Availableonlineatwww.sciencedirect.com ScienceDirect E噩≈RS ELSEVIER Joumal of the European Ceramic Society 27(2007)1449-1453 www.elsevier.comlocate/jeurceramsoc Effective fracture toughness in Al,O3-Al2O3/zrO laminates Tanja Lube a, * Javier Pascuala, Francis Chalvet b, Goffredo de portu b a Institut fiir Struktur- und Funkionskeramik, Montanuniversitat Leoben, Peter Tinner StraBe 5, Leoben A-8700, Austria b Istituto di Scienza e Technologia dei Materiali Ceramici-CNR Via Granarolo 64. 48018 Faenza, Italy Available online 30 May 2006 During the processing of laminar ceramics, biaxial residual stresses can arise due to the thermal mismatch between different layers. For ceramic multilayers, the beneficial consequences of compressive stresses at the surface are well known: increase in strength, apparent toughness and reliability. Nevertheless, the resulting tensile stresses may induce a negative influence in the effective fracture toughness if the tensile stresses are hi The weight function technique is used to assess the stress intensity factor corresponding to the residual stresses field. The infuence of geometrical parameters such as thickness, number of layers and tension/compression thickness ratio is analyzed. For different multilaye (AlO3-xAl2O3 /(1-x)ZrO2), effective R-curves are presented. The existence of an optimal architecture that maximizes the toughening is exposed as well as two tendencies on the apparent R-curve that define different fracture patterns: brittle failure or layer-by-layer fracture 2006 Elsevier Ltd. All rights reserved. Keywords: Composites; Toughening: Al2 O3: ZrO2: Laminate 1. Introductio This paper examines laminates with strong interfaces, in par ticular multilayers made of alumina(A)and an alumina-zirconia Ceramic composites have a broad range of industrial appli- composite(AZ). Those multilayers with an A-outer layer are cations. They have been extensively developed for structural shielded due to the minor thermal expansion of A compared to components in order to improve the mechanical, chemical and the composite AZ. thermal performance of engineering devices. However, despite Although fracture toughness of a layered composite can be a high hardness, an excellent oxidation resistance, and high tem- experimentally measured, it is only an apparent or effective value perature stability, ceramics are inherently brittle. One of the because of the influence of the residual stress. Besides, different laminates with residual stresses. 1,2gt strategies to decrease brittleness is through the design of ceramic shielding effects or intrinsic properties of the structure, such as bridging associated to grain size, rend difficult the interpretation Laminates can improve mechanical performance since sur- of toughness measurements. face compression introduces a closure stress that protects against The apparent R-curve of a laminate can be calculated con- faws. Two strategies of laminate design have been previ- sidering the equilibrium condition at the crack tip, i.e. crack ously presented: first, laminates with a weak interface that propagation is possible if the stress intensity at the crack tip deflects cracks, thus preventing catastrophic failure 4 and sec- Ktip, equals or exceeds the intrinsic material toughness Ko ond, laminates with strong interfaces. Since strong interfaces will transmit residual stresses during cooling from sintering Ktip(a)>Ke.o being Ktip(@)=Kappl(a)+Kres(a),(1) temperature, one can benefit of a phase transformation nermal mismatch to induce compressive stresses at the where Kapp(a)is the applied stress intensity and Kres(a)is the stress intensity contribution from the residual stress. Solving for Kappl(a) holds Kappl(a)>ke.0-Kres(a)=KR.effective Corresponding author. Tel. +43 3842 402 4111: fax: +43 3842 402 4102 E-mailaddresses:tanjalube@mu-leobenat(TLube),deport@istec.cnr.twhereKapp(a)equalsthedesiredeffectiveR-curve (G. de Portu). KReffective(a) 0955-2219/S-see front matter o 2006 Elsevier Ltd. All rights reserved. doi: 10. 1016/j-jeurceramsoc. 2006.04.063
Journal of the European Ceramic Society 27 (2007) 1449–1453 Effective fracture toughness in Al2O3–Al2O3/ZrO2 laminates Tanja Lube a,∗, Javier Pascual a, Francis Chalvet b, Goffredo de Portu b a Institut f ¨ur Struktur- und Funktionskeramik, Montanuniversit ¨at Leoben, Peter Tunner Straße 5, Leoben A-8700, Austria b Istituto di Scienza e Technologia dei Materiali Ceramici-CNR, Via Granarolo 64, 48018 Faenza, Italy Available online 30 May 2006 Abstract During the processing of laminar ceramics, biaxial residual stresses can arise due to the thermal mismatch between different layers. For ceramic multilayers, the beneficial consequences of compressive stresses at the surface are well known: increase in strength, apparent toughness and reliability. Nevertheless, the resulting tensile stresses may induce a negative influence in the effective fracture toughness if the tensile stresses are high. The weight function technique is used to assess the stress intensity factor corresponding to the residual stresses field. The influence of geometrical parameters such as thickness, number of layers and tension/compression thickness ratio is analyzed. For different multilayers (Al2O3 − xAl2O3/(1 − x)ZrO2), effective R-curves are presented. The existence of an optimal architecture that maximizes the toughening is exposed as well as two tendencies on the apparent R-curve that define different fracture patterns: brittle failure or layer-by-layer fracture. © 2006 Elsevier Ltd. All rights reserved. Keywords: Composites; Toughening; Al2O3; ZrO2; Laminate 1. Introduction Ceramic composites have a broad range of industrial applications. They have been extensively developed for structural components in order to improve the mechanical, chemical and thermal performance of engineering devices. However, despite a high hardness, an excellent oxidation resistance, and high temperature stability, ceramics are inherently brittle. One of the strategies to decrease brittleness is through the design of ceramic laminates with residual stresses.1,2 Laminates can improve mechanical performance since surface compression introduces a closure stress that protects against flaws. Two strategies of laminate design have been previously presented: first, laminates with a weak interface that deflects cracks, thus preventing catastrophic failure3,4 and second, laminates with strong interfaces. Since strong interfaces will transmit residual stresses during cooling from sintering temperature, one can benefit of a phase transformation4 or a thermal mismatch5 to induce compressive stresses at the surface. ∗ Corresponding author. Tel.: +43 3842 402 4111; fax: +43 3842 402 4102. E-mail addresses: tanja.lube@mu-leoben.at (T. Lube), deportu@istec.cnr.it (G. de Portu). This paper examines laminates with strong interfaces, in particular multilayers made of alumina (A) and an alumina–zirconia composite (AZ). Those multilayers with an A-outer layer are shielded due to the minor thermal expansion of A compared to the composite AZ. Although fracture toughness of a layered composite can be experimentally measured, it is only an apparent or effective value because of the influence of the residual stress. Besides, different shielding effects or intrinsic properties of the structure, such as bridging associated to grain size, rend difficult the interpretation of toughness measurements. The apparent R-curve of a laminate can be calculated considering the equilibrium condition at the crack tip, i.e. crack propagation is possible if the stress intensity at the crack tip, Ktip, equals or exceeds the intrinsic material toughness K0: Ktip(a) ≥ Kc,0 being Ktip(a) = Kappl(a) + Kres(a), (1) where Kappl(a) is the applied stress intensity and Kres(a) is the stress intensity contribution from the residual stress. Solving for Kappl(a) holds Kappl(a) ≥ Kc,0 − Kres(a) = KR,effective, (2) where Kappl(a) equals the desired effective R-curve. KR,effective(a). 0955-2219/$ – see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2006.04.063
T Lube et al. Joumal of the European Ceramic Sociery 27(2007)1449-1453 In fracture mechanics, both residual and applied stresses are Table I usually included in the crack driving force. However, it is useful Properties of the material layers to consider the residual stresses as part of the crack resistance E( atech(10-6K-) Ko(MPam Thus, in laminates with compressive stress at the surface, the (0-1150°C) higher resistance to failure results from a reduction of the crack 8 driving force rather than from an increase in the intrinsic material AZ (60A40Z) 305 0.2579.24 resistance to crack extension The term Kres(a)can-as an approximation- be assessed by means of the weight function approach, that allows us to calcu- layers, A=tAz/ta is the layer thickness ratio, and e= EA/EAZ late the stress intensity factor K(a), for an edge crack of length a The indexes make reference to the materials. Since the reason for an arbitrary stress distribution acting normal to the fracture of the residual stresses is a deformation constraint( due to the path. The weight function procedure developed by Bueckner thermal mismatch), the stress profile has to be proportional to simplifies the determination of K(a) since most of the numeri- the Youngs modulus in the corresponding layer. For the assess- cal methods require separate calculations for each given stress ment of the residual stress profile the different elastic moduli distribution and each crack length. This method is of particular were considered interest when the material is submitted to a"complicated"stress In this paper, symmetrical N-layer laminates with compres- profile such as creep, residual stresses in tempered glasses, or sive stresses at the surface were studied(N being an odd number esidual stresses in multilayers. Applying this concept to our to fulfil the condition of symmetry). All the layers made of the residual stress profile O res results same material(A or AZ, respectively) have the same thick ness, so the laminate is well defined by the thicknesses tA h(r, a)]res(x)dx (3) and [AZ, or the total thickness W and A. Through the paper, W will be considered constant and equals to W=1.5 mm, accord- where h(r, a) is the suitable weight function, a the crack length, ing to a possible design condition. The corresponding effective and x is the distance from the surface R-curves are calculated according to the procedure explained Previous works by Fett et al. 0, I validate the applicabili above. The influence of the residual stress field, defined by of this methodology to inhomogeneous materials. The weight geometrical and material properties, on the apparent R-curve function presented in Eq (4)was developed using the boundary is examined in detail. The results are expressed for the lami- collocation method. 12 It models materials with an homogeneous nated system Al2O3-xAl203/(1-x)ZrO2, but the conclusions Young's modulus It will be used as a first approximation For can be extended for any ceramic multilayer system with ideally inhomogeneous materials a suitable weight function will depend strong interfaces on E(). The consequences of using this simplified weight func- tion for a laminate will be discussed later 2. Experimental procedure The weight function is This study entailed the use of a high-purity (99.7%)alumina (x, a)-=Vrdvi-cal -(a/wo)i powder(Alcoa A16-SG, Alcoa Aluminium Co, New York, NY with an average particle size of 0.3 um, and a zirconia powder (TZ3Y-S, Tosoh Corp, Tokyo, Japan)doped with 3 mol% Y203 (-)2+4m(-2)"(G with an average particle size of 0.3 um. On the basis of previous experiments, > the different powders were mixed with organic (4) binders, dispersants, plasticizers, and solvents to obtain suitable where the coefficients A, can be found in 8, 12 w is the total slips for tape casting. Slurry compositions were the same for thickness. It is worth of note that is not dependent on Youngs both Al2 O3 and AlO3 /ZrO2 composite powders. Sheets of pure modulus exclusively in the case of a homogeneous material. alumina(A)and of the composite containing 60 vol %o alumina In order to calculate the residual stresses in a laminate the and 40 vol% zirconia(Az)were produced following approximation was used. Far away from the free Table I presents the material properties for the different surface, 4 the residual stress, OR, in each layer is uniform and layers, where E and v were measured by impulse excitation biaxial. For the different layers a or aZ technique, a by means of a dilatometer between 20 and 1200C ( single-edge-V-notch beam in four point bending test). 16. 7 re and the intrinsic toughness Ko following the VAMAS procedure 1+(N+1)/(N-1)(e/入) tA (N +l) 3. Results and discussion As shown by previous authors, the apparent R-curve in where E=E/(I-v), v being the Poisson's ratio, Aa= multilayers presents an oscillating behaviour.4(see Fig. 1) (aAz -aA)the difference of the thermal expansion coefficients The toughness increases in of AZ and A, respectively, Tsf the temperature below which the increasing crack length and reaches a local maximum at the inter residual stresses arise, To the room temperature, N the number of face. It decreases in the tensile layers reaching a local minimum
1450 T. Lube et al. / Journal of the European Ceramic Society 27 (2007) 1449–1453 In fracture mechanics, both residual and applied stresses are usually included in the crack driving force. However, it is useful to consider the residual stresses as part of the crack resistance. Thus, in laminates with compressive stress at the surface, the higher resistance to failure results from a reduction of the crack driving force rather than from an increase in the intrinsic material resistance to crack extension. The term Kres(a) can – as an approximation – be assessed by means of the weight function approach,6 that allows us to calculate the stress intensity factor K(a), for an edge crack of length a for an arbitrary stress distribution acting normal to the fracture path. The weight function procedure developed by Bueckner7 simplifies the determination of K(a) since most of the numerical methods require separate calculations for each given stress distribution and each crack length. This method is of particular interest when the material is submitted to a “complicated” stress profile such as creep,8 residual stresses in tempered glasses,9 or residual stresses in multilayers.2 Applying this concept to our residual stress profile σres results: Kres(a) = a 0 h(x, a)σres(x) dx, (3) where h(x, a) is the suitable weight function, a the crack length, and x is the distance from the surface. Previous works by Fett et al.10,11 validate the applicability of this methodology to inhomogeneous materials. The weight function presented in Eq. (4) was developed using the boundary collocation method.12 It models materials with an homogeneous Young’s modulus. It will be used as a first approximation. For inhomogeneous materials a suitable weight function will depend on E(x). The consequences of using this simplified weight function for a laminate will be discussed later. The weight function is h(x, a) = 2 πa 1 √1 − (x/a)(1 − (a/W))1.5 × 1 − a W 1.5 +Aνμ 1 − x a ν+1 a W μ , (4) where the coefficients Aνμ can be found in.8,12 W is the total thickness. It is worth of note that is not dependent on Young’s modulus exclusively in the case of a homogeneous material. In order to calculate the residual stresses in a laminate the following approximation was used.13 Far away from the free surface,14 the residual stress, σR, in each layer is uniform and biaxial. For the different layers A or AZ: σres,A = −E A Tsf T0 α dT 1 + ((N + 1)/(N − 1)(e/λ)) and σres,AZ = −σR,A tA tAZ (N + 1) (N − 1), (5) where E = E/(1 − ν), ν being the Poisson’s ratio, α = (AZ − αA) the difference of the thermal expansion coefficients of AZ and A, respectively, Tsf the temperature below which the residual stresses arise, T0 the room temperature, N the number of Table 1 Properties of the material layers E (GPa) ν αtech (10−6 K−1) (0–1150 ◦C) K0 (MPa m1/2) A 391 0.241 8.64 3.8 AZ (60A40Z) 305 0.257 9.24 4.28 layers, λ = tAZ/tA is the layer thickness ratio, and e = E A/E AZ. The indexes make reference to the materials. Since the reason of the residual stresses is a deformation constraint (due to the thermal mismatch), the stress profile has to be proportional to the Young’s modulus in the corresponding layer. For the assessment of the residual stress profile the different elastic moduli were considered. In this paper, symmetrical N-layer laminates with compressive stresses at the surface were studied (N being an odd number to fulfil the condition of symmetry). All the layers made of the same material (A or AZ, respectively) have the same thickness, so the laminate is well defined by the thicknesses tA and tAZ, or the total thickness W and λ. Through the paper, W will be considered constant and equals to W = 1.5 mm, according to a possible design condition. The corresponding effective R-curves are calculated according to the procedure explained above. The influence of the residual stress field, defined by geometrical and material properties, on the apparent R-curve is examined in detail. The results are expressed for the laminated system Al2O3 − xAl2O3/(1 − x)ZrO2, but the conclusions can be extended for any ceramic multilayer system with ideally strong interfaces. 2. Experimental procedure This study entailed the use of a high-purity (99.7%) alumina powder (Alcoa A16-SG, Alcoa Aluminium Co., New York, NY) with an average particle size of 0.3 m, and a zirconia powder (TZ3Y-S, Tosoh Corp., Tokyo, Japan) doped with 3 mol% Y2O3 with an average particle size of 0.3m. On the basis of previous experiments,15 the different powders were mixed with organic binders, dispersants, plasticizers, and solvents to obtain suitable slips for tape casting. Slurry compositions were the same for both Al2O3 and Al2O3/ZrO2 composite powders. Sheets of pure alumina (A) and of the composite containing 60 vol% alumina and 40 vol% zirconia (AZ) were produced. Table 1 presents the material properties for the different layers, where E and ν were measured by impulse excitation technique, α by means of a dilatometer between 20 and 1200 ◦C and the intrinsic toughness K0 following the VAMAS procedure (single-edge-V-notch beam in four point bending test).16,17 3. Results and discussion As shown by previous authors, the apparent R-curve in multilayers presents an oscillating behaviour3,4 (see Fig. 1). The toughness increases in the layers under compression with increasing crack length and reaches a local maximum at the interface. It decreases in the tensile layers reaching a local minimum
T. Lube et al. / Journal of the European Ceramic Society 27(2007)1449-1453 1451 日 toughness >>1 KoAlo. -3.8 MPam"2 2-1./t 0 a=a/w Fig. 1. Influence of the thickness ratio A=taz/tA on the effective R-curve. The Fig. 2. Two clear tendencies provoking different fracture process. situation W=1.5 mm and N=7 layers has been chosen to present the result to a situation with homogeneous stiffness, the A-layers carries at the interface. It can be stated that the compressive stresses more load and the Az-layers less load, so that the calculated hield the material against flaws, while the tensile stresses have apparent toughness is overestimated in the alumina. a detrimental effect on the effective r-curve A second conclusion worth of note concerns the fracture pro- As it derives from Eq (5), the architecture(1)defines the cess. As shown in Fig. 2, two clearly different behaviours are residual stress field. It was the aim of this investigation to under- observed In both cases, while the crack is propagating through stand how the architecture influences the maximum shielding. layers under compression the shielding is increasing, reachin In Fig. 1, apparent R-curves are presented for different values a maximum at the interface, but the overall tendencies are dif- of a in the range 0.2-25. Low values of A corresponds to thin ferent. There are laminates for which the effective toughness alumina layers ta in comparison to tAz, and thus high compres- presents an overall increase with crack length, while there are sive stresses are present in these layers. That is the reason why laminates that show an overall decrease the shielding increases so steep in the alumina layers and a high Roughly speaking, those laminates in which the A stress intensity factor has to be applied to fail the specimen. For compressive stress is higher than the AZ-tensile stress, will high values of A, the thickness of alumina layers is much big- present a tendency of toughness increase as long as the crack ger than that of the AZ composite layers and as a result, high grows. Those laminates with a higher tensile stress present a ten- tensile stresses arise in the Az layers, while almost no compres- dency of toughness decrease, even reaching fictitious negative sive stress appears. That is the reason that the effective toughness values of effective toughness In the latter type of laminates, the drops in the AZ layers for these laminates. This kind of multilay- fracture process results in unstable failure after reaching a peak ers,could even present for all the crack lengths a lower apparent in the R-curve. On the other hand in laminates with a tendency of toughness, so its mechanical performance is not so interesting toughness increase, a controlled layer-by-layer fracture pattern as compared to laminates with A<I is observed. This behaviour has been experimentally observed An interesting conclusion drawn from Fig. I is the existence carrying out 4-point bending tests. 8 of an architecture that maximizes the shielding in the first inter The architecture A =hopt that maximizes the shielding in the face. Opposite to what could be expected, the highest surface first interface, also deserves some attention. In Fig 3 compressive stress(the highest A) does not correspond to the lope is presented covering the maximum shielding for each x highest shielding in the first layer. Since the maximum shield- Obviously all the maxima of these envelopes correspond to opt ing in the first layer is obtained at a distance equal to the outer Fig. 3 also presents the infuence of the different architecture layer thickness, the thickness ta plays an important role parameters(N and W)on shielding N modifies the residual stres This architecture that maximizes the apparent toughness at field thus influencing the shielding and w normalizes the crack the first interlayer is especially interesting when short cracks depth in the effective R-curve. The envelopes can be obtained are expected. Otherwise, for long cracks a laminate with A<1 by evaluating the effective R-curve at the first interface for each could be more adequate due to the overall increase of toughness architecture. The reader should keep in mind that for this work that is present in this type of multilayer. the stress field considered is given by Eq. (5)that introduces We caution the reader about the fact that a weight function some error in the outer layer since does not consider free sur that applies to a homogeneous material (E constant) has been face. FEM calculations demonstrate that the difference is not considered. This approximation results in an error of maximal significant in our case. 8 10% for the calculated stress intensity factor. The A/AZ lami- As one can appreciate from Fig 3 the architecture does not nate contains an AZ core that is less stiff than the A Compared influence the position of the maximum. This means that the
T. Lube et al. / Journal of the European Ceramic Society 27 (2007) 1449–1453 1451 Fig. 1. Influence of the thickness ratio λ = tAZ/tA on the effective R-curve. The situation W = 1.5 mm and N= 7 layers has been chosen to present the results. at the interface. It can be stated that the compressive stresses shield the material against flaws, while the tensile stresses have a detrimental effect on the effective R-curve. As it derives from Eq. (5), the architecture (λ) defines the residual stress field. It was the aim of this investigation to understand how the architecture influences the maximum shielding. In Fig. 1, apparent R-curves are presented for different values of λ in the range 0.2–25. Low values of λ corresponds to thin alumina layers tA in comparison to tAZ, and thus high compressive stresses are present in these layers. That is the reason why the shielding increases so steep in the alumina layers and a high stress intensity factor has to be applied to fail the specimen. For high values of λ, the thickness of alumina layers is much bigger than that of the AZ composite layers and as a result, high tensile stresses arise in the AZ layers, while almost no compressive stress appears. That is the reason that the effective toughness drops in the AZ layers for these laminates. This kind of multilayers, could even present for all the crack lengths a lower apparent toughness, so its mechanical performance is not so interesting as compared to laminates with λ < 1. An interesting conclusion drawn from Fig. 1 is the existence of an architecture that maximizes the shielding in the first interface. Opposite to what could be expected, the highest surface compressive stress (the highest λ) does not correspond to the highest shielding in the first layer. Since the maximum shielding in the first layer is obtained at a distance equal to the outer layer thickness, the thickness tA plays an important role. This architecture that maximizes the apparent toughness at the first interlayer is especially interesting when short cracks are expected. Otherwise, for long cracks a laminate with λ 1 could be more adequate due to the overall increase of toughness that is present in this type of multilayer. We caution the reader about the fact that a weight function that applies to a homogeneous material (E constant) has been considered. This approximation results in an error of maximal 10% for the calculated stress intensity factor.5 The A/AZ laminate contains an AZ core that is less stiff than the A. Compared Fig. 2. Two clear tendencies provoking different fracture process. to a situation with homogeneous stiffness, the A-layers carries more load and the AZ-layers less load, so that the calculated apparent toughness is overestimated in the alumina. A second conclusion worth of note concerns the fracture process. As shown in Fig. 2, two clearly different behaviours are observed. In both cases, while the crack is propagating through layers under compression the shielding is increasing, reaching a maximum at the interface, but the overall tendencies are different. There are laminates for which the effective toughness presents an overall increase with crack length, while there are laminates that show an overall decrease. Roughly speaking, those laminates in which the Acompressive stress is higher than the AZ-tensile stress, will present a tendency of toughness increase as long as the crack grows. Those laminates with a higher tensile stress present a tendency of toughness decrease, even reaching fictitious negative values of effective toughness. In the latter type of laminates, the fracture process results in unstable failure after reaching a peak in the R-curve. On the other hand in laminates with a tendency of toughness increase, a controlled layer-by-layer fracture pattern is observed. This behaviour has been experimentally observed carrying out 4-point bending tests.18 The architecture λ = λopt that maximizes the shielding in the first interface, also deserves some attention. In Fig. 3, an envelope is presented covering the maximum shielding for each λ. Obviously all the maxima of these envelopes correspond to λopt. Fig. 3 also presents the influence of the different architecture parameters (Nand W) on shielding.N modifies the residual stress field thus influencing the shielding and W normalizes the crack depth in the effective R-curve. The envelopes can be obtained by evaluating the effective R-curve at the first interface for each architecture. The reader should keep in mind that for this work the stress field considered is given by Eq. (5) that introduces some error in the outer layer since does not consider free surface. FEM calculations demonstrate that the difference is not significant in our case.18 As one can appreciate from Fig. 3 the architecture does not influence the position of the maximum. This means that the
1452 T Lube et al. Journal of the European Ceramic Society 27(2007)1449-1453 maximum shielding=12 MPa m for 1=2.6 x alumina volume fraction 12 E三2598935,日 N, number of layer E22 Fig. 4. Influence of the AZ-composite chemistry on the maximum shielding of maximum shielding= 13 MPa m the outer A-layer. w. total thickness [ mm] e'=EA/E, elastic ratio 9>5×日 Fig 3. Influence of architecture on shielding.(a)N: number of layers and(b) kness optimal architecture Aopt is exclusively defined by the elastic constants. It also shows that shielding is more protective with a (a) A=121 low number of layers and for thicker specimens. However, for relatively thick layers the authors expect a non-uniform stress field within the layers(Saint Venant principle)and the stress E 16) Aa=(a-a)10, thermal mismatch field considered here(Eq (5)) would not apply The influence of the materials properties on the residual stress field is evident by Eq (5). Fig 4 presents the maximum shielding in A/AZ laminates for several compositions of the composite da=1.25 AZ. As one can observe the maximum for each composition is obtained for a different AoptAopt varies from 2.25 for 95 vol% 3 alumina to 2.7 for 50 vol% alumina. Properties of the different opposites were estimated by applying the rule of mixtures,to the values presented in Table 1 A more detailed analysis results in that exclusively the Youngs modulus ratio influences and not the thermal 0.25 expansion mismatch. Fig 5a reveals how a stiffer material than alumina in the inner layer will increase the toughness. It results com Fig. 5b, the higher the thermal mismatch is, the higher is (b) the compression in the outer layer and therefore, the higher is Fig. 5. Influence of the Young's modulus E and of the coefficient of thermal the shielding expansion a on the maximum shielding
1452 T. Lube et al. / Journal of the European Ceramic Society 27 (2007) 1449–1453 Fig. 3. Influence of architecture on shielding. (a) N: number of layers and (b) W: total thickness. optimal architecture λopt is exclusively defined by the elastic constants. It also shows that shielding is more protective with a low number of layers and for thicker specimens. However, for relatively thick layers the authors expect a non-uniform stress field within the layers (Saint Venant principle) and the stress field considered here (Eq. (5)) would not apply. The influence of the materials properties on the residual stress field is evident by Eq.(5). Fig. 4 presents the maximum shielding in A/AZ laminates for several compositions of the composite AZ. As one can observe the maximum for each composition is obtained for a different λopt. λopt varies from 2.25 for 95 vol% alumina to 2.7 for 50 vol% alumina. Properties of the different composites were estimated by applying the rule of mixtures, to the values presented in Table 1. A more detailed analysis results in that exclusively the Young’s modulus ratio influences λopt, and not the thermal expansion mismatch. Fig. 5a reveals how a stiffer material than alumina in the inner layer will increase the toughness. It results from Fig. 5b, the higher the thermal mismatch is, the higher is the compression in the outer layer and therefore, the higher is the shielding. Fig. 4. Influence of the AZ-composite chemistry on the maximum shielding of the outer A-layer. Fig. 5. Influence of the Young’s modulus E and of the coefficient of thermal expansion α on the maximum shielding
T Lube et al. /Journal of the European Ceramic Society 27(2007)1449-1453 1453 ered alumina-zirconia composites. J. A. Ceram. Soc., 2002, 85, 1505- Attendingtostructuralconsiderationsanoptimalarchitecture6.Fett,T.andMunz,DStressIntensityFactorandWeightFunctions.com- is presented for ceramic multilayers. An overall increasing ten- putational Mechanics Publications, 1997 7. Bueckner, A novel principle for the computation of stress intensity factors. dency is observed in laminates with high compressive stresses ZAMM,1970.50.529-546. that can provoke a controlled fracture process. Results are pre-8. Fett, T and Munz, D, Determination of fracture toughness at high tem- sented for a system alumina/composite alumina-zirconia for peratures after subcritical crack extension. J Am. Ceram Soc., 1992, 75, which realistic effective toughness up to 13 MPam 2 can be 3133-3136. 9. sglavo. V. M. Larentis. L. and Green, D. J, Flaw-insensitive ion- exchanged glass. I. Theoretical aspects. J. Am. Ceram Soc., 2001, 84, 1827- Acknowledgments 10. Fett, T, Munz, D. and Yang, Y. Y, Applicability of the extended Petroski Achenbach weight function procedure to graded materials. Eng. Fract. Work supported in part by the European Communitys Mechan,2000,65,393-403 Human Potential Programme under contract HPRN-CT-2002- IL. Fett, T, Munz, D and Yang, Y Y, Direct adjustment procedure for weight 00203. Javier Pascual and Francis Chalvet acknowledge the functions of graded materials. Fatigue Fract. Eng. Mater. Struct, 2000, 23, 191-198. financial support provided through the European Communitys 12. Fett, T, Stress Intensity Factors and Weight Functions for the Edge Cracked Human Potential Programme under contract HPRN-CT-2002- late Calculated by the Boundary Collocation Method. Kfk 4791. Kem 00203 forschungszentrum, Karlsruhe, 1990 13. Oil, H. J. and Frechette, V. D, Stress distribution in multiphase system L. Composites with planar interfaces. J. Am. Ceram. Soc., 1967, 50, 542- References 14. Sergo, V, Lipkin, D. M, de Portu, G and Clarke, D.R. stresse 1. Chan, H. M, Layered ceramics: processing and mechanical behaviour. in alumina/zirconia laminates. J. Am. Ceram. Soc. 1997 Annu. Rev. Mater Sci. 1997.27.249-282 2. Lugovy, M, Slyunyayev, V, Orlovskaya, N, Blugan, G, Kuebler, J and 15. Tarlazzi, A, Roncari, E, Pinasco, P, Guicciardi, S, Melandri, C and de Lewis, M, Apparent fracture toughness of Si3 Ny-based laminates with Portu, G, Tribological behaviour of Al2O3/LrOz-ZrOz laminated compos- residual compressive or tensile stresses in surface layers Act. Mater, 2005 tes.Wear,2000.,24,2940. 53.289-296 16. Kubler. J, Procedure for Determining the Fracture Toughness of Ceram- 3. Blanks, K.S., Kristoffersson, A, Carlstrom, E. and Clegg, w.J., Crack cs Using the Single- Edge-V-Notched Beam (SEVNB) Method. GKsS deflection in ce laminates using porous interlayers. J. Eur. Ceran orschungszentrum on behalf of the European Structural Integrity Socie Soc,1998,18,1945-1951. 2000 4. Lakshminarayanan, R, Shetty, D. K and Cutler, R. A, Toughening of lay- 17. Damani, R, Gstrein, R. and Danzer, R, Critical notch-root radius effect composites with residual surface compression. J. Am. Ceran SENB-S fracture toughness testing. J. Eur: Ceram Soc., 1996, 16. 695- Soc,1996,79,7987 5. Moon, RJ. Hoffman, M, Hilden, J, Bowman, K.J. Trumble, K P and 18. Pascual. J. Chalvet, F. Lube, T. and de portu, G, R-curves in Rodel, J, Weight function analysis on the R-curve behavior of multilay- Al2O3-AlO/ZrO2 laminates. Key Eng Mater, 2005, 290, 214-221
T. Lube et al. / Journal of the European Ceramic Society 27 (2007) 1449–1453 1453 4. Summary Attending to structural considerations an optimal architecture is presented for ceramic multilayers. An overall increasing tendency is observed in laminates with high compressive stresses that can provoke a controlled fracture process. Results are presented for a system alumina/composite alumina–zirconia for which realistic effective toughness up to 13 MPa m1/2 can be expected. Acknowledgments Work supported in part by the European Community’s Human Potential Programme under contract HPRN-CT-2002- 00203. Javier Pascual and Francis Chalvet acknowledge the financial support provided through the European Community’s Human Potential Programme under contract HPRN-CT-2002- 00203. References 1. Chan, H. M., Layered ceramics: processing and mechanical behaviour. Annu. Rev. Mater. Sci., 1997, 27, 249–282. 2. Lugovy, M., Slyunyayev, V., Orlovskaya, N., Blugan, G., Kuebler, J. and Lewis, M., Apparent fracture toughness of Si3N4-based laminates with residual compressive or tensile stresses in surface layers. Act. Mater., 2005, 53, 289–296. 3. Blanks, K. S., Kristoffersson, A., Carlstrom, E. and Clegg, W. J., Crack ¨ deflection in ceramic laminates using porous interlayers. J. Eur. Ceram. Soc., 1998, 18, 1945–1951. 4. Lakshminarayanan, R., Shetty, D. K. and Cutler, R. A., Toughening of layered ceramic composites with residual surface compression. J. Am. Ceram. Soc., 1996, 79, 79–87. 5. Moon, R. J., Hoffman, M., Hilden, J., Bowman, K. J., Trumble, K. P. and Rodel, J., Weight function analysis on the ¨ R-curve behavior of multilayered alumina–zirconia composites. J. Am. Ceram. Soc., 2002, 85, 1505– 1511. 6. Fett, T. and Munz, D., Stress Intensity Factor and Weight Functions. Computational Mechanics Publications, 1997. 7. Bueckner, A novel principle for the computation of stress intensity factors. ZAMM, 1970, 50, 529–546. 8. Fett, T. and Munz, D., Determination of fracture toughness at high temperatures after subcritical crack extension. J. Am. Ceram. Soc., 1992, 75, 3133–3136. 9. Sglavo, V. M., Larentis, L. and Green, D. J., Flaw-insensitive ionexchanged glass. I. Theoretical aspects. J. Am. Ceram. Soc., 2001, 84, 1827– 1831. 10. Fett, T., Munz, D. and Yang, Y. Y., Applicability of the extended PetroskiAchenbach weight function procedure to graded materials. Eng. Fract. Mechan., 2000, 65, 393–403. 11. Fett, T., Munz, D. and Yang, Y. Y., Direct adjustment procedure for weight functions of graded materials. Fatigue Fract. Eng. Mater. Struct., 2000, 23, 191–198. 12. Fett, T., Stress Intensity Factors and Weight Functions for the Edge Cracked Plate Calculated by the Boundary Collocation Method. Kfk 4791. Kernforschungszentrum, Karlsruhe, 1990. 13. Oel, H. J. and Fr ¨ echette, V. D., Stress distribution in multiphase systems: ´ I. Composites with planar interfaces. J. Am. Ceram. Soc., 1967, 50, 542– 549. 14. Sergo, V., Lipkin, D. M., de Portu, G. and Clarke, D. R., Edge stresses in alumina/zirconia laminates. J. Am. Ceram. Soc., 1997, 80, 1633– 1638. 15. Tarlazzi, A., Roncari, E., Pinasco, P., Guicciardi, S., Melandri, C. and de Portu, G., Tribological behaviour of Al2O3/ZrO2–ZrO2 laminated composites. Wear, 2000, 24, 29–40. 16. Kubler, J., ¨ Procedure for Determining the Fracture Toughness of Ceramics Using the Single-Edge-V-Notched Beam (SEVNB) Method. GKSSForschungszentrum on behalf of the European Structural Integrity Society, 2000. 17. Damani, R., Gstrein, R. and Danzer, R., Critical notch-root radius effect in SENB-S fracture toughness testing. J. Eur. Ceram. Soc., 1996, 16, 695– 702. 18. Pascual, J., Chalvet, F., Lube, T. and de Portu, G., R-curves in Al2O3–Al2O3/ZrO2 laminates. Key Eng. Mater., 2005, 290, 214–221
