《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_alumina-mullite

J.Am. Ceran.Soe,88102826-2832(2005) Dol:l0.l11551-2916.2005.00479x journal C) 2005 The American Ceramic Society Tailored Residual Stresses in High Reliability Alumina-Mullite Ceramic Laminates Vincenzo m. sglavo, * I Massimo Paternoster, and Massimo bertoldi Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita di Trento, 38050 Trento, Italy a design and processing approach to fabricate ceramic lami- As an alternative fracture behavior of ceramics has been im- nates with high mechanical reliability, i. e, high failure resist- proved by introducing low-energy paths for growing cracks in e, limited strength scatter, and increased damage tolerance is laminated structures. This has been achieved using either sented in this paper. Different ceramic layers are stacked rous or weak interlayer. 4to promote delamination and crack together to develop a specific residual stress profile after sinte- deflection. In this way the strength is usually not increased, but ing. By changing the composition of the laminae and the com- the deformation and the energy absorbed before failure are am- architecture it is possible to produce a material with plified many times. In other cases, sandwiched structures de redefined failure stress which can be evaluated from the frac- signed to improve the mechanical performance were proposed ture toughness curve correlated to the residual stresses. In ad- based on other microstructural mechanisms. 5, 6 urface defects can be forced to grow in a stable way before reaching the critical tures in which the strength is controlled by the presence of com- condition, thus obtaining a unique-value strength ceramic ma- pressive residual stresses. Laminates presenting threshold terial Laminates composed of alumina mullite composite layers strength, i.e a minimum stress value below which rupture are designed and created in this work by the implementation of does not occur, have been successfully produced by lange and he proposed approach. The material obtained shows a"con- o-workers by alternating thin compressive layers and thicker stant"strength of 456 MPa(standard deviation <7%) even tensile layers. The most significant limitations of such laminates when large surface damage is produced by vickers indentation. is that they can be used only with specific orientations to the applied load and, for example, they require complex manufac- turing to produce shells or tubes as usually required in typical L. Introduction ROBABly the fundamental reason for the scarce employ of The idea that surface stresses can hinder the growth of surface ceramic materials in structural applications is their limited cracks has been extensively exploited in the past especially on mechanical reliability. Although ceramics possess many glasses. 0, II It is important to point out that surface flaws rep- tive properties suitable for different applications, such materials resent the most typical defects in ceramic and glasses: in fact, have low fracture toughness. In addition, processing and dam- once the processing procedures are optimized to reduce or elim- age and degradation in service, results in flaws of varying sizes hate heterogeneities that can produce volume defects, sur- The resulting strength scatter is usually too large to allow safe ace flaws are normally generated during surface finishing or design, unless statistical approaches embodying acceptable min- when a body is subjected to bending and not to tension, as is imum failure risk are used. In addition, fracture usually occurs in a catastrophic manner in absence of any warning of the usually, the case in ceramic components. Recently, Sglavo and Green have proposed that the creation of a residual stress profile Much effort has been made in the past to overcome such prob- with a maximum compression at a certain depth from the sur lems. Solutions proposed to improve the mechanical behavior of and limited strength variability. 4 This approach has been ap- defects, or to increase fracture toughness by microstructural con- plied to silicate glasses by producing the residual stress field via a trol. Higher fracture toughness has been achieved through the double ion-e exploitation of the reinforcing action of grain anisotropy or sec- Residual stresses in ceramic materials can arise either from ond phases or the promotion of crack shielding effects associated differences in the thermal expansion coefficient of the constitut- to phase-transformation or micro-cracking. Unfortunately, all ing grains or phases, from uneven sintering rates or from mar- these solutions overcome the problem of the wide strength scatter tensitic phase transformations associated to specific volume to a limited extent only. Moreover, a precise microstructure con- lange. As described in the present paper, if the development trol is always required and this is achievable only with a careful of the residual stresses in ceramic multilayer is opportunely con- control of starting material and process conditions. The same trolled, materials characterized by high fracture resistance and limited strength scatter can be designed and produced. By var- strict requirements are needed when the reduction of flaw severity ying the nature, the thickness and the stacking order of the lam- which allows cutting the low-stress tail of critical flaw popula- inae, the residual stress profile developed after sintering can be tion.Nevertheless, costs associated with the preloading of all the tailored to promote the growth of surface cracks in a stable bodies are usually too high for most applications ibrated and varied as required is obtained by changing of the multilayer"structure". This approach, as described in this pa- per, has been implemented for the production of alur Manuscript No. 20268 Received July 31, 2004: approved March 7, 2005. Il. Theory and design Procedure n order to analyze the effect of residual stresses on crack Author to whom correspondence should be addressed. e-mail: sglavo a ingunitn.it agation and resistance failure in brittle material, the

Tailored Residual Stresses in High Reliability Alumina-Mullite Ceramic Laminates Vincenzo M. Sglavo,* ,w Massimo Paternoster, and Massimo Bertoldi Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita` di Trento, 38050 Trento, Italy A design and processing approach to fabricate ceramic lami￾nates with high mechanical reliability, i.e., high failure resist￾ance, limited strength scatter, and increased damage tolerance is presented in this paper. Different ceramic layers are stacked together to develop a specific residual stress profile after sinte￾ring. By changing the composition of the laminae and the com￾posite architecture it is possible to produce a material with predefined failure stress which can be evaluated from the frac￾ture toughness curve correlated to the residual stresses. In ad￾dition, by tailoring the fracture toughness curve, surface defects can be forced to grow in a stable way before reaching the critical condition, thus obtaining a unique-value strength ceramic ma￾terial. Laminates composed of alumina/mullite composite layers are designed and created in this work by the implementation of the proposed approach. The material obtained shows a ‘‘con￾stant’’ strength of 456 MPa (standard deviation o7%) even when large surface damage is produced by Vickers indentation. I. Introduction PROBABLY the fundamental reason for the scarce employ of ceramic materials in structural applications is their limited mechanical reliability. Although ceramics possess many attrac￾tive properties suitable for different applications, such materials have low fracture toughness. In addition, processing and dam￾age and degradation in service, results in flaws of varying sizes. The resulting strength scatter is usually too large to allow safe design, unless statistical approaches embodying acceptable min￾imum failure risk are used. In addition, fracture usually occurs in a catastrophic manner in absence of any warning of the incipient rupture.1 Much effort has been made in the past to overcome such prob￾lems. Solutions proposed to improve the mechanical behavior of ceramics aimed either to reduce the presence or the severity of defects, or to increase fracture toughness by microstructural con￾trol. Higher fracture toughness has been achieved through the exploitation of the reinforcing action of grain anisotropy or sec￾ond phases or the promotion of crack shielding effects associated to phase-transformation or micro-cracking.1 Unfortunately, all these solutions overcome the problem of the wide strength scatter to a limited extent only. Moreover, a precise microstructure con￾trol is always required and this is achievable only with a careful control of starting material and process conditions. The same strict requirements are needed when the reduction of flaw severity is pursued. In some cases, the sole solution is the ‘‘proof testing’’ which allows cutting the low-stress tail of critical flaw popula￾tion.1 Nevertheless, costs associated with the preloading of all the bodies are usually too high for most applications. As an alternative, fracture behavior of ceramics has been im￾proved by introducing low-energy paths for growing cracks in laminated structures. This has been achieved using either po￾rous2 or weak interlayer3,4 to promote delamination and crack deflection. In this way the strength is usually not increased, but the deformation and the energy absorbed before failure are am￾plified many times. In other cases, sandwiched structures de￾signed to improve the mechanical performance were proposed based on other microstructural mechanisms.5,6 A different approach has been proposed for laminated struc￾tures in which the strength is controlled by the presence of com￾pressive residual stresses.7–9 Laminates presenting threshold strength, i.e., a minimum stress value below which rupture does not occur, have been successfully produced by Lange and co-workers9 by alternating thin compressive layers and thicker tensile layers. The most significant limitations of such laminates is that they can be used only with specific orientations to the applied load and, for example, they require complex manufac￾turing to produce shells or tubes as usually required in typical applications. The idea that surface stresses can hinder the growth of surface cracks has been extensively exploited in the past especially on glasses.10,11 It is important to point out that surface flaws rep￾resent the most typical defects in ceramic and glasses: in fact, once the processing procedures are optimized to reduce or elim￾inate heterogeneities that can produce volume defects,12,13 sur￾face flaws are normally generated during surface finishing or upon service. In addition, surface defects only become critical when a body is subjected to bending and not to tension, as is usually the case in ceramic components. Recently, Sglavo and Green have proposed that the creation of a residual stress profile with a maximum compression at a certain depth from the sur￾face can arrest surface cracks and result in higher failure stress and limited strength variability.14 This approach has been ap￾plied to silicate glasses by producing the residual stress field via a double ion-exchange process.15,16 Residual stresses in ceramic materials can arise either from differences in the thermal expansion coefficient of the constitut￾ing grains or phases, from uneven sintering rates or from mar￾tensitic phase transformations associated to specific volume change. As described in the present paper, if the development of the residual stresses in ceramic multilayer is opportunely con￾trolled, materials characterized by high fracture resistance and limited strength scatter can be designed and produced. By var￾ying the nature, the thickness and the stacking order of the lam￾inae, the residual stress profile developed after sintering can be tailored to promote the growth of surface cracks in a stable manner before final failure. Thus, the strength that can be cal￾ibrated and varied as required is obtained by changing of the multilayer ‘‘structure’’. This approach, as described in this pa￾per, has been implemented for the production of alumina/mul￾lite composite laminates. II. Theory and Design Procedure In order to analyze the effect of residual stresses on crack prop￾agation and resistance failure in brittle material, the simple Journal J. Am. Ceram. Soc., 88 [10] 2826–2832 (2005) DOI: 10.1111/j.1551-2916.2005.00479.x r 2005 The American Ceramic Society 2826 S. J. Glass—contributing editor Supported by University of Trento (Italy). Originally presented at the 2004 Annual Meeting in the symposium in honor of Ed Fuller. *Member, American Ceramic Society. w Author to whom correspondence should be addressed. e-mail: sglavo@ing.unitn.it Manuscript No. 20268. Received July 31, 2004; approved March 7, 2005

October 2005 Tailored Residual Stresses in Ceramic laminates 2827 model depicted in Fig. I can be considered. The residual stress, Ores(x) which is a function of the distance from the surface, x ores (n only, is correlated with a stress intensity factor defined as 1)/v(x/c)ore(x)dx (1) crack length and y a function The generic system in Fig. I can be al ected to external loads, correlated with the stress intensity factor, Kext. Crack ture toughness, Kc, of the material around the crack tip. ll s propagation occurs when the sum(Kres+ Kext equals the esidual stresses are hypothesized as a material characteristic Kc( he apparent fracture toughness can be defined by combining Ko th the stress intensity factor correlated with K Thus, crack propagates when Kext =kc. It is clear that com- pressive (i.e, negative) residual stresses have a beneficial effect on crack propagation resistance. If the simple situation where the residual stress possesse ve ed in Fig. 2 is considere calculated For an edge crack in a semi-infinite body subjected to residual stresses, Eq. (I)can be rewritten as: X1 vccr Fig. 2. Plot of the step residual stress profile(a) and of the correspond- ng apparent fracture toughness(b). The dashed tangent straight line is drawn to calculate the failure stress for crack lengths lower than ccr. with Y a 1. 12. It is correct to point out here that this is not slight dependence on x/c. Nevertheless, such approximation sition; then, by using the principle of s nae of different compo- rigorously true for non-uniform loading, since Y maintains a a ceramic laminate constituted by lar corre- simplifies the calculations while avoiding the loss of generality sponding apparent fracture toughness can be evaluated The apparent fracture toughness correlated with the residual Referring to the generic step profile shown in Fig. 1, if each stress profile shown in Fig. 2(a) becomes step has an amplitude o,=of-1+Ao the apparent fracture toughness in layer i(xi_I <x< x) can be defined Kc=k 0<x<x Kc=kc+2) ()(-amcm() x1<x<+∞ kci=ko Assuming the presence of surface cracks smaller than a critical length, cer, the material strength, of, can be calculated by means of the graphical construction reported in Fig. 2(b)from the tan- In the calculations carried out to obtain Eq(the approxima- gent line correlated with the applied stress intensity factor de- tion is made that the elastic modulus of the different layers constant. Nevertheless. it has been demonstrated elsewhere that the approximation in Kci estimate does not exceed 10% if Kex=Yor√re the Young modulus variation is less than 33%.4One should note that the hypotheses made purport that perfect adhesion The addition or subtraction of step profiles such as in exists between layers and no delamination occurs; such hypoth ig 2(a)allows the reproduction of the stress generated within eses have been experimentally verified as reported later in the resent paper The residual stress profile that develops within a ceramic laminate is related either to the composition/microstructure and thickness of the laminae and to their stacking order. i.e. the composite architecture. According to the theory of composite plies, in order to maintain flatness during in-plane loading, as in the case of biaxial residual stresses developed during produc- tion, laminate structure must conform to a number of symmetry conditions. If each layer is isotropic, like ceramic laminae with 4乙 layer i fine and randomly oriented crystalline microstructure, and the tacking order is symmetrical, the laminate remains fat upon ering and being orthotropic, its response to loading is sim- to that of a homogeneous plate Regardless of the physical source of residual stresses, their presence in a co-sintered multilayer is related to constraining effect. When the different layers perfectly adhere to each other every lamina must deform similarly and at the same rate as the others The difference between free deformation or free defor- Fig1. Schematic representation of the model used for the calculation mation rate of the single lamina with respect to the average val- of the apparent fracture toughness in a multilayered body subjected to ue of the whole laminate accounts for the creation of residual residual stresses, Ore(x), with a surface crack (length=c) tresses Such stresses can be either viscous or elastic in nature

model depicted in Fig. 1 can be considered. The residual stress, sres(x), which is a function of the distance from the surface, x, only, is correlated with a stress intensity factor defined as: Kres ¼ 2 c p
0:5 Z c 0 cðx=cÞsresðxÞ dx (1) being c the crack length and c a function of x/c. 17 The generic system in Fig. 1 can be also subjected to external loads, correlated with the stress intensity factor, Kext. Crack propagation occurs when the sum (Kres1Kext) equals the frac￾ture toughness, KC, of the material around the crack tip. If the residual stresses are hypothesized as a material characteristic, the apparent fracture toughness can be defined by combining KC with the stress intensity factor correlated with sres: K
C ¼ KC Kres (2) Thus, crack propagates when Kext ¼ K
C. It is clear that com￾pressive (i.e., negative) residual stresses have a beneficial effect on crack propagation resistance. If the simple situation where the residual stress possesses a simple step-profile as reported in Fig. 2 is considered, K
C can be calculated. For an edge crack in a semi-infinite body subjected to residual stresses, Eq. (1) can be rewritten as: Kres ¼ Y ðpcÞ 0:5 Z c 0 sresðxÞ 2c ðc2 x2Þ 0:5 dx (3) with Y 1.12. It is correct to point out here that this is not rigorously true for non-uniform loading, since Y maintains a slight dependence on x/c. Nevertheless, such approximation simplifies the calculations while avoiding the loss of generality. The apparent fracture toughness correlated with the residual stress profile shown in Fig. 2(a) becomes: K
C ¼ KC 0 < x < x1 K
C ¼ KC þ 2Y c p
0:5 sR p 2 arcsin x1 c

x1 < x < þ1 ( (4) Assuming the presence of surface cracks smaller than a critical length, ccr, the material strength, sf, can be calculated by means of the graphical construction reported in Fig. 2(b) from the tan￾gent line correlated with the applied stress intensity factor de- fined as: Kext ¼ Ysf ffiffiffiffiffi pc p (5) The addition or subtraction of step profiles such as in Fig. 2(a) allows the reproduction of the stress generated within a ceramic laminate constituted by laminae of different compo￾sition; then, by using the principle of superposition, the corre￾sponding apparent fracture toughness can be evaluated. Referring to the generic step profile shown in Fig. 1, if each step has an amplitude sj 5 sj11Dsj, the apparent fracture toughness in layer i (xi1 oxoxi) can be defined as: K
C;i ¼KC;i Xi j¼1 2Y c p
0:5 Dsres;j p 2 arcsin xj1 c h i
  (6) In the calculations carried out to obtain Eq. (3) the approxima￾tion is made that the elastic modulus of the different layers is constant.18 Nevertheless, it has been demonstrated elsewhere that the approximation in K
Ci; estimate does not exceed 10% if the Young modulus variation is less than 33%.19,20 One should note that the hypotheses made purport that perfect adhesion exists between layers and no delamination occurs; such hypoth￾eses have been experimentally verified as reported later in the present paper. The residual stress profile that develops within a ceramic laminate is related either to the composition/microstructure and thickness of the laminae and to their stacking order, i.e., the composite architecture. According to the theory of composite plies,21 in order to maintain flatness during in-plane loading, as in the case of biaxial residual stresses developed during produc￾tion, laminate structure must conform to a number of symmetry conditions. If each layer is isotropic, like ceramic laminae with fine and randomly oriented crystalline microstructure, and the stacking order is symmetrical, the laminate remains flat upon sintering and, being orthotropic, its response to loading is sim￾ilar to that of a homogeneous plate.21 Regardless of the physical source of residual stresses, their presence in a co-sintered multilayer is related to constraining effect. When the different layers perfectly adhere to each other, every lamina must deform similarly and at the same rate as the others. The difference between free deformation or free defor￾mation rate of the single lamina with respect to the average val￾ue of the whole laminate accounts for the creation of residual stresses. Such stresses can be either viscous or elastic in nature c xi −1 layer i σres(x) ∆σres,i xi σres,i Fig. 1. Schematic representation of the model used for the calculation of the apparent fracture toughness in a multilayered body subjected to residual stresses, sres(x), with a surface crack (length 5 c). x x1 σ res x c 1 KC * ( ) x ( ) x Yσ π f c ccr KC − σ KC * (a) (b) Fig. 2. Plot of the step residual stress profile (a) and of the correspond￾ing apparent fracture toughness (b). The dashed tangent straight line is drawn to calculate the failure stress for crack lengths lower than ccr. October 2005 Tailored Residual Stresses in Ceramic Laminates 2827

Journal of the American Ceramic Society-Sglavo et al. No.10 and can be relaxed or maintained within the material depending TableL. Materials Properties Used to Estimate the Stress ture, cooling rate, and material properties. With the exception of the edges, if thickness is much smaller than the Distribution and the Apparent Fracture Toughnes other dimensions. each lamina can be considered to be in a bi- Material E(GPa) Kc(MPam0)x(10-6°- axial stress state One fundamental task in the opportune designing of a sym- AMO 4(14)0 3.6(0.2) 7.75 metric multilayer is the estimate of the biaxial residual stresses. AM10378-3680.2340.2333.3(0.2) In the common case where stresses develop from differences in AM20 0.2380.2373.1(0.3) 7.30 thermal expansion coefficients only, the residual stress in the AM30 0.242-0.24126(0.2) 7.12 generic layer i(among n layers) can be written as: AM40 0.2460.2442.4(0.2) 88 Numbers between parenthesis correspond to the standard deviation. Elastic =E1(-m)△T (7) modulus and Poissons ratio values correspond to calculated Voigt-Reuss bounds for AMI0-AM40 composites vi(vi= Poissons ratic in order to promote the stable growth of surface defects as deep TSF-TRT (TSF =stress free temperature, TRT as≈l80um ture), and a is the average thermal expansion On the basis of the aforementioned analysis, once the Young whole laminate. defined as: ion coefficient, and fracture toughness for each layer are established, the residual stress distribution and the corresponding apparent fracture toughness curve for each =∑E1/∑Et laminate can be estimated In this study room temperature equal to 25.C and stress-free temperature equal to 1200C were es- with t; being the layer thickness. In this specific case the residual tablished as indicated in previous works. 2.23 The properties of stresses are therefore generated upon cooling after sintering. It the materials required for the calculation are summarized in Table I. Young modulus and Poissons ratio values for AMz has been shown in previous works that the TSF represents the composites shown in Table I temperature below which the material can be considered to be- bounds according to previous results, Young modulus and have as a perfectly elastic body and visco-elastic relaxation phe Poissons ratio equal to 229 GPa and 0.27 live nomena do not occu considered for pure mullite. Poisson's ratio equal to 0. 23 was Equation( 6) represents the fundamental tool for the design of a ceramic laminate with pre-defined mechanical properties. Dif- ssumed for pure alumina. The difference between the bounds s lower than 7% and 1.3% for elastic modulus and Poisson ferent ceramic layers can be stacked together in order to develop a specific residual stress profile after sintering that can be eval ratio, respectively, for mullite content below 40%0. Therefore, the average of the values reported in Table I has been used for uated by Eq. (7). Once the correlated kc curve is calculated by Eq(6), strength and fracture behavior are directly defined. By the evaluation of Eqs (7)and( 8)thus accepting an error equ hanging the stacking order and composition of the laminae it is well as the thermal expansion coefficient and fracture toughness stress. In addition, if the shape of kc is also tailored, reported below. The stress distribution was calculated by Eq. (7) defects can be forced to grow in a stable way before reaching the and the corresponding T-curve estimated according to Eq(6) ritical condition, thus obtaining single-value strength. As an example, a ceramic laminate composed of different The residual stress profile and the kc, curve for the engineered composite are shown in Fig 4. In the same graphs the applied ayers belonging to the alumina/mullite system has been de- stress intensity factor corresponding to the maximum stress igned and produced in the research work as documented in this paper. The architecture of the laminate is reported in Fig. 3 (strength) equal to N 400 MPa and the cracks depth interval Here the different alumina/ mullite composites are labeled are also shown. Since Kci was calculated step by step(Eq.(6)). alumina monolithic(AM)z where z corresponds to the volume the corresponding diagram is discontinuous at the boundary percent content of mullite. The composition and thickness of the between layers, this refecting the discontinuities in the ores d layers and the composite architecture are selected to produce a agram(Fig 4(a). One can easily suppose that the real kc, trend ceramic laminate with a" constant"strength of A 400 MPa are is continuous and that the discontinuities in Fig. 4 correspond to nathematical artifacts only. It is for this reason that the max- shown in Fig. 3. The apparent fracture toughness curve and imum sustainable stress was only calculated approximately correlated residual stress profile were correspondingly tailored equaling about 400 MP AMO, 41um AM20, 44um Ill. Experimental Procedure AM40, 43um Ceramic laminates corresponding to the material designed in the AM20, 44um previous section were produced and characterized. As previous- y pointed out, the thermal expansion coefficient as required for AM10,42um the development of the residual stress profile was tailored by considering composites in the alumina/mullite system for the production of the single lamina The ceramic powders used in the present work are reported AMO, 540 um in Table Il. a-alumina(ALCOA, Leetsdale, PA, A-16SG Dso=0.4 um) was considered as the fundamental starting ma- terial. High purity and fine mullite(KCM Corp, Nagoya, Japan, KM101, Dso=0.77 um) powder was chosen as the sec- symmetry axis Green laminae were produced by tape casting water-based Fig 3. Structure of the alumina/mullite multilayer designed and pro- vanC R. T. Vander Norwalk, CT)as dispersant and duced in the pi t work. The actual layers thickness and composition acrylic emulsions(B-1235, DURAMAX, Rohm Haas are reported(dimensions are not in scale Philadelphia, PA)as A lower-Tg acrylic emulsion(B-

and can be relaxed or maintained within the material depending on temperature, cooling rate, and material properties. With the exception of the edges, if thickness is much smaller than the other dimensions, each lamina can be considered to be in a bi￾axial stress state. One fundamental task in the opportune designing of a sym￾metric multilayer is the estimate of the biaxial residual stresses. In the common case where stresses develop from differences in thermal expansion coefficients only, the residual stress in the generic layer i (among n layers) can be written as: si ¼ E
i ða
aiÞDT (7) where ai is the thermal expansion coefficient, E
i ¼ Ei=ð1 niÞ(ni 5 Poisson’s ratio, Ei 5 Young modulus), DT 5 TSF–TRT (TSF 5 stress free temperature, TRT 5 room tempera￾ture), and a
is the average thermal expansion coefficient of the whole laminate, defined as: a
¼ Xn 1 E
i ti ai= Xn 1 E
i ti (8) with ti being the layer thickness. In this specific case the residual stresses are therefore generated upon cooling after sintering. It has been shown in previous works that the TSF represents the temperature below which the material can be considered to be￾have as a perfectly elastic body and visco-elastic relaxation phe￾nomena do not occur.22 Equation (6) represents the fundamental tool for the design of a ceramic laminate with pre-defined mechanical properties. Dif￾ferent ceramic layers can be stacked together in order to develop a specific residual stress profile after sintering that can be eval￾uated by Eq. (7). Once the correlated K
C curve is calculated by Eq. (6), strength and fracture behavior are directly defined. By changing the stacking order and composition of the laminae it is therefore possible to produce a material with predefined failure stress. In addition, if the shape of K
C is also tailored, surface defects can be forced to grow in a stable way before reaching the critical condition, thus obtaining single-value strength. As an example, a ceramic laminate composed of different layers belonging to the alumina/mullite system has been de￾signed and produced in the research work as documented in this paper. The architecture of the laminate is reported in Fig. 3. Here the different alumina/mullite composites are labeled as alumina monolithic (AM)z where z corresponds to the volume percent content of mullite. The composition and thickness of the layers and the composite architecture are selected to produce a ceramic laminate with a ‘‘constant’’ strength of 400 MPa are shown in Fig. 3. The apparent fracture toughness curve and correlated residual stress profile were correspondingly tailored in order to promote the stable growth of surface defects as deep as 180 mm. On the basis of the aforementioned analysis, once the Young modulus, thermal expansion coefficient, and fracture toughness for each layer are established, the residual stress distribution and the corresponding apparent fracture toughness curve for each laminate can be estimated. In this study room temperature equal to 251C and stress-free temperature equal to 12001C were es￾tablished as indicated in previous works.22,23 The properties of the materials required for the calculation are summarized in Table I. Young modulus and Poisson’s ratio values for AMz composites shown in Table I correspond to Voigt–Reuss bounds;17 according to previous results,24 Young modulus and Poisson’s ratio equal to 229 GPa and 0.27, respectively, were considered for pure mullite. Poisson’s ratio equal to 0.23 was assumed for pure alumina.17 The difference between the bounds is lower than 7% and 1.3% for elastic modulus and Poisson’s ratio, respectively, for mullite content below 40%. Therefore, the average of the values reported in Table I has been used for the evaluation of Eqs (7) and (8) thus accepting an error equal to 4% at the highest. The elastic modulus for pure alumina as well as the thermal expansion coefficient and fracture toughness for AMz composites were measured on monolithic samples as reported below. The stress distribution was calculated by Eq. (7) and the corresponding T-curve estimated according to Eq. (6). The residual stress profile and the K
C;i curve for the engineered composite are shown in Fig. 4. In the same graphs the applied stress intensity factor corresponding to the maximum stress (strength) equal to 400 MPa and the cracks depth interval are also shown. Since K
C;i was calculated step by step (Eq. (6)), the corresponding diagram is discontinuous at the boundary between layers, this reflecting the discontinuities in the sres di￾agram (Fig. 4(a)). One can easily suppose that the real K
C;i trend is continuous and that the discontinuities in Fig. 4 correspond to mathematical artifacts only. It is for this reason that the max￾imum sustainable stress was only calculated approximately, equaling about 400 MPa. III. Experimental Procedure Ceramic laminates corresponding to the material designed in the previous section were produced and characterized. As previous￾ly pointed out, the thermal expansion coefficient as required for the development of the residual stress profile was tailored by considering composites in the alumina/mullite system for the production of the single laminae. The ceramic powders used in the present work are reported in Table II. a-alumina (ALCOA, Leetsdale, PA, A-16SG, D50 5 0.4 mm) was considered as the fundamental starting ma￾terial. High purity and fine mullite (KCM Corp., Nagoya, Japan, KM101, D50 5 0.77 mm) powder was chosen as the sec￾ond phase. Green laminae were produced by tape casting water-based slurries. Suspensions were prepared by using NH4-PMA (Dar￾van Cs R. T. Vanderbilt Inc., Norwalk, CT) as dispersant and acrylic emulsions (B-1235, DURAMAXs , Rohm & Haas, Philadelphia, PA) as binder. A lower-Tg acrylic emulsion (B￾AM0, 41µm AM20, 44µm AM30, 48µm AM40, 43µm AM20, 44µm AM10, 42µm AM0, 540 µm symmetry axis Fig. 3. Structure of the alumina/mullite multilayer designed and pro￾duced in the present work. The actual layers thickness and composition are reported (dimensions are not in scale). Table I. Materials Properties Used to Estimate the Stress Distribution and the Apparent Fracture Toughness Material E (GPa) n KC (MPa  m0.5) a (106 1C1 ) AM0 394 (14) 0.23 3.6 (0.2) 7.75 AM10 378–368 0.234–0.233 3.3 (0.2) 7.63 AM20 361–344 0.238–0.237 3.1 (0.3) 7.30 AM30 345–324 0.242–0.241 2.6 (0.2) 7.12 AM40 328–306 0.246–0.244 2.4 (0.2) 6.88 Numbers between parenthesis correspond to the standard deviation. Elastic modulus and Poisson’s ratio values correspond to calculated Voigt–Reuss bounds for AM10–AM40 composites. 2828 Journal of the American Ceramic Society—Sglavo et al. Vol. 88, No. 10

October 20 Tailored Residual Stresses in Ceramic laminates 2829 depth(um) the initial viscosity. After adding some drops of concentrated NH4OH to increase pH, suspensions were filtered through a 40 m polyethylene filter and de-aired using a low-vacuum Venturi pump to remove air entrapped during the milling stage Acrylic binder emulsion and plasticizer were then added to the dispersion and slowly mixed for 30 min to obtain the nec- essary homogeneity, applying great care to avoid the formation of new air bubbles. The final organic content was about 21 vol%. A similar preparation procedure was used for composite slurries, although some modifications of the dispersion process re introduced in order to obtain limited thixotropy and high fluidity. In this case, mullite powder was added after dispersing alumina for 16 h in the same conditions described for pure alu- mina and then ball milled for a further 24 h. All suspension were produced with a powder content of 39 vol %. It should be noted that the volume of powders in the first dispersing stage depth(um) was obviously higher, ranging from 49 to 51 vol%, as the ae 100 dition of the acrylic emulsions supplies also solvent(water )to the slurry and thus dilutes the system. Just before casting, slur ries were filtered again at 60 um to ensure the elimination of any bubbles or clusters of flocculated polymer. A flow chart of the overall process is shown in Fig. 5. Tape casting was conducted using a double doctor-blade as- 皇 sembly(DDB-1-6, 6 in wide, Richard E Mistler Inc, Yardley, PA)at a speed of I m/min for a length of about 1000 mm. A omposite three-layer film(PET12/Al7/LDPE60, BP Europack Vicenza, Italy) was used as a substrate in order to make the re- moval of the dried green tape easier. For this reason the poly ethylene hydrophobic side of the film was placed side-up. The (depth)o5(umo.5) substrate was placed on a rigid float glass sheet in order to en- sure a flat surface and properly fixed with adhesive tape to the sign residual stress profile(a) and corresponding apparent borders. The relative humidity of the over-standing environment was controlled and set to about 80% during casting and drying line shows the construction used for the calculation to avoid the excessively quick evaporation of the solvent and (σr≈400MPa) possible cracking of green tapes because of shrinkage stresses Casting of suspensions was performed using two different blade Table ll Ceramic powders used in this work heights, 250 and 100 um, respectively. Drops of a 10 wt% wet ting agent water solution (NHa-lauryl sulphate, code 09887 BET specific Purity Fluka Chemie AG, Buchs, Switzerland) were added to the slur- Material Code ries to help the casting tape spread on the substrate when re- - Ale O3 A-16SG. ALCOA 8.6 quired, particularly in the case of thinner tapes 3AlO32SiO2 KM1Ol, KCM 8.4 Green tapes of nominal dimension 60 mm x 45 mm wer punched using a hand-cutter, stacked together and thermo-com pressed at 70C using a pressure of 30 MPa for 15 min applied by a universal mechanical testing machine (MTS Systems minneapolis, MN, mod. 810). Two 100 um thick PET layers 1000, DURAMAX) was also added in 1: 2 by weight ratio with were placed between the laminate and the die to make the re- espect to the binder content as plasticizer to increase the green moval easier For the mechanical characterization bars of nom- flexibility and to reduce cracks occurrence in the dried tape. Th inal dimensions 60 mm x 7.5 mm 1.5 mm were cut after the organic ingredients used in this work are listed in Table lll. thermo-compression stage and then re-laminated2before ther The alumina powder suspension was obtained by using a two- mal treatment to avoid any delamination promoted by localized stage process. In order to enhance the electrostatic interaction shear stresses developed upon cutting between the positive charges on the powder surface and the Bars(6 mm x 48 mm) of the AM engineered composite were negative sites on the polymer chains, an initially slightly acid obtained after sintering. The edges were slightly chamfered to water solution (pH=4) was used. An optimum dispersant remove macroscopic defects and geometrical irregularities. No content equal to 1.5 wt% with respect to the powder was es- further polishing and finishing operations were performed on tablished by static sedimentation. This value corresponds to he sample surfaces or edges to avoid any artificial reduction of about 0. 4 mg/m of active matter per unit area, corresponding in he severity of flaws. Monolithic bars(thickness a 1.5 mm) turn to values suggested by greenwood et al.- for the same were produced in the same way for the measurement of thermal material. a ball milling stage using alumina spheres of 9 expansion coefficient, a, elastic modulus, E, and fracture tough mm nominal diameter was carried out in polyethylene bottles ness, Kc. The thermal expansion coefficient was measured in the for 16-24 h to break down all powder aggregates. The suspen range 30-1000.C by using a silica dilatometer and a heating sion was ultrasonicated for 10 min before ball milling to redu te of 2C/ lastic modulus was measured by four-points Table lll. Organic Ingredients Used for the Preparation of the Slurries NH4-PMA Darvan C.R.t. vanderbilt Inc Dispersant 7.5-90 High-Tg acrylic emulsion B-1235 DURAMAX Low-Tg acrylic emulsion B-1000, DURAMAX Plasticizer 55.0

1000, DURAMAXs ) was also added in 1:2 by weight ratio with respect to the binder content as plasticizer to increase the green flexibility and to reduce cracks occurrence in the dried tape. The organic ingredients used in this work are listed in Table III. The alumina powder suspension was obtained by using a two￾stage process.25 In order to enhance the electrostatic interaction between the positive charges on the powder surface and the negative sites on the polymer chains, an initially slightly acid water solution (pH 5 4) was used.26 An optimum dispersant content equal to 1.5 wt% with respect to the powder was es￾tablished by static sedimentation. This value corresponds to about 0.4 mg/m2 of active matter per unit area, corresponding in turn to values suggested by Greenwood et al. 27 for the same material. A ball milling stage using alumina spheres of 6 and 9 mm nominal diameter was carried out in polyethylene bottles for 16–24 h to break down all powder aggregates. The suspen￾sion was ultrasonicated for 10 min before ball milling to reduce the initial viscosity. After adding some drops of concentrated NH4OH to increase pH, suspensions were filtered through a 40 mm polyethylene filter and de-aired using a low-vacuum Venturi pump to remove air entrapped during the milling stage. Acrylic binder emulsion and plasticizer were then added to the dispersion and slowly mixed for 30 min to obtain the nec￾essary homogeneity, applying great care to avoid the formation of new air bubbles.28 The final organic content was about 21 vol%. A similar preparation procedure was used for composites slurries, although some modifications of the dispersion process were introduced in order to obtain limited thixotropy and high fluidity. In this case, mullite powder was added after dispersing alumina for 16 h in the same conditions described for pure alu￾mina and then ball milled for a further 24 h. All suspensions were produced with a powder content of 39 vol%. It should be noted that the volume of powders in the first dispersing stage was obviously higher, ranging from 49 to 51 vol%, as the ad￾dition of the acrylic emulsions supplies also solvent (water) to the slurry and thus dilutes the system. Just before casting, slur￾ries were filtered again at 60 mm to ensure the elimination of any bubbles or clusters of flocculated polymer. A flow chart of the overall process is shown in Fig. 5. Tape casting was conducted using a double doctor-blade as￾sembly (DDB-1-6, 6 in. wide, Richard E. Mistler Inc., Yardley, PA) at a speed of 1 m/min for a length of about 1000 mm. A composite three-layer film (PET12/Al7/LDPE60, BP Europack, Vicenza, Italy) was used as a substrate in order to make the re￾moval of the dried green tape easier. For this reason the poly￾ethylene hydrophobic side of the film was placed side-up. The substrate was placed on a rigid float glass sheet in order to en￾sure a flat surface and properly fixed with adhesive tape to the borders. The relative humidity of the over-standing environment was controlled and set to about 80% during casting and drying to avoid the excessively quick evaporation of the solvent and possible cracking of green tapes because of shrinkage stresses. Casting of suspensions was performed using two different blade heights, 250 and 100 mm, respectively. Drops of a 10 wt% wet￾ting agent water solution (NH4-lauryl sulphate, code 09887, Fluka Chemie AG, Buchs, Switzerland) were added to the slur￾ries to help the casting tape spread on the substrate when re￾quired, particularly 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-com￾pressed at 701C using a pressure of 30 MPa for 15 min applied by a universal mechanical testing machine (MTS Systems, Minneapolis, MN, mod. 810). Two 100 mm thick PET layers were placed between the laminate and the die to make the re￾moval easier. For the mechanical characterization bars of nom￾inal dimensions 60 mm  7.5 mm  1.5 mm were cut after the thermo-compression stage and then re-laminated29 before ther￾mal treatment to avoid any delamination promoted by localized shear stresses developed upon cutting. Bars (6 mm  48 mm) of the AM engineered composite were obtained after sintering. The edges were slightly chamfered to remove macroscopic defects and geometrical irregularities. No further polishing and finishing operations were performed on the sample surfaces or edges to avoid any artificial reduction of the severity of flaws. 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 tough￾ness, KC. The thermal expansion coefficient was measured in the range 301–10001C by using a silica dilatometer and a heating rate of 21C/min. Elastic modulus was measured by four-points − 400 − 300 − 200 − 100 0 100 200 0 5 10 15 20 25 residual stress, σres (MPa) (depth)0.5 (µm0.5) 0 5 10 15 20 25 (depth)0.5 (µm0.5) 20 100 400 50 200 depth (µm) 0 2 4 6 8 10 12 apparent fracture toughness, KC (MPa m0.5) 20 100 400 50 200 (b) depth (µm) (a) * Fig. 4. Design residual stress profile (a) and corresponding apparent fracture toughness (b) for the monolithic engineered laminate. The dashed tangent line shows the construction used for the calculation of the failure stress (sf 400 MPa). Table II. Ceramic Powders Used in this Work Material Code, producer BET specific area (m2 /g) Purity (%) a-Al2O3 A-16SG, ALCOA 8.6 499.8 3Al2O3  2SiO2 KM101, KCM Corp. 8.4 499.7 Table III. Organic Ingredients Used for the Preparation of the Slurries Substance Name, producer Function Tg (1C) pH Active matter (wt%) NH4-PMA Darvan Cs , R. T. Vanderbilt Inc. Dispersant 7.5–9.0 25.0 High-Tg acrylic emulsion B-1235, DURAMAXs Binder 14 8.3 46.5 Low-Tg acrylic emulsion B-1000, DURAMAXs Plasticizer 26 9.4 55.0 October 2005 Tailored Residual Stresses in Ceramic Laminates 2829

2830 Journal of the American Ceramic Society-Sglavo et al. VoL. 88. No. 10 Table IV. Mechanical Properties of the Engineered AM powder, water, dispersant Laminate and Monolithic Alumina ng pH control Monolithic alumina 418+45 2.1±0.8 Engineered AM laminate 457±32 17.0±1.1 ball milling The average bending strength measured on the engineered filtering AM laminates is equal to 458 and the standard deviation is 32 MPa, corresponding to a coefficient of variation of 6.9%. The de-airing binder emulsion Average bending strength of the monolithic samples(AMO) is 45 MPa has been calculated and this corresponds to a coefficient of variation of 10.9%. One can easily observe that the strengt values measured on the AM laminate represent a clear indica suspension tion of a reliable ("constant") failure stress. The average strength is slightly greater than the design value( 400 MPa) for the engineered AM laminate, which, conversely, is in opti contro um conformity with the minimum measured strength value equal to 405 MPa. This effect is probably related to the fact that slow-mixing and homogeNize large surface cracks experience some stable growth before final catastrophic propagation while smaller flaws, not included in the stability range identified in Fig 4, lead to immediate failure at higher applied stresses. In any case, the obtained results confirm the reliability of the material, correlated with a designed strength that corresponds to a minimum failure resistance. One furthe comment regards the unusual greater strength of AM composite slurry ready to cast compared with alumina monolith, although in the former the surface is subjected to a tension of a 80 MPa and both mate- rials have an AlO3 surface. This effect is correlated with the ig his worlw chart of the two-stages surry preparaton procedure used specific shape of the kc, curve(Fig. 4(b)with respect to the final failure bending tests(spans equal to 40 and 20 mm) by using a cali- The strength variability in brittle materials is often described brated extensometer (MTS Systems)to measure the deflection as by the Weibull modulus, which is a stress exponent that de- a function of applied load. Fracture toughness was determined scribes the relation between failure probability and the applied by the conventional indentation fracture method. The length, c, stress. On the basis of Fig 6, Weibull modulus equal to 12. 1+0.8 of radial cracks produced by vickers indentations(maximum has been calculated for AMo monolithic laminate. which is sim- load P=49 N)was measured and Kc was calculated with the ilar to other advanced ceramic materials. For the engineered following equation AM laminate Weibull modulus equal to 17.0+1. I was obtained and this clearly underlines again the high reliability of the en- Kc=0.016(E/H)03 (9) gineered composite material. It is clear again that if the flaw size pulation was completely included in the stability range iden- tified in Fig 4 higher Weibull modulus could have been where H is the vickers hardness btained urteen samples were broken by four-points bending tests Figure 6 shows the strength of indented samples as a function n order to establish the invariance of strength with flaw size of indentation load. It is clear that the failure stress of engi- some specimens were also pre-cracked by Vickers indentation neered AM laminates is independent from the initial flaw size using loads ranging from 10 to 100 N. Three indentations were produced in the center of the perspective tensile surface. AMO amples were also produced and tested in the same conditions for comparison. Results and discussion 合0 F monolith(AMC The mechanical properties of the engineered AM laminate are mpared with those of the monolithic alumina in Table IV and in the Weibull diagram shown in Fig. 6. The proposed compar- ison is thought to be effective since the surface layer of the en- gineered laminated is made by pure alumina and is subjected to quite small tensile stresses. For the construction of the Weibul diagram(Fig. 6), the failure probability was calculated as s0-=d 5.85.96.06.16.26.3 re n and N represent the rank in the ascending ordere I diagram for the engineered laminate(AM)an AMO). Straight lines represent fitting curves use ngth distribution and the total number of specimens, respec- Weibull modulus. Raw strength data(in MPa

bending tests (spans equal to 40 and 20 mm) by using a cali￾brated extensometer (MTS Systems) to measure the deflection as a function of applied load. Fracture toughness was determined by the conventional indentation fracture method. The length, c, of radial cracks produced by Vickers indentations (maximum load, P 5 49 N) was measured and KC was calculated with the following equation:30 KC ¼ 0:016 ð Þ E=H 0:5 P c1:5 (9) where H is the Vickers hardness. Fourteen samples were broken by four-points bending tests. In order to establish the invariance of strength with 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 center of the perspective tensile surface. AM0 samples were also produced and tested in the same conditions for comparison. IV. Results and Discussion The mechanical properties of the engineered AM laminate are compared with those of the monolithic alumina in Table IV and in the Weibull diagram shown in Fig. 6. The proposed compar￾ison is thought to be effective since the surface layer of the en￾gineered laminated is made by pure alumina and is subjected to quite small tensile stresses. For the construction of the Weibull diagram (Fig. 6), the failure probability was calculated as: F ¼ n 0:5 N (10) where n and N represent the rank in the ascending ordered strength distribution and the total number of specimens, respec￾tively.17 The average bending strength measured on the engineered AM laminates is equal to 458 and the standard deviation is 32 MPa, corresponding to a coefficient of variation of 6.9%. The average bending strength of the monolithic samples (AM0) is equal to 418 MPa. More interestingly, a standard deviation of 45 MPa has been calculated and this corresponds to a coefficient of variation of 10.9%. One can easily observe that the strength values measured on the AM laminate represent a clear indica￾tion of a reliable (‘‘constant’’) failure stress. The average strength is slightly greater than the design value ( 400 MPa) for the engineered AM laminate, which, conversely, is in opti￾mum conformity with the minimum measured strength value, equal to 405 MPa. This effect is probably related to the fact that large surface cracks experience some stable growth before final catastrophic propagation while smaller flaws, not included in the stability range identified in Fig. 4, lead to immediate failure at higher applied stresses. In any case, the obtained results confirm the reliability of the material, correlated with a designed strength that corresponds to a minimum failure resistance. One further comment regards the unusual greater strength of AM composite compared with alumina monolith, although in the former the surface is subjected to a tension of 80 MPa and both mate￾rials have an Al2O3 surface. This effect is correlated with the specific shape of the K
C;i curve (Fig. 4(b)) with respect to the initial flaws and to the presence of crack stable growth before final failure. The strength variability in brittle materials is often described by the Weibull modulus, which is a stress exponent that de￾scribes the relation between failure probability and the applied stress. On the basis of Fig 6, Weibull modulus equal to 12.170.8 has been calculated for AM0 monolithic laminate, which is sim￾ilar to other advanced ceramic materials. For the engineered AM laminate Weibull modulus equal to 17.071.1 was obtained and this clearly underlines again the high reliability of the en￾gineered composite material. It is clear again that if the flaw size population was completely included in the stability range iden￾tified in Fig. 4 an even higher Weibull modulus could have been obtained. Figure 6 shows the strength of indented samples as a function of indentation load. It is clear that the failure stress of engi￾neered AM laminates is independent from the initial flaw size powder, water, dispersant ultrasonicating ball milling filtering de-airing slow-mixing and homogenizing filtering suspension slurry ready to cast pH control pH control binder emulsion Stage I Stage II Fig. 5. Flow chart of the two-stages slurry preparation procedure used in this work. − 4 − 3 − 2 − 1 0 1 2 5.8 5.9 6.0 6.1 6.2 6.3 6.4 ln ln (1/(1-F)) ln σf (ln MPa) engineered laminate (AM) monolith (AM0) Fig. 6. Weibull diagram for the engineered laminate (AM) and mon￾olithic sample (AM0). Straight lines represent fitting curves used for the evaluation of the Weibull modulus. Raw strength data (in MPa) for the two materials are reported in the inserted table. Table IV. Mechanical Properties of the Engineered AM Laminate and Monolithic Alumina sf (MPa) m Monolithic alumina 418745 12.170.8 Engineered AM laminate 457732 17.071.1 2830 Journal of the American Ceramic Society—Sglavo et al. Vol. 88, No. 10

October 2005 Tailored Residual Stresses in Ceramic laminates engineered laminate(AM) 450 wM 15 monolith(AMO 1 mm 100 Fig. 7. Failure stress data as function of the indentation load for the engineered laminates(AM)and monolithic samples(AMO). Each point Fig 9. Optical micrographs showing the typical fracture surface of ar corresponds to the average of five samples. Straight lines correspond te linear fitting curves in the log-log diagram. indicate the surface faw where fracture initiated the black arrows indi- cate the arrested crack in the engineered laminate while, as expected, the strength of monolithic laminates is relat- that the material shows also some warning before final failur d to the indentation load as described by This phenomenon is quite unusual in brittle materials. Figure 9 shows the typical fracture surface of an engineered or pl The markings on the fracture surface show that the surface e (11) AM laminate compared with that of a ceramic monolith(AM where k, in the specific case, calculated by linear fitting (in the extended at first along the surface, being arrested by the engi- log-log diagram), is equal to 0.28, corresponding closely to the peered residual stress profile in the in-depth propagation; then, theoretical value(N 0.3 after this stable growth stage only, the through-thickness notch To further emphasize this point becomes unstable and leads to the sample failure. Conversely one should note also that the strength of indented AM laminates corresponds closely to the design value( a 400 MPa). From the growth of surface cracks in the ceramic monolith is typically Fig. 7, it appears surprising that the standard deviation of n as the critical load is reached figure 9 shows strength for indented alumina samples is smaller than for AM also the perfect adhesion of the various layers both in the whole- composites; such a result can be probably related in part to the alumina and in the engineered laminate indicating a satisfacto- limited number of samples(five)tested at each indentation load rily implemented thermo-compression and sintering process. In although further investigations are certainly needed addition, detailed observations did not reveal any delamination The presence of stable crack growth phenomena was ob- effect. By comparing Figs 8 and 9 it should be noted that orig- served in the engineered AM laminates. Samples subjected to inal surface flaws, natural or produced by indentation, propa- bending loads exhibited in fact multiple cracking before final gate along the tensile surface and arrest at around the same failure. i.e. several cracks are formed on the tensile surface of depth. Any of the resulting through-thickness cracks can then he sample above a specific threshold stress( a 200 MPa). Such lead to ultimate failure, this specific event being therefore racks are arrested or undergo stable growth and only one lead onger related to the initial faw size to the failure of the body. Figure 8 shows clearly that surface stable cracks derive either from indentation faws or surface pores; interestingly, the critical fracture does not necessarily V. Conclusions start from the larger indentation flaws. Such behavior indicates This study shows that it is possible to produce highly reliable ceramic materials whose"" strength can be a priori de fined and controlled through an innovative design procedi arrested cracks 1 mm The material can be also designed to support bending loads more efficiently than homogeneous materials, since the material is improved only where required, i.e., near the surface In the present work ceramic laminates composed of alumina/ mullite composite layers have been designed to possess strength equal to A 400 MPa and to promote the stable growth of cracks as deep as 180 um. The material has been then produced by stacking and sintering together laminae obtained by tape asting. The engineered composite showed strength is equal to 458+32 MPa thus confirming the validity of the experimental approach adopted. The stable growth of surface cracks, deriving either from natural defects and indentation flaws has also been observe indentation precrack The laminated bodies here presented are therefore natural andidates for structural applications, particularly when high mechanical reliability and damage tolerance in severe conditions re required, as in the case of load-bearing components in the Fig 8. Optical micrograph showing the arrested cracks produced upo automotive and aircraft industries, biomedical prostheses, chem- ending on indented alt ical plant linings and safety systems even when more complex d=100N shapes like plates, shells or tubes are required

while, as expected, the strength of monolithic laminates is relat￾ed to the indentation load as described by: sf Pk ¼ constant (11) where k, in the specific case, calculated by linear fitting (in the log-log diagram), is equal to 0.28, corresponding closely to the theoretical value ( 0.33).1,17 To further emphasize this point one should note also that the strength of indented AM laminates corresponds closely to the design value ( 400 MPa). From Fig. 7, it appears surprising that the standard deviation of strength for indented alumina samples is smaller than for AM composites; such a result can be probably related in part to the limited number of samples (five) tested at each indentation load although further investigations are certainly needed. The presence of stable crack growth phenomena was ob￾served in the engineered AM laminates. Samples subjected to bending loads exhibited in fact multiple cracking before final failure, i.e., several cracks are formed on the tensile surface of the sample above a specific threshold stress ( 200 MPa). Such cracks are arrested or undergo stable growth and only one leads to the failure of the body. Figure 8 shows clearly that surface stable cracks derive either from indentation flaws or surface pores; interestingly, the critical fracture does not necessarily start from the larger indentation flaws. Such behavior indicates that the material shows also some warning before final failure. This phenomenon is quite unusual in brittle materials. Figure 9 shows the typical fracture surface of an engineered AM laminate compared with that of a ceramic monolith (AM0). The markings on the fracture surface show that the surface flaw, extended at first along the surface, being arrested by the engi￾neered residual stress profile in the in-depth propagation; then, after this stable growth stage only, the through-thickness notch becomes unstable and leads to the sample failure. Conversely, the growth of surface cracks in the ceramic monolith is typically unstable as soon as the critical load is reached. Figure 9 shows also the perfect adhesion of the various layers both in the whole￾alumina and in the engineered laminate indicating a satisfacto￾rily implemented thermo-compression and sintering process. In addition, detailed observations did not reveal any delamination effect. By comparing Figs 8 and 9 it should be noted that orig￾inal surface flaws, natural or produced by indentation, propa￾gate along the tensile surface and arrest at around the same depth. Any of the resulting through-thickness cracks can then lead to ultimate failure, this specific event being therefore no longer related to the initial flaw size. V. Conclusions This study shows that it is possible to produce highly reliable ceramic materials whose ‘‘constant’’ strength can be a priori de- fined and controlled through an innovative design procedure. The material can be also designed to support bending loads more efficiently than homogeneous materials, since the material is improved only where required, i.e., near the surface. In the present work ceramic laminates composed of alumina/ mullite composite layers have been designed to possess strength equal to 400 MPa and to promote the stable growth of cracks as deep as 180 mm. The material has been then produced by stacking and sintering together laminae obtained by tape casting. The engineered composite showed strength is equal to 458732 MPa thus confirming the validity of the experimental approach adopted. The stable growth of surface cracks, deriving either from natural defects and indentation flaws, has also been observed. The laminated bodies here presented 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 industries, biomedical prostheses, chem￾ical plant linings and safety systems even when more complex shapes like plates, shells or tubes are required. 0 150 300 450 600 10 100 failure stress, σf (MPa) indentation load (N) engineered laminate (AM) monolith (AM0) Fig. 7. Failure stress data as function of the indentation load for the engineered laminates (AM) and monolithic samples (AM0). Each point corresponds to the average of five samples. Straight lines correspond to linear fitting curves in the log–log diagram. Fig. 8. Optical micrograph showing the arrested cracks produced upon bending on indented alumina monolithic specimen (indentation load 5 100 N). Fig. 9. Optical micrographs showing the typical fracture surface of an engineered laminate (a) and of a ceramic monolith (b). The white arrows indicate the surface flaw where fracture initiated; the black arrows indi￾cate the arrested crack in the engineered laminate. October 2005 Tailored Residual Stresses in Ceramic Laminates 2831

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