《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_THICKNESS RATIO-A-Z

Availableonlineatwww.sciencedirectcom Science Direct Acta materialia ELSEVIER Acta Materialia 54(2006)4745-4757 www.actamat-journals.com Residual stresses, strength and toughness of laminates with different layer thickness ratios R Bermejo, Y. Torres A.J. Sanchez-Herencia, C Baudin M. Anglada, L Llanes Departamento de Ciencia de los Materiales e Ingenieria Metalurgica, ETSEIB, Universidad Politecnica de cataluria Anda. Diagonal 647, E-08028 Barcelona, Spain ito de Ceramica y Vidrio(CSIC), C/Kelsen 5, 28049 Madrid, Spain Received 10 February 2006: received in revised form 3 June 2006: accepted 3 June 2006 Abstract The effect of residual stresses on the strength, toughness and work of fracture of Al2O3-5 wt %tZrO,/Al2O3-30 wt % mZrO2 layered ceramics with different thickness ratios has been investigated The laminates, as well as a monolithic AlO3-5 wt taro used as refer ence material, were fabricated by sequential slip casting Residual stresses were estimated experimentally using indentation techniques and analytically using a three-dimensional finite element model. Flexural strength was evaluated by means of four-point bending tests on specimens with natural and artificial (indentation) flaws. Experimental findings show the existence of a threshold strength in the lam- inates whose value depends on the layer thickness ratio. Crack growth resistance behaviour was studied by crack opening displacement controlled tests and by recourse to a weight function analytical approach. The high compressive stresses in the internal layers yield a that of the reference monolith r in the laminates. Regarding work of fracture, it is found to be enhanced to levels up to about six times pronounced R-curve behavi on the basis of the compromise between threshold strength and energy absorption capability associated with crack bifurcation mecha nisms occurring at fracture o 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Multilayers; Residual stresses; Fracture: Threshold strength; Toughness 1. Introduction limits their use for load-bearing applications. In the last three decades. remarka ble advances have been achieved Design against brittle- like fracture assumes that materi- to overcome the lack of toughness of structural ceramics als contain defects either within the bulk or at the surface, Several processing routes have emerged which do not recall resulting from processing and/or machining procedures. conventional "flaw elimination"approaches, but rather This is specifically true for ceramic components where"flaw tolerant'ones based on the operability of energy intrinsic or extrinsic flaws are the common source of failure release mechanisms aiming to improve strength reliability due to the stress concentration associated with them. From Among those doping, fibre and/or particle reinforcement this perspective, it is well established that the stress concen- functional grading and layered architectural design may tration at a crack tip depends on crack geometry; hence, be highlighted. Particularly, alumina-zirconia [1, 2] and the size and type of these defects will condition the mechan- mullite-alumina [3] ceramic composites with a layered ical strength of the material. As a result, structural ceram- structure, among others, have been reported to exhibit ics exhibit a statistically variable brittle fracture which increased apparent fracture toughness and energy absorp- +34934011083;fax:+34934016706 One of the most used multilayer designs that ensures E-mail address anes(@upc.edu(L. Llanes). higher apparent toughness is that which combines layers 1359-6454/$30.00 O 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Residual stresses, strength and toughness of laminates with different layer thickness ratios R. Bermejo a , Y. Torres a , A.J. Sa´nchez-Herencia b , C. Baudı´n b , M. Anglada a , L. Llanes a,* a Departamento de Ciencia de los Materiales e Ingenierı´a Metalu´rgica, ETSEIB, Universidad Polite´cnica de Catalun˜a, Avda. Diagonal 647, E-08028 Barcelona, Spain b Instituto de Cera´mica y Vidrio (CSIC), C/Kelsen 5, 28049 Madrid, Spain Received 10 February 2006; received in revised form 3 June 2006; accepted 3 June 2006 Abstract The effect of residual stresses on the strength, toughness and work of fracture of Al2O3–5 wt.% tZrO2/Al2O3–30 wt.% mZrO2 layered ceramics with different thickness ratios has been investigated. The laminates, as well as a monolithic Al2O3–5 wt.% tZrO2 used as refer￾ence material, were fabricated by sequential slip casting. Residual stresses were estimated experimentally using indentation techniques and analytically using a three-dimensional finite element model. Flexural strength was evaluated by means of four-point bending tests on specimens with natural and artificial (indentation) flaws. Experimental findings show the existence of a threshold strength in the lam￾inates whose value depends on the layer thickness ratio. Crack growth resistance behaviour was studied by crack opening displacement￾controlled tests and by recourse to a weight function analytical approach. The high compressive stresses in the internal layers yield a pronounced R-curve behaviour in the laminates. Regarding work of fracture, it is found to be enhanced to levels up to about six times that of the reference monolith. The results are discussed in terms of the optimum layered architectural design for structural applications on the basis of the compromise between threshold strength and energy absorption capability associated with crack bifurcation mecha￾nisms occurring at fracture. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Multilayers; Residual stresses; Fracture; Threshold strength; Toughness 1. Introduction Design against brittle-like fracture assumes that materi￾als contain defects either within the bulk or at the surface, resulting from processing and/or machining procedures. This is specifically true for ceramic components where intrinsic or extrinsic flaws are the common source of failure due to the stress concentration associated with them. From this perspective, it is well established that the stress concen￾tration at a crack tip depends on crack geometry; hence, the size and type of these defects will condition the mechan￾ical strength of the material. As a result, structural ceram￾ics exhibit a statistically variable brittle fracture which limits their use for load-bearing applications. In the last three decades, remarkable advances have been achieved to overcome the lack of toughness of structural ceramics. Several processing routes have emerged which do not recall conventional ‘‘flaw elimination’’ approaches, but rather ‘‘flaw tolerant’’ ones based on the operability of energy release mechanisms aiming to improve strength reliability. Among those, doping, fibre and/or particle reinforcement, functional grading and layered architectural design may be highlighted. Particularly, alumina–zirconia [1,2] and mullite–alumina [3] ceramic composites with a layered structure, among others, have been reported to exhibit increased apparent fracture toughness and energy absorp￾tion, as well as non-catastrophic failure behaviour. One of the most used multilayer designs that ensures higher apparent toughness is that which combines layers 1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.06.008 * Corresponding author. Tel.: +34 93 4011083; fax: +34 93 4016706. E-mail address: luis.miguel.llanes@upc.edu (L. Llanes). www.actamat-journals.com Acta Materialia 54 (2006) 4745–4757

R Bermejo et al. Acta Materialia 54(2006)4745-4757 with different volume changes during cooling from the sin- ized methods are available to evaluate the fracture tough- tering temperature. Under these conditions, an alternate ness in layered composites, a fracture mechanics weight tensile-compressive residual stress state develops with spe- function analysis was effectively used to estimate the crack cific location of the compressive layers, either at the surface growth resistance behaviour(R-curve)as a function of or internally, depending on the attempted design approach, position within the layered architectures investigated based on either mechanical resistance or damage tolerance, Additionally, crack opening displacement (COD)- respectively. In the former case, the effect of the compres- controlled tests were conducted to determine the work of sive residual stresses on the nominally applied stress results fracture in monoliths and laminates. Finally, a discussion in a higher, but single-value, apparent fracture toughness of the optimum multilayered architectural design is pro- gether with enhanced strength( the main goal) and some vided in terms of threshold strength, toughness and energy improved reliability [4, 5]. On the other hand, in the latter absorption capability associated with energy-dissipating case, the internal compressive layer is microstructurally mechanisms operative during initial crack extension up to designed to rather act as stopper of any potential process- final catastrophic failure ing flaw at surface layers, independent of original size and location, such that failure tends to take place under condi- 2. Experimental tions of maximum crack growth resistance. As a conse- ce, strength becomes flawsize independent and 2. 1. Materials bility is significantly increased. Within this framework an"extreme"case is the possibility of developing materials The following starting powders were used: (i)a-alu- hibiting a threshold strength", i.e. a stress below which mina( Condea, HPAO5, USA)with 0. 29 um average par failure would not occur despite the presence of relatively ticle size and 8.5 m/g specific surface area (N2 large cracks, as reported for alumina-alumina mullite adsorption; BET method),(iiY2O3-free and Y2O3 .7] or alumina-alumina zirconia multilayered systems (3 wt %)-stabilized zirconia(TZ-0 and TZ-3YS, Tosoh [8]. From this viewpoint, much effort has been expended Japan)with 0.60 and 0. 37 um average particle size and on the fabrication of laminates with a tailored residual 14.0 and 6.7 m-g specific surface area, respectively. a stress profile arising from mismatch of thermal expansion slurry composed of AlO3/5 vol. Y2O3-stabilized Zro coefficients between layers, selective phase transformation (t-ZrO2), referred to as ATZ, was used to form all the and/or chemical reactions [7, 9, 10]. In these investigations, thicker layers. The t-ZrO2 was utilized to control the zirconia-containing laminar ceramics have been employed grain size of the Al_O3 during sintering. In order to form develop compressive stresses in the internal layers by the thin layers a slurry containing Al2O3 /30 vol %Y2O means of the tetragonal to monoclinic phase transforma- free ZrO2(m-ZrO2), named AMZ, was employed. Each tion that takes place in the zirconia phase when cooling suspension was re-used every time to form the successive down during sintering. The corresponding volume increase layers of the corresponding composition. The content of associated with such transformation determines the resid- non-stabilized zirconia in these layers was selected to pro- ual stress field within the multilayer. Under certain condi- mote high residual compressive stresses, as studied in pre- tions, these compressive stresses may act as a barrier to vious works [15, 17, 18]. Preparation of the batches has crack propagation. In other cases, crack deflection at the already been detailed elsewhere [19]. Wall thickness vs. interface of dissimilar materials [11-13]and/or crack bifur- time curves were experimentally determined on monolithic cation due to the high compressive stresses in the internal samples for both slurries and then used to calculate the layers of the composite [14, 15]result in an increase of frac- time for sequential slip casting of three different multilay ture toughness and energy absorption capability [16]. The ered systems named A, B and C, with the same composi- search of laminar ceramic composites for structural appli- tion but different layer thickness ratios [20]. Laminates cations must be focused on"flaw tolerance"materials, were composed in all cases of five thick ATZ layers alter where reliability gets significantly enhanced, exhibiting a nated with four thin AMZ layers. Cast specimens were fairly high resistance to failure. carefully removed from the moulds, dried at room tem- The purpose of the investigation reported here was to perature for 48 h, and finally fired at 1550C for 2 h using optimize the design of alumina-zirconia layered ceramics heating and cooling rates of 5 C/min Rectangular plates obtain flaw-tolerant materials with pronounced crack of approximately 60 mm x 60 mm x 4 mm were obtained growth resistance and work of fracture. In doing so, three for the three multilayered architectures. The thickness of multilayered architectures of the same composition but dif- the layers resulting for each case was measured by optical experimental and analytically using the indentation tech- are listed in Table 1. The outer ATZ layers were cast nique and a three-dimensional finite element model, respec- thicker than the inner ones to allow grinding and polish tively. Four-point bending tests were performed on virgin ing procedures. Density measurements were carried out and indented samples to account for the existence of a for both ATZ monoliths and laminates, yielding values threshold strength in the laminates. Although no standard- of 99.5% and 99.3%, respectively

with different volume changes during cooling from the sin￾tering temperature. Under these conditions, an alternate tensile–compressive residual stress state develops with spe￾cific location of the compressive layers, either at the surface or internally, depending on the attempted design approach, based on either mechanical resistance or damage tolerance, respectively. In the former case, the effect of the compres￾sive residual stresses on the nominally applied stress results in a higher, but single-value, apparent fracture toughness together with enhanced strength (the main goal) and some improved reliability [4,5]. On the other hand, in the latter case, the internal compressive layer is microstructurally designed to rather act as stopper of any potential process￾ing flaw at surface layers, independent of original size and location, such that failure tends to take place under condi￾tions of maximum crack growth resistance. As a conse￾quence, strength becomes flawsize independent and reliability is significantly increased. Within this framework, an ‘‘extreme’’ case is the possibility of developing materials exhibiting a ‘‘threshold strength’’, i.e. a stress below which failure would not occur despite the presence of relatively large cracks, as reported for alumina–alumina mullite [6,7] or alumina–alumina zirconia multilayered systems [8]. From this viewpoint, much effort has been expended on the fabrication of laminates with a tailored residual stress profile arising from mismatch of thermal expansion coefficients between layers, selective phase transformation and/or chemical reactions [7,9,10]. In these investigations, zirconia-containing laminar ceramics have been employed to develop compressive stresses in the internal layers by means of the tetragonal to monoclinic phase transforma￾tion that takes place in the zirconia phase when cooling down during sintering. The corresponding volume increase associated with such transformation determines the resid￾ual stress field within the multilayer. Under certain condi￾tions, these compressive stresses may act as a barrier to crack propagation. In other cases, crack deflection at the interface of dissimilar materials [11–13] and/or crack bifur￾cation due to the high compressive stresses in the internal layers of the composite [14,15] result in an increase of frac￾ture toughness and energy absorption capability [16]. The search of laminar ceramic composites for structural appli￾cations must be focused on ‘‘flaw tolerance’’ materials, where reliability gets significantly enhanced, exhibiting a fairly high resistance to failure. The purpose of the investigation reported here was to optimize the design of alumina–zirconia layered ceramics to obtain flaw-tolerant materials with pronounced crack growth resistance and work of fracture. In doing so, three multilayered architectures of the same composition but dif￾ferent layer thickness ratios fabricated by slip casting were studied. The residual stress profile was determined both experimental and analytically using the indentation tech￾nique and a three-dimensional finite element model, respec￾tively. Four-point bending tests were performed on virgin and indented samples to account for the existence of a threshold strength in the laminates. Although no standard￾ized methods are available to evaluate the fracture tough￾ness in layered composites, a fracture mechanics weight function analysis was effectively used to estimate the crack growth resistance behaviour (R-curve) as a function of position within the layered architectures investigated. Additionally, crack opening displacement (COD)- controlled tests were conducted to determine the work of fracture in monoliths and laminates. Finally, a discussion of the optimum multilayered architectural design is pro￾vided in terms of threshold strength, toughness and energy absorption capability associated with energy-dissipating mechanisms operative during initial crack extension up to final catastrophic failure. 2. Experimental 2.1. Materials The following starting powders were used: (i) a-alu￾mina (Condea, HPA05, USA) with 0.29 lm average par￾ticle size and 8.5 m2 /g specific surface area (N2 adsorption; BET method), (ii) Y2O3-free and Y2O3 (3 wt.%)-stabilized zirconia (TZ-0 and TZ-3YS, Tosoh, Japan) with 0.60 and 0.37 lm average particle size and 14.0 and 6.7 m2 /g specific surface area, respectively. A slurry composed of Al2O3/5 vol.% Y2O3-stabilized ZrO2 (t-ZrO2), referred to as ATZ, was used to form all the thicker layers. The t-ZrO2 was utilized to control the grain size of the Al2O3 during sintering. In order to form the thin layers a slurry containing Al2O3/30 vol.% Y2O3- free ZrO2 (m-ZrO2), named AMZ, was employed. Each suspension was re-used every time to form the successive layers of the corresponding composition. The content of non-stabilized zirconia in these layers was selected to pro￾mote high residual compressive stresses, as studied in pre￾vious works [15,17,18]. Preparation of the batches has already been detailed elsewhere [19]. Wall thickness vs. time curves were experimentally determined on monolithic samples for both slurries and then used to calculate the time for sequential slip casting of three different multilay￾ered systems named A, B and C, with the same composi￾tion but different layer thickness ratios [20]. Laminates were composed in all cases of five thick ATZ layers alter￾nated with four thin AMZ layers. Cast specimens were carefully removed from the moulds, dried at room tem￾perature for 48 h, and finally fired at 1550 C for 2 h using heating and cooling rates of 5 C/min. Rectangular plates of approximately 60 mm · 60 mm · 4 mm were obtained for the three multilayered architectures. The thickness of the layers resulting for each case was measured by optical microscopy on polished samples, and the experimental values, including the corresponding layer thickness ratios, are listed in Table 1. The outer ATZ layers were cast thicker than the inner ones to allow grinding and polish￾ing procedures. Density measurements were carried out for both ATZ monoliths and laminates, yielding values of 99.5% and 99.3%, respectively. 4746 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757

R Bermejo et al. Acta Materialia 54(2006)4745-4757 Table I and used to calculate the residual stresses, res, through Layer thickness and thickness ratio of the multilayered systems A, B andc the I Multilayer Layer thickness (um) Thickness ratio (ATZ: AMZ) AMZ Vvc 650士10140±546 B 540±1095±55.7 where co and c are the indentation crack lengths in the atz 570±10 60±5 monolith and in the aTz layers of the laminate, respec- c k -shape factor that alculated for a given geometry (in this case y=0.90, as determined for 2.2 Residual stress determination a similar multilayer composite on a previous study [25]) and Klc is the fracture toughness obtained by the indenta- n every case where dissimilar materials are sealed tion method in the corresponding ATZ monolithic material together and subsequently undergo differential dimensional [8]. change, stresses arise between them [21]. For a multilayered Additionally, a finite element analysis previously devel- system composed of n layers of composition X and thick- oped [26] was implemented in order to determine the resid- ual stress profile within the tri-dimensional multilayered struc ly the residual stress values in the bulk of each layer may were modelled as representative of the samples utilized in the experiments for material characterization. The sintering E (1) step was simulated attempting to quantify the thermal strain mismatch during cooling and the corresponding residual stress field in the layered materials under investiga E (2) tion. The finite element model employed was a nine-layer structure, whose layer properties, i.e. Youngs modulus and thermal expansion coefficient, were taken as those of where E=Ei/(1-vi), E; being Youngs modulus and vi the monolithic ATZ and AMZ samples. All materials were Poissons ratio of a given layer. As evidenced from the assumed to be isotropic so that only two independent above equation, the magnitude of the residual stresses ,y ratio, had to be provided. Young's moduli for the ATZ n- mechanical properties, Youngs modulus and Poissons erated in these systems depends on both the relative th less of the layers(ts/ty)and the difference in thermal strain and AMZ layers were taken as those experimentally deter- between adjacent layers, AE. As mentioned before, this mined by the impulse excitation technique on the corre residual thermal strain may be due to mismatch of thermal sponding monoliths [25], i.e. 390 and 280 GPa, expansion coefficients between layers, selective phase trans- respectively. A Poisson,s ratio of 0.22 was used for all the formations and/or chemical reactions. In this investigation, layers. Regarding thermal properties, the thermal expan non-stabilized zirconia has been utilized in the thin AMz sion coefficients (oATz=9.82 x 10K and aAMZ layers to generate a significant thermal mismatch between 802x 10-6K-) were discretely introduced in the model layers due to the t-m zirconia phase transformation from data corresponding to dilatometry curves, consider occurring when cooling down during sintering. This mar- ing 1250C as the reference stress-free state i.e. the tem tensitic transformation is accompanied by an increase in perature above which residual stresses are negligible [25] volume which modifies the cooling shrinkage behaviour The residual stress profile was computed both at the centre of the laminate, developing compressive stresses inside of the laminates and at the surface, in order to account for the thin layers and tensile stresses in the thicker ones the edge stress effects in the composites [27] In order to evaluate experimentally the residual stress profile in the multilayers investigated, the indentation tech- 2.3. Flexural strength tests ue was employed. Several Vickers indentations with a load of 30 N were applied in the three laminates at different The modulus of rupture(MOR)of the three laminates distances from the ATZ/AMZ interface. The cracks nor- was evaluated under four-point bending tests performed mal to the ATZ/AMZ interface, emanating from such on prismatic bars and compared to that of the atz mono- indentations, were measured using interference contrast. lith, taken as reference. Five specimens of each kind were To determine the crack tip position for each indentation used for strength determination. In doing so, a fully artic- crack, the light beam was reduced so that the crack tip ulated test jig with inner and outer spans of 10 and 20 mm, ras in the dark field next to the beam area. The magnitude respectively, was used. Tests were carried out under load f the residual stresses in the inner and outer ATZ layers of control using a servohydraulic testing machine(model each laminate was determined by equating the critical 1341, Instron Ltd. with a load cell of 20 kN at a rate of stress intensity factor, Klc, for indentation cracks on a 100 N/s. All the fractured specimens were inspected using stress-free ceramic [23] and on a ceramic within a residual both reflected light optical microscopy and scanning elec- stress field [24]. Thus, The following equation is obtained tron microscopy (JEOL JMS 6400) to determine the type

2.2. Residual stress determination In every case where dissimilar materials are sealed together and subsequently undergo differential dimensional change, stresses arise between them [21]. For a multilayered system composed of n layers of composition X and thick￾ness tx and n 1 layers of composition Y and thickness ty, the residual stress values in the bulk of each layer may be estimated as [22] rx ¼ De E0 x 1 þ E0 xntx E0 y ðn1Þty ð1Þ ry ¼ De E0 y 1 þ E0 y ðn1Þty E0 xntx ð2Þ where E0 i ¼ Ei=ð1 miÞ, Ei being Young’s modulus and mi Poisson’s ratio of a given layer. As evidenced from the above equation, the magnitude of the residual stresses gen￾erated in these systems depends on both the relative thick￾ness of the layers (tx/ty) and the difference in thermal strain between adjacent layers, De. As mentioned before, this residual thermal strain may be due to mismatch of thermal expansion coefficients between layers, selective phase trans￾formations and/or chemical reactions. In this investigation, non-stabilized zirconia has been utilized in the thin AMZ layers to generate a significant thermal mismatch between layers due to the t ! m zirconia phase transformation occurring when cooling down during sintering. This mar￾tensitic transformation is accompanied by an increase in volume which modifies the cooling shrinkage behaviour of the laminate, developing compressive stresses inside the thin layers and tensile stresses in the thicker ones. In order to evaluate experimentally the residual stress profile in the multilayers investigated, the indentation tech￾nique was employed. Several Vickers indentations with a load of 30 N were applied in the three laminates at different distances from the ATZ/AMZ interface. The cracks nor￾mal to the ATZ/AMZ interface, emanating from such indentations, were measured using interference contrast. To determine the crack tip position for each indentation crack, the light beam was reduced so that the crack tip was in the dark field next to the beam area. The magnitude of the residual stresses in the inner and outer ATZ layers of each laminate was determined by equating the critical stress intensity factor, KIc, for indentation cracks on a stress-free ceramic [23] and on a ceramic within a residual stress field [24]. Thus, The following equation is obtained and used to calculate the residual stresses, rres, through the layers of the laminates: rres ¼ 1 w ffiffi c p KIc 1 co c 3=2   ð3Þ where co and c are the indentation crack lengths in the ATZ monolith and in the ATZ layers of the laminate, respec￾tively, w is a crack-shape factor that can be calculated for a given geometry (in this case w = 0.90, as determined for a similar multilayer composite on a previous study [25]), and KIc is the fracture toughness obtained by the indenta￾tion method in the corresponding ATZ monolithic material [8]. Additionally, a finite element analysis previously devel￾oped [26] was implemented in order to determine the resid￾ual stress profile within the tri-dimensional multilayered structures. In doing so, prismatic bar-shaped specimens were modelled as representative of the samples utilized in the experiments for material characterization. The sintering step was simulated attempting to quantify the thermal strain mismatch during cooling and the corresponding residual stress field in the layered materials under investiga￾tion. The finite element model employed was a nine-layer structure, whose layer properties, i.e. Young’s modulus and thermal expansion coefficient, were taken as those of the monolithic ATZ and AMZ samples. All materials were assumed to be isotropic so that only two independent mechanical properties, Young’s modulus and Poisson’s ratio, had to be provided. Young’s moduli for the ATZ and AMZ layers were taken as those experimentally deter￾mined by the impulse excitation technique on the corre￾sponding monoliths [25], i.e. 390 and 280 GPa, respectively. A Poisson’s ratio of 0.22 was used for all the layers. Regarding thermal properties, the thermal expan￾sion coefficients (aATZ = 9.82 · 106 K1 and aAMZ = 8.02 · 106 K1 ) were discretely introduced in the model from data corresponding to dilatometry curves, consider￾ing 1250 C as the reference stress-free state, i.e. the tem￾perature above which residual stresses are negligible [25]. The residual stress profile was computed both at the centre of the laminates and at the surface, in order to account for the edge stress effects in the composites [27]. 2.3. Flexural strength tests The modulus of rupture (MOR) of the three laminates was evaluated under four-point bending tests performed on prismatic bars and compared to that of the ATZ mono￾lith, taken as reference. Five specimens of each kind were used for strength determination. In doing so, a fully artic￾ulated test jig with inner and outer spans of 10 and 20 mm, respectively, was used. Tests were carried out under load control using a servohydraulic testing machine (model 1341, Instron Ltd.) with a load cell of 20 kN at a rate of 100 N/s. All the fractured specimens were inspected using both reflected light optical microscopy and scanning elec￾tron microscopy (JEOL JMS 6400) to determine the type, Table 1 Layer thickness and thickness ratio of the multilayered systems A, B and C Multilayer Layer thickness (lm) Thickness ratio (ATZ:AMZ) ATZ AMZ A 650 ± 10 140 ± 5 4.6 B 540 ± 10 95 ± 5 5.7 C 570 ± 10 60 ± 5 9.5 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757 4747

R Bermejo et al. Acta Materialia 54(2006)4745-4757 size and location of the failure-controlling natural flaws. 3. Results and discussion The mechanical strength for the three laminates, af and of, and the reference monolith, o fTz, is based on the 3. 1. Residual stress profile evaluation of the failure stress at the location of the dis- cerned critical natural flaw. The stress distribution under The variation of the experimentally measured indenta four-point bending on a prismatic bar formed by layers tion crack length for the three laminates, as a function of with different elastic properties was taken into account fol- the distance to the interlayer, is presented in Fig. 1. The lowing the expression given by [28] magnitude and distribution of the residual stresses within the inner and outer ATZ layers of the laminates, deter- ()(y-Ja) (4) mined using Eq (3), are shown in Fig. 2. For the internal ATz lay where E; is Youngs modulus of the corresponding layer, M obtained, reaching a maximum value close to the atz/ is the moment for the case of four-point bending tests AMZ interfaces. On the other hand, for the outer layers, (M= FL, where Fis the applied load and I the distance be- residual stresses decrease when the free surface is tween inner and outer spans), yna is the position of the neu- approached. Experimental limitations due to the small tral axis on a multilayer, y is the specimen depth where the dimensions of the AMZ layers hindered the study of the failure stress is to be determined (at the location of the crit- empiric residual stress profile in these thin compressive ical flaw)and EI is the flexural rigidity of the layered com- layers posite calculated for bending perpendicular to the layer It is well known that stresses at the free surface of lay ered materials are different from those within the bulk In order to evaluate the threshold strength and R-curve While the stresses determined by the indentation method behaviour in the laminates investigated, four specimens are valid for the surface of the specimens, the stress profile from each multilayered system were ground and polished calculated with the three-dimensional finite element model up to 3 um both at the surface and at one of their lateral describes the residual stress distribution through the layers faces. Four different combinations of vickers indentations both in the bulk and at the surface of the three laminates were placed longitudinally on each specimen surface with an offset separation distance of 2 mm to avoid any crack teraction:(a)200,200,100,50N;(b)150,150,100, 50N;(c)100,100,50,30N;and(d)50,50,30,30N. Inner ATZ layers The same procedure was conducted on ATZ monoliths for comparative purposes. The indentation crack length 目100 was measured using an optical microscope by recourse to Nomarski interference contrast. Finally, all the specimens were fractured under four-point bending. The failure stress for the indented specimens (oRi) was calculated using Eq 马兰 (4), which for the case of the laminates takes into account the different elastic properties of the corresponding layers ATZ monolith In all cases, a post-mortem examination was made to con firm failure initiation from the indentation sites and not 0100200300400500600 from either interface defects or other surface flaws Distance to ATZ/AMZ interface [um) l10 Outer Atz layers 2. 4. Tests under COd control The work of fracture of the laminates and the reference ATZ monolith was determined by testing notched samples in three-point bending under COD control, at a rate of I um/s. Identical specimens for monoliths and laminates were notched using a razor blade automatic machine Notches were machined to enter a small depth, 150 un 叫土 into the aTZ phase, and a COD-gauge was attached to the specimen surface at the notch site to register the 0100200300400500600 COD data. Additionally, the extension of the crack in the Distance to ATZ/AMZ interface [um) single-edge-V-notch-bend (SEVNB) specimens was contin uously monitored using a long-distance focal optical Fig. I. Experimentally measured values of the indentation crack length, as microscope(Questar QM1OO)with an effective magnifica- of the systems A(4), B(O C() and ATZ monolith(): and (i)outer tion of x1000, and the data recorded by software(Labview ATZ layers for the three systems A(), B(O), c(V) and for the aTZ 6. 1) coupled to the testing set-up monolith(■)

size and location of the failure-controlling natural flaws. The mechanical strength for the three laminates, rA f , rB f and rC f , and the reference monolith, rATZ f , is based on the evaluation of the failure stress at the location of the dis￾cerned critical natural flaw. The stress distribution under four-point bending on a prismatic bar formed by layers with different elastic properties was taken into account fol￾lowing the expression given by [28] ri;y ¼ EiM ðEIÞ ðy ynaÞ ð4Þ where Ei is Young’s modulus of the corresponding layer, M is the moment for the case of four-point bending tests (M = Fl, where F is the applied load and l the distance be￾tween inner and outer spans), yna is the position of the neu￾tral axis on a multilayer, y is the specimen depth where the failure stress is to be determined (at the location of the crit￾ical flaw) and EI is the flexural rigidity of the layered com￾posite calculated for bending perpendicular to the layer plane. In order to evaluate the threshold strength and R-curve behaviour in the laminates investigated, four specimens from each multilayered system were ground and polished up to 3 lm both at the surface and at one of their lateral faces. Four different combinations of Vickers indentations were placed longitudinally on each specimen surface with an offset separation distance of 2 mm to avoid any crack interaction: (a) 200, 200, 100, 50 N; (b) 150, 150, 100, 50 N; (c) 100, 100, 50, 30 N; and (d) 50, 50, 30, 30 N. The same procedure was conducted on ATZ monoliths for comparative purposes. The indentation crack length was measured using an optical microscope by recourse to Nomarski interference contrast. Finally, all the specimens were fractured under four-point bending. The failure stress for the indented specimens (rRi) was calculated using Eq. (4), which for the case of the laminates takes into account the different elastic properties of the corresponding layers. In all cases, a post-mortem examination was made to con- firm failure initiation from the indentation sites and not from either interface defects or other surface flaws. 2.4. Tests under COD control The work of fracture of the laminates and the reference ATZ monolith was determined by testing notched samples in three-point bending under COD control, at a rate of 1 lm/s. Identical specimens for monoliths and laminates were notched using a razor blade automatic machine. Notches were machined to enter a small depth, 150 lm, into the ATZ phase, and a COD-gauge was attached to the specimen surface at the notch site to register the COD data. Additionally, the extension of the crack in the single-edge-V-notch-bend (SEVNB) specimens was contin￾uously monitored using a long-distance focal optical microscope (Questar QM100) with an effective magnifica￾tion of ·1000, and the data recorded by software (Labview 6.1) coupled to the testing set-up. 3. Results and discussion 3.1. Residual stress profile The variation of the experimentally measured indenta￾tion crack length for the three laminates, as a function of the distance to the interlayer, is presented in Fig. 1. The magnitude and distribution of the residual stresses within the inner and outer ATZ layers of the laminates, deter￾mined using Eq. (3), are shown in Fig. 2. For the internal ATZ layers a symmetrical parabolic distribution is obtained, reaching a maximum value close to the ATZ/ AMZ interfaces. On the other hand, for the outer layers, residual stresses decrease when the free surface is approached. Experimental limitations due to the small dimensions of the AMZ layers hindered the study of the empiric residual stress profile in these thin compressive layers. It is well known that stresses at the free surface of lay￾ered materials are different from those within the bulk. While the stresses determined by the indentation method are valid for the surface of the specimens, the stress profile calculated with the three-dimensional finite element model describes the residual stress distribution through the layers both in the bulk and at the surface of the three laminates 0 100 200 300 400 500 600 60 70 80 90 100 110 Crack length, c ( μm) Distance to ATZ/AMZ interface [μm] Inner ATZ layers ATZ monolith A B C 0 100 200 300 400 500 600 60 70 80 90 100 110 Crack length, c ( μm) Distance to ATZ/AMZ interface [μm] Outer ATZ layers ATZ monolith A B C (i) (ii) Fig. 1. Experimentally measured values of the indentation crack length, as a function of the distance to ATZ/AMZ interface, in: (i) inner ATZ layers of the systems A (m), B (d), C (.) and ATZ monolith (j); and (ii) outer ATZ layers for the three systems A (n), B (s), C ($) and for the ATZ monolith (j). 4748 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757

R Bermejo et al. Acta Materialia 54(2006)4745-4757 AMZ AMZ AMZ Inner ATZ layers (a)2 ATZ ATZATZ ATZA四 l00 l00 80 300 -400 600 Surface 200300400500600 Distance to ATZ/AMZ interface(um) 0.00.5101.5202.53.03.5 Gi)140 (b) Outer ATZ layers A 100 Surface 0030040050060 0.00.51.015202.53.0 Distance to ATZAMZ interface(um) Fig. 2. Plot of the experimentally measured residual stress profile in (i) inner ATZ layers of the multilayers A(A), B(O), C(; and (ii)outer ATZ layers of the three systems A(A), B(O), C(V) 100 ( Fig 3). From the referred plots it can be inferred that the residual stress profile at the surface is similar to that deter- -400 mined experimentally with indentations. On the other -500 hand. stresses in the bulk show the same distribution within 600 each layer, ranging from 60 to 120 MPa in the tensile layers and from -720 to -680 MPa in the compressive ones 0.00.51.01.520 depending on the laminate studied. These values are in Distance in thickness direction(mm) good agreement with those calculated using Eqs. (1)and (2), as listed in Table 2. As expected, increasing thickness Fig 3. Stress distribution through the layers in the bulk and at the surface ratio results in a strong decrease of the tensile stresses in dimensional finite element model the atz layers together with a slightly rise of the compres- sive stresses in the amz ones from a residual stress view point, multilayer type C would be the best candidate for Table 2 ructural applications, among the ones studied here, since Analytical residual stresses calculated in the bulk material for the A.B and it combines the highest compressive stresses in the internal C multilayered systems layers with the lowest tensile ones at the surface Multilayer Tensile residual 3. 2. fracture behauiour -691 3.2.1. Strength and fractograph Fractographic observations of the fractured specimens showed differences in the natural flaw populations for diameters ranging from 30 to 75 um, less irregular, and ATZ monoliths and laminates. Fig. 4 shows the fracture located closer to the surfaces(Fig 4a). On the other hand, surfaces and the natural defects of some representative pores in the laminates( Fig. 4b-d)were much larger, with ens tested under four-point bending. Even though maximum diameters ranging from 90 to 185 um, and more pores were the critical defects in both series of materials, irregular, such as those formed by differential sintering in those present in the monoliths were smaller, with maximum compacts with large agglomerates. It is clear that removal

(Fig. 3). From the referred plots it can be inferred that the residual stress profile at the surface is similar to that deter￾mined experimentally with indentations. On the other hand, stresses in the bulk show the same distribution within each layer, ranging from 60 to 120 MPa in the tensile layers and from 720 to 680 MPa in the compressive ones, depending on the laminate studied. These values are in good agreement with those calculated using Eqs. (1) and (2), as listed in Table 2. As expected, increasing thickness ratio results in a strong decrease of the tensile stresses in the ATZ layers together with a slightly rise of the compres￾sive stresses in the AMZ ones. From a residual stress view￾point, multilayer type C would be the best candidate for structural applications, among the ones studied here, since it combines the highest compressive stresses in the internal layers with the lowest tensile ones at the surface. 3.2. Fracture behaviour 3.2.1. Strength and fractography Fractographic observations of the fractured specimens showed differences in the natural flaw populations for ATZ monoliths and laminates. Fig. 4 shows the fracture surfaces and the natural defects of some representative specimens tested under four-point bending. Even though pores were the critical defects in both series of materials, those present in the monoliths were smaller, with maximum diameters ranging from 30 to 75 lm, less irregular, and located closer to the surfaces (Fig. 4a). On the other hand, pores in the laminates (Fig. 4b–d) were much larger, with maximum diameters ranging from 90 to 185 lm, and more irregular, such as those formed by differential sintering in compacts with large agglomerates. It is clear that removal 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 Residual Stress (MPa) Distance to ATZ/AMZ interface (μm) Inner ATZ layers A B C 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 Residual stresses (MPa) Distance to ATZ/AMZ interface (μm) Outer ATZ layers A B C (i) (ii) Fig. 2. Plot of the experimentally measured residual stress profile in: (i) inner ATZ layers of the multilayers A (m), B (d), C (.); and (ii) outer ATZ layers of the three systems A (n), B (s), C (,). 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -700 -600 -500 -400 -300 -200 -100 0 100 200 AMZ AMZ AMZ ATZ ATZ Center Surface Residual Stress (MPa) ATZ AMZ (a) ATZ ATZ ATZ ATZ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -700 -600 -500 -400 -300 -200 -100 0 100 200 Center Surface Residual Stress (MPa) (b) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -700 -600 -500 -400 -300 -200 -100 0 100 200 Center Surface Distance in thickness direction (mm) Residual Stress (MPa) (c) Fig. 3. Stress distribution through the layers in the bulk and at the surface of the multilayers (a) A, (b) B, and (c) C, calculated using a three￾dimensional finite element model. Table 2 Analytical residual stresses calculated in the bulk material for the A, B and C multilayered systems Multilayer Tensile residual stress (MPa) Compressive residual stress (MPa) A 116 678 B 97 691 C 60 718 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757 4749

R Bermejo et al. Acta Materialia 54(2006)4745-4757 AT b YST.A SYST. B 100m YST. C d 4. Scanning electron micrographs of fracture sites for the ATZ monolith and laminates A, B and C. Natural flaws in the laminates(b-d) are located at rent locations within the outer most ATZ layer and are larger than those in the aTZ monolith(a). The propagation of the critical flaws in systems A and B is more stepped than in system C, whereas it may be described as flat for the case of the atz monolith. of these agglomerates, formed during the sequential casting Klc= Yarviae step, should be a key action for optimizing the processing procedure of the laminates investigated here where Klc is the plane strain fracture toughness, or is the 6 Following the above ideas, a description of the fracture fracture resistance and y represents a geometrical factor aviour of ATZ monoliths and laminates was attempted that depends on the configuration of the flawed sample in terms of unstable propagation of natural flaws within a and the manner in which the loads are applied. Although linear elastic fracture mechanics(LEFM) framework. Such in applying LEFM criteria it is common to assume frac an approach was implemented by considering monoliths ture-controlling flaws as if they were circular cracks, it is and laminates as brittle materials and their fracture occur- clear from Fig. 4 that failure origins for the materials ring from pre-existing natural flaws of critical size 2ac, studied here are pores, i.e. defects with aspect quite differ according to nship ent from such simple geometry. Within this context, one

of these agglomerates, formed during the sequential casting step, should be a key action for optimizing the processing procedure of the laminates investigated here. Following the above ideas, a description of the fracture behaviour of ATZ monoliths and laminates was attempted in terms of unstable propagation of natural flaws within a linear elastic fracture mechanics (LEFM) framework. Such an approach was implemented by considering monoliths and laminates as brittle materials and their fracture occur￾ring from pre-existing natural flaws of critical size 2ac, according to the generic relationship KIc ¼ Y rf ffiffiffiffiffiffiffi pac p ð5Þ where KIc is the plane strain fracture toughness, rf is the fracture resistance and Y represents a geometrical factor that depends on the configuration of the flawed sample and the manner in which the loads are applied. Although in applying LEFM criteria it is common to assume frac￾ture-controlling flaws as if they were circular cracks, it is clear from Fig. 4 that failure origins for the materials studied here are pores, i.e. defects with aspect quite differ￾ent from such simple geometry. Within this context, one Fig. 4. Scanning electron micrographs of fracture sites for the ATZ monolith and laminates A, B and C. Natural flaws in the laminates (b–d) are located at different locations within the outer most ATZ layer and are larger than those in the ATZ monolith (a). The propagation of the critical flaws in systems A and B is more stepped than in system C, whereas it may be described as flat for the case of the ATZ monolith. 4750 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757

R Bermejo et al. Acta Materialia 54(2006)4745-4757 interesting approach is the consideration of the whole flaw extension of about twice the microstructural scale of the (with an effective crack extension of 2a) as an spherical de- ATZ under consideration. fect(pore of diameter 2R) acting as a stress concentrator Concerning the laminates, as a first approach the value on a circumferential"small""crack(of length b) around it of 3. 2 MPa m"was considered as the intrinsic fracture [29,30]. Various studies are available on the stress intensity toughness of the aTZ layers of the three multilayered sys factor for such a configuration [29, 31, 32]. For simplicity, tems. Under these conditions, the expected applied stress at the relation between the"normalized stress intensity fac- fracture for each multilayered architecture, annl, could be tor"(K/a)and the"normalized crack length"(b/R), as estimated using Eq(7), once the residual stress state inher given in Fig. 4 of Ref. [29] is here fitted to the following ent to the outer ATZ layers(as reported in Table 2)is taken equation nto account. Thus, fracture of laminates originating at g(b/R251+2346/R pores might be described as 1+387(b/R) [g(b/R)l(ores +oa and directly implemented within a relationship as the one given in Eq. (5), but under the consideration of critical flaw where K is assumed to be the Klc for the Atz material size in terms of the length of the circumferential crack at g(b/) is given by Eq.(6)under the consideration of the failure (b) ffective critical flaw sizes experimentally discerned at the K=g(b/R)√mb (1 the sponding fracture surfaces, Ores is the tensile stress in the outer ATZ layer for each layered system and be is taken ndeed, this is an important variable in the model because, as 5 um. The critical appl values extracted from Eq (8)are upon load application, it sets the value of the applied stress listed in Table 3 and would represent the expected failure intensity factor around each pore. As it has been previously stress of each multilayered architecture ng that: (i) stated for other polycrystalline ceramics [33-36), a correct propagation of natural flaws becomes unstable within the outer ATZ layer, and thus, controls failure in these layered tive evaluation of the microstructure at the fracture origin. systems; and(ii) the intrinsic fracture behaviour of this For the particular case of the ATZ investigated, with AlO3 layer is exactly the same as the one exhibited by the bulk and ZrO grain sizes of 2.0-3.0 and 0.3-0.6 um, respec- ATZ monolith. Table 3 also includes, for comparative pur determine the extension, and even the existence, of four-point bending ntal fracture strength or obtained under its intrinsic fine microstructure makes it difficult to poses, the experime cracks. However, they may be speculated to exist once From the data given in Table 3, several aspects may be thermal expansion mismatch between neighbouring grains highlighted. First, the critical appl values predicted for the and phase transformation of zirconia particles, upon cool- laminates, considering their fracture behaviour as governed ing from processing, are accounted for. In this work the by the atz outer layer mechanical properties, are 4-17%o appropriate size of the crack length was first estimated lower than the failure stress r obtained under four-point from calibration of the fracture mechanics model within bending tests. Such a finding suggests that the layered the residual stress-free ATZ monolith, and subsequently structure itself(below the failure-controlling defect)acts implemented for analysing the fracture behaviour of the as reinforcement in terms of strength, with respect to the laminates. In doing so, direct experimental data for the ATZ monolithic material, despite the tensile residual stres- ATZ monolith (i.e. flexural strength and critical flaw size, ses induced within the outer ATZ layer. Second, although as given in Table 3; and a fracture toughness value of the experimental failure stress for the AtZ monolith is 3.2 MPam/2. as measured by the SEVNB method in a pre- higher than for the multilayered materials, as associated vious work [8] were incorporated as inputs within Eq (7), with the different critical defect size above discussed, the yielding as a result a best-fitting b value of 5 um, i.e. a crack corresponding strength scatter decreases in the latter, from 13-14% to about 3-5%. Indeed this is sound evidence of the beneficial effect induced by the layered architectural Table 3 design from a damage tolerance perspective(as discussed Effective failure strength parameters for the laminates and the monolithic below). The strength values measured on the laminates rep- resent a clear indication of a reliable failure stress as of(MPa) Ores(MPa) oapr(MPa) 2ae (um) reported for other multilayered structures designed with ATZ 482±65 487±47 58+15 internal compressive stresses where the strength variability 271#21 145#40 described by the Weibull modulus underlined the high reli- Laminate b360±1497 299士22 128+35 ability of the layered materials [7). Within this context, very interesting observation came from the fact that the Experimentally measured flexural strength of, residual stress each ATZ layer; expected critical applied stress afp considering the within examined fracture surfaces of the laminates showed initial and range of critical natural faw sizes 2ac as discerned from scanning bea growth of the natural flaws up to the first AMZ layer, failure-related external ATZ layers in the laminates as ATZ monoliths: re catastrophic failure, as seen in Fig. 5. Hence, the electron microscopy fractographic examination. true critical flaw size ae (at fracture) became as deep as

interesting approach is the consideration of the whole flaw (with an effective crack extension of 2a) as an spherical de￾fect (pore of diameter 2R) acting as a stress concentrator on a circumferential ‘‘small’’ crack (of length b) around it [29,30]. Various studies are available on the stress intensity factor for such a configuration [29,31,32]. For simplicity, the relation between the ‘‘normalized stress intensity fac￾tor’’ (K/r) and the ‘‘normalized crack length’’ (b/R), as given in Fig. 4 of Ref. [29], is here fitted to the following equation: gðb=RÞ ¼ 2:51 þ 2:34ðb=RÞ 1 þ 3:87ðb=RÞ ð6Þ and directly implemented within a relationship as the one given in Eq. (5), but under the consideration of critical flaw size in terms of the length of the circumferential crack at failure (bc): KIc ¼ gðb=RÞrf ffiffiffiffiffiffiffi pbc p ð7Þ Indeed, this is an important variable in the model because, upon load application, it sets the value of the applied stress intensity factor around each pore. As it has been previously stated for other polycrystalline ceramics [33–36], a correct approximation of the size of this crack requires an exhaus￾tive evaluation of the microstructure at the fracture origin. For the particular case of the ATZ investigated, with Al2O3 and ZrO2 grain sizes of 2.0–3.0 and 0.3–0.6 lm, respec￾tively, its intrinsic fine microstructure makes it difficult to clearly determine the extension, and even the existence, of such cracks. However, they may be speculated to exist once thermal expansion mismatch between neighbouring grains and phase transformation of zirconia particles, upon cool￾ing from processing, are accounted for. In this work the appropriate size of the crack length was first estimated from calibration of the fracture mechanics model within the residual stress-free ATZ monolith, and subsequently implemented for analysing the fracture behaviour of the laminates. In doing so, direct experimental data for the ATZ monolith (i.e. flexural strength and critical flaw size, as given in Table 3; and a fracture toughness value of 3.2 MPa m1/2, as measured by the SEVNB method in a pre￾vious work [8]) were incorporated as inputs within Eq. (7), yielding as a result a best-fitting b value of 5 lm, i.e. a crack extension of about twice the microstructural scale of the ATZ under consideration. Concerning the laminates, as a first approach the value of 3.2 MPa m1/2 was considered as the intrinsic fracture toughness of the ATZ layers of the three multilayered sys￾tems. Under these conditions, the expected applied stress at fracture for each multilayered architecture, rc appl, could be estimated using Eq. (7), once the residual stress state inher￾ent to the outer ATZ layers (as reported in Table 2) is taken into account. Thus, fracture of laminates originating at pores might be described as Kc ¼ ½gðb=RÞðrres þ rc applÞ ffiffiffiffiffiffiffi pbc p ð8Þ where Kc is assumed to be the KIc for the ATZ material, g(b/R) is given by Eq. (6) under the consideration of the effective critical flaw sizes experimentally discerned at the corresponding fracture surfaces, rres is the tensile stress in the outer ATZ layer for each layered system and bc is taken as 5 lm. The critical rc appl values extracted from Eq. (8) are listed in Table 3 and would represent the expected failure stress of each multilayered architecture assuming that: (i) propagation of natural flaws becomes unstable within the outer ATZ layer, and thus, controls failure in these layered systems; and (ii) the intrinsic fracture behaviour of this layer is exactly the same as the one exhibited by the bulk ATZ monolith. Table 3 also includes, for comparative pur￾poses, the experimental fracture strength rf obtained under four-point bending. From the data given in Table 3, several aspects may be highlighted. First, the critical rc appl values predicted for the laminates, considering their fracture behaviour as governed by the ATZ outer layer mechanical properties, are 4–17% lower than the failure stress rf obtained under four-point bending tests. Such a finding suggests that the layered structure itself (below the failure-controlling defect) acts as reinforcement in terms of strength, with respect to the ATZ monolithic material, despite the tensile residual stres￾ses induced within the outer ATZ layer. Second, although the experimental failure stress for the ATZ monolith is higher than for the multilayered materials, as associated with the different critical defect size above discussed, the corresponding strength scatter decreases in the latter, from 13–14% to about 3–5%. Indeed, this is sound evidence of the beneficial effect induced by the layered architectural design from a damage tolerance perspective (as discussed below). The strength values measured on the laminates rep￾resent a clear indication of a reliable failure stress, as reported for other multilayered structures designed with internal compressive stresses where the strength variability described by the Weibull modulus underlined the high reli￾ability of the layered materials [7]. Within this context, a very interesting observation came from the fact that the examined fracture surfaces of the laminates showed initial crack growth of the natural flaws up to the first AMZ layer, before catastrophic failure, as seen in Fig. 5. Hence, the true critical flaw size ac (at fracture) became as deep as Table 3 Effective failure strength parameters for the laminates and the monolithic ATZ Material rf (MPa) rres (MPa) rc appl (MPa) 2ac (lm) ATZ 482 ± 65 0 487 ± 47 58 ± 15 Laminate A 326 ± 15 116 271 ± 21 145 ± 40 Laminate B 360 ± 14 97 299 ± 22 128 ± 35 Laminate C 343 ± 12 60 329 ± 16 142 ± 32 Experimentally measured flexural strength rf; residual stress rres within each ATZ layer; expected critical applied stress rc appl considering the failure-related external ATZ layers in the laminates as ATZ monoliths; and range of critical natural flaw sizes 2ac as discerned from scanning electron microscopy fractographic examination. R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757 4751

4752 R Bermejo et al. Acta Materialia 54(2006)4745-4757 the thickness of the outer ATZ layer of the corresponding straight fracture surface was discerned(Fig. 4). On the multilayered system, i.e. the initial flaw is able to experience other hand, the three laminates showed a step-like fracture, an initial extension up to the ATZ/AMZ interface, with y being more pronounced in systems A and B than in system changing as the crack dimensions increase. The effective C (as seen in Fig 4). The main reason for such observation geometrical factor Y ascribed to such critical flaw was eval- may be found in the evidence of deflection and/or bifurca uated from the empirical equations proposed by Newman tion when the corresponding propagating crack interacts and Raju [37] for a semielliptical surface crack of depth a with the thin AMZ layers under compression, as seen in and width 2c, by using a crack geometry aspect ratio(alc) Fig. 6 for laminate type B. The bright regions in the top- of about l, as determined from experimentally measured view of Fig. 6 shows the extent of such crack bifurcation values in the fracture specimens. Within this framework, along the AMZ layers. This phenomenon might increase the LEFM approach was also implemented through Eq. the fracture energy and thus the toughness of the material, (5)to estimate the stress intensity factor K evaluated at as demonstrated by other authors for other multilayered he ATZ/AMZ interface of each laminate, using the failure systems[12, 16]. From this viewpoint, it should be empha stress value calculated at the flaw site given by Eq. (4). The sized that bifurcation was observed at fracture for all the results are shown in Table 4. Although there were no clear laminated materials studied. Such a finding was expected differences in Ke among the three layered systems, there for multilayers type A and B, since edge cracking had been exists a signific in the apparent fracture tough- previously developed in these two systems along the centre less of the laminates with respect to that evaluated for the of the AMZ compressive layers [6, 14, 17]. On the other ATZ monolith. This increase in toughness must be related hand, although system C did not show a very pronounced to the presence of the thin AMZ compressive layers, which step-like fracture surface(see Fig 4), crack bifurcation was act as a well-defined barrier to flaw propagation through also encountered even for specimens where edge cracking the material. It leads to a"single-value"critical flaw size had not been previously detected. This Important at failure, and consequently would suggest the presence finding since these two mechanisms have been always beer of a threshold strength in the laminates investigated. More- thought to be related [38, 39]. Following the above consid- over, observation of the fracture surfaces revealed a differ- erations, the mechanical characterization study was further ent pattern on the crack propagation when comparing the extended in the layered architectures to evaluate the exis- ATZ monolith and the laminates. In the former, similar to tence of a threshold strength and the corresponding crack the finding expected in conventional brittle materials, a growth resistance(R-curve) behaviour 3.2.2. Threshold strength and R-curve behaviour Indentation strength tests were carried out to evaluate the presence of a threshold strength in the laminates, as suggested by the above discussion due to the crack arrest experienced by the natural flaws at the first Atz layer, i.e. existence of a"single-value"flaw size associated with the failure of the specimens. Fig. 7 represents the variation of the failure stress with the indentation load applied for the atz monoliths and for the three laminates studied Fig. 5. Detail of the initial growth of a natural flaw up to the first AMz the best fit for the experimental data. As it can be inferred ecrease in Table 4 Fracture mechanics data and work of fracture for the laminates and monolithic atz Inclined view Gr(MPa) at fiaw site (um) (MPa m2)(J/m2) Top view ATZ Laminate a240±15 50±1073± Laminate b250±14540±107.5±0 Laminate c254±12 570±1073±0.2 Critical stress intensity factor values, Ke, are calculated by recourse to Eq (5), considering the outer ATZ layer thickness as the critical flaw size ac, for the laminates: or by implementing Eq. (7), as related to an intrins defect of effective flaw size 2ac. for the monolithic ATZ. In all the cases 500pm failure stress at the faw site was determined through Eq (4). Finally, work of fracture, woF, was estimated from the integration of the registered Fig. 6. Views of a multilayered type B fracture site. Step-like fracture is load-displacement curve per unit volume for the ATZ monolith as well as observed due to the bifurcation of the propagating crack when entering for the three laminates the AMz layers(bright contour at the top view

the thickness of the outer ATZ layer of the corresponding multilayered system, i.e. the initial flaw is able to experience an initial extension up to the ATZ/AMZ interface, with Y changing as the crack dimensions increase. The effective geometrical factor Y ascribed to such critical flaw was eval￾uated from the empirical equations proposed by Newman and Raju [37] for a semielliptical surface crack of depth a and width 2c, by using a crack geometry aspect ratio (a/c) of about 1, as determined from experimentally measured values in the fracture specimens. Within this framework, the LEFM approach was also implemented through Eq. (5) to estimate the stress intensity factor Kc evaluated at the ATZ/AMZ interface of each laminate, using the failure stress value calculated at the flaw site given by Eq. (4). The results are shown in Table 4. Although there were no clear differences in Kc among the three layered systems, there exists a significant increase in the apparent fracture tough￾ness of the laminates with respect to that evaluated for the ATZ monolith. This increase in toughness must be related to the presence of the thin AMZ compressive layers, which act as a well-defined barrier to flaw propagation through the material. It leads to a ‘‘single-value’’ critical flaw size at failure, and consequently would suggest the presence of a threshold strength in the laminates investigated. More￾over, observation of the fracture surfaces revealed a differ￾ent pattern on the crack propagation when comparing the ATZ monolith and the laminates. In the former, similar to the finding expected in conventional brittle materials, a straight fracture surface was discerned (Fig. 4). On the other hand, the three laminates showed a step-like fracture, being more pronounced in systems A and B than in system C (as seen in Fig. 4). The main reason for such observation may be found in the evidence of deflection and/or bifurca￾tion when the corresponding propagating crack interacts with the thin AMZ layers under compression, as seen in Fig. 6 for laminate type B. The bright regions in the top￾view of Fig. 6 shows the extent of such crack bifurcation along the AMZ layers. This phenomenon might increase the fracture energy and thus the toughness of the material, as demonstrated by other authors for other multilayered systems [12,16]. From this viewpoint, it should be empha￾sized that bifurcation was observed at fracture for all the laminated materials studied. Such a finding was expected for multilayers type A and B, since edge cracking had been previously developed in these two systems along the centre of the AMZ compressive layers [6,14,17]. On the other hand, although system C did not show a very pronounced step-like fracture surface (see Fig. 4), crack bifurcation was also encountered even for specimens where edge cracking had not been previously detected. This is an important finding since these two mechanisms have been always been thought to be related [38,39]. Following the above consid￾erations, the mechanical characterization study was further extended in the layered architectures to evaluate the exis￾tence of a threshold strength and the corresponding crack growth resistance (R-curve) behaviour. 3.2.2. Threshold strength and R-curve behaviour Indentation strength tests were carried out to evaluate the presence of a threshold strength in the laminates, as suggested by the above discussion due to the crack arrest experienced by the natural flaws at the first ATZ layer, i.e. existence of a ‘‘single-value’’ flaw size associated with the failure of the specimens. Fig. 7 represents the variation of the failure stress with the indentation load applied for the ATZ monoliths and for the three laminates studied. A linear regression analysis was implemented to obtain the best fit for the experimental data. As it can be inferred from the plot, the failure stress values, rf, decrease in the Fig. 5. Detail of the initial growth of a natural flaw up to the first AMZ layer for a multilayer type B, before catastrophic failure. Table 4 Fracture mechanics data and work of fracture for the laminates and monolithic ATZ Material rf (MPa) at flaw site ac (lm) Kc (MPa m1/2) cWOF (J/m2 ) ATZ 482 ± 65 29 ± 15 3.2 ± 0.2 22 Laminate A 240 ± 15 650 ± 10 7.3 ± 0.3 77 Laminate B 250 ± 14 540 ± 10 7.5 ± 0.2 126 Laminate C 254 ± 12 570 ± 10 7.3 ± 0.2 102 Critical stress intensity factor values, Kc, are calculated by recourse to Eq. (5), considering the outer ATZ layer thickness as the critical flaw size ac, for the laminates; or by implementing Eq. (7), as related to an intrinsic defect of effective flaw size 2ac, for the monolithic ATZ. In all the cases, failure stress at the flaw site was determined through Eq. (4). Finally, work of fracture, cWOF, was estimated from the integration of the registered load–displacement curve per unit volume for the ATZ monolith as well as for the three laminates. Fig. 6. Views of a multilayered type B fracture site. Step-like fracture is observed due to the bifurcation of the propagating crack when entering the AMZ layers (bright contour at the top view). 4752 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757

R Bermejo et al. Acta Materialia 54(2006)4745-4757 475 204-20 175d=178P xv+l/a +>ay where W is the specimen thickness, and the coefficients Ayu and exponents v and u are determined using the " boundary collocation method, as described elsewhere [41]. Integrat- ing this weight function for the geometries under study, the apparent fracture toughness was determined as a function l00 of a crack length parameter a, defined as Yva, with Y given Indentation Load, P(N by[42] af, with the indentation load, P, for indented ATZ monoliths ()and the Y(a)1.99-a(1-a)(2.15-3.93x+2.702 Fig. 7. Plot of the variation of the failure stress under four-point bending W (1+2x)(1-x) multilayered systems A(▲),B● and c(★). Fig. 8 represents the Kapt.c curve corresponding to a multi- ATZ monoliths with the indentation load applied, P, fol- layered B architecture. The trend of the Kapt. c curve is in lowing a power law, oroe P, with k=0.31. This value good agreement with previous analysis on multilayered is very close to 1/3, which corresponds to the behaviour structures reported in the literature [43-45]. It can be ob. expected in brittle materials exhibiting a flat R-curve served that Kapt.c decreases in the layers with a tensile res single-valued toughness)[40]. On the other hand, the ual stress state and increases rapidly within the layers with exponent k values for the three laminates are much lower compressive residual stresses as a increases. In this regard, than 1/3, suggesting a very steep R-curve behaviour More- although microstructure-related mechanisms such as crack over, the almost constant value of or in the laminates points bridging may influence the increase in the crack growth out the existence of a threshold strength, regardless of the resistance in multilayered alumina-zirconia composites dentation flaw size, reaching its highest value for multi-(as demonstrated by Moon et al. [44), the main contribu layers type C, i.e. layered architectures with relatively tion is due to the macroscopic residual compressive stres- higher compressive stresses. From these findings, it can ses. Within this context, the conditions for stable/ be concluded that threshold strength is dictated by the unstable crack growth in the laminate can be directly estab- magnitude of the compressive stresses present in the thin lished from Fig. 8, as has been nicely presented in recent AMZ layers and, from this perspective, material type C work by Lugovy et al. [45]. Under a far-field applied stress results to be the optimum"flaw tolerance" design in terms intensity factor, Kapp, given by the straight lines in Fig. 8, a of strength crack with a crack length parameter P(i.e. below @)will Although no standardized methods are available to experience unstable propagation once the applied stress evaluate the fracture toughness in layered composites, a gets higher than op On the other hand, a crack with a fracture mechanics weight function analysis has been effec- crack length parameter R (i.e. above @)will grow abruptly tively used to estimate the crack growth resistance behav- at a stress level or, between points R and S, since the seg iour(R-curve)as a function of the position of an edge ment RS lies above the Kapt. c. However, at point S, the crack within each multilayered system investigated with a residual stress distribution, res(x). The so-called apparent fracture toughness (since it is influenced by the residual stresses),Kapt.c, may be defined as follows ATZ AMZ Kle-/h(a,x)ores(x)dr where Klc is the intrinsic fracture toughness of each individ- ual layer calculated by the SEVnb method in the corre- sponding monoliths(2.6 and 3.2 MPa for the amz and aTz layers, respectively), x is the distance along the crack length measured from the surface, a is the crack length, and h(a, x)is a weight function, as developed by 020.040.060.080.10 Fett and Munz [41] for an edge crack in a bar, commonly employed in the evaluation of R-curve behaviour for mul- Fig.8. Conditions for stable/unstable crack propagation in a layered tilayered systems. The corresponding weight function is gi- structure type B with R-curve behaviour determined analytically using the weight function approach, as a function of a crack length parameter a

ATZ monoliths with the indentation load applied, P, fol￾lowing a power law, rf  Pk , with k = 0.31. This value is very close to 1/3, which corresponds to the behaviour expected in brittle materials exhibiting a flat R-curve (single-valued toughness) [40]. On the other hand, the exponent k values for the three laminates are much lower than 1/3, suggesting a very steep R-curve behaviour. More￾over, the almost constant value of rf in the laminates points out the existence of a threshold strength, regardless of the indentation flaw size, reaching its highest value for multi￾layers type C, i.e. layered architectures with relatively higher compressive stresses. From these findings, it can be concluded that threshold strength is dictated by the magnitude of the compressive stresses present in the thin AMZ layers and, from this perspective, material type C results to be the optimum ‘‘flaw tolerance’’ design in terms of strength. Although no standardized methods are available to evaluate the fracture toughness in layered composites, a fracture mechanics weight function analysis has been effec￾tively used to estimate the crack growth resistance behav￾iour (R-curve) as a function of the position of an edge crack within each multilayered system investigated with a residual stress distribution, rres(x). The so-called apparent fracture toughness (since it is influenced by the residual stresses), Kapt,c, may be defined as follows: Kapt;c ¼ KIc Z a 0 hða; xÞrresðxÞdx ð9Þ where KIc is the intrinsic fracture toughness of each individ￾ual layer calculated by the SEVNB method in the corre￾sponding monoliths (2.6 and 3.2 MPa m1/2 for the AMZ and ATZ layers, respectively), x is the distance along the crack length measured from the surface, a is the crack length, and h(a,x) is a weight function, as developed by Fett and Munz [41] for an edge crack in a bar, commonly employed in the evaluation of R-curve behaviour for mul￾tilayered systems. The corresponding weight function is gi￾ven by hða; xÞ ¼ 2 pa  1=2 1 1 x a 1=2 1 a W 3=2  1 a W 3=2 þXAml 1 x a mþ1 a W l   ð10Þ where W is the specimen thickness, and the coefficients Aml and exponents m and l are determined using the ‘‘boundary collocation method’’, as described elsewhere [41]. Integrat￾ing this weight function for the geometries under study, the apparent fracture toughness was determined as a function of a crack length parameter ^a, defined as Y ffiffiffi a p , with Y given by [42] Y ðaÞ ¼ 1:99 að1 aÞð2:15 3:93a þ 2:7a2 ð1 þ 2aÞð1 aÞ 3=2 " #; a ¼ a=W ð11Þ Fig. 8 represents the Kapt,c curve corresponding to a multi￾layered B architecture. The trend of the Kapt,c curve is in good agreement with previous analysis on multilayered structures reported in the literature [43–45]. It can be ob￾served that Kapt,c decreases in the layers with a tensile resid￾ual stress state and increases rapidly within the layers with compressive residual stresses as ^a increases. In this regard, although microstructure-related mechanisms such as crack bridging may influence the increase in the crack growth resistance in multilayered alumina–zirconia composites (as demonstrated by Moon et al. [44]), the main contribu￾tion is due to the macroscopic residual compressive stres￾ses. Within this context, the conditions for stable/ unstable crack growth in the laminate can be directly estab￾lished from Fig. 8, as has been nicely presented in recent work by Lugovy et al. [45]. Under a far-field applied stress intensity factor, Kapp, given by the straight lines in Fig. 8, a crack with a crack length parameter P (i.e. below Q) will experience unstable propagation once the applied stress gets higher than rp. On the other hand, a crack with a crack length parameter R (i.e. above Q) will grow abruptly at a stress level rr, between points R and S, since the seg￾ment RS lies above the Kapt,c. However, at point S, the 50 100 150 200 250 100 125 150 175 200 225 σ A f =167P -0.041 σ B f =178P -0.013 σ C f =210P -0.023 Fracture Strength, σ f(MPa) Indentation Load, P(N) σ ATZ f =575P -0.310 Fig. 7. Plot of the variation of the failure stress under four-point bending rf, with the indentation load, P, for indented ATZ monoliths (j) and the multilayered systems A (m), B (d) and C (w). 0.00 0.02 0.04 0.06 0.08 0.10 -4 0 4 8 12 16 σr σp T S R Q B K apt,c (MPa m1/2) Crack length parameter, â (m1/2) ATZ AMZ σth P Kapp Fig. 8. Conditions for stable/unstable crack propagation in a layered structure type B with R-curve behaviour determined analytically using the weight function approach, as a function of a crack length parameter ^a. R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757 4753

R Bermejo et al. Acta Materialia 54(2006)4745-4757 crack growth would become stable up to point T, i.e. any cerned for systems B and C. However, the decrease in Kapt further crack advance will require an increase in the ap- is not so pronounced in system C since the tensile stresses plied stress. Point T is a maximum value of Kapt.c and it in the corresponding atZ layer are lower than in the other is located at the interface between the first AMZ and the two systems. The negative values for Kapt. c within the first second ATZ layer. As a consequence, it determines the ATZ layer of systems A and B would suggest spontaneous threshold stress value, oth, above which the crack propa- crack growth when the crack reached a certain crack gates unstably up to failure. For cracks with crack length length. As a matter of fact, this phenomenon has been parameters above T, crack extension takes place in a simi- experimentally observed and reported by the authors in a lar way as explained above, and the specimen failure is then previous work [8]. In contrast, multilayered system C did dictated by the maximum value of Kapt.c attained at the not show negative values for Kapt. c, and consequently it interface of the second AMz and third atz layers did not reveal spontaneous crack growing in the experi- Following the above ideas, small surface cracks located ments just discussed. Experimental data supporting the in the region of unstable growth will cause the catastrophic above ideas have been recently assessed by the authors failure of the material when the fracture conditions forfor notched specimens, which showed no continuous crack extension are satisfied, i.e. for an applied stress above growth of the initial crack [8]. Instead, the crack arising enough to fall within the region of initial crack growth, will then gets arrested and finally continues its growth agate, the threshold stress. However, all cracks which are long from the notch in the first ATZ layer starts to prop unstably propagate at the same stress level Oth, i.e. the This crack arrest results in a"pop-in"event on the load- threshold strength. This prediction is sustained by the limit displacement curve, where an instantaneous drop in load strength experimentally encountered for indented layered may be observed specimens, as shown in Fig. 7, where the failure stress of In general, the estimated apparent fracture toughness all specimens converged to the same value, regardless of values, Kapt. c, revealed an enhancement in the multilayer he initial indentation flaw size fracture behaviour with respect to the ATZ monolithic This study has been extended to the other multilayered material taken as reference. However, no significant differ geometries, i.e. systems A and C, and all the results for ence among the three layered structures was noted. In all Kapt. c are shown in Fig 9. It can be seen that Kapt.c follows cases, Kapt.c was calculated at the first AMZ compressive a similar trend for the three laminates investigated, show- layer, which acted as a barrier to any crack propagation. ing a steep R-curve behaviour within the first AMZ com- When the impinging crack entered this layer, bifurcation pressive layer. Nonetheless, some differences may be and/or deflection phenomena were discerned, yielding as discerned. For the cases of laminates A and B, apparent a result a step-like fracture(Fig. 4). This is clear evidence fracture toughness decreases from 3.2 MPa m"to nega- of the complex mode of loading to which these materials tive values within the first ATZ layer until the crack reaches may be subjected during fracture and thus the difficulty he first interface. This is explained by the relatively high in the evaluation of the real fracture toughness of the residual tensile stresses present in the ATZ layers. Once multilayered structures. Hence, in order to assess the con- the crack reaches the first interface, apparent toughness tribution of the rest of the layers to the crack resistance increases in the thin compressive layer region. The maxi- behaviour of each laminate system, COD-controlled tests mum Kapt.c is observed for laminate A, due to the relatively were performed and the work of fracture evaluated for thicker compressive AMZ layer, where the R-curve devel- each multilayered architecture ops up to a value of 9.7 MPa m".It decreases again within the second aTZ tensile layer. The same trend may be dis- 3.2.3. Work of fracture The COD-controlled tests carried out on atz mono- liths and laminates allowed one to evaluate the work of fractu ed to break the samples. In the case of ATZ monolith, the fracture initiated at the notch tip when 12 reaching a certain opening displacement. As expected for a brittle material exhibiting a flat R-curve behaviour failure associated with such first crack extension was already cat ophic(Fig. 10a). For the case of the laminates, crack growth originated also at the notch tip but at a stress value below the maximum one reached by the monolithic sample, B as is clearly discerned from the first load drops in Fig. 10b- d. As has been discussed before, these differences are spec- 0.000.020.040.060.080.10 ulated to come from the tensile residual stresses inherent to the laminate at the notch site. which increase the effective Fig. 9. Apparent fracture toughness, Kapt.c, calculated analytically using stress intensity factor at that point. However, even though the weight function approach, considering the three different layered the crack started to grow at lower stress levels for the lam architectures. A. B and C. inates, it did not produce catastrophic failure as in the case

crack growth would become stable up to point T, i.e. any further crack advance will require an increase in the ap￾plied stress. Point T is a maximum value of Kapt,c and it is located at the interface between the first AMZ and the second ATZ layer. As a consequence, it determines the threshold stress value, rth, above which the crack propa￾gates unstably up to failure. For cracks with crack length parameters above T, crack extension takes place in a simi￾lar way as explained above, and the specimen failure is then dictated by the maximum value of Kapt,c attained at the interface of the second AMZ and third ATZ layers. Following the above ideas, small surface cracks located in the region of unstable growth will cause the catastrophic failure of the material when the fracture conditions for crack extension are satisfied, i.e. for an applied stress above the threshold stress. However, all cracks which are long enough to fall within the region of initial crack growth, will unstably propagate at the same stress level rth, i.e. the threshold strength. This prediction is sustained by the limit strength experimentally encountered for indented layered specimens, as shown in Fig. 7, where the failure stress of all specimens converged to the same value, regardless of the initial indentation flaw size. This study has been extended to the other multilayered geometries, i.e. systems A and C, and all the results for Kapt,c are shown in Fig. 9. It can be seen that Kapt,c follows a similar trend for the three laminates investigated, show￾ing a steep R-curve behaviour within the first AMZ com￾pressive layer. Nonetheless, some differences may be discerned. For the cases of laminates A and B, apparent fracture toughness decreases from 3.2 MPa m1/2 to nega￾tive values within the first ATZ layer until the crack reaches the first interface. This is explained by the relatively high residual tensile stresses present in the ATZ layers. Once the crack reaches the first interface, apparent toughness increases in the thin compressive layer region. The maxi￾mum Kapt,c is observed for laminate A, due to the relatively thicker compressive AMZ layer, where the R-curve devel￾ops up to a value of 9.7 MPa m1/2. It decreases again within the second ATZ tensile layer. The same trend may be dis￾cerned for systems B and C. However, the decrease in Kapt,c is not so pronounced in system C since the tensile stresses in the corresponding ATZ layer are lower than in the other two systems. The negative values for Kapt,c within the first ATZ layer of systems A and B would suggest spontaneous crack growth when the crack reached a certain crack length. As a matter of fact, this phenomenon has been experimentally observed and reported by the authors in a previous work [8]. In contrast, multilayered system C did not show negative values for Kapt,c, and consequently it did not reveal spontaneous crack growing in the experi￾ments just discussed. Experimental data supporting the above ideas have been recently assessed by the authors for notched specimens, which showed no continuous growth of the initial crack [8]. Instead, the crack arising from the notch in the first ATZ layer starts to propagate, then gets arrested and finally continues its growth again. This crack arrest results in a ‘‘pop-in’’ event on the load– displacement curve, where an instantaneous drop in load may be observed. In general, the estimated apparent fracture toughness values, Kapt,c, revealed an enhancement in the multilayer fracture behaviour with respect to the ATZ monolithic material taken as reference. However, no significant differ￾ence among the three layered structures was noted. In all cases, Kapt,c was calculated at the first AMZ compressive layer, which acted as a barrier to any crack propagation. When the impinging crack entered this layer, bifurcation and/or deflection phenomena were discerned, yielding as a result a step-like fracture (Fig. 4). This is clear evidence of the complex mode of loading to which these materials may be subjected during fracture and thus the difficulty in the evaluation of the real fracture toughness of the multilayered structures. Hence, in order to assess the con￾tribution of the rest of the layers to the crack resistance behaviour of each laminate system, COD-controlled tests were performed and the work of fracture evaluated for each multilayered architecture. 3.2.3. Work of fracture The COD-controlled tests carried out on ATZ mono￾liths and laminates allowed one to evaluate the work of fracture required to break the samples. In the case of the ATZ monolith, the fracture initiated at the notch tip when reaching a certain opening displacement. As expected for a brittle material exhibiting a flat R-curve behaviour, failure associated with such first crack extension was already cat￾astrophic (Fig. 10a). For the case of the laminates, crack growth originated also at the notch tip but at a stress value below the maximum one reached by the monolithic sample, as is clearly discerned from the first load drops in Fig. 10b– d. As has been discussed before, these differences are spec￾ulated to come from the tensile residual stresses inherent to the laminate at the notch site, which increase the effective stress intensity factor at that point. However, even though the crack started to grow at lower stress levels for the lam￾inates, it did not produce catastrophic failure as in the case 0.00 0.02 0.04 0.06 0.08 0.10 -4 0 4 8 12 16 A B C K apt,c (MPa m1/2) Crack length parameter, ã ATZ AMZ KATZ σ th Fig. 9. Apparent fracture toughness, Kapt,c, calculated analytically using the weight function approach, considering the three different layered architectures, A, B and C. 4754 R. Bermejo et al. / Acta Materialia 54 (2006) 4745–4757