Availableonlineatwww.sciencedirect.com Science Direct E噩≈RS ELSEVIER Joumal of the European Ceramic Society 28(2008)1575-1583 www.elsevier.com/locate/jeurceramsoc Optimal strength and toughness of Al2O3-Zro2 laminates designed with external or internal compressive layers Raul bermejo Javier Pascual, Tanja Lube, Robert Danzer Institut fiir Struktur- und Funktionskeramik, Montanuniversitdr Leoben, Peter-Tiunner StraBe 5. A-8700 Leoben, austria Received 25 July 2007; received in revised form 25 October 2007; accepted 2 November 2007 Available online 4 March 2008 Abstract Layered ceramics have been proposed as an alternative choice for the design of structural ceramics with improved fracture toughness, strength and reliability. The use of residual compressive stresses, either at the surface or in the intermal layers, may improve the strength as well as the crack resistance of the material during crack growth. In this work, two alumina-zirconia laminates designed with external(ECs-laminates)and internal (ICS-laminates) compressive stresses have been investigated using a fracture mechanics weight function analysis. An optimal architecture that naximises material toughness and strength has been found for each design as a function of geometry. From a flaw tolerant viewpoint, ECS-laminates are suitable for ceramic components with small cracks or flaws which are embedded in or near the potential tensile surface of the piece On the other hand, the existence of large cracks or defects suggests the use of ICS-laminates to attain a more reliable response o 2007 Elsevier Ltd. All rights reserved. Keywords: Composites: Toughness and toughening: Strength; AlO3-ZrO2: Weight function 1. ntroduction ing crack growth resistance, i.e. R-curve behaviour. Ceramics that exhibit this behaviour can show not only reduced scat- The increased number of engineering design constraints, ter in fracture strength(higher reliability) but also, in some driven by the growing product requirements, as well as the cases, higher fracture loads compared to brittle materials with greater range of advanced materials now available face the no crack-growth resistance. A commonly used multilayer design designer with complex choices for selecting a material to meet is that which combines layers with different densification dur the performance of a particular system. The outcome of com- ing cooling from the sintering temperature, yielding as a result petition between various classes of materials is given not only a tensile-compressive residual stress distribution in the lami- by the combination of their intrinsic properties but also by the nate. The specific location of the compressive layers, either at processing capability that they may offer for being tailored for the surface or internal, is associated with the attempted design pecific tasks. The development and implementation of multilay- approach, based on either mechanical resistance or damage ered ceramics for structural applications is an excellent example tolerance, respectively. In the former case, the effect of the com- of the above design and material selection approach.-+ pressive residual stresses results in a higher, but single-value, Layered ceramic composites have been proposed as an alter- apparent fracture toughness together with enhanced strength native design to enhance the strength reliability of ceramic(the goal) and some improved reliability. -On the components as well as to improve their fracture toughness by other hand, in the latter case, the internal compressive layers means of energy release mechanisms, such as crack deflection are microstructurally designed to rather act as stopper of any or crack bifurcation. -10 A direct consequence of these energy- potential processing and/or machining flaw at the surface lay dissipating toughening mechanisms, which reduce the crack ers, independent of original defect size(threshold strength), such driving force at the crack tip, is the development of an increas- that failure tends to take place under conditions of maximum crack growth resistance. - From this viewpoint, much effort has been put in the fabrication of laminates with a tailored resid- Corresponding author. Tel: +43 4115: fax: +43 38424024102. ual stress profile arising from mismatch of elastic properties and E-mail address: raul bermejo @ mu-leoben at(R. Bermejo). hermal expansion coefficients between layers, selective phase 0955-2219/S-see front matter o 2007 Elsevier Ltd. All rights reserved. doi: 10.1016/j-jeurceramsoc20071 1.003
Available online at www.sciencedirect.com Journal of the European Ceramic Society 28 (2008) 1575–1583 Optimal strength and toughness of Al2O3–ZrO2 laminates designed with external or internal compressive layers Raul Bermejo ´ ∗, Javier Pascual, Tanja Lube, Robert Danzer Institut f ¨ur Struktur- und Funktionskeramik, Montanuniversit ¨at Leoben, Peter-Tunner Straße 5, A-8700 Leoben, Austria Received 25 July 2007; received in revised form 25 October 2007; accepted 2 November 2007 Available online 4 March 2008 Abstract Layered ceramics have been proposed as an alternative choice for the design of structural ceramics with improved fracture toughness, strength and reliability. The use of residual compressive stresses, either at the surface or in the internal layers, may improve the strength as well as the crack resistance of the material during crack growth. In this work, two alumina–zirconia laminates designed with external (ECS-laminates) and internal (ICS-laminates) compressive stresses have been investigated using a fracture mechanics weight function analysis. An optimal architecture that maximises material toughness and strength has been found for each design as a function of geometry. From a flaw tolerant viewpoint, ECS-laminates are suitable for ceramic components with small cracks or flaws which are embedded in or near the potential tensile surface of the piece. On the other hand, the existence of large cracks or defects suggests the use of ICS-laminates to attain a more reliable response. © 2007 Elsevier Ltd. All rights reserved. Keywords: Composites; Toughness and toughening; Strength; Al2O3–ZrO2; Weight function 1. Introduction The increased number of engineering design constraints, driven by the growing product requirements, as well as the greater range of advanced materials now available face the designer with complex choices for selecting a material to meet the performance of a particular system. The outcome of competition between various classes of materials is given not only by the combination of their intrinsic properties but also by the processing capability that they may offer for being tailored for specific tasks. The development and implementation of multilayered ceramics for structural applications is an excellent example of the above design and material selection approach.1–4 Layered ceramic composites have been proposed as an alternative design to enhance the strength reliability of ceramic components as well as to improve their fracture toughness by means of energy release mechanisms, such as crack deflection or crack bifurcation.5–10 A direct consequence of these energydissipating toughening mechanisms, which reduce the crack driving force at the crack tip, is the development of an increas- ∗ Corresponding author. Tel.: +43 3842 402 4115; fax: +43 3842 402 4102. E-mail address: raul.bermejo@mu-leoben.at (R. Bermejo). ing crack growth resistance, i.e. R-curve behaviour. Ceramics that exhibit this behaviour can show not only reduced scatter in fracture strength (higher reliability) but also, in some cases, higher fracture loads compared to brittle materials with no crack-growth resistance. A commonly used multilayer design is that which combines layers with different densification during cooling from the sintering temperature, yielding as a result a tensile-compressive residual stress distribution in the laminate. The specific location of the compressive layers, either at the surface or internal, is associated with the attempted design approach, based on either mechanical resistance or damage tolerance, respectively. In the former case, the effect of the compressive residual stresses results in a higher, but single-value, apparent fracture toughness together with enhanced strength (the main goal) and some improved reliability.11–13 On the other hand, in the latter case, the internal compressive layers are microstructurally designed to rather act as stopper of any potential processing and/or machining flaw at the surface layers, independent of original defect size (threshold strength), such that failure tends to take place under conditions of maximum crack growth resistance.14–17 From this viewpoint, much effort has been put in the fabrication of laminates with a tailored residual stress profile arising from mismatch of elastic properties and thermal expansion coefficients between layers, selective phase 0955-2219/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2007.11.003
R. Bermejo et al. / Journal of the European Ceramic Sociery 28(2008)1575-1583 b AZ 200pm Fig. 1. Cross-section detail of the two alumina-zirconia layered architectures investigated, designed with(a)external compressive layers(ECS-laminates)and (b) internal compressive layers (ICS-laminates) transformation and/or chemical reactions. 18-20 Within this con- sion, a, by means of a dilatometer between 20 and 1200C text, alumina-zirconia layered systems have been extensively and the intrinsic toughness Ko following the VAMAS procedure investigated as an alternative route for enhancing the mechani-(single-edge -V-notch beam in four-point bending test).29, 30 cal response of alumina-based monolithic ceramics in terms of strength and/or fracture 19,21-26 2.2. Residual stresses e aim of this work is to optimise the architectural design of ceramic multilayered systems as a function of its potential appli As a result of the thermo-elastic mismatch between adjacent cation. In doing so, two alumina-zirconia systems designed with layers occurring during sintering, a uniform and biaxial resid external or internal compressive stresses respectively are com- ual stress distribution parallel to the layer plane appears in the pared using a fracture mechanics weight function analysis. An laminate far away from the free surfaces(Fig. 1). For the case example of such layered architectures can be seen in Fig. 1, of ECS-laminates the thermal mismatch between layers is given where tailored residual compressive stresses were introduced in by the different thermal expansion capability of the Az layers the laminates during sintering, either in the surface layers or with respect to the A layers, due to the zirconia content of the in the internal ones. The material designed with external com- former. On the other hand for the ICs-laminates the significant ressive stresses, named ECS-laminate, consists of alternated thermal mismatch between adjacent layers is associated with tape cast sheets of alumina/stabilised-zirconia(AZ) compos- the zirconia phase transformation occurring in the AMZ layers te and sheets of pure-alumina(A), following the sequence during cooling down from sintering. The magnitude of these /AZIA..... A/AZ/A 27 The material fabricated with internal residual stresses can be assessed by I compressive stresses, referred to as ICS-laminate, is made of alumina/pure-zirconia(AMZ) layers sequentially slip cast with s△adT alumina/stabilised-zirconia(ATZ) layers as ATZIAMZATZ res, int=-E [1+(N-1)/(N+1)](e/) ATZIAMZ/ATZ 28 An optimal architecture that maximises both material tough- Ores,ext --Ores, int (N +1) ness and strength is sought for each layered design as a function of its layer thickness ratio. The influence of elastic properties where E=E/(1-v),v being the Poissons ratio, and number of layers is also discussed Aa=(aext-aint) is the difference of the thermal expan- sion coefficients between two adjacent layers, Tsf is the 2. Experimental procedure temperature below which the residual stresses arise(considered to be 1200C), To is the room temperature, and e= Eext/E 2.1 Laminates of study It is known that the residual stress state associated with the above-mentioned parameters may condition the crack growth In this work, symmetrical laminates fabricated with nine alternated layers and a fixed total thickness of w=3 mm, accord- Table 1 ing to a possible design condition, were studied. All the layers Material properties corresponding to the layers of both ECS-and ICS-laminates made of the same material(A, Az, ATZ or AMZ, respectively) Material E(GPa) v &(10-6K-)(20-1200C) Ko(MPam/2 have the same thickness, so that the laminate is well defined by the number of layers, N, and the layer thickness ratio, A =tin/text. AZ 0.248.64 3.8 305 The indexes"ext"and"int refer to the external and first internal 0.269.24 ATZ 9.82 layer for each case. Table 1 summarises the material proper- AMZ 280 0.228.02a ties corresponding to the layers of both laminates, where the The low thermal oung's modulus, E, and Poissons ratio, v, were measured by associated with the t-m zirconia phase transformation in the AMZ layers impulse excitation technique, the coefficient of thermal expan- during cooli
1576 R. Bermejo et al. / Journal of the European Ceramic Society 28 (2008) 1575–1583 Fig. 1. Cross-section detail of the two alumina–zirconia layered architectures investigated, designed with (a) external compressive layers (ECS-laminates) and (b) internal compressive layers (ICS-laminates). transformation and/or chemical reactions.18–20 Within this context, alumina–zirconia layered systems have been extensively investigated as an alternative route for enhancing the mechanical response of alumina-based monolithic ceramics in terms of strength and/or fracture toughness.19,21–26 The aim of this work is to optimise the architectural design of ceramic multilayered systems as a function of its potential application. In doing so, two alumina–zirconia systems designed with external or internal compressive stresses respectively are compared using a fracture mechanics weight function analysis. An example of such layered architectures can be seen in Fig. 1, where tailored residual compressive stresses were introduced in the laminates during sintering, either in the surface layers or in the internal ones. The material designed with external compressive stresses, named ECS-laminate, consists of alternated tape cast sheets of alumina/stabilised-zirconia (AZ) composite and sheets of pure-alumina (A), following the sequence A/AZ/A, ..., A/AZ/A.27 The material fabricated with internal compressive stresses, referred to as ICS-laminate, is made of alumina/pure-zirconia (AMZ) layers sequentially slip cast with alumina/stabilised-zirconia (ATZ) layers as ATZ/AMZ/ATZ, ..., ATZ/AMZ/ATZ.28 An optimal architecture that maximises both material toughness and strength is sought for each layered design as a function of its layer thickness ratio. The influence of elastic properties and number of layers is also discussed. 2. Experimental procedure 2.1. Laminates of study In this work, symmetrical laminates fabricated with nine alternated layers and a fixed total thickness of W = 3 mm, according to a possible design condition, were studied. All the layers made of the same material (A, AZ, ATZ or AMZ, respectively) have the same thickness, so that the laminate is well defined by the number of layers, N, and the layer thickness ratio, λ = tint/text. The indexes “ext” and “int” refer to the external and first internal layer for each case. Table 1 summarises the material properties corresponding to the layers of both laminates, where the Young’s modulus, E, and Poisson’s ratio, ν, were measured by impulse excitation technique, the coefficient of thermal expansion, α, by means of a dilatometer between 20 and 1200 ◦C and the intrinsic toughness K0 following the VAMAS procedure (single-edge-V-notch beam in four-point bending test).29,30 2.2. Residual stresses As a result of the thermo-elastic mismatch between adjacent layers occurring during sintering, a uniform and biaxial residual stress distribution parallel to the layer plane appears in the laminate far away from the free surfaces (Fig. 1). For the case of ECS-laminates the thermal mismatch between layers is given by the different thermal expansion capability of the AZ layers with respect to the A layers, due to the zirconia content of the former. On the other hand for the ICS-laminates the significant thermal mismatch between adjacent layers is associated with the zirconia phase transformation occurring in the AMZ layers during cooling down from sintering.28 The magnitude of these residual stresses can be assessed by31: σres,int = −E int Tsf T0 α dT [1 + (N − 1)/(N + 1)](e/λ) (1a) σres,ext = −σres,int (N − 1) (N + 1) λ (1b) where E = E/(1 − ν), ν being the Poisson’s ratio, α = (αext − αint) is the difference of the thermal expansion coefficients between two adjacent layers, Tsf is the temperature below which the residual stresses arise (considered to be 1200 ◦C), T0 is the room temperature, and e = E ext/E int. It is known that the residual stress state associated with the above-mentioned parameters may condition the crack growth Table 1 Material properties corresponding to the layers of both ECS- and ICS-laminates Material E (GPa) ν α¯ (10−6 K−1) (20–1200 ◦C) K0 (MPa m1/2) A 391 0.24 8.64 3.8 AZ 305 0.26 9.24 4.3 ATZ 390 0.22 9.82 3.2 AMZ 280 0.22 8.02a 2.6 a The low thermal expansion coefficient value is due to the volume increase associated with the t→m zirconia phase transformation in the AMZ layers during cooling28.
R. Bermejo et al. /Journal of the European Ceramic Society 28(2008)1575-1583 resistance of the multilayered system. 4-16. 23,24 In this work, Table 2 the layer thickness ratio() will be the parameter of study. a Weight function coefficients (Arp)for a 3-point bend bar determined by the fracture mechanics analysis will be performed to optimise the fracture response for each design H=3 132 3272 18.12 -12.64 The apparent fracture toughness of a laminate with a residual stress distribution can be calculated considering the equilibrium condition at the crack tip, i.e. crack propagation is possible if the ICS-laminates and in the A layers of the ECS-laminates, the stress intensity factor at the crack tip equals or exceeds the owed to the lower stiffness of the adjacent AMZ and AZ lay- residual stresses, the stress intensity factor at the crack tip as a bee respectively. 35.36 In this regard, an alternative procedure has intrinsic material toughness, Ko. In the case of materials with en proposed elsewhere, 3 to predict in a more accurate way the function of the crack length, Ktip(a), can be given as the exter- fracture toughness of multilayered ceramics whose layers have nally applied stress intensity factor Kappl (a)plus the contribution is beyond the scope of this work. The apparent fracture toughness, KR(a), was calculated Ktip(a)=Kapp(a)+ kres(a) (2) according to the procedure explained above, integrating Eq (4) Thus, solving Eq (2)for Kappl(a), the crack propagation criterion by means of analytical software Mathematica.5. 1. The influ- is fulfilled when ence of the different residual stress states, given by the layer thickness ratio(), on the apparent fracture toughness of the Kappl(a)> Ko- kres(a)=Kr(a) (3) laminates has been examined in detail aiming to obtain archi- lectures which yield the maximum shielding effect. within this The term Kres(a) can be assessed by means of the weight context, a linear elastic fracture mechanics analysis based on function approach, which allows us to calculate the apparent experimental flexural tests has also been implemented in order toughness KR(a) for an edge crack of length a for an arbitrary to provide an optimal design combining toughness and strength stress distribution acting normal to the prospective fracture path The results are expressed for both ECS and ICS layered system KR(a)=Ko- h(x, a)ores(r)d (4) 3. Results and discussion where Ko is the intrinsic fracture toughness of each individual 3.. Layer thickness ratio for maximum shielding mmer (given in Table 1), x is the distance along the crack length measured from the surface, a is the crack length, and h(a, r)is he apparent fracture toughness for different the weight function, as developed by Fett 'for an edge crack in layer thickness ratios(.)in the layered architectures designed a 3-point bend bar, commonly employed in the evaluation of the with external(Fig 2a)and internal(Fig. 2b) compressive layers, R-curve behaviour for multilayered systems. The corresponding as a function of a crack length parameter a, expressed as Y, with y defined for an edge in a crack 3-point bend bar and given h(a, x)= ma)(1-x/a)/2(1-a/W)/ Y(6-[1.99-8(1-8(215-3938+2782) (1+28)(1-8)312 d≈a As it can be inferred from Eq (1), the architectural parameter where Wis the specimen thickness, and the coefficients Awu and toughness is represented for different values of A(until the crack exponents v and u determined using the"boundary collocation length a being approximately half of the specimen thickness)in method"34 are listed in Table 2. We caution the reader about order to determine the geometry that provides the maximum the fact that a weight function that applies to a homogeneous shielding in both laminates material(with constant elastic properties)has been here con- As shown by previous authors the apparent toughness curves idered. This approximation may lead to an overestimation of of multilayers show an oscillating behaviour. 2,24,39-4 For the the calculated apparent fracture toughness in the ATZ layers of laminates with external compressive residual stresses, ECS laminates, the toughness increases in the external layers with I In this paper, edge crack refers to a straight crack running from the tensile Increasing crack length and reaches a local maximum at the urface of the laminate normal to the layer plane. It should not be confused A/AZ interface, whereas it decreases in the tensile layers with edge cracking phenomena occurring in some laminates due to the residual reaching a local minimum at the AZ/A interface. For the ics- stresses laminates toughness decreases within the external layer up to the
R. Bermejo et al. / Journal of the European Ceramic Society 28 (2008) 1575–1583 1577 resistance of the multilayered system.14–16,23,24 In this work, the layer thickness ratio (λ) will be the parameter of study. A fracture mechanics analysis will be performed to optimise the fracture response for each design. 2.3. Weight function analysis The apparent fracture toughness of a laminate with a residual stress distribution can be calculated considering the equilibrium condition at the crack tip, i.e. crack propagation is possible if the stress intensity factor at the crack tip equals or exceeds the intrinsic material toughness, K0. In the case of materials with residual stresses, the stress intensity factor at the crack tip as a function of the crack length, Ktip(a), can be given as the externally applied stress intensity factorKappl(a) plus the contribution of the residual stresses Kres(a): Ktip(a) = Kappl(a) + Kres(a) (2) Thus, solving Eq.(2)forKappl(a), the crack propagation criterion is fulfilled when: Kappl(a) ≥ K0 − Kres(a) = KR(a) (3) The term Kres(a) can be assessed by means of the weight function approach, which allows us to calculate the apparent toughness KR(a) for an edge crack1 of length a for an arbitrary stress distribution acting normal to the prospective fracture path as33: KR(a) = K0 − a 0 h(x, a)σres(x) dx (4) where K0 is the intrinsic fracture toughness of each individual layer (given in Table 1), x is the distance along the crack length measured from the surface, a is the crack length, and h(a,x) is the weight function, as developed by Fett34 for an edge crack in a 3-point bend bar, commonly employed in the evaluation of the R-curve behaviour for multilayered systems. The corresponding weight function is given by h(a, x) = 2 a 1/2 1 (1 − x/a) 1/2(1 − a/W) 3/2 × 1 − a W 3/2 + Aνμ 1 − x a ν+1 a W μ (5) where W is the specimen thickness, and the coefficients Aνμ and exponents ν and μ determined using the “boundary collocation method”34 are listed in Table 2. We caution the reader about the fact that a weight function that applies to a homogeneous material (with constant elastic properties) has been here considered. This approximation may lead to an overestimation of the calculated apparent fracture toughness in the ATZ layers of 1 In this paper, edge crack refers to a straight crack running from the tensile surface of the laminate normal to the layer plane. It should not be confused with edge cracking phenomena occurring in some laminates due to the residual stresses.32 Table 2 Weight function coefficients (Aνμ) for a 3-point bend bar determined by the “boundary collocation method”34 μ= 0 μ= 1 μ= 2 μ= 3 μ= 4 ν = 0 0.50 2.45 0.07 1.32 −3.07 ν = 1 0.54 −5.08 24.35 −32.72 18.12 ν = 2 −0.19 2.56 −12.64 19.76 −10.99 the ICS-laminates and in the A layers of the ECS-laminates, owed to the lower stiffness of the adjacent AMZ and AZ layers, respectively.35,36 In this regard, an alternative procedure has been proposed elsewhere,37 to predict in a more accurate way the fracture toughness of multilayered ceramics whose layers have different elastic properties. Nevertheless, this level of accuracy is beyond the scope of this work. The apparent fracture toughness, KR(a), was calculated according to the procedure explained above, integrating Eq. (4) by means of analytical software Mathematica© V.5.1. The influence of the different residual stress states, given by the layer thickness ratio (λ), on the apparent fracture toughness of the laminates has been examined in detail aiming to obtain architectures which yield the maximum shielding effect. Within this context, a linear elastic fracture mechanics analysis based on experimental flexural tests has also been implemented in order to provide an optimal design combining toughness and strength. The results are expressed for both ECS and ICS layered systems. 3. Results and discussion 3.1. Layer thickness ratio for maximum shielding Fig. 2 shows the apparent fracture toughness for different layer thickness ratios (λ) in the layered architectures designed with external (Fig. 2a) and internal (Fig. 2b) compressive layers, as a function of a crack length parameter aˆ, expressed as Y √a, with Y defined for an edge in a crack 3-point bend bar and given by38: Y(δ) = 1.99 − δ(1 − δ)(2.15 − 3.93δ + 2.7δ2) (1 + 2δ)(1 − δ) 3/2 , δ = a W (6) As it can be inferred from Eq. (1), the architectural parameter λ influences the residual stress field. Thus, the apparent fracture toughness is represented for different values of . λ (until the crack length a being approximately half of the specimen thickness) in order to determine the geometry that provides the maximum shielding in both laminates. As shown by previous authors the apparent toughness curves of multilayers show an oscillating behaviour.12,24,39–41 For the laminates with external compressive residual stresses, ECSlaminates, the toughness increases in the external layers with increasing crack length and reaches a local maximum at the A/AZ interface, whereas it decreases in the tensile layers reaching a local minimum at the AZ/A interface. For the ICSlaminates toughness decreases within the external layer up to the
R. Bermejo et al. / Journal of the European Ceramic Sociery 28(2008)1575-1583 w-3 mr 0 Crack length parameter, d=ya [m"1 Crack length parameter, d=Ya [m"1 Fig. 2. Apparent toughness as a function of the layer thickness ratio(A)in the layered architectures designed with(a)external and(b) intemal compressive layers. ATZ/AMZ interface, due to the negative contribution of the sec- high compressive stresses and thick ATZ layers with negligible ond term in Eq (4)to the intrinsic fracture toughness of the ATz tensile stresses, as inferred from Eq (1). On the other hand, rel- layers. In some cases, the apparent fracture toughness of the lam- ative high A values lead to significant tensile residual stresses inate predicted by the weight function analysis may even result in in the aTZ layers which may be detrimental for the material negative values(see shaded area in Fig. 2b), owed to the signifi- integrity. In any case, the shielding effect is provided by the inter- ant tensile residual stresses in the thick ATZ layers. However, as nal AMZ compressive layers and, similar to the ECS-laminate soon as the crack enters the compressive AMZ layer, the appar- design, an optimal apparent toughness(93 MPa"2)is found ent toughness rises up to a maximum value at the AMziatz for a geometry that combines high compressive stresses in the interface. It can be stated that the compressive stresses shield AMZ internal layers of a relative thick thickness. A maximal the material against flaws, while the tensile stresses have a detri- parameter of Amax 0.2 is found in such case, which would cor- mental effect in the effective apparent toughness. Regarding the respond to ATZ layers of tATz 520 um and AMZ layers of shielding effects as a function of the different geometries, i.e. tAMZ 100 um. The residual stresses associated with this lay various A, the following aspects may be inferred from Fig. 2. ered architecture, calculated using Eq (1), yield tensile stresses For the ECs-laminates A is defined as tAZ/ta in the range of N+109 MPa in the atz layers and compressive stresses of of 1-25. Therefore, high values of A correspond to thin A lay- N-682 MPa in the AMZ layers. The fracture behaviour of this ers in comparison to the Az layers, and thus high compressive particular architecture has been experimentally assessed in stresses are present in the former according to Eg. (1). That is the reason why the shielding increases so steeply in the A lay- 3.2. Residual stresses in the laminates of study ers and a high stress intensity factor should be applied to lead the specimen to failure(Fig. 2a). However, for low values of As explained above, the different residual stress state in the a, the thickness of the a layers is much bigger than that of the laminates is associated with the layer thickness ratio between AZ layers and as a result, high tensile stresses arise in these layers(). Table 3 represents the magnitude of the biaxial resid- AZ layers. Hence, the effective toughness drops remarkably in ual stresses which develop in the layers of both ECS-and the Az layers for these laminates. An interesting conclusion drawn from Fig. 2a is the existence of an architecture that max- Table 3 imises the shielding at the first interface. Opposite to what could Magnitude of the biaxial residual stresses which develop in the layers of both be expected, the highest surface compressive stress(the high- ECS-and ICS-laminates for several geometries as a function of the layer thick est n)does not correspond to the highest shielding in the first ness ratio (a) layer. Since the maximum shielding in the first layer is obtained Residual stress(MPa) to the outer layer thickness, the thickness Ratio() ECS-Iaminates ICS-Iaminates tA plays an important role. In this case, a maximum shield- ing factor at the first interface is achieved for geometries with ATZ AMZ a Amax 2.5, where a compromise between high compressive 0.05 stresses and relative thick layer thickness applies, leading to an 0.10 719 pparent toughness of 10.6 MPam". In terms of layer thick- 0.20 682 ness, this will correspond to A layers of tA 200 um and Az 177 -633 layers of tAZ 500 um. The residual stresses corresponding to 0.5 236 591 this layered architecture can be calculated using Eq (1), yielding 25 compressive stresses of a-224 MPa in the A layers and tensile 5 stresses of A+112 MPa in the Az layers For the ICS-laminates A is defined as tamzltaTz in the range 20 of 0.05-0.5. Low 2 values yield very thin AMZ layers with 25
1578 R. Bermejo et al. / Journal of the European Ceramic Society 28 (2008) 1575–1583 Fig. 2. Apparent toughness as a function of the layer thickness ratio (λ) in the layered architectures designed with (a) external and (b) internal compressive layers. ATZ/AMZ interface, due to the negative contribution of the second term in Eq. (4) to the intrinsic fracture toughness of the ATZ layers. In some cases, the apparent fracture toughness of the laminate predicted by the weight function analysis may even result in negative values (see shaded area in Fig. 2b), owed to the signifi- cant tensile residual stresses in the thick ATZ layers. However, as soon as the crack enters the compressive AMZ layer, the apparent toughness rises up to a maximum value at the AMZ/ATZ interface. It can be stated that the compressive stresses shield the material against flaws, while the tensile stresses have a detrimental effect in the effective apparent toughness. Regarding the shielding effects as a function of the different geometries, i.e. various λ, the following aspects may be inferred from Fig. 2. For the ECS-laminates λ is defined as tAZ/tA in the range of 1–25. Therefore, high values of λ correspond to thin A layers in comparison to the AZ layers, and thus high compressive stresses are present in the former according to Eq. (1). That is the reason why the shielding increases so steeply in the A layers and a high stress intensity factor should be applied to lead the specimen to failure (Fig. 2a). However, for low values of λ, the thickness of the A layers is much bigger than that of the AZ layers and as a result, high tensile stresses arise in these AZ layers. Hence, the effective toughness drops remarkably in the AZ layers for these laminates. An interesting conclusion drawn from Fig. 2a is the existence of an architecture that maximises the shielding at the first interface. Opposite to what could be expected, the highest surface compressive stress (the highest λ) does not correspond to the highest shielding in the first layer. Since the maximum shielding in the first layer is obtained at a distance equal to the outer layer thickness, the thickness tA plays an important role. In this case, a maximum shielding factor at the first interface is achieved for geometries with a λmax ≈ 2.5, where a compromise between high compressive stresses and relative thick layer thickness applies, leading to an apparent toughness of ≈10.6 MPa m1/2. In terms of layer thickness, this will correspond to A layers of tA ≈ 200m and AZ layers of tAZ ≈ 500m. The residual stresses corresponding to this layered architecture can be calculated using Eq.(1), yielding compressive stresses of ≈−224 MPa in the A layers and tensile stresses of ≈+112 MPa in the AZ layers. For the ICS-laminates λ is defined as tAMZ/tATZ in the range of 0.05–0.5. Low λ values yield very thin AMZ layers with high compressive stresses and thick ATZ layers with negligible tensile stresses, as inferred from Eq. (1). On the other hand, relative high λ values lead to significant tensile residual stresses in the ATZ layers which may be detrimental for the material integrity. In any case, the shielding effect is provided by the internal AMZ compressive layers and, similar to the ECS-laminate design, an optimal apparent toughness (≈9.3 MPa m1/2) is found for a geometry that combines high compressive stresses in the AMZ internal layers of a relative thick thickness. A maximal parameter of λmax ≈ 0.2 is found in such case, which would correspond to ATZ layers of tATZ ≈ 520m and AMZ layers of tAMZ ≈ 100m. The residual stresses associated with this layered architecture, calculated using Eq. (1), yield tensile stresses of ≈+109 MPa in the ATZ layers and compressive stresses of ≈−682 MPa in the AMZ layers. The fracture behaviour of this particular architecture has been experimentally assessed in.17 3.2. Residual stresses in the laminates of study As explained above, the different residual stress state in the laminates is associated with the layer thickness ratio between layers (λ). Table 3 represents the magnitude of the biaxial residual stresses which develop in the layers of both ECS- and Table 3 Magnitude of the biaxial residual stresses which develop in the layers of both ECS- and ICS-laminates for several geometries as a function of the layer thickness ratio (λ) Residual stress (MPa) Ratio (λ) ECS-laminates ICS-laminates A AZ ATZ AMZ 0.05 – – 30 −740 0.10 – – 57.5 −719 0.20 – – 109 −682 0.35 – – 177 −633 0.5 – – 236 −591 1 −142 177 – – 2.5 −224 112 – – 5 −278 69 – – 10 −315 39 – – 20 −338 21 – – 25 −343 17 – –
R. Bermejo et al. /Journal of the European Ceramic Society 28(2008)1575-1583 1579 ICS-laminates for several geometries. The values were calcu the elastic and thermal properties were taken from Table 1 The maximum shielding in both ecs- and ics-laminates is given by an optimal combination of compressive stresses and layer thickness. However, the tensile residual stresses which bal ance the layered architecture must also be taken into account. In this case, however, the corresponding tensile stresses are about C100 MPafor both ECS-and lCS-laminates(see Table 3), which should not affect the integrity of the layered structure. This is an important factor to take into account, since a high tensile stress state could lead to the appearance of closed transverse cracks so-called tunnelling cracks, which might negatively affect the material mechanical response Crack length parameter, a(m) 3.3. Implications of maximum shielding on strength Fig 3. Optimal apparent toughness and strength as a function of the layer thick ness ratio(A)in the layered architectures designed with external compressive layers. The range of fiaw size experimental found (ae )is also represented. The weight function analysis performed above yields optimal design geometries in terms of maximum shielding for layered shielding is achieved at the first A/AZ interface of the external ceramics with tailored external/internal compressive stresses. In both cases, relative thick compressive layers are required to impressive layer A, for a design corresponding to a layer thick- ness ratio of入 rovide a maximum crack growth resistance for an edge crack max=2.5. Experimental flexural tests carried out under a tensile stress field. Due to the large variety of flaw sizes in some ECS-laminate geometries along with the corresponding inspection of the fracture specimens revealed a homogeneous and population which may be encountered in a real ceramic surface defect population within the first A layer. Abnormally component, flexural strength tests are often performed toidentify grown grains were identified as failure origins having a critical both the shape and the kind of the critical defects causing the size of ac =15-60 um. 46 This flaw range is represented in Fig 3 failure as well as their location within the specimen. It is well in terms of the crack length parameter a(0.0076-0015 m), known that the failure stress variability of ceramic components assuming the geometric factor Y given by Eq(6). We caution often recalls the use of Weibull statistics to evaluate the strength the reader that other critical flaws such as embedded flaws or of the material+ For some of the multilayered geometries small semi-elliptical cracks may also be found in this type of here investigated, experimental four-point bending strength tests laminates. Such defects are not as critical as the edge cracks have been carried out in previous works, aiming to discern the here considered, which yields a certain overestimation of the type and size of critical flaws causing the material failure as critical parameter a, namely, a safer design condition well as to understand the fracture process of a crack propagating through the layered structure. 7.24. 25, The straight lines in Fig. 3 represent a given applied stress Within the crack resistance context assessed in Section 3.1 intensity factor Kapp which increases linearly as the crack length alysis is here emploved to better parameter a rises, and whose slope corresponds to the applied understand the implications of the maximum shielding provided by the layered geometries above described on the strength and Kapp(a)=Appl Y va= dapple fracture behaviour of both designs(ECS-laminates and ICS- laminates). In this regard, additionally to Eq (3)which dictates When this line intersects the effective apparent toughness the conditions for crack growth, a stable/unstable crack propa- of the material (KR), Eq. ( 3)is fulfilled and crack propagation gation criterion is given by the following equation, defined for occurs. In addition, if Eq (7)is satisfied, the crack propagates each layer except at the interfaces in an unstable manner until it reaches a region were Eq.(7) dKappl (a). dKR, effective(a) may no longer apply. For the particular geometry of maximum (7) shielding(=2.5), and considering the largest critical flaw found experimentally(a0.015 2), the crack propagation will take when Eq. (7)is fulfilled, unstable crack propagation will occur. place when the applied stress intensity factor Kappl overcomes Whether or not the crack propagation yields to catastrophic fail- the apparent toughness of the laminate according to Eq.(3), ure will be associated with the capability of the layered structure represented by point S in Fig 3. Moreover, since Eq. (7)is also to arrest the approaching crack fulfilled at this point, crack propagation will be unstable leading to catastrophic failure. Hence, the slope of this line(represent 33. ECS-laminates ing the applied stress, O appl)can be considered as the failure Fig 3 represents the crack growth resistance of several ECS- stress of the laminate. An interesting observation can be inferred ninates(with different A)as a function of the crack length from Fig 3 when estimating the failure stress corresponding parameter d in the region of maximum shielding. As reported to other geometries(such as A=10) for the same critical flaw in the previous sections, for the ECS-laminates, the maximum size. Within this context, the applied stress intensity factor nec
R. Bermejo et al. / Journal of the European Ceramic Society 28 (2008) 1575–1583 1579 ICS-laminates for several geometries. The values were calculated using Eq. (1), and the elastic and thermal properties were taken from Table 1. The maximum shielding in both ECS- and ICS-laminates is given by an optimal combination of compressive stresses and layer thickness. However, the tensile residual stresses which balance the layered architecture must also be taken into account. In this case, however, the corresponding tensile stresses are about ≈100 MPa for both ECS- and ICS-laminates (seeTable 3), which should not affect the integrity of the layered structure. This is an important factor to take into account, since a high tensile stress state could lead to the appearance of closed transverse cracks, so-called tunnelling cracks, which might negatively affect the material mechanical response.42 3.3. Implications of maximum shielding on strength The weight function analysis performed above yields optimal design geometries in terms of maximum shielding for layered ceramics with tailored external/internal compressive stresses. In both cases, relative thick compressive layers are required to provide a maximum crack growth resistance for an edge crack under a tensile stress field. Due to the large variety of flaw sizes and population which may be encountered in a real ceramic component, flexural strength tests are often performed to identify both the shape and the kind of the critical defects causing the failure as well as their location within the specimen. It is well known that the failure stress variability of ceramic components often recalls the use of Weibull statistics to evaluate the strength of the material.43–45 For some of the multilayered geometries here investigated, experimental four-point bending strength tests have been carried out in previous works, aiming to discern the type and size of critical flaws causing the material failure as well as to understand the fracture process of a crack propagating through the layered structure.17,24,25,46 Within the crack resistance context assessed in Section 3.1, a simple fracture mechanics analysis is here employed to better understand the implications of the maximum shielding provided by the layered geometries above described on the strength and fracture behaviour of both designs (ECS-laminates and ICSlaminates). In this regard, additionally to Eq. (3) which dictates the conditions for crack growth, a stable/unstable crack propagation criterion is given by the following equation, defined for each layer except at the interfaces: dKappl(a) da ≥ dKR,effective(a) da (7) when Eq. (7) is fulfilled, unstable crack propagation will occur. Whether or not the crack propagation yields to catastrophic failure will be associated with the capability of the layered structure to arrest the approaching crack. 3.3.1. ECS-laminates Fig. 3 represents the crack growth resistance of several ECSlaminates (with different λ) as a function of the crack length parameter aˆ in the region of maximum shielding. As reported in the previous sections, for the ECS-laminates, the maximum Fig. 3. Optimal apparent toughness and strength as a function of the layer thickness ratio (λ) in the layered architectures designed with external compressive layers. The range of flaw size experimental found (a exp c ) is also represented. shielding is achieved at the first A/AZ interface of the external compressive layer A, for a design corresponding to a layer thickness ratio of λmax = 2.5. Experimental flexural tests carried out in some ECS-laminate geometries along with the corresponding inspection of the fracture specimens revealed a homogeneous surface defect population within the first A layer. Abnormally grown grains were identified as failure origins having a critical size of ac = 15–60m.46 This flaw range is represented in Fig. 3 in terms of the crack length parameter aˆ(0.0076–0.015 m1/2), assuming the geometric factor Y given by Eq. (6). We caution the reader that other critical flaws such as embedded flaws or small semi-elliptical cracks may also be found in this type of laminates. Such defects are not as critical as the edge cracks here considered, which yields a certain overestimation of the critical parameter aˆ, namely, a safer design condition. The straight lines in Fig. 3 represent a given applied stress intensity factor Kappl which increases linearly as the crack length parameter aˆ rises, and whose slope corresponds to the applied stress σappl, according to the following equation: Kappl(a) = σapplY √a = σapplaˆ (8) When this line intersects the effective apparent toughness of the material (KR), Eq. (3) is fulfilled and crack propagation occurs. In addition, if Eq. (7) is satisfied, the crack propagates in an unstable manner until it reaches a region were Eq. (7) may no longer apply. For the particular geometry of maximum shielding (λ = 2.5), and considering the largest critical flaw found experimentally (aˆ ≈ 0.015 m1/2), the crack propagation will take place when the applied stress intensity factor Kappl overcomes the apparent toughness of the laminate according to Eq. (3), represented by point S in Fig. 3. Moreover, since Eq. (7) is also fulfilled at this point, crack propagation will be unstable leading to catastrophic failure. Hence, the slope of this line (representing the applied stress, σappl) can be considered as the failure stress of the laminate. An interesting observation can be inferred from Fig. 3 when estimating the failure stress corresponding to other geometries (such as λ = 10) for the same critical flaw size. Within this context, the applied stress intensity factor nec-