《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