《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_Design and production of ceramic laminates-A-M

Availableonlineatwww.sciencedirectcom Science Direct Acta materialia ELSEVIER Acta Materialia 54(2006)4929-4937 www.actamat-journals.com Design and production of ceramic laminates with high mechanical resistance and reliability Vincenzo m. sglavo. Massimo bertoldi Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Unitersita degli Studi di Trento, Via Mesiano 77, Trento 38050, Italy Received 27 December 2005: received in revised form 31 May 2006: accepted 14 June 2006 Available online Il September 2006 This paper is dedicated to the memory of Luigi Sglavo, father of vi M. Sglavo, a great person. Abstract a design and processing approach for high failure resistance and increased damage tolerance in laminated ceramic structures is pre- sented. Layers of different compositions are stacked in order to develop a specific residual stress profile by the sintering process. The fracture toughness of the laminate is related to the residual stress. The fracture toughness behaviour can be tailored so that surface efects are forced to grow in a stable way before becoming critical. In this way a ceramic with a unique value of fracture strength is obtained. Laminates composed of alumina/ mullite and alumina/zirconia layers have been designed and fabricated. These materials pos- ss a strength of 700 MPa with a standard deviation of <4%. The strength is insensitive to surface damage and in good agreement with the design value o 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved Keywords: Ceramics: Toughness: Layered structures; Fracture: Ceramic composite 1. Introduction la laminates [3, 4] these strategies promote delamina tion and crack deflection [5, 6]. These approaches, however, The application of brittle materials, like ceramics and provide only a limited relief from the variability in fracture glasses, is often limited by the reliability of their mechanical strength and place high demands on process control for esistance. The variability in strength arises from flaws gen- achieving desired microstructures erated either during processing or arising from damage and In a different approach [7-9] the strength of laminated degradation when in service. The variability is usually too structures is controlled by introducing residual stresses large to allow safe design. In addition, fracture can occur For example, laminates of high strength have been pro- in a catastrophic manner without warning [1]. duced by Lange and co-workers [9] using alternating thin Efforts have been made to reduce the severity of defects compressive layers and thicker tensile layers. An important or to increase fracture toughness by microstructural con- limitation of such laminates is that they can be used only trol. Higher fracture toughness has been achieved via with specific orientations to the applied load; they are not grain-shape anisotropy, by introducing suitable for producing plates, shells or tubes as required and by promoting crack shielding by phase transformation in typical applications or microcracking [1]. As an alternative, fracture behaviour More recently, Orlovskaya and co-worke produced has been improved by introducing low-energy paths for high-toughness Si3 N4 laminates by alternating layers of dif- crack propagation in using porous [2] or within weak inter- ferent composition that resulted in alternating compressive and tensile residual stresses after sintering [10-12]. Fracture Corresponding author. Fax: +39 0461881945 toughness values of up to 17 E-mail address However, the high residual compressive stresses in these 1359-6454/$30.00 O 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. do: 10. 1016/j.actamat. 2006.06.019

Design and production of ceramic laminates with high mechanical resistance and reliability Vincenzo M. Sglavo *, Massimo Bertoldi Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita` degli Studi di Trento, Via Mesiano 77, Trento 38050, Italy Received 27 December 2005; received in revised form 31 May 2006; accepted 14 June 2006 Available online 11 September 2006 This paper is dedicated to the memory of Luigi Sglavo, father of Vincenzo M. Sglavo, a great person. Abstract A design and processing approach for high failure resistance and increased damage tolerance in laminated ceramic structures is pre￾sented. Layers of different compositions are stacked in order to develop a specific residual stress profile by the sintering process. The fracture toughness of the laminate is related to the residual stress. The fracture toughness behaviour can be tailored so that surface defects are forced to grow in a stable way before becoming critical. In this way a ceramic with a unique value of fracture strength is obtained. Laminates composed of alumina/mullite and alumina/zirconia layers have been designed and fabricated. These materials pos￾sess a strength of 700 MPa with a standard deviation of <4%. The strength is insensitive to surface damage and in good agreement with the design value. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ceramics; Toughness; Layered structures; Fracture; Ceramic composite 1. Introduction The application of brittle materials, like ceramics and glasses, is often limited by the reliability of their mechanical resistance. The variability in strength arises from flaws gen￾erated either during processing or arising from damage and degradation when in service. The variability is usually too large to allow safe design. In addition, fracture can occur in a catastrophic manner without warning [1]. Efforts have been made to reduce the severity of defects or to increase fracture toughness by microstructural con￾trol. Higher fracture toughness has been achieved via grain-shape anisotropy, by introducing second phases and by promoting crack shielding by phase transformation or microcracking [1]. As an alternative, fracture behaviour has been improved by introducing low-energy paths for crack propagation in using porous [2] or within weak inter￾layers in laminates [3,4]; these strategies promote delamina￾tion and crack deflection [5,6]. These approaches, however, provide only a limited relief from the variability in fracture strength and place high demands on process control for achieving desired microstructures. In a different approach [7–9] the strength of laminated structures is controlled by introducing residual stresses. For example, laminates of high strength have been pro￾duced by Lange and co-workers [9] using alternating thin compressive layers and thicker tensile layers. An important limitation of such laminates is that they can be used only with specific orientations to the applied load; they are not suitable for producing plates, shells or tubes as required in typical applications. More recently, Orlovskaya and co-workers produced high-toughness Si3N4 laminates by alternating layers of dif￾ferent composition that resulted in alternating compressive and tensile residual stresses after sintering [10–12]. Fracture toughness values of up to 17 MPa m1/2 were measured. However, the high residual compressive stresses in these 1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.06.019 * Corresponding author. Fax: +39 0461881945. E-mail address: vincenzo.sglavo@unitn.it (V.M. Sglavo). www.actamat-journals.com Acta Materialia 54 (2006) 4929–4937

V.M. Solaro, M. Bertoldi Acta Materialia 54(2006)4929-4937 laminates can lead to defects in the form of tunnel cracks [13] and fracture in the ceramic laminate[10]. The use of near-surface stresses that hinder the growth of surface cracks has been extensively exploited in glasses 4, 15]. Surface flaws represent typical defects in ceramics and glasses: in fact, once the process has been optimised reduce or eliminate volume defects [16, 17]. surface flav which are normally generated during surface finishing and in service, become strength limiting. Furthermore, surface defects are important when bodies are subjected to bend ing, as is often the case in ceramic components. Recently, Sglavo et al. have proposed that creation of a residual a maximum compression at a certain Fig. I. T-curve that allows the stable growth phenomenon in the interval lepth from the surface can arrest surface cracks [18]. This co, Cr). Straight ines represent various Keat values and are used to pproach has been applied to silicate glasses by producing evaluate the stable growth interval and final strength,oF the residual stress field through a double ion-exchange process [19, 20]. the interval co, ce] and subjected to Kext= T(c1), will prop- Residual stresses in ceramic materials can arise from dif- agate instantaneously up to a length c2 within the interval ferences in the thermal expansion coefficient of the consti- [co, CF] and then grow stably up to cp for higher Kext values tuting grains or phases, uneven sintering rates or phase The presence of residual stresses inside the material can transformations associated with specific volume change. be responsible for a T-curve like that shown in Fig. 1. If the As described below, the residual stress profile developed simple model represented in Fig. 2 is considered, residual after sintering can be controlled by changing the thickness stresses, ores are responsible for the stress intensity factor and the stacking order of the layers. In this approach a pre- [21,22 dictable strength can be obtained by changing the multi- layer"architecture". In the present work this approach Kres o(x)(2,)d applied to the design and the production of alumina/ ZirconIa compo aminates where h is a weight function and w is the width of the body. In the present analysis discontinuous stepwise stress pro file is adopted and perfect adhesion between different lam 2. Theory inae is hypothesised. In addition, it is assumed that each layer is characterised by a constant fracture toughness The first step in the approach mentioned above is to value. Ki develop a procedure for designing ceramic components Under the influence of the external load(Kext, crack ith high mechanical reliability. These components ar propagation occurs when the sum(Kres t Kext) equals the characterised by narrow scatter in fracture strength, which fracture toughness, Kc, of the material at the crack tip is obtained by stable growth of defects before final failure. Including the residual stresses as a part of the crack resis- In this way an invariant final strength, which is indepen- tance of the material, the"apparent"fracture toughness dent of the initial flaw size can be attained can be defined Stable crack propagation is possible when fracture toughness, T, is a growing function of crack length, c, stee. T=ki-Kres (3) per than the applied stress intensity factor, Kext, which is It is clear from Eqs.(2)and (3)that for compressive generally defined as Kext=yac., where y is the shape fac- residual stresses(negative) there is a beneficial effect on tor and o the applied stress. Analytically, stable growth T. In addition, given a proper residual stress profile, it occurs when the following condition is satisfied [1, 213 T(c), a It has been demonstrated elsewhere that the range of stable crack growth is finite [18]. This is shown schemati 白 cally in Fig. I where the interval [co, cF]represents the range where cracks can grow in a stable fashion: all defect included in such interval propagate to the same maximum △ores value before final failure, thus leading to a unique strength value(F in Fig. 1). More precisely, if kinetic effects are eglected the stable crack growth interval can be extended down to co: in fact, a flaw with generic size, CI, enclosed in Fig. 2. Crack model considered in the present work

laminates can lead to defects in the form of tunnel cracks [13] and fracture in the ceramic laminate [10]. The use of near-surface stresses that hinder the growth of surface cracks has been extensively exploited in glasses [14,15]. Surface flaws represent typical defects in ceramics and glasses: in fact, once the process has been optimised to reduce or eliminate volume defects [16,17], surface flaws, which are normally generated during surface finishing and in service, become strength limiting. Furthermore, surface defects are important when bodies are subjected to bend￾ing, as is often the case in ceramic components. Recently, Sglavo et al. have proposed that creation of a residual stress profile with a maximum compression at a certain depth from the surface can arrest surface cracks [18]. This approach has been applied to silicate glasses by producing the residual stress field through a double ion-exchange process [19,20]. Residual stresses in ceramic materials can arise from dif￾ferences in the thermal expansion coefficient of the consti￾tuting grains or phases, uneven sintering rates or phase transformations associated with specific volume change. As described below, the residual stress profile developed after sintering can be controlled by changing the thickness and the stacking order of the layers. In this approach a pre￾dictable strength can be obtained by changing the multi￾layer ‘‘architecture’’. In the present work this approach is applied to the design and the production of alumina/ mullite/zirconia composite laminates. 2. Theory The first step in the approach mentioned above is to develop a procedure for designing ceramic components with high mechanical reliability. These components are characterised by narrow scatter in fracture strength, which is obtained by stable growth of defects before final failure. In this way an invariant final strength, which is indepen￾dent of the initial flaw size, can be attained. Stable crack propagation is possible when fracture toughness, T, is a growing function of crack length, c, stee￾per than the applied stress intensity factor, Kext, which is generally defined as Kext = wrc 0.5, where w is the shape fac￾tor and r the applied stress. Analytically, stable growth occurs when the following condition is satisfied [1,21]: Kext ¼ T ðcÞ; dKext dc 6 dT ðcÞ dc : ( ð1Þ It has been demonstrated elsewhere that the range of stable crack growth is finite [18]. This is shown schemati￾cally in Fig. 1 where the interval [c0, cF] represents the range where cracks can grow in a stable fashion: all defects included in such interval propagate to the same maximum value before final failure, thus leading to a unique strength value (rF in Fig. 1). More precisely, if kinetic effects are neglected, the stable crack growth interval can be extended down to c 0; in fact, a flaw with generic size, c1, enclosed in the interval ½c 0; cF and subjected to Kext = T(c1), will prop￾agate instantaneously up to a length c2 within the interval [c0, cF] and then grow stably up to cF for higher Kext values. The presence of residual stresses inside the material can be responsible for a T-curve like that shown in Fig. 1. If the simple model represented in Fig. 2 is considered, residual stresses, rres, are responsible for the stress intensity factor [21,22]: Kres ¼ Z c 0 rresðxÞh x c ; c w dx; ð2Þ where h is a weight function and w is the width of the body. In the present analysis discontinuous stepwise stress pro- file is adopted and perfect adhesion between different lam￾inae is hypothesised. In addition, it is assumed that each layer is characterised by a constant fracture toughness value, Ki C. Under the influence of the external load (Kext), crack propagation occurs when the sum (Kres + Kext) equals the fracture toughness, Ki C, of the material at the crack tip. Including the residual stresses as a part of the crack resis￾tance of the material, the ‘‘apparent’’ fracture toughness can be defined as T i ¼ Ki C  Kres: ð3Þ It is clear from Eqs. (2) and (3) that for compressive residual stresses (negative) there is a beneficial effect on T. In addition, given a proper residual stress profile, it K ψ σ c cF c0 T F c0 * c1 c2 Fig. 1. T-curve that allows the stable growth phenomenon in the interval (c0, cF). Straight lines represent various Kext values and are used to evaluate the stable growth interval and final strength, rF. c res(x) res,i x σ σ Δσ i xi-1 layer i res,i Fig. 2. Crack model considered in the present work. 4930 V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937

V M. Sglavo, M. Bertoldi Acta Materialia 54(2006 )4929-4937 should be possible to obtain Representing a steep growing ity interval width increases. Since both high strength and a function of c. Moreover, as only surface flaws have been large stable growth interval are desirable, an intermediate onsidered, the T-curve is unique for any defect and, there- value of x has to be adopted in the laminate design. On fore, it can be considered as fixed with respect to the sur- the other hand, an increase of or is useful for increasing face of the body. Consequently, crack length (c) and both the stable growth range and the maximum stres depth from the surface (x) can be regarded as identical Also, if Kc increases, the maximum stress is higher but quantities in the following analysi the stability range decreases; note that Kc is a parameter In order to understand the effect of residual stress inten- that depends on the material selection and is treated as a sity and location on the apparent fracture toughness, it is constant in the design procedure useful to analyse some special cases. First, if the reference A more realistic residual stress shape is the sq model(Fig. 2)corresponds to an edge crack in a semi- profile(Fig 4) defined as infinite body, Eq (2)can be simplified as 0<x<x1 Ores(x) r<x<x (c2-x2)0 x2<x<+∞ where Ya 1.215. One could point out that such a simpli- In this case the T-curve can be calculated both analytically fication is an approximation, as Y maintains a slight depen- and by using the principle of superposition [1, 21]. The dence on x/c[22]. Nevertheless, this allows the calculations square-wave profile can be considered in fact as the sum to be effected in a closed form without the loss of two simple step profiles with stresses of generality tude but opposite sign placed at different depths(xI and One very simple situation corresponds to the step profile x2). The apparent fracture toughness becomes defined 0 0,0<x<x T=Kc-2Y(9 aRIE-arcsin() x<x<x T=Kc-2Y(9 aR[arcsin(2) and shown in Fig. 3a for various Ores values where or is a generic positive stress value. In this case T can be analyti- (8) cally calculated from Eq (4)as A single compressive layer of the appropriate thickness, 0<x<x1 able for ting a stable growth range for surface T=Kc+2Y( oRE-arcsin()),x1<x<+oo defects. Unfortunately, this simple solution is not applica- (6 ble because the force equilibrium in the component is not satisfied. Furthermore, the compressive stress required to by assuming a constant fracture toughness achieve the higher strength is often very high and localised As shown in Fig. 3b, a stability range exists between xi it can generate intense interlaminar shear stresses, which and the tangent point between Kext and T. One can observe can cause delamination between layers. Edge cracking that by increasing x, the strength decreases and the stabil- can occur at the interface between highly compressed x2 a T x√E Fig 3. Step residual stress profile(a) and corresponding apparent fracture toughness(b). The effect of intensity (left) and location (right) of the Fig. 4. Square-wave stress profile and corresponding apparent fracture residual stress is she

should be possible to obtain T representing a steep growing function of c. Moreover, as only surface flaws have been considered, the T-curve is unique for any defect and, there￾fore, it can be considered as fixed with respect to the sur￾face of the body. Consequently, crack length (c) and depth from the surface (x) can be regarded as identical quantities in the following analysis. In order to understand the effect of residual stress inten￾sity and location on the apparent fracture toughness, it is useful to analyse some special cases. First, if the reference model (Fig. 2) corresponds to an edge crack in a semi￾infinite body, Eq. (2) can be simplified as Kres ¼ Y ðpcÞ 0:5 Z c 0 rresðxÞ 2c ðc2  x2Þ 0:5 dx; ð4Þ where Y  1.1215. One could point out that such a simpli- fication is an approximation, as Y maintains a slight depen￾dence on x/c [22]. Nevertheless, this allows the calculations to be effected in a closed form without the loss of generality. One very simple situation corresponds to the step profile defined as rres ¼ 0; 0 : ð7Þ In this case the T-curve can be calculated both analytically and by using the principle of superposition [1,21]. The square-wave profile can be considered in fact as the sum of two simple step profiles with stresses of identical ampli￾tude but opposite sign placed at different depths (x1 and x2). The apparent fracture toughness becomes T ¼ KC; 0 : ð8Þ A single compressive layer of the appropriate thickness, placed at a certain depth from the surface, is therefore suit￾able for generating a stable growth range for surface defects. Unfortunately, this simple solution is not applica￾ble because the force equilibrium in the component is not satisfied. Furthermore, the compressive stress required to achieve the higher strength is often very high and localised; it can generate intense interlaminar shear stresses, which can cause delamination between layers. Edge cracking can occur at the interface between highly compressed x1 x x1 –σ σ –σ σ ψ ψ res R x, c x1 KC Y σR K x x1 res R x, c x1 KC Y K a b T T Fig. 3. Step residual stress profile (a) and corresponding apparent fracture toughness (b). The effect of intensity (left) and location (right) of the residual stress is shown. x1 x, c K ψ σ σ x2 KC ψ x x1 – res x2 R T Fig. 4. Square-wave stress profile and corresponding apparent fracture toughness. V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937 4931

V.M. Solaro, M. Bertoldi Acta Materialia 54(2006)4929-4937 layers; this was observed in previous work [23] when the layers maintain with respect to the layer previously encoun- layer thickness was greater than a critical value, te=kc/ tered by the propagating crack. The equations contain 2n 0.34(1+vo, oc being the compressive stress and v Pois- parameters(x;, Aoi). Two conditions have to be satisfied son's ratio. Layer thickness and compressive stress are (forces equilibrium and equivalence between the sum of therefore mutually dependent and it is not possible to single-layer thickness and the total laminate thickness), lesign the desired mechanical behaviour by using only a which leaves 2n-2 degrees of freedom for defining the de square-wave stress(single layer) profile. Fortunately, these sired T-curve problems can be overcome by considering a multilayered It is important to note that in Eq (9)the elastic modulus structure of the different layers is assumed to be the same. It has been Before considering a complex multilayer profile, it is demonstrated elsewhere that the error in estimating T is useful to analyse another simple case. Consider two stress less than 10% if the Youngs modulus variation amongst profiles obtained by the combination of simple square- the layers is less than 33%[23, 24]. wave profiles of diffe nd identical exte sion(Fig. 5). This situation corresponds to laminates with 3. Design of the laminate wo layers of difTerent composition and identical thickness. The actual order of the two layers is the only difference Eq (9) suggests guidelines for the properties of the stress between the two examined profiles. It is clear from profile which would promote stable growth of surface ig. 5 that the order of the compressive layers is impor- cracks. The T-curve should be a monotonically increasing tant both for the final strength and the stability interval. function of c, which requires a continuous increase of the Such a consideration is general and the final conclusion compressive stresses from the surface towards the internal can be drawn that the compression intensity in successive layers. A stress-free or slightly tensile stressed layer is pre- layers must grow continuously to obtain a properly ferred on the surface since this allows the lower boundary designed T-curve. of the stable growth interval to move towards the surfac At this point, the principle of superposition can be used which envelopes the smaller flaws within such an interval calculate the T-curve for a general multi-step profile. We The risk of edge cracking and delamination phenomena onsider n layers, with n steps of amplitude Ao;(Fig. 2), is reduced by using multi-step profiles, which reduces the equal to the stress increase of layer j with respect to the pre- thickness of the most stressed layer vious one. A general equation, which defines the apparent The residual stress profile that develops within a ceramic fracture toughness for layer i in the interval [xi-l, xi] laminate is related to the composition/microstructure and (Fig. 2), can be obtained thickness of the layers and to their stacking order. Accord ing to the theory of composite plies [25], in order to main- tain flatness during in-plane loading, as in the case of biaxial residual stresses developed upon processing, lami- xi_I<x<x (9) nate structures must possess a number of symmetri properties. If each layer is isotropic, as is the case for where i indicates the layer rank and x is the starting depth ramiCs w tions the sum being calculated for a diferent number structure, and i出 is s ymm etrical, then th terms for each i. This represents a mathematical transla- pic, its response to loading is similar to that of a homoge- tion of the"memory"effect of stress history that deeper neous plate [25]. Regardless of the physical source of residual stresses their presence in a co-sintered multilayer is related to the constraining effect. As perfectly adherent layers, every layer must deform similarly and at the same rate as the others. The difference between free deformation or free deforma- tion rate of one layer with respect to the average value of V4, V5 5 V stresses Such stresses can be either viscous or elastic in nat ure and can be relaxed or maintained within the material depending on temperature, cooling rate and material prop- erties. With the exception of the edges, if thickness is much smaller than the other dimensions, each layer can be con- sidered to be in a biaxial stress state At this point the fundamental task in properly designing a symmetric multilayer is the estimation of the biaxial Fig. 5. Residual stress and corresponding T-curve for two simple square- residual stresses In the common case of stresses developed wave profiles placed in different order. from differences in thermal expansion coefficients only, the

layers; this was observed in previous work [23] when the layer thickness was greater than a critical value, tc ¼ K2 C= ½0:34ð1 þ mÞr2 c , rc being the compressive stress and m Pois￾son’s ratio. Layer thickness and compressive stress are therefore mutually dependent and it is not possible to design the desired mechanical behaviour by using only a square-wave stress (single layer) profile. Fortunately, these problems can be overcome by considering a multilayered structure. Before considering a complex multilayer profile, it is useful to analyse another simple case. Consider two stress profiles obtained by the combination of simple square￾wave profiles of different amplitude and identical exten￾sion (Fig. 5). This situation corresponds to laminates with two layers of different composition and identical thickness. The actual order of the two layers is the only difference between the two examined profiles. It is clear from Fig. 5 that the order of the compressive layers is impor￾tant both for the final strength and the stability interval. Such a consideration is general and the final conclusion can be drawn that the compression intensity in successive layers must grow continuously to obtain a properly designed T-curve. At this point, the principle of superposition can be used to calculate the T-curve for a general multi-step profile. We consider n layers, with n steps of amplitude Dri (Fig. 2), equal to the stress increase of layer j with respect to the pre￾vious one. A general equation, which defines the apparent fracture toughness for layer i in the interval [xi1,xi] (Fig. 2), can be obtained: T ¼ Ki C Xi j¼1 2Y c p 0:5 Drres;j p 2  arcsin xj1 c h i xi1 < x < xi; ð9Þ where i indicates the layer rank and xj is the starting depth of layer j. Eq. (9) represents a short notation of n different equations, the sum being calculated for a different number of terms for each i. This represents a mathematical transla￾tion of the ‘‘memory’’ effect of stress history that deeper layers maintain with respect to the layer previously encoun￾tered by the propagating crack. The equations contain 2n parameters (xi,Dri). Two conditions have to be satisfied (forces equilibrium and equivalence between the sum of single-layer thickness and the total laminate thickness), which leaves 2n  2 degrees of freedom for defining the de￾sired T-curve. It is important to note that in Eq. (9) the elastic modulus of the different layers is assumed to be the same. It has been demonstrated elsewhere that the error in estimating T is less than 10% if the Young’s modulus variation amongst the layers is less than 33% [23,24]. 3. Design of the laminate Eq. (9) suggests guidelines for the properties of the stress profile which would promote stable growth of surface cracks. The T-curve should be a monotonically increasing function of c, which requires a continuous increase of the compressive stresses from the surface towards the internal layers. A stress-free or slightly tensile stressed layer is pre￾ferred on the surface since this allows the lower boundary of the stable growth interval to move towards the surface, which envelopes the smaller flaws within such an interval. The risk of edge cracking and delamination phenomena is reduced by using multi-step profiles, which reduces the thickness of the most stressed layer. The residual stress profile that develops within a ceramic laminate is related to the composition/microstructure and thickness of the layers and to their stacking order. Accord￾ing to the theory of composite plies [25], in order to main￾tain flatness during in-plane loading, as in the case of biaxial residual stresses developed upon processing, lami￾nate structures must possess a number of symmetrical properties. If each layer is isotropic, as is the case for ceramics with fine and randomly oriented crystalline micro￾structure, and the stacking order is symmetrical, then the laminate remains flat upon sintering and, being orthotro￾pic, its response to loading is similar to that of a homoge￾neous plate [25]. Regardless of the physical source of residual stresses, their presence in a co-sintered multilayer is related to the constraining effect. As perfectly adherent layers, every layer must deform similarly and at the same rate as the others. The difference between free deformation or free deforma￾tion rate of one layer with respect to the average value of the whole laminate accounts for the creation of residual stresses. Such stresses can be either viscous or elastic in nat￾ure and can be relaxed or maintained within the material depending on temperature, cooling rate and material prop￾erties. With the exception of the edges, if thickness is much smaller than the other dimensions, each layer can be con￾sidered to be in a biaxial stress state. At this point the fundamental task in properly designing a symmetric multilayer is the estimation of the biaxial residual stresses. In the common case of stresses developed from differences in thermal expansion coefficients only, the x x1 x2 x3 R 2σ R x1 x2 x3 x1 x, c K ψ x2 x3 x x1 res x2 x3 K ψ –σ res –σ R 2σ R x, c T T σ σ Fig. 5. Residual stress and corresponding T-curve for two simple square￾wave profiles placed in different order. 4932 V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937

V M. Sglavo, M. Bertoldi Acta Materialia 54(2006 )4929-4937 following conditions (related to forces equilibrium, com- 4z30, 35 Hm patibility and constitutive law) must be satisfied 6.88 Grsst=0 7.75 1=e1+x△T=E, (10) a; being the thermal expansion coefficient, E=E/(l-vi) (Vi is Poissons ratio, Ei is Youngs modulus), e i the elastic strain and &i the deformation. The system defined by AZ40,520m Eq(10) represents a set of 3n t l equations and 3n+ 1 ppm/°C ns(o, ei, Ei, e). The solution of this linea ar system allows the residual stress in the ith layer to be calculated a ds=E(-x)△T where AT= TSF- TRT(TSE is stress-free temperature, TRT is room temperature)and a is the average thermal expan- Fig. 6. Architecture of the AMZ laminate. Layer thickness, composition sion coefficient of the whole laminate. defined as and thermal expansion coefficient( Fig. 7)are reported(dimensions are not ∑E Erti (12) order to promote the stable growth of surface defects as where f; is the layer thickness. In this instance the residual stresses are therefore generated upon cooling after sinter On the basis of the aforementioned analysis, once the Youngs modulus, Poissons ratio, thermal expansion coef- ng. It has been shown in previous studies that SE repre- ficient and fracture toughness for each layer are determined sents the temperature below which the material can b considered to behave elastically without viscoelastic relax the residual stress distribution and the corresponding appar- ent fracture toughness curve for each laminate can be esti mated. In this study, room temperature is 25C and the q. (9)represents the fundamental tool for the stress-free condition is assumed at 1200 C as discussed in designing a ceramic laminate with predefined mechanical earlier works [26, 27]. The properties of the materials properties. Different ceramic layers can be stacked together in order to develop a specific residual strese required for the calculation are summarised in Table I and in Fig. 7. Youngs modulus and Poissons ratio values for profile from sintering, by using Eq (11). Since the stress AM and AZ composites shown in Table I correspond to level in Eq (11)does not depend on stacking order, the Voigt-Reuss bounds [21]; according to previous results sequence of laminae can still be changed provided the [281. Young's modulus and Poisson's ratio equal to symmetry condition is maintained. Once the stress pro- 229 GPa and 0.27, respectively, were considered for pure file is defined, the apparent fracture toughness can be mullite. The elastic modulus for pure alumina and zirconia estimated from Eq.(9). By changing the stacking order and composition of the layers, i.e. the laminate architec- was measured on monolithic samples as reported elsewhere ture, it is therefore possible to produce a material with a unique and predefined failure stress Table 1 ceramic laminates composed of layers belonging to the Materials properties used to estimate stress distribution and apparent alumina/zirconia and alumina/mullite systems were designed in the work reported here. The thermal expansion Material E(GPa) stress profile was tailored by changing the composition of At0 394(14) coefficient required for the development of the residual AN 36(0.2) 0.23 0.2340.233 the single laminae. The architecture of the engineered lam- AM20 3.1(0.3) 0.2380.237 0.242-0.241 inate is reported in Fig. 6. The notation"AZw/y"or AM40 0.246-0.244 AMw/y stands for alumina(A), zirconia(Z) or mullite AZl0 3.5(0.3) (M), while w corresponds to the volume percent content A220 0.242-0.240 AZ30 of zirconia or mullite and y to the layer thickness in micro- AZ40 337-308 3.9(0.3) 0.2480.245 metres. The composition and thickness of the layers and 318-287 4.5(0.3) 0.2540.251 their stacking order were selected to produce ceramic lam Numbers in parentheses correspond to the standard deviation. Elastic inates with a"constant"strength, aF, approximately equal modulus and Poisson,'s ratio values correspond to calculated Voigt-Reuss to 700 MPa. The apparent fracture toughness curve and bounds for AM10-AM40 composite corresponding residual stress profile were also tailored in Ref.[27]

following conditions (related to forces equilibrium, com￾patibility and constitutive law) must be satisfied: Pn i¼1 rres;iti ¼ 0; ei ¼ ei þ aiDT ¼ e; ri ¼ E i ei; 8 >>>>>: ð10Þ ai being the thermal expansion coefficient, E i ¼ Ei=ð1  miÞ (mi is Poisson’s ratio, Ei is Young’s modulus), ei the elastic strain and ei the deformation. The system defined by Eq. (10) represents a set of 3n + 1 equations and 3n + 1 unknowns (ri, ei,ei,e). The solution of this linear system allows the residual stress in the ith layer to be calculated as rres;i ¼ E i ða  aiÞDT ; ð11Þ where DT = TSF  TRT (TSF is stress-free temperature, TRT is room temperature) and a is the average thermal expan￾sion coefficient of the whole laminate, defined as a ¼ Xn 1 E i tiai ,Xn 1 E i ti; ð12Þ where ti is the layer thickness. In this instance the residual stresses are therefore generated upon cooling after sinter￾ing. It has been shown in previous studies that TSF repre￾sents the temperature below which the material can be considered to behave elastically without viscoelastic relax￾ation [26]. Eq. (9) represents the fundamental tool for the designing a ceramic laminate with predefined mechanical properties. Different ceramic layers can be stacked together in order to develop a specific residual stress profile from sintering, by using Eq. (11). Since the stress level in Eq. (11) does not depend on stacking order, the sequence of laminae can still be changed provided the symmetry condition is maintained. Once the stress pro- file is defined, the apparent fracture toughness can be estimated from Eq. (9). By changing the stacking order and composition of the layers, i.e. the laminate architec￾ture, it is therefore possible to produce a material with a unique and predefined failure stress. Ceramic laminates composed of layers belonging to the alumina/zirconia and alumina/mullite systems were designed in the work reported here. The thermal expansion coefficient required for the development of the residual stress profile was tailored by changing the composition of the single laminae. The architecture of the engineered lam￾inate is reported in Fig. 6. The notation ‘‘AZw/y’’ or ‘‘AMw/y stands for alumina (A), zirconia (Z) or mullite (M), while w corresponds to the volume percent content of zirconia or mullite and y to the layer thickness in micro￾metres. The composition and thickness of the layers and their stacking order were selected to produce ceramic lam￾inates with a ‘‘constant’’ strength, rF, approximately equal to 700 MPa. The apparent fracture toughness curve and corresponding residual stress profile were also tailored in order to promote the stable growth of surface defects as deep as 150 lm. On the basis of the aforementioned analysis, once the Young’s modulus, Poisson’s ratio, thermal expansion coef- ficient and fracture toughness for each layer are determined, the residual stress distribution and the corresponding appar￾ent fracture toughness curve for each laminate can be esti￾mated. In this study, room temperature is 25 C and the stress-free condition is assumed at 1200 C, as discussed in earlier works [26,27]. The properties of the materials required for the calculation are summarised in Table 1 and in Fig. 7. Young’s modulus and Poisson’s ratio values for AM and AZ composites shown in Table 1 correspond to Voigt–Reuss bounds [21]; according to previous results [28], Young’s modulus and Poisson’s ratio equal to 229 GPa and 0.27, respectively, were considered for pure mullite. The elastic modulus for pure alumina and zirconia was measured on monolithic samples as reported elsewhere AZ30, 35 µm AZ0, 40 µm AM40, 90 µm AZ0, 40 µm AZ40, 520 µm symmetry axis 8.37 7.75 6.88 7.75 8.68 (ppm / ˚C) α Fig. 6. Architecture of the AMZ laminate. Layer thickness, composition and thermal expansion coefficient (Fig. 7) are reported (dimensions are not to scale). Table 1 Materials properties used to estimate stress distribution and apparent fracture toughness Material E (GPa) KC (MPa m1/2) m AM0/AZ0 394 (14) 3.6 (0.2) 0.23a AM10 378–368 3.3 (0.2) 0.234–0.233 AM20 361–344 3.1 (0.3) 0.238–0.237 AM30 345–324 2.6 (0.2) 0.242–0.241 AM40 328–306 2.4 (0.2) 0.246–0.244 AZ10 375–360 3.5 (0.3) 0.236–0.235 AZ20 356–332 3.6 (0.2) 0.242–0.240 AZ30 337–308 3.9 (0.3) 0.248–0.245 AZ40 318–287 4.5 (0.3) 0.254–0.251 AZ100 204 (8) – 0.29a Numbers in parentheses correspond to the standard deviation. Elastic modulus and Poisson’s ratio values correspond to calculated Voigt–Reuss bounds for AM10–AM40 composites. a Ref. [27]. V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937 4933

V.M. Sglaco, M. Bertoldi Acta Materialia 54(2006)4929-4937 depth(um) -DAM -C-AZ 15 E Fig. 7. Thermal expansion coefficient for AZ and AM composites. (depth)(um Fig. 9. Apparent fracture toughness of the AMZ engineered laminate. [29]. The difference between the elastic modulus bounds is The dashed line is used to calculate the final strength less than 7% and 10%, respectively, for mullite and zirconia content below 40%. For the Poisson's ratios the difference less than 1.5%. Therefore, the average of the values reported 4. Experimental in Table I has been used for the evaluation of Eqs. (11)and a-Alumina(ALCOA, A-16SG, Dso=0.4 um) was the (12), with an error range of 5%. The thermal expansion coef- ficient and fracture toughness for AM and AZ composites primary starting material. High-purity mullite(KCM Corp, KM101, D50=0.77 um) and yttria (3 mol%)- were measured on monolithic samples as reported previ- stabilised zirconia(TOSOH, TZ-3YS, D50=0.4 um)pow- ously [29]. The residual stress profile and the T-curve for the aMz ders were chosen as second phases to vary the thermal oefficient with respect to pu re engineered laminate are shown in Fig 8. The applied stress Green layers were produced by tape casting water-based stress(strength) and the crack depth interval are also (Darvan C.R. T. Vanderbilt Inc )as dispersant and acrylic shown in Fig 9. Since T was calculated step by step emulsions(B-1235, DURAMAX")as binder. A lower-T, (Eq.(9)), the corresponding diagram is disc continuous acrylic emulsion(B-1000, DURAMAX was also adde the boundary between layers(Fig 8). One can easily sup- in a 1: 2 by weight ratio with respect to the binder content tinuous and that the discontinuities in Fig. 9 are merely occurrence of cracks in the dried tape. The alumina powder mathematical artefacts dispersion was obtained using a two-stage process [30,31] In order to enhance the electr depth(um) sites on the polymer chains, a slightly acid 00200 400 (pH 4)was used [32]. An optimal dispersant content equal to 1. 5 wt %o with respect to the powder was establish by sta- tic sedimentation. This value corresponds to about 0. 4 mg natter per unit area, which corresponds closely with values suggested by Greenwood et al. [30]for the same material. a ball milling stage using alumina spheres of 6 and 9 mm in diameter was carried out in polyethylene bot tles for 16-24 h to break down the aggregates. Suspensions -400 were ultrasonicated for 10 min before ball milling to reduce the starting viscosity. After adding some drops of concen- trated NH,OH to increase pH, suspensions were filtered with a 40 um polyethylene net and de-aired using a low- vacuum Venturi pump to remove air entrapped during (depth)s(um) the milling stage Acrylic binder emulsion and plasticiser were then added Fig 8. Residual stress profile in the surface region of the AMZ engineered to the suspension and slowly mixed for 30 min to reach good homogeneity, using great care to avoid the formation

[29]. The difference between the elastic modulus bounds is less than 7% and 10%, respectively, for mullite and zirconia content below 40%. For the Poisson’s ratios the difference is less than 1.5%. Therefore, the average of the values reported in Table 1 has been used for the evaluation of Eqs. (11) and (12), with an error range of 5%. The thermal expansion coef- ficient and fracture toughness for AM and AZ composites were measured on monolithic samples as reported previ￾ously [29]. The residual stress profile and the T-curve for the AMZ engineered laminate are shown in Fig. 8. The applied stress intensity factor corresponding to the predefined maximum stress (strength) and the crack depth interval are also shown in Fig. 9. Since T was calculated step by step (Eq. (9)), the corresponding diagram is discontinuous at the boundary between layers (Fig. 8). One can easily sup￾pose that the real apparent fracture toughness trend is con￾tinuous and that the discontinuities in Fig. 9 are merely mathematical artefacts. 4. Experimental a-Alumina (ALCOA, A-16SG, D50 = 0.4 lm) was the primary starting material. High-purity mullite (KCM Corp., KM101, D50 = 0.77 lm) and yttria (3 mol.%)- stabilised zirconia (TOSOH, TZ-3YS, D50 = 0.4 lm) pow￾ders were chosen as second phases to vary the thermal expansion coefficient with respect to pure alumina. Green layers were produced by tape casting water-based slurries. Suspensions were prepared using NH4-PMA (Darvan C, R.T. Vanderbilt Inc.) as dispersant and acrylic emulsions (B-1235, DURAMAX) as binder. A lower-Tg acrylic emulsion (B-1000, DURAMAX) was also added in a 1:2 by weight ratio with respect to the binder content as plasticiser to increase green flexibility and to reduce the occurrence of cracks in the dried tape. The alumina powder dispersion was obtained using a two-stage process [30,31]. In order to enhance the electrostatic interaction between the positive charges on the powder surface and the negative sites on the polymer chains, a slightly acid water solution (pH 4) was used [32]. An optimal dispersant content equal to 1.5 wt.% with respect to the powder was establish by sta￾tic sedimentation. This value corresponds to about 0.4 mg/ m2 active matter per unit area, which corresponds closely with values suggested by Greenwood et al. [30] for the same material. A ball milling stage using alumina spheres of 6 and 9 mm in diameter was carried out in polyethylene bot￾tles for 16–24 h to break down the aggregates. Suspensions were ultrasonicated for 10 min before ball milling to reduce the starting viscosity. After adding some drops of concen￾trated NH4OH to increase pH, suspensions were filtered with a 40 lm polyethylene net and de-aired using a low￾vacuum Venturi pump to remove air entrapped during the milling stage. Acrylic binder emulsion and plasticiser were then added to the suspension and slowly mixed for 30 min to reach good homogeneity, using great care to avoid the formation 4 6 8 10 12 0 20 40 60 80 100 AM AZ α (10-6 ˚C) mullite or zirconia content (vol%) Fig. 7. Thermal expansion coefficient for AZ and AM composites. -800 -600 -400 -200 0 200 400 0 5 10 15 20 25 σ res (MPa) (depth)0.5 (µm0.5) 20 100 400 50 200 depth (µm) Fig. 8. Residual stress profile in the surface region of the AMZ engineered laminate. 0 5 10 15 20 0 5 10 15 20 25 T (MPa m0.5) (depth)0.5 (µm0.5) 20 100 400 50 200 depth (µm) Fig. 9. Apparent fracture toughness of the AMZ engineered laminate. The dashed line is used to calculate the final strength. 4934 V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937

V M. Sglavo, M. Bertoldi Acta Materialia 54(2006)4929-4937 of air bubbles [31]. The final organic content was about Monolithic bars(thickness M1.5 mm)were produced in 21 vol %. A similar preparation procedure was used for the same way for the measurement of thermal expansion composite slurries, though some modifications of the dis- coefficient, a, elastic modulus, E, and fracture toughness, persion process were introduced in order to obtain limited Kc. The thermal expansion coefficient was measured in thixotropy and high fluidity. AZ suspensions were pre- the range 30-1000C using a silica dilatometer and a heat pared by dispersing the zirconia powder in a slightly acidic ing rate of 2C/min. Elastic modulus was measured using HCI solution and then by adding the alumina powder. four-point bending tests (spans equal to 40 The slurry was ball milled using a high-efficiency mixer 20 mm) with a calibrated extensometer(MTS Systems, (Turbula T2F, W.A. BACHOFEN AG, CH) for 4-8h. USA) to measure the deflection as a function of applied The dispersant was also added in two steps, using an load. Fracture toughness was determined by the conven- amount of 1. 2 wt. with respect to zirconia In the case tional indentation fracture method [1, 21] of AM composites, mullite powder was added after dispers- Sixteen samples were fractured by four-point bending ng alumina for 16 h in the same conditions described for tests. In order to establish the invariance of strength with pure alumina and ball milled for further 24 h All suspen- respect to flaw size, some specimens were also pre-cracked sions were produced with a powder content of 39 vol%. by Vickers indentation using loads ranging from 10 to The volume of powders in the first dispersing stage was 100 N. Three indentations were produced in the centre of higher, ranging from 49 to 51 vol % as the addition of the the perspective tensile surface before applying the bending acrylic emulsions also supplies the solvent(water) to the test Monolithic samples(Azo and AZ40)were also pro- slurry and dilutes the system. Just before casting, slurries duced and tested under the same conditions for were filtered again at 60 um to ensure the elimination of comparison. any bubbles or clusters of flocculated polymer Tape casting was carried out using a double doctor- 5. Results and discussion olade assembly(DDB-1-6, 6 in wide, Richard E Mistler Inc,USA)at a speed of I m/min for a length of about Fig. 10 shows the architecture of the produced AMZ 1000 mm. A composite three-layer film(PETI2/Al7/ ceramic laminate observed using scanning electron micros- LDPE60, BP Europack, Italy) was used as substrate in copy(SEM). One can easily appreciate the perfect adhesion order to make the al of the dried green tape easier. among different layers as hypothesised in the theoretical For this reason the polyethylene hydrophobic side of film was placed side-up. The substrate was placed on a rigid section of this pape The average bending stre measured for the Amz float glass plate in order to ensure a flat surface. The rela- samples was equal to 692 and the standard deviation was tive humidity of the over-standing environment was con- 25 MPa, i.e. lower than 4%. The bending strength of the trolled and set to about 80% during casting and monolithic samples was equal to 418 and 741 MPa for successive drying to avoid fast evaporation of the solvent AZo and AZ40 laminates, respectively. more interestingly and possible cracking of green tapes due to shrinkage stres- standard deviations equal to 43 and 86 MPa were calcu- es. Suspension casting was carried out using two diferent lated, correspondingly It is evident that the strength values blade heights, 250 and 100 um Drops of a 10 wt% wetting measured on the aMz laminate correlate closely to the agent water solution(NH4-lauryl sulphate, code 09887, design value and represent a clear indication of a reliable FLUKA CHEMIE AG, CH) were added to the slurries ("constant")failure stress to help the casting tape to spread on the substrate when The strength variability in brittle materials is often needed, especially in the case of thinner tapes described by the Weibull modulus, which is a stress expo- Green tapes of nominal dimension 60 mm x 45 mm were nent that describes the relation between a failure probabil- punched using a hand-cutter, stacked together and thermo ity function and the applied stress: the higher the strength compressed at 70C under a pressure of 30 MPa for 15 min variability, the lower the Weibull modulus. The strength applied by a universal mechanical testing machine (MTs data measured in this work are graphically represented Systems, model 810, USA). Two 100 um thick poly(ethyl- on a Weibull plot as shown in Fig. ll. The failure proba- ene terephthalate)layers were placed between the laminate bility is evaluated as [1, 21] and the die to make the removal easier. For mechani cal characterisation bars of nominal dimensions 60 mmx F 7.5 mm x 1-2 mm were cut after the thermo-compression and then re-laminated [29] before final thermal treatment where N is the total number of samples for each set and n is to avoid any delamination promoted by localised shear the rank in the ascending ordered distribution. Fitting of stresses developed upon cutting. Samples were finally sin- the strength data shown in Fig. Il, using linear regression, tered at 1600C for 2h. After sintering the edges were allows a calculation of the Weibull modulus that corre- lightly chamfered to remove macroscopic defects and geo- sponds to each strength distribution. Values equal to metrical irregularities. No further polishing and finishing 12t I and 10+ I were obtained for Azo and AZ40 mono- operations were performed on the sample surfaces or edges liths, respectively, similar to other advanced ceramic mate- in order to avoid any artificial reduction of flaw severity. rials. For the engineered AMZ laminate, a Weibull

of air bubbles [31]. The final organic content was about 21 vol.%. A similar preparation procedure was used for composite slurries, though some modifications of the dis￾persion process were introduced in order to obtain limited thixotropy and high fluidity. AZ suspensions were pre￾pared by dispersing the zirconia powder in a slightly acidic HCl solution and then by adding the alumina powder. The slurry was ball milled using a high-efficiency mixer (Turbula T2F, W.A. BACHOFEN AG, CH) for 4–8 h. The dispersant was also added in two steps, using an amount of 1.2 wt.% with respect to zirconia. In the case of AM composites, mullite powder was added after dispers￾ing alumina for 16 h in the same conditions described for pure alumina and ball milled for further 24 h. All suspen￾sions were produced with a powder content of 39 vol.%. The volume of powders in the first dispersing stage was higher, ranging from 49 to 51 vol.%, as the addition of the acrylic emulsions also supplies the solvent (water) to the slurry and dilutes the system. Just before casting, slurries were filtered again at 60 lm to ensure the elimination of any bubbles or clusters of flocculated polymer. Tape casting was carried out using a double doctor￾blade assembly (DDB-1-6, 6 in wide, Richard E. Mistler Inc., USA) at a speed of 1 m/min for a length of about 1000 mm. A composite three-layer film (PET12/Al7/ LDPE60, BP Europack, Italy) was used as substrate in order to make the removal of the dried green tape easier. For this reason the polyethylene hydrophobic side of the film was placed side-up. The substrate was placed on a rigid float glass plate in order to ensure a flat surface. The rela￾tive humidity of the over-standing environment was con￾trolled and set to about 80% during casting and successive drying to avoid fast evaporation of the solvent and possible cracking of green tapes due to shrinkage stres￾ses. Suspension casting was carried out using two different blade heights, 250 and 100 lm. Drops of a 10 wt.% wetting agent water solution (NH4-lauryl sulphate, code 09887, FLUKA CHEMIE AG, CH) were added to the slurries to help the casting tape to spread on the substrate when needed, especially in the case of thinner tapes. Green tapes of nominal dimension 60 mm · 45 mm were punched using a hand-cutter, stacked together and thermo￾compressed at 70 C under a pressure of 30 MPa for 15 min applied by a universal mechanical testing machine (MTS Systems, model 810, USA). Two 100 lm thick poly(ethyl￾ene terephthalate) layers were placed between the laminate and the die to make the removal easier. For mechani￾cal characterisation bars of nominal dimensions 60 mm · 7.5 mm · 1–2 mm were cut after the thermo-compression and then re-laminated [29] before final thermal treatment to avoid any delamination promoted by localised shear stresses developed upon cutting. Samples were finally sin￾tered at 1600 C for 2 h. After sintering the edges were slightly chamfered to remove macroscopic defects and geo￾metrical irregularities. No further polishing and finishing operations were performed on the sample surfaces or edges in order to avoid any artificial reduction of flaw severity. Monolithic bars (thickness 1.5 mm) were produced in the same way for the measurement of thermal expansion coefficient, a, elastic modulus, E, and fracture toughness, KC. The thermal expansion coefficient was measured in the range 30–1000 C using a silica dilatometer and a heat￾ing rate of 2 C/min. Elastic modulus was measured using four-point bending tests (spans equal to 40 mm and 20 mm) with a calibrated extensometer (MTS Systems, USA) to measure the deflection as a function of applied load. Fracture toughness was determined by the conven￾tional indentation fracture method [1,21]. Sixteen samples were fractured by four-point bending tests. In order to establish the invariance of strength with respect to flaw size, some specimens were also pre-cracked by Vickers indentation using loads ranging from 10 to 100 N. Three indentations were produced in the centre of the perspective tensile surface before applying the bending test. Monolithic samples (AZ0 and AZ40) were also pro￾duced and tested under the same conditions for comparison. 5. Results and discussion Fig. 10 shows the architecture of the produced AMZ ceramic laminate observed using scanning electron micros￾copy (SEM). One can easily appreciate the perfect adhesion among different layers as hypothesised in the theoretical section of this paper. The average bending strength measured for the AMZ samples was equal to 692 and the standard deviation was 25 MPa, i.e. lower than 4%. The bending strength of the monolithic samples was equal to 418 and 741 MPa for AZ0 and AZ40 laminates, respectively. More interestingly, standard deviations equal to 43 and 86 MPa were calcu￾lated, correspondingly. It is evident that the strength values measured on the AMZ laminate correlate closely to the design value and represent a clear indication of a reliable (‘‘constant’’) failure stress. The strength variability in brittle materials is often described by the Weibull modulus, which is a stress expo￾nent that describes the relation between a failure probabil￾ity function and the applied stress: the higher the strength variability, the lower the Weibull modulus. The strength data measured in this work are graphically represented on a Weibull plot as shown in Fig. 11. The failure proba￾bility is evaluated as [1,21] F ¼ n  0:5 N ; ð13Þ where N is the total number of samples for each set and n is the rank in the ascending ordered distribution. Fitting of the strength data shown in Fig. 11, using linear regression, allows a calculation of the Weibull modulus that corre￾sponds to each strength distribution. Values equal to 12 ± 1 and 10 ± 1 were obtained for AZ0 and AZ40 mono￾liths, respectively, similar to other advanced ceramic mate￾rials. For the engineered AMZ laminate, a Weibull V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937 4935

V.M. Solaro, M. Bertoldi Acta Materialia 54(2006)4929-4937 AMZ Az40 Azo Fig 12. Failure stress as a function of the indentation load for the aMz engineered laminate and the reference monolithic ceramics. Fig. 10. SEM micrograph showing the architecture of the produced the AMZ laminate allows the calculation of B. Values equal to 0. 27 and 0.30 were obtained for AZo and AZ40 samples, respectively, modulus equal to 35+2 was calculated, clearly highlighted and both are substantially close to the theoretical value. by the very steep interpolating line shown in Fig. Il; this Conversely, for AZM B is equal to 0.01, confirming the result proves the high reliability of the engineered laminate independence of the strength from indentation load, i.e. produced in this work. Fracture strengths measured for samples subjected to AM ramin ates in a dpan gthe strengthes wt ln den te Irface damage by Vickers indentation are shown in design value Fig. 12. The he failure stress of engineered AMZ laminates appears to be independent of the indentation load, i.e. from the initial flaw size. Conversely, as expected, the strength of monolithic laminates is strongly dependent on the size of the indentation load, P, through the relation [1, 21] of where a is a constant depending on hardness, elastic mod- ulus and fracture toughness of the material and B=1/3 Fitting of the strength results for AZo and AZ40 shown in Fig. 12, using linear regression(in the log-log diagram) mm AMZ Az40 5.6586.0 X65 260M 45 SEI In g.(In MPa) Fig. 13. Typical fracture surfaces of the engineered laminate as observed Fig. Il. Weibull plot for the AMz engineered laminate and the reference by (a) optical microscopy and (b) scanning electron microscopy. The AZo and AZ40 monolithic ceramics surface in tension during the bending tests is marked as"t

modulus equal to 35 ± 2 was calculated, clearly highlighted by the very steep interpolating line shown in Fig. 11; this result proves the high reliability of the engineered laminate produced in this work. Fracture strengths measured for samples subjected to surface damage by Vickers indentation are shown in Fig. 12. The failure stress of engineered AMZ laminates appears to be independent of the indentation load, i.e. from the initial flaw size. Conversely, as expected, the strength of monolithic laminates is strongly dependent on the size of the indentation load, P, through the relation [1,21] rf ¼ a P b ; ð14Þ where a is a constant depending on hardness, elastic mod￾ulus and fracture toughness of the material and b = 1/3. Fitting of the strength results for AZ0 and AZ40 shown in Fig. 12, using linear regression (in the log–log diagram), allows the calculation of b. Values equal to 0.27 and 0.30 were obtained for AZ0 and AZ40 samples, respectively, and both are substantially close to the theoretical value. Conversely, for AZM b is equal to 0.01, confirming the independence of the strength from indentation load, i.e. from crack size. In addition, the strength of indented AMZ laminates (720 MPa) again compares well to the design value. Fig. 10. SEM micrograph showing the architecture of the produced the AMZ laminate. -4 -3 -2 -1 0 1 2 5.6 6.0 6.2 6.4 6.6 6.8 7.0 5.8 ln ln (1/(1-F)) ln σf (ln MPa) AMZ AZ0 AZ40 300 400 500 600 800 1000 σf (MPa) F (%) 99 90 50 20 10 5 Fig. 11. Weibull plot for the AMZ engineered laminate and the reference AZ0 and AZ40 monolithic ceramics. 0 200 400 600 800 10 100 σ f (MPa) indentation load (N) AMZ AZ40 AZ0 Fig. 12. Failure stress as a function of the indentation load for the AMZ engineered laminate and the reference monolithic ceramics. Fig. 13. Typical fracture surfaces of the engineered laminate as observed by (a) optical microscopy and (b) scanning electron microscopy. The surface in tension during the bending tests is marked as ‘‘t’’. 4936 V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937

V M. Sglavo, M. Bertoldi Acta Materialia 54(2006 )4929-4937 Fig. 13 shows typical fracture surfaces of the engineered [2] Davis JB, Kristoffersson A, Carlstrom E, Clegg WJ. J Am Ceram Soc laminate(AMZ) subjected to bending tests. The markings 2000:83:2369-7 on the fracture surface show that the surface flaw extends B] Clegg WJ, Kendall K, Alford McN. Nature (London)1990: 347 at first along the surface and is then arrested by the engi-[4 Kriven wM, Kuo D-H. US Patent 5,948.5167 September1999 peered residual stress profile in the in-depth propagation; [5]Mistler RE. US Patent 3,652.,378: 28 March 1972. then, after such stable growth stage only, the through 6 Harmer MP, Chan HM, Miller GA. J Am Ceram Soc 1992: 75: 1715-28 thickness notch can become instable and lead to sample [7 Russo CJ, Harmer MP, Chan HM, Miller GA. J Am Ceram Soc failure. Such behaviour demonstrates further the insensi 1992:75:3396400 tiveness of the engineered laminate to surface defects [8]Latkshminarayanan R, Shetty DK, Cutler RA. J Am Ceram Soc 1996;79:79-87 9]Rao MP, Sanchez- Herencia AJ, Beltz GE, McMeeking RM, Lange FF. Science 1999:286:102-5. 6. Conclusions [0] Orlovskaya N, Lugovy M, Subbotin V, Radchenko O. Adams J, Chheda M. et al. J Mater Sci 2005: 40- 5483-90 The present study shows that it is possible to produce [ll] Orlovskaya N, Kuebler J, Subbotin V, Lugovy M. J Mater Sci highly reliable ceramic materials whose"constant 2005:40:5443-50 strength can be a priori defined and controlled through [2 mugovy M. slyunyayev v orlovskaya N, Blugan G, Kuebler ), Lewis an innovative design procedure. The material can be also [13] Cai PZ, Green DJ, Messing GL. J Am Ceram Soc 1997: 80: 1929-39 designed to support bending loads in a more efficient way [14] Donald w. J Mater Sci 1989: 24:4177-208 than homogeneous materials, since it is improved only [15] Bartolomew RF, Garfinkel HM. In: Uhlmann DR, Kreidl NJ where needed, i.e. near the surface. These laminates are editors. Glass science and technology, vol 5. New York(NY) :Aca- therefore natural candidates for structural applications, demic Press: 1980 particularly when high mechanical reliability and damage [16 Lange FF. J Am Ceram Soc 1989: 72: 3-15 ge[17] Yu BC, Lange FF. Adv Mater 2001 tolerance in severe conditions are required, as in the case [18]Sglavo VM, Larentis L, Green DJ. J Am Ceram Soc 2001: 84: 1827-31 of load-bearing components in the automotive and aircraft [19] Sglavo VM, Green DJ. J Am Ceram Soc 2001: 84: 1832-8 industry, biomedical prostheses, chemical plant linings and [20] Green DJ, Tandon R, Sglavo VM Science 1999 283: 1295-7 safety systems [21] Green DJ. An introduction to the mechanical properties of ceram- Cambridge: Cambridge University Press: 1998 It is important to point out that the principle outlined is [22]Sglavo VM, Bertoldi M. In: Proceedings of the 29th international general. It can be applied to different material systems and conference on advanced ceramics and composites, 23-28 January production processes. The design requires knowledge of the 2005. Cocoa Beach(FL): American Ceramic Society: 2005 arce of the residual stresses and the availability of suit- [23] Moon RJ, Hoffman M, Hilden J, Bowman KJ, Trumble KP, Rodel J able processing techniques to assemble layers with different Eng fract Mech 2002: 69: 1647-65 composition and/or microstructure 224] Chung TJ, Neubrand A, Rodel J, Fett T. Ceram Trans 2001:114:78996 225] Halpin JC. Primer on composite materials analysis. 2nd ed. Lancas- ter(PA): Technomic: 1992. Acknowledgements [28] Ledbetter H, Kim S, Crudele DB, Kriven W. J Am Ceram Soc 1998:8l:1025-8. Te acknowledge the University of Trento for financial [27] Sergo V, Wang X, Becher PF, Clarke DR. J Am Ceram Soc 1995; support and Massimo Paternoster for technical assistance Professor Rishi Raj( Colorado University, USA)is 28] Ledbetter H, Kim S, Crudele DB, Kriven w JAm Ceram Soc 1998:8l:1025-8. acknowledged for reviewing the manuscript aternoster M. Sglavo VM. Ceram Tr 2003;153:89-102 [0] Greenwood R, Roncari E, Galassi C. J Eur Ceram Soc References 31] Mistler RE, Twiname ER. Tape casting: theory and practice. Wes- []Lawn BR. Fracture of brittle solids. 2nd ed. Cambridge: Cambridge berville(OH): American Ceramic Society: 2000. University Press: 1993 32] Cesarano Ill J, Aksay IA, Bleier A. J Am Ceram Soc 1988: 71: 250-5

Fig. 13 shows typical fracture surfaces of the engineered laminate (AMZ) subjected to bending tests. The markings on the fracture surface show that the surface flaw extends at first along the surface and is then arrested by the engi￾neered residual stress profile in the in-depth propagation; then, after such stable growth stage only, the through￾thickness notch can become instable and lead to sample failure. Such behaviour demonstrates further the insensi￾tiveness of the engineered laminate to surface defects. 6. Conclusions The present study shows that it is possible to produce highly reliable ceramic materials whose ‘‘constant’’ strength can be a priori defined and controlled through an innovative design procedure. The material can be also designed to support bending loads in a more efficient way than homogeneous materials, since it is improved only where needed, i.e. near the surface. These laminates are therefore natural candidates for structural applications, particularly when high mechanical reliability and damage tolerance in severe conditions are required, as in the case of load-bearing components in the automotive and aircraft industry, biomedical prostheses, chemical plant linings and safety systems. It is important to point out that the principle outlined is general. It can be applied to different material systems and production processes. The design requires knowledge of the source of the residual stresses and the availability of suit￾able processing techniques to assemble layers with different composition and/or microstructure. Acknowledgements We acknowledge the University of Trento for financial support and Massimo Paternoster for technical assistance. Professor Rishi Raj (Colorado University, USA) is acknowledged for reviewing the manuscript. References [1] Lawn BR. Fracture of brittle solids. 2nd ed. Cambridge: Cambridge University Press; 1993. [2] Davis JB, Kristoffersson A, Carlstrom E, Clegg WJ. J Am Ceram Soc 2000;83:2369–74. [3] Clegg WJ, Kendall K, Alford McN. Nature (London) 1990;347: 455–7. [4] Kriven WM, Kuo D-H. US Patent 5,948,516; 7 September 1999. [5] Mistler RE. US Patent 3,652,378; 28 March 1972. [6] Harmer MP, Chan HM, Miller GA. J Am Ceram Soc 1992;75:1715–28. [7] Russo CJ, Harmer MP, Chan HM, Miller GA. J Am Ceram Soc 1992;75:3396–400. [8] Latkshminarayanan R, Shetty DK, Cutler RA. J Am Ceram Soc 1996;79:79–87. [9] Rao MP, Sa´nchez-Herencia AJ, Beltz GE, McMeeking RM, Lange FF. Science 1999;286:102–5. [10] Orlovskaya N, Lugovy M, Subbotin V, Radchenko O, Adams J, Chheda M, et al. J Mater Sci 2005;40:5483–90. [11] Orlovskaya N, Kuebler J, Subbotin V, Lugovy M. J Mater Sci 2005;40:5443–50. [12] Lugovy M, Slyunyayev V, Orlovskaya N, Blugan G, Kuebler J, Lewis M. Acta Mater 2005;53:289–96. [13] Cai PZ, Green DJ, Messing GL. J Am Ceram Soc 1997;80:1929–39. [14] Donald W. J Mater Sci 1989;24:4177–208. [15] Bartolomew RF, Garfinkel HM. In: Uhlmann DR, Kreidl NJ, editors. Glass science and technology, vol. 5. New York (NY): Aca￾demic Press; 1980. [16] Lange FF. J Am Ceram Soc 1989;72:3–15. [17] Yu BC, Lange FF. Adv Mater 2001;13:276–80. [18] Sglavo VM, Larentis L, Green DJ. J Am Ceram Soc 2001;84:1827–31. [19] Sglavo VM, Green DJ. J Am Ceram Soc 2001;84:1832–8. [20] Green DJ, Tandon R, Sglavo VM. Science 1999;283:1295–7. [21] Green DJ. An introduction to the mechanical properties of ceram￾ics. Cambridge: Cambridge University Press; 1998. [22] Sglavo VM, Bertoldi M. In: Proceedings of the 29th international conference on advanced ceramics and composites, 23–28 January 2005. Cocoa Beach (FL): American Ceramic Society; 2005. [23] Moon RJ, Hoffman M, Hilden J, Bowman KJ, Trumble KP, Ro¨del J. Eng Fract Mech 2002;69:1647–65. [24] Chung TJ, Neubrand A, Ro¨del J, Fett T. Ceram Trans 2001;114:789–96. [25] Halpin JC. Primer on composite materials analysis. 2nd ed. Lancas￾ter (PA): Technomic; 1992. [28] Ledbetter H, Kim S, Crudele DB, Kriven W. J Am Ceram Soc 1998;81:1025–8. [27] Sergo V, Wang X, Becher PF, Clarke DR. J Am Ceram Soc 1995; 78:2213–4. [28] Ledbetter H, Kim S, Crudele DB, Kriven W. J Am Ceram Soc 1998;81:1025–8. [29] Bertoldi M, Paternoster M, Sglavo VM. Ceram Trans 2003;153:89–102. [30] Greenwood R, Roncari E, Galassi C. J Eur Ceram Soc 1997;17:1393–401. [31] Mistler RE, Twiname ER. Tape casting: theory and practice. Wes￾terville (OH): American Ceramic Society; 2000. [32] Cesarano III J, Aksay IA, Bleier A. J Am Ceram Soc 1988;71:250–5. V.M. Sglavo, M. Bertoldi / Acta Materialia 54 (2006) 4929–4937 4937