see white arrows on the internal ATZ layer in Fig. 5b), as compared with the flat character exhibited by the ATZ monolith (see Fig. 5a), leading to a toughness value of 14.7 MPa.m1/2 and indicating the relevant effect of the thin compressive layers impeding unstable propagation of natural flaws within the multi-layered structure. As commented above, the scatter in the laminates is much lower than in the ATZ monoliths. This might also be ex￾plained by the subcritical growth experienced by the nat￾ural flaws up to the first ATZ/AMZ inter-layer, regardless their initial size. This allows us to speculate on the exis￾tence of a threshold strength in this multi-layered system, as seen in other laminar structures reported in literature,6 below which catastrophic failure will not occur. CONCLUSIONS Based on the analysis of the mechanical behaviour of an Al2O3–5vol%tZrO2/Al2O3–30vol%mZrO2 multi￾layered system, the following main results and conclusions may be inferred: (i) The residual stresses developed in the multi-layer during sintering, evaluated using the indentation tech￾nique, reveal a difference in both magnitude and distri￾bution between external and internal ATZ layers. For the former, residual stresses decrease near the free surface. For the latter a symmetrical parabolic distribution is observed, reaching a maximum value close to the ATZ/AMZ inter￾faces. The mean value of these tensile residual stresses, that is ≈76 ± 10 MPa, is in good agreement with the re￾sults obtained with analytical calculations (74 MPa). Fol￾lowing a similar approach, a value of -695 MPa is found for the thin AMZ compressive layers. (ii) Flexural strength in the laminates (431 ± 8 MPa) is similar to that of the ATZ monoliths (422 ± 30 MPa). However, the scatter in the former is much lower. This along with the observation of the step-wise fracture sur￾face is explained by the subcritical growth experienced by the natural flaws, independently of their initial size, up to the first AMZ layer, which acts as a barrier due to its high compressive residual stresses inherent to the zirco￾nia phase transformation during sintering. This behaviour proposes the presence of a threshold strength, in this type of laminated, below which catastrophic failure will not occur. (iii) The increase in the fracture toughness of the multi￾layered material is found to be at least three times that of the reference Al2O3–5vol%tZrO2 monolith. The step-like fracture observed in the multi-layered structure shows the complex mode of loading to which this ma￾terial is subjected during fracture and thus the difficulty in the evaluation of the real fracture toughness of the multi-layer. Acknowledgments Financial support by the Ministerio de Ciencia y Tecnolog´ıa (MAT2002–00368 and MAT2003–00836), Spain, is acknowledged. Work supported in part by the European Community’s Human Potential Program un￾der contract HPRN-CT-2002–00203, [SICMAC]. The c 2006 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 29, 71–78

78 R. BERMEJo et a/ luthors thank M. Marsal for assisting with the electron 12 Pontin, M G, Rao, M P, Sanchez-Herencia, A J and Lange, Icroscopy activities. F. F(2002)Laminar ceramics utilizing the zirconia tragonal-to-monoclinic phase transformation to obtain REFERENCES threshold strength. 7. Am. Ceram. Soc. 85, 3041-3048 13 Requena, J, Moreno, R and Moya, J S (1989)Alumina and I Virkar, A. V, Huang, J. L and Cutler, R. A (1987 alumina/zirconia multilayer composites obtained by slip casting Strengthening of oxide ceramics by transformation-induced 3.Am.Cerm.Soc.72,1511-1513. stresses. f. Am. Ceram Soc. 70, 164-170 14 Garvie, R. C and Nicholson, P S (1972) Phase analysis in Marshall, D. B, Ratto, JJ and Lange, FF(1991) Enhanced zirconia system. ]. Am. Ceram. Soc. 55, 303-305 fracture toughness in layered microcomposites of Ce-ZrO2 and 15 Oel, H.J. and Frechette, V.D. (1967)Stress distribution in Al2O3.3.Am.Cerm.Soc.74,2979-2987 multiphase system: I, composites with planar interfaces. 7. Am. 3 Katsuki, H. and Hirata, Y. (1990) Coat of alumina sheet with Cerm.Soc.50,542-549 needle-like mullite. ]. Ceram. Soc. Japan 98, 1114-1119 16 Anstis, G. R, Chantikul, P, Lawn, B R and Marshall, D. B 4 Hansen, J.J., Cutler, R. A, Shetty, D. K and Virkar, A. V. (1981)A critical evaluation of indentation techniques for (1988)Indentation fracture response and damage resistance of measuring fracture toughness: I, direct crack measurements. 3. Al2O3- ZrO2 composites strengthened by Am.Cenm.Soc.64,533-538. transformation-induced residual stresses. 7. Am. Ceram. Soc. 71, 17 Marshall, D. B and Lawn, B. R (1979) Residual Stress Effects C-501-C-505 5 Lakshminarayanan, R,, Shetty, D K and Cutler, R. A (199 . Mater sci.14,2001-2012 Toughening of layered ceramic composites with residual 18 Smith, S. M. and Scattergood, O (1992)Crack-shape effects for surface compression. 7. Am. Ceram. Soc. 79, 79-87. dentation fracture toughness measurements. ]. Am. Ceram 6 Rao, M. P, Sanchez-Herencia, A.J., Beltz, G. E, McMeeking, So.75,305-31 R. M. and Lange, F. F (1999) Laminar ceramics that exhibit a 19 Roebben, G, Bollen, B, Rebels, A, Van Humbeeck, J and Val threshold strength. Science 286, 102-105 der Biest, O. (1997) Impulse excitation apparatus to measure 7 Cutler, R. A, Bright, J D, Virkar, A. V and Shetty, D.K. nce frequencies, elastic moduli and internal friction at (1987) Strength improvement in transformation-toughened room and high temperature. Rev. Sci. Instr: 68, 4511-4515 umina by selective phase transformation. 7. Am. Ceram. So 20 Ravichandran, K( 1994) Elastic properties of two phase 70,714718 sites.J. Am. Ceram. Soc. 77, 1178-1184 8 Hillman, C, Suo, Z G and Lange, F. F(1996)Cracking of ics of Materials. Van Nostrand minates subjected to biaxial tensile stresses. Am. Ceram. Soc Reinhold, New York, USA 2127-2133 22 Malzbender, J and Steinbrech, R w.(2004) Mechanical 9 Sanchez-Herencia, A.J., Moya, J S and Tomsia, A. P (1997) properties of coated materials and multi-layered composites Microstructural design in alumina-alumina/zirconia layered determined using bending methods. Surf. Coat. Tecb. 176 opposites. Scr. Mater. 38, 1-5 65-172 10 Sanchez-Herencia, A. J, Pascual, C, He, J and Lange,E.E. 23 She, J, Scheppokat, S, Janssen, R and Claussen, N. (1999) ZrO2/ZrO2 layered composites for crack bifurcation. 7. Determination of residual stresses in three-layer alu m.Ccrm.So.82,1512-1518 composites using an indentation technique. J. Mater. Sci. 34, 11 Sanchez-Herencia, A J, James, L and Lange, F. F (2000) 1823-1828 Bifurcation in alumina plates produced by a phase 24 Sergo, V, Lipkin, D. M, De Portu, G and Clarke, D. R ( 1997) transformation in central, alumina/zirconia thin layers. 7. Eur Edge stresses in alumina/zirconia laminates. 7. Am. Ceram. Soc Cea.Soc.20,1297-130 80.1633-1638. @2006 Blackwell Publishing Ltd. Fatigue Fact Engng Mater Struct 29, 71-78

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