《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_9Loading configuration effects on the strength reliability of a-z

Availableonlineatwww.sciencedirect.com COMPOSITES ScienceDirect SCIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 68(2008)244-250 w.elsevier. com/locate/compscitech Loading configuration effects on the strength reliability of alumina-zirconia multilayered ceramics Raul bermejo. y adir Torres Luis llanes Departamento de Ciencia de los materiales e Ingenieria Metalirgica, ETSEIB, Universitat Politecnica de Catalunya, Auda. Diagonal 647. Barcelona, 08028, spain Received 15 February 2007: received in revised form 29 March 2007: accepted 30 March 2007 Available online 24 April 2007 Abstract The loading configuration effects on the strength reliability of alumina/zirconia multilayered systems, designed with internal compres- sive stresses, have been investigated. The existence of a threshold strength behaviour, as previously assessed under longitudinal flexure. has been evaluated by indentation-strength tests under transverse flexure. Additionally, the influence of flaw interactions on the strength eliability under both loading configurations has also been studied. Experimental findings show a higher strength level under transverse flexure, as far as the failure-controlling flaw is located between two compressive layers. It is found however that multiple artificial and values result from this configuration, a more reliable design is rather attained when the loading axis is applied normal to the layer plane, a loading mode where similar effects are negligible c 2007 Elsevier Ltd. All rights reserved Keywords: A. Layered structures; B Strength; C. Damage tolerance; C. Transverse cracking: Loading configuration 1. Introduction forced ceramics, where the better mechanical performance is associated with not only the second phase or layer addi Ceramic materials exhibit a relatively wide strength dis- tion, but also the arrangement of the fibres or the layer tribution owed to the quite variable characteristics of the assemblage with respect to the loading axis, as well as the laws induced during their processing and/or machining, sliding resistance of the fibre-matrix interface or the inter- i.e. nature, geometry and size, together with their relative layer fracture energy, respectively [7, 12, 13]. According to orientation with respect to the applied loads. This broad these studies, when the crack front is oriented parallel to range of strength values and their inherent brittleness have the aligned fibres, the crack propagates catastrophically limited the use of ceramics in structural applications. How- through the composite at the initial cracking stress, i.e ever,as a direct consequence of remarkable progress in there is not any crack shielding from the fibres arranged terms of microstructural design and advanced processing normal to the loading direction. On the other hand, when [1-3], toughness and reliability of structural ceramics have the fibres are oriented perpendicular to the crack front een increasingly enhanced by recourse to crack shielding cracks originated at the outer ceramic layer get arrested ulting from microstructure-related mechanisms [4-11]. at the ceramic-fibre interfaces, providing a higher resis- Particular attention has been paid to fibre and layered rein- tance to crack propagation As an extension of this laminar ceramic/fibre-reinforced sponding author. Present address: Institut fur Struktur- und concept, multilayered architectural designs have also been keramik, Montanuniversitat Leoben, Peter-Tunner Strasse 5 attempted in many ways aiming to improve both the resis- ben. Austria. Tel: +43 402 4115: fax: +43 3842 402 4102 tance to crack propagation and the mechanical reliability address: raul bermejo@mu-leoben at(R. Bermejo) of ceramic components [11, 14-17. This approach has 0266-3538/- see front matter e 2007 Elsevier Ltd. All rights reserved doi: 10.1016/j. compscitech. 2007.03.042

Loading configuration effects on the strength reliability of alumina–zirconia multilayered ceramics Rau´l Bermejo *, Yadir Torres, Luis Llanes Departamento de Ciencia de los Materiales e Ingenierı´a Metalu´rgica, ETSEIB, Universitat Polite`cnica de Catalunya, Avda. Diagonal 647, Barcelona, 08028, Spain Received 15 February 2007; received in revised form 29 March 2007; accepted 30 March 2007 Available online 24 April 2007 Abstract The loading configuration effects on the strength reliability of alumina/zirconia multilayered systems, designed with internal compres￾sive stresses, have been investigated. The existence of a threshold strength behaviour, as previously assessed under longitudinal flexure, has been evaluated by indentation-strength tests under transverse flexure. Additionally, the influence of flaw interactions on the strength reliability under both loading configurations has also been studied. Experimental findings show a higher strength level under transverse flexure, as far as the failure-controlling flaw is located between two compressive layers. It is found however that multiple artificial and natural flaws may interact affecting the strength of the specimen under transverse loading. As a consequence, although higher strength values result from this configuration, a more reliable design is rather attained when the loading axis is applied normal to the layer plane, a loading mode where similar effects are negligible. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Layered structures; B. Strength; C. Damage tolerance; C. Transverse cracking; Loading configuration 1. Introduction Ceramic materials exhibit a relatively wide strength dis￾tribution owed to the quite variable characteristics of the flaws induced during their processing and/or machining, i.e. nature, geometry and size, together with their relative orientation with respect to the applied loads. This broad range of strength values and their inherent brittleness have limited the use of ceramics in structural applications. How￾ever, as a direct consequence of remarkable progress in terms of microstructural design and advanced processing [1–3], toughness and reliability of structural ceramics have been increasingly enhanced by recourse to crack shielding resulting from microstructure-related mechanisms [4–11]. Particular attention has been paid to fibre and layered rein￾forced ceramics, where the better mechanical performance is associated with not only the second phase or layer addi￾tion, but also the arrangement of the fibres or the layer assemblage with respect to the loading axis, as well as the sliding resistance of the fibre–matrix interface or the inter￾layer fracture energy, respectively [7,12,13]. According to these studies, when the crack front is oriented parallel to the aligned fibres, the crack propagates catastrophically through the composite at the initial cracking stress, i.e. there is not any crack shielding from the fibres arranged normal to the loading direction. On the other hand, when the fibres are oriented perpendicular to the crack front, cracks originated at the outer ceramic layer get arrested at the ceramic–fibre interfaces, providing a higher resis￾tance to crack propagation. As an extension of this laminar ceramic/fibre-reinforced concept, multilayered architectural designs have also been attempted in many ways aiming to improve both the resis￾tance to crack propagation and the mechanical reliability of ceramic components [11,14–17]. This approach has 0266-3538/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.03.042 * Corresponding author. Present address: Institut fu¨r Struktur- und Funktionskeramik, Montanuniversita¨t Leoben, Peter-Tunner Strasse 5, 8700 Leoben, Austria. Tel.: +43 3842 402 4115; fax: +43 3842 402 4102. E-mail address: raul.bermejo@mu-leoben.at (R. Bermejo). www.elsevier.com/locate/compscitech Available online at www.sciencedirect.com Composites Science and Technology 68 (2008) 244–250 COMPOSITES SCIENCE AND TECHNOLOGY

Composites Science and Technology 68(2008)244-250 demonstrated to be less cost effective than the one based on conia laminated system can be arrested by the first internal fibre structures and more accurate in terms of tailoring thin compressive layer when extending under longitudinal mechanical requirements. Within this context, a commonly flexure [24]. As a result of such crack -layer architecture sed multilayered structural design is that associated with interaction, these laminates exhibit an almost constant fail- the presence of compressive residual stresses developed in ure stress regardless of the size of the pre-existing cracks the laminate during cooling from sintering [11, 18, 19], as(artificially introduced by recourse to indentation tech- related to differences in elastic or thermal properties niques), i.e. a threshold stress below which the probability (Youngs modulus, thermal expansion coefficient, etc. of failure is nearly zero. As it is shown in Fig 4 from Ref. and/or chemical reactions within them [8, 15, 20]. In partic- experienced by monolithic alumina-based brittle ceramics, ular, ceramic composites with a layered structure such as where the flexural strength continuously decreases with alumina/zirconia have been reported to exhibit relatively increasing indentation load, i. e. flaw size. Because this large apparent fracture toughness, energy absorption capa- interesting finding (i.e. the existence of a threshold stress bility and, consequently, non-catastrophic failure behav- has been discerned only under longitudinal flexure ur[8,14,15,21,2 (Fig. la), an immediate query is raised whether such a In addition to the architectural design, loading condi- mechanical response would also apply under conditions tions(Fig. 1)may strongly affect the mechanical response where the load axis is set parallel to the layers, i.e. in trans- of a layered structure [14]. Although it is well-documented verse flexure(Fig. Ib) that multilayered cs exhibit an enhanced fracture The purpose of this work is to investigate the loading behaviour, independent of the specific loading configura- configuration effects on the strength reliability of an opti- on under consideration, i. e with loading axis either paral- mally designed alumina/zirconia multilayered system [22] lel(transverse flexure)[Il] or perpendicular (longitudinal In doing so, the existence of a threshold strength behaviour flexure)[17, 23, 24] to the layer plane, studies where the under conditions of transverse flexure is assessed. Addi- mechanical strength of such multilayered systems are tionally, the infuence of flaw interactions on the strength directly compared as a function of loading orientation reliability under both loading configurations is also are quite scarce. In this regard, a recent work from Moon addressed et al. [25]on alumina-zirconia multilayered composites has shown that relative layer orientation with respect to the 2. Experimental procedure crack-tip front exerts a pronou inced influence on the crack growth resistance behaviour of the material, thus pointing 2.1. Material of study out the need for further investigation from this perspective if these materials are to be properly implemented in struc- Starting powders were submicron-sized alumina(HPa applications. 0.5, Condea, USA)with a mean particle size (dso) of Furthermore, although a single crack within a thick ten- 0.3 um, tetragonal zirconia polycryst Y-TZP) with sile layer can be arrested by thin compressive layers, there 3 mol% of Y2O3 (TZ-3YS, Tosoh, Japan) with dso is a possibility that other cracks and/or flaws may coexist 0.4 um, and pure zirconia (Tz-0, Tosoh, Japan)with Dse to each other, either in the same or in adjacent layers, dso=0.3 um. Slurries were prepared to a solid loading of varying in certain cases the critical failure scenario for the 36.5 vol% by mixing starting powders with DI water, con- material. Within this context, the effective stress intensity taining a 0.8 wt% of a commercial acrylic based polyelectro- factor for interacting cracks has been the topic of research lyte(Duramax D-3021, Rohm&Haas, USA)used for of several studies following both analytical [26-28] and stabilisation. Sequential slip casting [30,31] was used to fab experimental [29]approaches. In general, it has been found ricate laminates composed of five thick layers, referred to as that two closely spaced cracks can interact to increase the ATZ, alternated with four thin layers, named as AMZ. The stresses at the corresponding crack tips, thus affecting the thickness of the layers was controlled from the measure- fracture response of the component in the zone where the ment of the wall thickness after different casting times for both ATZ and AMz suspensions. A slurry composed of n a previous work, the authors have shown that a single Al,O3/5 vol%Y2O3-stabilised ZrO2(t-ZrO2), was used to crack, located at the outer tensile layer of an alumina-zir- form the thick ATZ layers. The t-Zro2 was employed to control the grain size of the Al,O3 during densification. In order to form the thin AMz layers a slurry containing b AlO3/30 vol% ZrO2(m-ZrO2), was utilised. Details of the colloidal processing procedure may be found elsewhere 32]. The laminate plates were sintered at 1550C for 2h in air. Several bar-shaped specimens (3.8 mm x 3.2 mm x Fig. 1. Scheme of a testing configuration where the loading axis is applied 25 mm)were cut from the plates and the top and lateral (a) perpendicular(longitudinal flexure)and(b) parallel(transverse flexure) surfaces of each sample polished to a 3 um finish with a to the layer plane. diamond abrasive. A homogeneous layer thickness, i.e

demonstrated to be less cost effective than the one based on fibre structures and more accurate in terms of tailoring mechanical requirements. Within this context, a commonly used multilayered structural design is that associated with the presence of compressive residual stresses developed in the laminate during cooling from sintering [11,18,19], as related to differences in elastic or thermal properties (Young’s modulus, thermal expansion coefficient, etc.) between the layers, as well as to phase transformations and/or chemical reactions within them [8,15,20]. In partic￾ular, ceramic composites with a layered structure such as alumina/zirconia have been reported to exhibit relatively large apparent fracture toughness, energy absorption capa￾bility and, consequently, non-catastrophic failure behav￾iour [8,14,15,21,22]. In addition to the architectural design, loading condi￾tions (Fig. 1) may strongly affect the mechanical response of a layered structure [14]. Although it is well-documented that multilayered ceramics exhibit an enhanced fracture behaviour, independent of the specific loading configura￾tion under consideration, i.e. with loading axis either paral￾lel (transverse flexure) [11] or perpendicular (longitudinal flexure) [17,23,24] to the layer plane, studies where the mechanical strength of such multilayered systems are directly compared as a function of loading orientation are quite scarce. In this regard, a recent work from Moon et al. [25] on alumina–zirconia multilayered composites has shown that relative layer orientation with respect to the crack-tip front exerts a pronounced influence on the crack growth resistance behaviour of the material, thus pointing out the need for further investigation from this perspective if these materials are to be properly implemented in struc￾tural applications. Furthermore, although a single crack within a thick ten￾sile layer can be arrested by thin compressive layers, there is a possibility that other cracks and/or flaws may coexist close to each other, either in the same or in adjacent layers, varying in certain cases the critical failure scenario for the material. Within this context, the effective stress intensity factor for interacting cracks has been the topic of research of several studies following both analytical [26–28] and experimental [29] approaches. In general, it has been found that two closely spaced cracks can interact to increase the stresses at the corresponding crack tips, thus affecting the fracture response of the component in the zone where the cracks are located. In a previous work, the authors have shown that a single crack, located at the outer tensile layer of an alumina–zir￾conia laminated system can be arrested by the first internal thin compressive layer when extending under longitudinal flexure [24]. As a result of such crack – layer architecture interaction, these laminates exhibit an almost constant fail￾ure stress regardless of the size of the pre-existing cracks (artificially introduced by recourse to indentation tech￾niques), i.e. a threshold stress below which the probability of failure is nearly zero. As it is shown in Fig. 4 from Ref. [24], this is completely different from the failure behaviour experienced by monolithic alumina-based brittle ceramics, where the flexural strength continuously decreases with increasing indentation load, i.e. flaw size. Because this interesting finding (i.e. the existence of a threshold stress) has been discerned only under longitudinal flexure (Fig. 1a), an immediate query is raised whether such a mechanical response would also apply under conditions where the load axis is set parallel to the layers, i.e. in trans￾verse flexure (Fig. 1b). The purpose of this work is to investigate the loading configuration effects on the strength reliability of an opti￾mally designed alumina/zirconia multilayered system [22]. In doing so, the existence of a threshold strength behaviour under conditions of transverse flexure is assessed. Addi￾tionally, the influence of flaw interactions on the strength reliability under both loading configurations is also addressed. 2. Experimental procedure 2.1. Material of study Starting powders were submicron-sized alumina (HPA 0.5, Condea, USA) with a mean particle size (d50) of 0.3 lm, tetragonal zirconia polycrystals (Y-TZP) with 3 mol% of Y2O3 (TZ-3YS, Tosoh, Japan) with d50 = 0.4 lm, and pure zirconia (TZ-0, Tosoh, Japan) with d50 = 0.3 lm. Slurries were prepared to a solid loading of 36.5 vol% by mixing starting powders with DI water, con￾taining a 0.8 wt% of a commercial acrylic based polyelectro￾lyte (Duramax D-3021, Rohm&Haas, USA) used for stabilisation. Sequential slip casting [30,31] was used to fab￾ricate laminates composed of five thick layers, referred to as ATZ, alternated with four thin layers, named as AMZ. The thickness of the layers was controlled from the measure￾ment of the wall thickness after different casting times for both ATZ and AMZ suspensions. A slurry composed of Al2O3/5 vol% Y2O3-stabilised ZrO2 (t-ZrO2), was used to form the thick ATZ layers. The t-ZrO2 was employed to control the grain size of the Al2O3 during densification. In order to form the thin AMZ layers a slurry containing Al2O3/30 vol% ZrO2 (m-ZrO2), was utilised. Details of the colloidal processing procedure may be found elsewhere [32]. The laminate plates were sintered at 1550 C for 2 h in air. Several bar-shaped specimens (3.8 mm · 3.2 mm · 25 mm) were cut from the plates and the top and lateral surfaces of each sample polished to a 3 lm finish with a diamond abrasive. A homogeneous layer thickness, i.e. Fig. 1. Scheme of a testing configuration where the loading axis is applied (a) perpendicular (longitudinal flexure) and (b) parallel (transverse flexure) to the layer plane. R. Bermejo et al. / Composites Science and Technology 68 (2008) 244–250 245

R Bermejo et al. / Composites Science and Technology 68(2008 )244-250 540+ 10 um and 95+ 5 um, was obtained for both atz where Fis the applied load at fracture, s and si are the out and AMz layers respectively, resulting in a symmetrical er and inner spans, respectively, B is the specimen width multilayered architecture. As a result of the non-stabilised and h is the specimen height. Fractured surfaces were in- zirconia content in the thin AMZ layers, a significant ther- spected by scanning electron microscopy (JEOL JMS mal mismatch between layers was generated owed to the 6400, Germany) to determine the source of failure for each f- m zirconia phase transformation occurring when cool- tested specimen ing down during sintering. This martensitic transformation is accompanied by an increase in volume which modifies the 3. Results and discussion this case compressive stresses inside the thin layers and ten- 3. 1. Strength on specimens containing a single crack sile stresses in the thicker ones [18]. The magnitude of these residual stresses has been calculated for this architecture in A constant strength value was encountered for the case thermal mismatch between adjacent layers resulted in a previous work [24]. In these cases, it was observed how all AE=0.00212, and the corresponding Youngs modulus of the initial indentation cracks propagated up to the first the atz and aMz compacts were 390 GPa and 280 GPa, compressive layer, where they got arrested before cata- respectively [32] strophic failure occurred, yielding an effective"threshold stress"level (170+8 MPa) below which the probability of failure is nearly zero. For the laminates indented the central thick layer and subjected to transverse flexura In order to evaluate the possible threshold stress under loading, cracks emanating from the indentation extended ransverse flexure, pre-cracks were introduced in the central towards the two thin compressive layers and got arrested thick layer of the laminate using a Vickers indenter, as ( Fig. 3), before further propagating through the rest of illustrated in Fig 2a. All pre-cracks were induced using a the laminate. As a result, a constant strength of Vickers indenter and applied loads within a range between 401 t 10 MPa was obtained, regardless of the size of the 50N and 200 N. Additionally, attempting to assess crack initial indentation crack, as it is represented in Fig 4 Nev interaction effects under both loading orientations, inden- ertheless, in some cases, and although artificial cracks had tations of 100N were placed with an offset separation x been introduced in the central ATZ layer of the tested spec- ranging from 0 mm(coplanar-cracks)to 3 mm, either at imens, fracture was found to initiate from natural flaws the internal ATZ layers(Fig. 2a)or at the top surface located in the outer most ATZ layer(Fig. 5), yielding fail- (Fig. 2b). The relative distance between cracks for both ure stress levels of 265+ 25 MPa. From this point of view, cases was measured by means of an optical microsco a threshold stress under transverse configuration may be Four-point bending tests were performed under both defined as far as the failure-controlling flaw is located configurations with a fully articulated test jig with outer between two compressive layers. In these cases, the initial and inner spans of 20 mm and 10 mm respectively. Tests growth experienced by such defect upon loading is inhib were carried out under load control using a servo-hydraulic ited by two thin compressive AMz layers, which act as testing machine(Model 8511, Instron Ltd. with a load cell physical barrier to crack propagation, as it was shown in of 10 kN, at a testing rate of 100 N/s. The failure stress for Fig. 3. In order to rationalise this behaviour, a linear elastic the indented specimens, oRi, was determined through the following expression Crack bifurcatio b atz Crack arrest. 300um Fig 3. Optical micrograph illustrating the crack arrest at the ATZ/AMZ Fig. 2. Testing configurations imposed on single and multiple indented interfaces of a layered specimen under loading parallel to the layer plane. specimens (x being the offset separation between cracks)corresponding to Crack bifurcation within the compressive layers can be also observed applied loading axis(a) parallel and (b) normal to the layer pl during the fracture process

540 ± 10 lm and 95 ± 5 lm, was obtained for both ATZ and AMZ layers respectively, resulting in a symmetrical multilayered architecture. As a result of the non-stabilised zirconia content in the thin AMZ layers, a significant ther￾mal mismatch between layers was generated owed to the t ! m zirconia phase transformation occurring when cool￾ing down during sintering. This martensitic transformation is accompanied by an increase in volume which modifies the cooling shrinkage behaviour of the laminate, developing in this case compressive stresses inside the thin layers and ten￾sile stresses in the thicker ones [18]. The magnitude of these residual stresses has been calculated for this architecture in a previous work [24], resulting in 690 MPa for the thin AMZ layers and 100 MPa for the ATZ ones. The measured thermal mismatch between adjacent layers resulted in De = 0.00212, and the corresponding Young’s modulus of the ATZ and AMZ compacts were 390 GPa and 280 GPa, respectively [32]. 2.2. Indentation-strength tests In order to evaluate the possible threshold stress under transverse flexure, pre-cracks were introduced in the central thick layer of the laminate using a Vickers indenter, as illustrated in Fig. 2a. All pre-cracks were induced using a Vickers indenter and applied loads within a range between 50 N and 200 N. Additionally, attempting to assess crack interaction effects under both loading orientations, inden￾tations of 100 N were placed with an offset separation x ranging from 0 mm (coplanar-cracks) to 3 mm, either at the internal ATZ layers (Fig. 2a) or at the top surface (Fig. 2b). The relative distance between cracks for both cases was measured by means of an optical microscope. Four-point bending tests were performed under both configurations with a fully articulated test jig with outer and inner spans of 20 mm and 10 mm respectively. Tests were carried out under load control using a servo-hydraulic testing machine (Model 8511, Instron Ltd.) with a load cell of 10 kN, at a testing rate of 100 N/s. The failure stress for the indented specimens, rRi, was determined through the following expression: rRi ¼ 3F ðSo SiÞ 2Bh2 ð1Þ where F is the applied load at fracture, so and si are the out￾er and inner spans, respectively, B is the specimen width and h is the specimen height. Fractured surfaces were in￾spected by scanning electron microscopy (JEOL JMS 6400, Germany) to determine the source of failure for each tested specimen. 3. Results and discussion 3.1. Strength on specimens containing a single crack A constant strength value was encountered for the case of laminates indented at the top surface and loaded perpen￾dicular to the layer plane (longitudinal flexure), as found in a previous work [24]. In these cases, it was observed how all the initial indentation cracks propagated up to the first compressive layer, where they got arrested before cata￾strophic failure occurred, yielding an effective ‘‘threshold stress’’ level (170 ± 8 MPa) below which the probability of failure is nearly zero. For the laminates indented at the central thick layer and subjected to transverse flexural loading, cracks emanating from the indentation extended towards the two thin compressive layers and got arrested (Fig. 3), before further propagating through the rest of the laminate. As a result, a constant strength of 401 ± 10 MPa was obtained, regardless of the size of the initial indentation crack, as it is represented in Fig. 4. Nev￾ertheless, in some cases, and although artificial cracks had been introduced in the central ATZ layer of the tested spec￾imens, fracture was found to initiate from natural flaws located in the outer most ATZ layer (Fig. 5), yielding fail￾ure stress levels of 265 ± 25 MPa. From this point of view, a threshold stress under transverse configuration may be defined as far as the failure-controlling flaw is located between two compressive layers. In these cases, the initial growth experienced by such defect upon loading is inhib￾ited by two thin compressive AMZ layers, which act as a physical barrier to crack propagation, as it was shown in Fig. 3. In order to rationalise this behaviour, a linear elastic Fig. 2. Testing configurations imposed on single and multiple indented specimens (x being the offset separation between cracks) corresponding to applied loading axis (a) parallel and (b) normal to the layer plane. Fig. 3. Optical micrograph illustrating the crack arrest at the ATZ/AMZ interfaces of a layered specimen under loading parallel to the layer plane. Crack bifurcation within the compressive layers can be also observed during the fracture process. 246 R. Bermejo et al. / Composites Science and Technology 68 (2008) 244–250

7 Composites Science and Technolog 008)244-250 450 Substituting into Eq (2)the value of the residual compres- sive stress ac, the average values of the thick(11) and thin 40,,, (2)layers, and the value of Klc for the AMz arrester layers i.e. 2.6+0. I MPam"-(evaluated in a previous work [24]), Indentation flaws the maximum predicted stress omax results in 336+9 MPa This stress level is lower than the measured strength of 401+ 10 MPa. Such discrepancy comes from the fact that Eq.(2)is derived for arrested cracks that fully extend through the compressive layers in a straight path, whereas Natural flaws the crack is experimentally observed to bifurcate(Fig 3) Such bifurcation process implies energy consumption asso- ciated with the deviation of the crack from mode i of frac- 100 ture, which also requires a higher stress level for further Indentation load, PINI crack propagation, as it was demonstrated in a previous Fig. 4. Plot of the measured four-point bending failure stress vs. work under longitudinal flexure [22]. We caution the reader indentation load in the laminate tested under transverse flexure Specimens about the fact that different elastic modulus between the that failed through indentations located in the central ATZ layer show an two layers may also affect the absolute threshold stress val almost constant value, whereas the ones failing owed to the natural flaws ues predicted by Eq.(2), as assessed by finite element stud ies taking into account the elastic anisotropy of the layered architecture [34 Lowever. since the elastic ratio be- tween tensile and compressive layers is not very significant in this case, i.e. E/E2 N 1.4, the maximum stress value con- sidering the material anisotropy should not differ much from that predicted by Eq(2) 50μm For the particular case of transverse flexure configura tion when the fracture initiating defect is embedded within the outer ATZ layer, failure stress levels are much lower than the corresponding threshold stress predicted by (2). This fact can be explained by considering that under this layered architectural design only one compressive layer 500μm may act as a crack arrester for these propagating critical defects. Hence, although larger artificial faws are intro- Fig. 5 micrograph showing the source of failure (natl duced in the central layer, the stress intensity factor associ encounter the outer most ATZ layer"f, despite the in ated with the outer natural flaws governs the material crack ed in the central layer. A detail of the failure-co fracture, yielding a flaw-size dependence mechanical natural flaw is also presented. strength. In order to avoid such crack location effect under such a configuration, a similar stress state in both inner and fracture mechanics analysis, as carried out by Rao et al. outer thick layers must be guaranteed, a situation that may [16] on an alumina/alumina- mullite system, was imple if the la ed with mented in this work. Following such ideas, for the case sive layers, as if the composite were to be used in contact of a well-developed crack of size 2a extended sidewise into related applications. This design concept may be suggested two surrounding compressive layers, the maximum stress as an option for preserving relative constant strength val needed to cause the crack to break through the compressive ues. and thus. for layers occurs as 2a= 2t2+t,(being tI and t2 the thickness loading conditio enhancing reliability under transverse of the ATZ and AMZ layers, respectively), and the subse quent catastrophic failure takes place when the stress inten- 3. 2. Strength on specimens containing several defects ty factor at the crack tip K overcomes the toughness of the thin compressive layers. Hence, the largest strength Failure stress values were determined for multi-cracked (omax) for further crack propagation is associated with specimens following a similar testing procedure as for the the toughness(Kle) and the magnitude of the compressive single-cracked samples. All the experimental results under stresses(ac) of such thin layers according to [16,33 both testing configurations were expressed in terms of K stress using Eq (1) and are shown, in a combined format, 21, in Fig. 6 Under longitudinal flexure testing it was observed that, t, although the strength of laminates was slightly affected 1+ (2) by crack interactions if the other, i.e. 0.5+0. 2 mm apart( Fig. 6a), a constant failure

fracture mechanics analysis, as carried out by Rao et al. [16] on an alumina/alumina-mullite system, was imple￾mented in this work. Following such ideas, for the case of a well-developed crack of size 2a extended sidewise into two surrounding compressive layers, the maximum stress needed to cause the crack to break through the compressive layers occurs as 2a = 2t2 + t1 (being t1 and t2 the thickness of the ATZ and AMZ layers, respectively), and the subse￾quent catastrophic failure takes place when the stress inten￾sity factor at the crack tip K overcomes the toughness of the thin compressive layers. Hence, the largest strength (rmax) for further crack propagation is associated with the toughness (KIc) and the magnitude of the compressive stresses (rc) of such thin layers according to [16,33]: rmax ¼ KIc ffiffiffiffiffiffi p t1 2 q 1 þ 2t2 t1  þ rc 1 1 þ t2 t1   2 p sin1 1 1 þ 2t2 t1 " # ! ð2Þ Substituting into Eq. (2) the value of the residual compres￾sive stress rc, the average values of the thick (t1) and thin (t2) layers, and the value of KIc for the AMZ arrester layers, i.e. 2.6 ± 0.1 MPam1/2 (evaluated in a previous work [24]), the maximum predicted stress rmax results in 336 ± 9 MPa. This stress level is lower than the measured strength of 401 ± 10 MPa. Such discrepancy comes from the fact that Eq. (2) is derived for arrested cracks that fully extend through the compressive layers in a straight path, whereas the crack is experimentally observed to bifurcate (Fig. 3). Such bifurcation process implies energy consumption asso￾ciated with the deviation of the crack from mode I of frac￾ture, which also requires a higher stress level for further crack propagation, as it was demonstrated in a previous work under longitudinal flexure [22]. We caution the reader about the fact that different elastic modulus between the two layers may also affect the absolute threshold stress val￾ues predicted by Eq. (2), as assessed by finite element stud￾ies taking into account the elastic anisotropy of the layered architecture [34,35]. However, since the elastic ratio be￾tween tensile and compressive layers is not very significant in this case, i.e. E1/E2 1.4, the maximum stress value con￾sidering the material anisotropy should not differ much from that predicted by Eq. (2). For the particular case of transverse flexure configura￾tion when the fracture initiating defect is embedded within the outer ATZ layer, failure stress levels are much lower than the corresponding threshold stress predicted by Eq. (2). This fact can be explained by considering that under this layered architectural design only one compressive layer may act as a crack arrester for these propagating critical defects. Hence, although larger artificial flaws are intro￾duced in the central layer, the stress intensity factor associ￾ated with the outer natural flaws governs the material fracture, yielding a flaw-size dependence mechanical strength. In order to avoid such crack location effect under such a configuration, a similar stress state in both inner and outer thick layers must be guaranteed, a situation that may be achieved if the laminate is designed with outer compres￾sive layers, as if the composite were to be used in contact￾related applications. This design concept may be suggested as an option for preserving relative constant strength val￾ues; and thus, for enhancing reliability under transverse loading conditions. 3.2. Strength on specimens containing several defects Failure stress values were determined for multi-cracked specimens following a similar testing procedure as for the single-cracked samples. All the experimental results under both testing configurations were expressed in terms of stress using Eq. (1) and are shown, in a combined format, in Fig. 6. Under longitudinal flexure testing it was observed that, although the strength of laminates was slightly affected by crack interactions if they were relatively close to each other, i.e. 0.5 ± 0.2 mm apart (Fig. 6a), a constant failure Fig. 4. Plot of the measured four-point bending failure stress vs. indentation load in the laminate tested under transverse flexure. Specimens that failed through indentations located in the central ATZ layer show an almost constant value, whereas the ones failing owed to the natural flaws present a lower value with a higher scatter. Fig. 5. SEM micrograph showing the source of failure (natural flaw) encountered at the outer most ATZ layer ‘‘f’’, despite the indentation crack ‘‘i’’ located in the central layer. A detail of the failure-controlling natural flaw is also presented. R. Bermejo et al. / Composites Science and Technology 68 (2008) 244–250 247

R Bermejo et al. Composites Science and Technology 68(2008)244-250 nearby flaws (located at different ATZ layers)do have an effect on the strength for multi-cracked specimens tested 350 under transverse flexure(Fig. 6b). Attempting to under- stand the described different crack interaction effects as function of loading mode, an extensive and detailed inspec- tion of the fracture surfaces of the broken indented speci- 点250 mens was conducted. Different from the case of the specimens tested under longitudinal flexure, interaction of 目2001a) the indentation cracks with intrinsic defects, such as pores or agglomerates, was often evidenced at fracture when the offset separation distance resulted to be less than 0.6 mm. In general, interacting natural flaws introduced during the 0.00.51.01.52.02.53.0 processing step were encountered within one of the adja- Offset separation distance, x[mm] cent ATZ layers near the indentation crack; and in all the cases. both the intrinsic defect and the indentation crack axis (a) perpendicular and (b) parallel to the layer plane. In the experienced an initial growth up to the corresponding g r, faw interaction effects are almost negligible and thus, from this ATZ/AMZ interfaces where they got arrested(as evi perspective, such a factor should not affect the high strength reliability denced in Fig 8)owed to the high compressive stresses in assessed under this loading configuration. In the later, natural flaws are the thin AMZ layers. Then, by increasing the applied load, bserved to interact with indentation cracks under certain offset separa- the critical stress intensity factor of the AMz compressive tion distances, reducing the strength levels encountered for single-cracked layer was finally overcome, and both defects coalesced and propagated unstably up to catastrophic failure at a stress level below the one resulted for the single-crack specimen, stress value similar to the case of a single-crack was as reported in Fig. 6b. Hence, it is suggested that the rela achieved regardless of the crack offset separation. As a tively higher prominence of multiple cracking effects on matter of fact, for the particular case of co-planar cracks, failure stress under transverse flexure is directly related to i.e. with zero offset separation distance, they were found the effective capability of the existing defects to interact coalesce at a certain load and behave as one single crack, with each other at regions close to the specimen surface as it can be inferred from Fig. 7. In such case, failure stress subjected to nominally maximum tensile stresses. Such fell within the scatter of the threshold stress value encoun- interacting capability is expected to be enhanced under tered for single-cracked specimens. Regarding crack loading parallel to the layer plane as a direct consequence growth mechanisms as related to the laminated architec- of the operation of the natural energy absorption mecha ture, a fracture surface exhibiting a similar step-wise profile nisms for these laminated ceramics, i.e. crack bifurcation as for the case of single-cracked specimens was also appre- and deflection within the thin aMz layers. This is not ciated(Fig. 7) the case under loading perpendicular to the layer plane Concerning transverse flexure testing, although qualitatively similar to the one described above a because similar crack interactions could only occur in the interior of the specimen, i.e. at locations where the levels influence of flaw interaction was also discerned, in agree- ment with the results reported by Moon et al. [29] for an alumina-mullite laminar composite, two particular obser- vations should be highlighted. First, relative differences in strength are somehow more pronounced under loading parallel to the layer plane than under longitudinal flexure testing(maximum decrease of about 15% in the former as compared to values close to 9%o in the latter). Second, 500 um 00 Fig. 8. Fracture site of two specimens where the indentation crack"i Fig. 7. Step-wise fracture of a laminate with co-planar indentations interacts with a natural flaw "f, located in the adjacent layer. As a located at the outer ATZ layer. A detail of the penny-like indentation consequence, the corresponding failure stress level is lower than that of specimens with a single crack in the central layer

stress value similar to the case of a single-crack was achieved regardless of the crack offset separation. As a matter of fact, for the particular case of co-planar cracks, i.e. with zero offset separation distance, they were found to coalesce at a certain load and behave as one single crack, as it can be inferred from Fig. 7. In such case, failure stress fell within the scatter of the threshold stress value encoun￾tered for single-cracked specimens. Regarding crack growth mechanisms as related to the laminated architec￾ture, a fracture surface exhibiting a similar step-wise profile as for the case of single-cracked specimens was also appre￾ciated (Fig. 7). Concerning transverse flexure testing, although a trend qualitatively similar to the one described above on the influence of flaw interaction was also discerned, in agree￾ment with the results reported by Moon et al. [29] for an alumina-mullite laminar composite, two particular obser￾vations should be highlighted. First, relative differences in strength are somehow more pronounced under loading parallel to the layer plane than under longitudinal flexure testing (maximum decrease of about 15% in the former as compared to values close to 9% in the latter). Second, nearby flaws (located at different ATZ layers) do have an effect on the strength for multi-cracked specimens tested under transverse flexure (Fig. 6b). Attempting to under￾stand the described different crack interaction effects as a function of loading mode, an extensive and detailed inspec￾tion of the fracture surfaces of the broken indented speci￾mens was conducted. Different from the case of the specimens tested under longitudinal flexure, interaction of the indentation cracks with intrinsic defects, such as pores or agglomerates, was often evidenced at fracture when the offset separation distance resulted to be less than 0.6 mm. In general, interacting natural flaws introduced during the processing step were encountered within one of the adja￾cent ATZ layers near the indentation crack; and in all the cases, both the intrinsic defect and the indentation crack experienced an initial growth up to the corresponding ATZ/AMZ interfaces where they got arrested (as evi￾denced in Fig. 8) owed to the high compressive stresses in the thin AMZ layers. Then, by increasing the applied load, the critical stress intensity factor of the AMZ compressive layer was finally overcome, and both defects coalesced and propagated unstably up to catastrophic failure at a stress level below the one resulted for the single-crack specimen, as reported in Fig. 6b. Hence, it is suggested that the rela￾tively higher prominence of multiple cracking effects on failure stress under transverse flexure is directly related to the effective capability of the existing defects to interact with each other at regions close to the specimen surface, subjected to nominally maximum tensile stresses. Such interacting capability is expected to be enhanced under loading parallel to the layer plane as a direct consequence of the operation of the natural energy absorption mecha￾nisms for these laminated ceramics, i.e. crack bifurcation and deflection within the thin AMZ layers. This is not the case under loading perpendicular to the layer plane, because similar crack interactions could only occur in the interior of the specimen, i.e. at locations where the levels Fig. 6. Failure stress values calculated under four-point bending with loading axis (a) perpendicular and (b) parallel to the layer plane. In the former, flaw interaction effects are almost negligible and thus, from this perspective, such a factor should not affect the high strength reliability assessed under this loading configuration. In the later, natural flaws are observed to interact with indentation cracks under certain offset separa￾tion distances, reducing the strength levels encountered for single-cracked specimens. Fig. 7. Step-wise fracture of a laminate with co-planar indentations located at the outer ATZ layer. A detail of the penny-like indentation cracks is also presented. Fig. 8. Fracture site of two specimens where the indentation crack ‘‘i’’ interacts with a natural flaw ‘‘f’’, located in the adjacent layer. As a consequence, the corresponding failure stress level is lower than that of specimens with a single crack in the central layer. 248 R. Bermejo et al. / Composites Science and Technology 68 (2008) 244–250