Availableonlineatwww.sciencedirect.com DIRECT e REFRACTORy METALS HARD MAtERials ELSEVIER International Journal of Refractory Metals Hard Materials 23(2005)375-381 elsevier. com/locate/ijrmhm Surface contact degradation of multilayer ceramics under cyclic subcritical loads and high number of cycles L.Ceseracciu, F Chalvet b,G de Portu b, M. Anglada E. Jimenez-pique a Departamento de Ciencia de Materiales e Ingenieria Metalurgica, Universitat Politecnica de Catalunya, Aoda. Diagonal 647(ETSEIB) 08028 Barcelona, Spain b National Research Council(CNR), Institute of Science and Technology for Ceramics(ISTEC), 48018 Faenza(RA), Italy Received ll November 2004: accepted 31 May 2005 Abstract lumina/alumina-zirconia ceramic laminated composites produced by tape casting present a compressive residual stress at the alumina surface due to the thermal expansion mismatch between layers developed during processing. Because of this residual stress the mechanical properties at the surface, such as wear or surface fracture, have proven to be better than the properties of a mono- lithic stress-free alumina. In a previous work, it was shown that this laminate composite has better resistance to the development of a ring crack when loaded with a spherical indenter, under both cyclic and static loads below the critical load for cone cracking. In this work, cyclic Hertzian indentations with subcritical loads are performed on the same laminate ceramic and a monolithic alumina, but with a higher number of cycles than the necessary to provoke the first damage(ring crack). Results show that for low and interme diate number of cycles, the laminated composite presents better resistance to damage than the monolithic alumina. However, for high number of cycles, spalling at the surface of the laminate material appears, whereas the monolithic alumina develops secondary cone cracking. This difference is attributed to the fact that laminate ceramics present an enhanced apparent fracture toughness of the material, which implies a higher quasi-plasticity due to shear driven microcracking. For a high number of cycles, these microcracks grow until coalescence at the surface, provoking exfoliation of the material at the contact area, enhanced by the fact that the indented and the indenter material have different elastic properties o 2005 Elsevier Ltd. All rights reserved Keywords: Contact; Fatigue; Alumina; Multilayer 1. Introduction The mechanical behaviour of the surface of ceramics different from the behaviour of the volumetric mate- Ceramic materials have excellent chemical stability; rial. In the latter case, the structural integrity of the cera- wear resistance, high stiffness and hardness. However, mic will be determined by their long-crack toughness, due to their ionic or covalent molecular bonding, they usually with a fully developed R-curve. However, when are intrinsically brittle. In order to take advantage of the ceramic is used as a surface material, its structural these beneficial properties, while avoiding their low integrity will be dictated by, not a single crack, but by toughness, ceramics are designed to be used at the sur- short cracks and quasi-plasticity due to shear driver face of components, using ceramic coatings on me cking [1] substrates, which bear the loading It is then important to increase the structural integrity of ceramics, not only at the bulk of the material, but also at the surface. One of the ways to achieve this objective Corresponding author. Tel. +34 934054454: fax: +34934016706. is to introduce a compressive residual stress at the sur- ress:. jimenez@ upc es(E. Jimenez-Pique) face. which will tend to close initial flaws and defects /s- see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.016/ irmin2005.05.019
Surface contact degradation of multilayer ceramics under cyclic subcritical loads and high number of cycles L. Ceseracciu a , F. Chalvet b , G. de Portu b , M. Anglada a , E. Jime´nez-Pique´ a,* a Departamento de Ciencia de Materiales e Ingenierı´a Metalu´rgica, Universitat Polite´cnica de Catalunya, Avda. Diagonal 647 (ETSEIB), 08028 Barcelona, Spain b National Research Council (CNR), Institute of Science and Technology for Ceramics (ISTEC), 48018 Faenza (RA), Italy Received 11 November 2004; accepted 31 May 2005 Abstract Alumina/alumina–zirconia ceramic laminated composites produced by tape casting present a compressive residual stress at the alumina surface due to the thermal expansion mismatch between layers developed during processing. Because of this residual stress, the mechanical properties at the surface, such as wear or surface fracture, have proven to be better than the properties of a monolithic stress-free alumina. In a previous work, it was shown that this laminate composite has better resistance to the development of a ring crack when loaded with a spherical indenter, under both cyclic and static loads below the critical load for cone cracking. In this work, cyclic Hertzian indentations with subcritical loads are performed on the same laminate ceramic and a monolithic alumina, but with a higher number of cycles than the necessary to provoke the first damage (ring crack). Results show that for low and intermediate number of cycles, the laminated composite presents better resistance to damage than the monolithic alumina. However, for high number of cycles, spalling at the surface of the laminate material appears, whereas the monolithic alumina develops secondary cone cracking. This difference is attributed to the fact that laminate ceramics present an enhanced apparent fracture toughness of the material, which implies a higher quasi-plasticity due to shear driven microcracking. For a high number of cycles, these microcracks grow until coalescence at the surface, provoking exfoliation of the material at the contact area, enhanced by the fact that the indented and the indenter material have different elastic properties. 2005 Elsevier Ltd. All rights reserved. Keywords: Contact; Fatigue; Alumina; Multilayer 1. Introduction Ceramic materials have excellent chemical stability; wear resistance, high stiffness and hardness. However, due to their ionic or covalent molecular bonding, they are intrinsically brittle. In order to take advantage of these beneficial properties, while avoiding their low toughness, ceramics are designed to be used at the surface of components, using ceramic coatings on metal substrates, which bear the loading. The mechanical behaviour of the surface of ceramics is different from the behaviour of the volumetric material. In the latter case, the structural integrity of the ceramic will be determined by their long-crack toughness, usually with a fully developed R-curve. However, when the ceramic is used as a surface material, its structural integrity will be dictated by, not a single crack, but by short cracks and quasi-plasticity due to shear driven microcracking [1]. It is then important to increase the structural integrity of ceramics, not only at the bulk of the material, but also at the surface. One of the ways to achieve this objective is to introduce a compressive residual stress at the surface, which will tend to close initial flaws and defects, 0263-4368/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2005.05.019 * Corresponding author. Tel.: +34 934054454; fax: +34 934016706. E-mail address: emilio.jimenez@upc.es (E. Jime´nez-Pique´). International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381 www.elsevier.com/locate/ijrmhm
L Ceseracciu et al International Journal of Refractory Metals& Hard Materials 23(2005)375-381 increasing, thus, the apparent fracture toughness of the produced by cyclic Hertzian indentation was either cone material. This can be achieved by several ways, such cracking or quasi-plasticity (due to microcracking as ion tempering, temperature quenching, variation of depending on the material type and the size of the the microstructure at the surface(functionally graded microstructure materials)or by the use of laminated composites [2, 3]. The objective of this study is to characterize the con- The residual stress at the surface of laminated com- tact resistance of an alumina-based laminated compos posites is usually achieved by alternating materials with ite, with compressive residual stresses at the surface, different thermal expansion behaviour, so, when joined subjected to cyclic loading, in comparison to a mono- at high temperature and later cooled to room tempera- lithic stress-free alumina. This is done because ceramic ture, they develop residual stresses due to the different surfaces, specially when employed as hard materials, hrinkage behaviour of the different materials. It is also are more susceptible to cracking by contact loading than possible to use other mechanisms of expansion mis- by external remote loading. Moreover, contact loading match for achieving residual stresses, such as martensitic applied during a relatively long time can degrade the transformation of zirconia, which implies a 4% volume materials even if the load is below the threshold for change [4]. These multilayers normally have a symmet inducing damage cal stacking in order to avoid unbalanced stresses, which In a previous work[15], we studied, for the same lam would result in bending of the sample inated composites, the resistance to the development of Among the ceramic laminated composites that can be ring cracking(considered as the first stage of damage) produced, one of the most preferred material combina- under both static and cyclic loading. This research tions is alumina and zirconia. Usually, at least one of showed that the laminate material presents a better he layers of the material is made of an alumina/zirconia behaviour under both types of loading than the mono- composite, in order to tailor the coefficient of thermal lithic alumina, and that both materials degrade more expansion(CTE)and, consequently, the residual stres- rapidly under cyclic loading due to the existence of ses. In this way, the channel cracking produced during fatigue sintering can be avoided The reason for choosing alu The objective of this work is to present the surface mina and zirconia as the constituent materials of cera- morphology of an alumina/zirconia laminated compos- mic laminates is normally because of the excellent ite, in comparison with a monolithic alumina, when sub bonding between the layers in the absence of excessive jected to cyclic loading with a number of cycles larger diffusion between components, their good thermo- than the critical one to produce the first damage. That mechanical properties and their relatively ease of is, while in a previous study the objective was to quan- processing tify the appearance of damage as a function of number Moreover, layered ceramics also present the of cycles and applied load, in this study we evaluate the ge that, under certain conditions, they have different surface fractographies and sub-surface damage proved long-crack resistance with respect to produced as the different materials are subjected, under monolithic counterparts [5]. This long-crack toughness a constant load, to different number of cycles improvement can be achieved by several mechanisms, such as weak interfaces [6], containment of martensitic transformation [7], existence of porous layers [8] or 2. Experimental crack deflection due to the elastic mismatch at the inter- face. In addition, the existence of residual compressive 2. 1. Sample preparation stresses also reduces the effective stress intensity factor consequently, the apparent fracture toughness / 8, of cracks located at the compressive layers, increasing, To obtain the ceramic sheets suitable for the prepara- tion of laminated composites, two powders were used One of the preferred ways of studying the contact high purity(99.7%)alumina(Alcoa A16-SG, Alcoa Alu damage is by Hertzian indentation. Hertzian indenta- minum Co., New York, USA) with an average particle tion presents the advantage over sharp indentations in size of 0. 3 um, and tetragonal zirconia polycrystal the fact that damage in the material can be produced (TZ3Y-S, Tosho Corp. Japan) containing 94.7% of in most cases without appreciable plastic deformation, ZrO2 and 3 mol% of Y2O3(usually referred to as 3Y which simplifies the analysis because fracture can occur TZP)with an average particle size of 0.3 um within an elastic field. Moreover. Hertzian indentations The different powders were mixed with organic bind- resemble more closely the real contact that the material rs, dispersant, plasticizers and solvents to obtain suit is expected to suffer in service. In recent years, there have able slips for tape casting. After mixing with organic been several studies on Hertzian contact fatigue of components, the slurry containing the ceramic powders ceramics, where the degradation of the material under was tape casted onto a mylar sheet moved at a constant clic loading has been evaluated by measuring the de- speed of 200 mm/min. Detail on this technique can be crease of strength of the material [12-14]. The damage found elsewhere [16]
increasing, thus, the apparent fracture toughness of the material. This can be achieved by several ways, such as ion tempering, temperature quenching, variation of the microstructure at the surface (functionally graded materials) or by the use of laminated composites [2,3]. The residual stress at the surface of laminated composites is usually achieved by alternating materials with different thermal expansion behaviour, so, when joined at high temperature and later cooled to room temperature, they develop residual stresses due to the different shrinkage behaviour of the different materials. It is also possible to use other mechanisms of expansion mismatch for achieving residual stresses, such as martensitic transformation of zirconia, which implies a 4% volume change [4]. These multilayers normally have a symmetrical stacking in order to avoid unbalanced stresses, which would result in bending of the sample. Among the ceramic laminated composites that can be produced, one of the most preferred material combinations is alumina and zirconia. Usually, at least one of the layers of the material is made of an alumina/zirconia composite, in order to tailor the coefficient of thermal expansion (CTE) and, consequently, the residual stresses. In this way, the channel cracking produced during sintering can be avoided. The reason for choosing alumina and zirconia as the constituent materials of ceramic laminates is normally because of the excellent bonding between the layers in the absence of excessive diffusion between components, their good thermomechanical properties and their relatively ease of processing. Moreover, layered ceramics also present the advantage that, under certain conditions, they have an improved long-crack resistance with respect to their monolithic counterparts [5]. This long-crack toughness improvement can be achieved by several mechanisms, such as weak interfaces [6], containment of martensitic transformation [7], existence of porous layers [8] or crack deflection due to the elastic mismatch at the interface. In addition, the existence of residual compressive stresses also reduces the effective stress intensity factor of cracks located at the compressive layers, increasing, consequently, the apparent fracture toughness [9–11]. One of the preferred ways of studying the contact damage is by Hertzian indentation. Hertzian indentation presents the advantage over sharp indentations in the fact that damage in the material can be produced in most cases without appreciable plastic deformation, which simplifies the analysis because fracture can occur within an elastic field. Moreover, Hertzian indentations resemble more closely the real contact that the material is expected to suffer in service. In recent years, there have been several studies on Hertzian contact fatigue of ceramics, where the degradation of the material under cyclic loading has been evaluated by measuring the decrease of strength of the material [12–14]. The damage produced by cyclic Hertzian indentation was either cone cracking or quasi-plasticity (due to microcracking), depending on the material type and the size of the microstructure. The objective of this study is to characterize the contact resistance of an alumina-based laminated composite, with compressive residual stresses at the surface, subjected to cyclic loading, in comparison to a monolithic stress-free alumina. This is done because ceramic surfaces, specially when employed as hard materials, are more susceptible to cracking by contact loading than by external remote loading. Moreover, contact loading applied during a relatively long time can degrade the materials even if the load is below the threshold for inducing damage. In a previous work [15], we studied, for the same laminated composites, the resistance to the development of ring cracking (considered as the first stage of damage) under both static and cyclic loading. This research showed that the laminate material presents a better behaviour under both types of loading than the monolithic alumina, and that both materials degrade more rapidly under cyclic loading due to the existence of fatigue. The objective of this work is to present the surface morphology of an alumina/zirconia laminated composite, in comparison with a monolithic alumina, when subjected to cyclic loading with a number of cycles larger than the critical one to produce the first damage. That is, while in a previous study the objective was to quantify the appearance of damage as a function of number of cycles and applied load, in this study we evaluate the different surface fractographies and sub-surface damage produced as the different materials are subjected, under a constant load, to different number of cycles. 2. Experimental 2.1. Sample preparation To obtain the ceramic sheets suitable for the preparation of laminated composites, two powders were used: high purity (99.7%) alumina (Alcoa A16-SG, Alcoa Aluminum Co., New York, USA) with an average particle size of 0.3 lm, and tetragonal zirconia polycrystals (TZ3Y-S, Tosho Corp. Japan) containing 94.7% of ZrO2 and 3 mol% of Y2O3 (usually referred to as 3YTZP) with an average particle size of 0.3 lm. The different powders were mixed with organic binders, dispersant, plasticizers and solvents to obtain suitable slips for tape casting. After mixing with organic components, the slurry containing the ceramic powders was tape casted onto a mylar sheet moved at a constant speed of 200 mm/min. Detail on this technique can be found elsewhere [16]. 376 L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381
L Ceseracciu et al. International Journal of Refractory Metals Hard Materials 23(2005)375-381 Sheets of pure alumina(hereinafter designated"A) as well as of the composite alumina-zirconia(hereinaf- ter designated"AZ")in the volume ratio 60/40 wer prepared. The thicknesses of the green tapes were lected in order to obtain, after sintering, layers of about 200 um(A)and 250 um(AZ). After drying, laminate of 50x 34 mm were cut from the different ceramic sheets Hybrid laminates were prepared by stacking and warm pressing the green sheets at 75C at a press 30 MPa for 30 min. Samples were obtained by alter (b) nately superimposing one layer of alumina and one lay of alumina-zirconia( this structure is hereinafter desig nated A/AZ). The structures were designed in order to have always an alumina layer in both the outer surfaces Debonding was carried out with a very slow heating rate up to 600C, followed by y sintering at 1550° for 1 h. thus obtained dense samples (97% of theoretical density) with a thickness of about 3.0 mm, contain ing layers with a thickness ratio of about 1/1.3. In the hybrid samples, due to lower thermal expansion coeffi- ient and shrinkage during sintering, the alumina layers undergo residual compressive stresses. As reference material (i.e. nominally stress free), pure monolithic alu mina(Ma)was prepared by cold isostatic pressing and sintering at 1550C for I h Fig. I shows a sample of the laminated ceramic com- posite and the sem picture of the interface between two lumina a Imina-zirconia. where it can be observed that the interface is properly bonded. It can be also observed that the alumina grains inside the alu- mina-zirconia layers are smaller than the ones in the pure alumina layers. This is a consequence of the con- strain effect that the zirconia grains produce on the growing of neighbouring alumina grains by preventing the diffusion of alumina between grains Fig. 1.(a) Picture of the multilayer where the different alumina and Once the laminated plates were produced, they were alumina-zirconia layers can be appreciated. (b) SEM pictures of th cut into prismatic bars of about 4 x 3 x 20 mm with a interface between alumina and alumina/zirconia layers of an A/AZ diamond saw. The top layer of alumina(which was in laminated composites. It can be observed that the interface is well ompression) was polished with diamond suspension up to 3 um with a low applied force in order to avoid excessive loss of material (30 um at most), and to pro- als are similar at the microstructural level, and that the samples. Several samples were polished in the cross sec- tion area and thermally etched (1500 C, 30 min)for inated architecture observing the microstructure of the material nearby the interface(Fig. 1). MA samples were polished in 2.2. Mechanical characterization the same way, and their microstructure was also ob- served by SEM. The mean grain size in the alumina lay Both surface hardness and toughness were evaluated ers of the laminates and in the monolithic alumina was by Vickers indentation [15] on the top alumina layer. measured to be 1.9+0.7 um and 1.1+0.8 um respec- The hardness of the outer alumina layer in the A/AZ tively. These differences are not sufficiently large to affect laminated composite(applied load I kg) was HA/AZ ignificantly the mechanical behaviour of the different 16.9+0.5 GPa, and the hardness of the monolithic alu materials. In addition, considering that both the lami- mina was H= 16.7+0.9 GPa. It can be seen that nates and the Ma materials have the same amount of both the Ma and the alumina layer have comparable porosity, it can be assumed that, apart from a possible values of hardness. Fracture toughness was evalu grain orientation in the laminated structures, the materi ated by measuring the crack lengths produced and by
Sheets of pure alumina (hereinafter designated ‘‘A’’) as well as of the composite alumina–zirconia (hereinafter designated ‘‘AZ’’) in the volume ratio 60/40 were prepared. The thicknesses of the green tapes were selected in order to obtain, after sintering, layers of about 200 lm (A) and 250 lm (AZ). After drying, laminate of 50 · 34 mm were cut from the different ceramic sheets. Hybrid laminates were prepared by stacking and warm pressing the green sheets at 75 C at a pressure of 30 MPa for 30 min. Samples were obtained by alternately superimposing one layer of alumina and one layer of alumina–zirconia (this structure is hereinafter designated A/AZ). The structures were designed in order to have always an alumina layer in both the outer surfaces. Debonding was carried out with a very slow heating rate up to 600 C, followed by sintering at 1550 C for 1 h. We thus obtained dense samples (97% of theoretical density) with a thickness of about 3.0 mm, containing layers with a thickness ratio of about 1/1.3. In the hybrid samples, due to lower thermal expansion coeffi- cient and shrinkage during sintering, the alumina layers undergo residual compressive stresses. As reference material (i.e. nominally stress free), pure monolithic alumina (MA) was prepared by cold isostatic pressing and sintering at 1550 C for 1 h. Fig. 1 shows a sample of the laminated ceramic composite and the SEM picture of the interface between two layers of alumina and alumina–zirconia, where it can be observed that the interface is properly bonded. It can be also observed that the alumina grains inside the alumina–zirconia layers are smaller than the ones in the pure alumina layers. This is a consequence of the constrain effect that the zirconia grains produce on the growing of neighbouring alumina grains by preventing the diffusion of alumina between grains. Once the laminated plates were produced, they were cut into prismatic bars of about 4 · 3 · 20 mm with a diamond saw. The top layer of alumina (which was in compression) was polished with diamond suspension up to 3 lm with a low applied force in order to avoid excessive loss of material (30 lm at most), and to produce a similar surface flaw size distribution for all the samples. Several samples were polished in the cross section area and thermally etched (1500 C, 30 min) for observing the microstructure of the material nearby the interface (Fig. 1). MA samples were polished in the same way, and their microstructure was also observed by SEM. The mean grain size in the alumina layers of the laminates and in the monolithic alumina was measured to be 1.9 ± 0.7 lm and 1.1 ± 0.8 lm respectively. These differences are not sufficiently large to affect significantly the mechanical behaviour of the different materials. In addition, considering that both the laminates and the MA materials have the same amount of porosity, it can be assumed that, apart from a possible grain orientation in the laminated structures, the materials are similar at the microstructural level, and that the differences in the mechanical behaviour can be mainly attributed to the presence of residual stresses in the laminated architecture. 2.2. Mechanical characterization Both surface hardness and toughness were evaluated by Vickers indentation [15] on the top alumina layer. The hardness of the outer alumina layer in the A/AZ laminated composite (applied load 1 kg) was H A=AZ v ¼ 16.9 0.5 GPa, and the hardness of the monolithic alumina was HMA v ¼ 16.7 0.9 GPa. It can be seen that both the MA and the alumina layer have comparable values of hardness. Fracture toughness was evaluated by measuring the crack lengths produced and by Fig. 1. (a) Picture of the multilayer where the different alumina and alumina–zirconia layers can be appreciated. (b) SEM pictures of the interface between alumina and alumina/zirconia layers of an A/AZ laminated composites. It can be observed that the interface is well bonded. L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381 377
L Ceseracciu et al International Journal of Refractory Metals& Hard Materials 23(2005)375-381 applying the equation proposed by Antsis et al.[17] yielding the values of KMA=3.5+0.8 MPa m /2for the 6.0±0.8MPam1/2 AAZ for the outer alumina layer in the laminated material. If this difference in apparent fracture toughness values is solely attributed to the existence of a homogeneous MA residual stress, the mean value of this residual stres in the zone of the surface interested by the crack can be evaluated to be 183 MPa [15]. Hertzian contact loads were applied on the laminated composites and in the reference MA material. This was carried out at the top layer with a wC-Co spherical in- denter of 2.5 mm. As expected due to the relative small grain size of the alumina, the main mechanism for dam- 10000 age showed to be cone cracking, and, for that particular Number of cycles indenter size, the critical load for cone cracking under Fig. 2. Applied indenter load against time for cyclic loading tests for monotonic loading rate was Pa=607+ 50N for the alumina(MA)and laminate(A/AZ), after[15] Ranges indicate alumina and PA/Az=675+50N for the alumina outer development of ring crack damage. Lines are best fits layer in A/AZ composite As before mentioned, the appearance of ring cracking in the sphere. Cyclic loading was carried out between [18, 19] in the surface of the samples was previously 50N and 500n by using a sinusoidal wave shape at determined as a function of number of cycles [15]. The a frequency of 10 Hz for different number of cycles experiment tal results of this study are summarized in (N= 10, 10, 10). The damaged surface of both ag.2. After these results, a load of 500N was selected laminated composite and monolithic alumina were sub- for studying the evolution of damage with increasing sequently observed, noting the different damage pro- number of cycles duced under repetitive contact loading. Fig 3 presents he typical surface damage on the samples after the cyc lic loading 23. Contact fatigue tests Several samples were also polished in the damaged surface after testing, in order to observe the microstruc Load was applied with a wC-Co sphere of 2.5 mm ture damage as a function of depth. This was done with diameter in a universal servohydraulic test machine a 30 um diamond suspension applying a low load. The (Instron 8500). Care was taken to properly hold the depth of material removal was measured with a microm pecimen in order to avoid small displacements and, eter of 10 um precision. Some samples were ground and consequently, fretting fatigue. The wC-Co sphere was finally polished in the perpendicular plane to the in- periodically inspected for damage, and rotated or re- dented surface in order to observe under Sem, the dam placed when some damage or deformation was observed age produced 10 cycles 10 cycles 10 cycles AAZ Fig. 3. Damage produced in A/AZ and MA by Hertzian fatigue tests under load of 500N and different numbers of cycles. Although A/AZ has a etter resistance to appearance of ring crack, it presents an apparent higher surface degradation(chipping) for severe conditions(N=10 cycles)
applying the equation proposed by Antsis et al. [17], yielding the values of KMA I c ¼ 3.5 0.8 MPa m1/2 for the monolithic alumina and KA=AZ I c ¼ 6.0 0.8 MPa m1/2 for the outer alumina layer in the laminated material. If this difference in apparent fracture toughness values is solely attributed to the existence of a homogeneous residual stress, the mean value of this residual stress, in the zone of the surface interested by the crack can be evaluated to be 183 MPa [15]. Hertzian contact loads were applied on the laminated composites and in the reference MA material. This was carried out at the top layer with a WC–Co spherical indenter of 2.5 mm. As expected, due to the relative small grain size of the alumina, the main mechanism for damage showed to be cone cracking, and, for that particular indenter size, the critical load for cone cracking under monotonic loading rate was P A c ¼ 607 50 N for the alumina and P A=AZ c ¼ 675 50 N for the alumina outer layer in A/AZ composite. As before mentioned, the appearance of ring cracking [18,19] in the surface of the samples was previously determined as a function of number of cycles [15]. The experimental results of this study are summarized in Fig. 2. After these results, a load of 500 N was selected for studying the evolution of damage with increasing number of cycles. 2.3. Contact fatigue tests Load was applied with a WC–Co sphere of 2.5 mm diameter in a universal servohydraulic test machine (Instron 8500). Care was taken to properly hold the specimen in order to avoid small displacements and, consequently, fretting fatigue. The WC–Co sphere was periodically inspected for damage, and rotated or replaced when some damage or deformation was observed in the sphere. Cyclic loading was carried out between 50 N and 500 N by using a sinusoidal wave shape at a frequency of 10 Hz for different number of cycles (N = 103 , 104 , 105 ). The damaged surface of both laminated composite and monolithic alumina were subsequently observed, noting the different damage produced under repetitive contact loading. Fig. 3 presents the typical surface damage on the samples after the cyclic loading. Several samples were also polished in the damaged surface after testing, in order to observe the microstructure damage as a function of depth. This was done with a 30 lm diamond suspension applying a low load. The depth of material removal was measured with a micrometer of 10 lm precision. Some samples were ground and finally polished in the perpendicular plane to the indented surface in order to observe under SEM, the damage produced. Fig. 2. Applied indenter load against time for cyclic loading tests for alumina (MA) and laminate (A/AZ), after [15]. Ranges indicate development of ring crack damage. Lines are best fits. Fig. 3. Damage produced in A/AZ and MA by Hertzian fatigue tests under load of 500 N and different numbers of cycles. Although A/AZ has a better resistance to appearance of ring crack, it presents an apparent higher surface degradation (chipping) for severe conditions (N = 105 cycles). 378 L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381
L Ceseracciu et al. International Journal of Refractory Metals Hard Materials 23(2005)375-381 3. Discussion According to the model proposed by rhee et al. [20] it is possible to predict the tendency to brittle or quasi Fig 3 presents the surface damage obtained for dif- plastic behaviour of a given material, as the ratio of the ferent number of cycles(N=103, 104, 105)on both critical loads for the appearance of the two kinds of materials for a fixed maximum load of 500N. At a damage( PY, critical load for quasi-plasticity; Pc, critical load for ring/cone cracking ), as crack appears in the alumina, while there is little appre. Py/Pe=(D/)(H/)(H/KI)r ciable damage in the A/AZ material. For an intermedi- ate number of cycles (N= 10), the cracking in the where D=(1. 11/3)[3(1-2)/4], C=C(v)from([21].H alumina becomes more severe, while there is only minor is the hardness, KIc is the fracture toughness of the ring cracking in the A/AZ. These results are consistent material (which, in our case is taken as the apparent with the previous ones [15], where it was shown that fracture toughness), r is the radius of the indenter and the laminate showed better resistance to contact E is the effective modulus of the system indenter- damage bitrate However, for large number of cycles(N=10), the type of damage is essentially different in the A/AZ E laminated composite than in the monolithic alumina: while in the alumina, secondary ring cracks appear at where E and v are Young modulus of the indented mate- the surface, together with radial cracking, in the A/Az rial (no subscript) and indenter(subscript i) material there is a off surface around ring Eq (1)implies that, when the ratio PY/Pc is high, the cracking, that is, there is a mild chipping in the contact damage produced in the material will be mainly ring and 2 This may be due to the fact that there is more quasi- dominant damage will be quasi-plasticity cone cracking, while when the ratio PY/Pc is low the pre- plastic damage under the contact loading than in In our case, as has been shown before both materials monolithic alumina, due to the higher apparent tough- present similar values of hardness and elastic properties less of the laminated material. The presence of a (E, v), which imply similar values of parameters D and juasi-plasticity can suggest the formation of a shear C. Moreover, the indenter size and material used are driven microcracking volume under the contact area he same for both materials. The only difference is in which will provoke an inelastic deformation. the apparent toughness, which equals to approximately Fig 4 presents the microstructure observed in the A/ 3.5 MPa m /2 in the monolithic alumina and 6.0 AZ material beneath the indentation site for 10 cycles, MPa m /2 in the laminated composite together with the microstructure of the same material This difference in apparent fracture toughness for the away from the indentation. It can be seen that beneath two materials implies that the ratio Px/pe for the lami the indentation site, a large amount of microcracking nated material is approximately three times smaller can be found, in comparison with the relative crack-free than the ratio for monolithic alumina. That means microstructure. This microcracking is produced by the that the A/AZ material has a more pronounced quasi strong shear stresses generated in that volume during plastic behaviour than the MA. This behaviour, as said the indentation, which results in a macroscopic inelastic before is a consequence of the more extensive micro- deformation, that is, in quasi-plasticity cracking produced in the A/AZ material due to the μm Fig 4. Scanning electron microscope pictures of the alumina layer in A/AZ composite showing: (a)damage zone underneath the indenter, where the evere microcracking produced by shear loading can be appreciated (b) undamaged microstructure of the same material away from the indentation site. Both pictures have been taken at a depth of 50 um from the surface
3. Discussion Fig. 3 presents the surface damage obtained for different number of cycles (N = 103 , 104 , 105 ) on both materials for a fixed maximum load of 500 N. At a low number of cycles (N = 103 ), it is seen that a ring crack appears in the alumina, while there is little appreciable damage in the A/AZ material. For an intermediate number of cycles (N = 104 ), the cracking in the alumina becomes more severe, while there is only minor ring cracking in the A/AZ. These results are consistent with the previous ones [15], where it was shown that the laminate showed better resistance to contact damage. However, for large number of cycles (N = 106 ), the type of damage is essentially different in the A/AZ laminated composite than in the monolithic alumina: while in the alumina, secondary ring cracks appear at the surface, together with radial cracking, in the A/AZ material there is a spalled off surface around ring cracking, that is, there is a mild chipping in the contact area. This may be due to the fact that there is more quasiplastic damage under the contact loading than in the monolithic alumina, due to the higher apparent toughness of the laminated material. The presence of a quasi-plasticity can suggest the formation of a shear driven microcracking volume under the contact area, which will provoke an inelastic deformation. Fig. 4 presents the microstructure observed in the A/ AZ material beneath the indentation site for 105 cycles, together with the microstructure of the same material away from the indentation. It can be seen that beneath the indentation site, a large amount of microcracking can be found, in comparison with the relative crack-free microstructure. This microcracking is produced by the strong shear stresses generated in that volume during the indentation, which results in a macroscopic inelastic deformation, that is, in quasi-plasticity. According to the model proposed by Rhee et al. [20], it is possible to predict the tendency to brittle or quasiplastic behaviour of a given material, as the ratio of the critical loads for the appearance of the two kinds of damage (PY, critical load for quasi-plasticity; Pc, critical load for ring/cone cracking), as: P Y=Pc ¼ ðD=CÞðH=E0 ÞðH=KI c Þ 2 r ð1Þ where D = (1.1p/3)3 [3(1 m 2 )/4]2 , C = C(m) from [21], H is the hardness, KIC is the fracture toughness of the material (which, in our case is taken as the apparent fracture toughness), r is the radius of the indenter and E0 is the effective modulus of the system indenter– substrate: E0 ¼ 1 m2 E þ 1 m2 i Ei ð2Þ where E and m are Young modulus of the indented material (no subscript) and indenter (subscript i). Eq. (1) implies that, when the ratio PY/Pc is high, the damage produced in the material will be mainly ring and cone cracking, while when the ratio PY/Pc is low the predominant damage will be quasi-plasticity. In our case, as has been shown before, both materials present similar values of hardness and elastic properties (E, m), which imply similar values of parameters D and C. Moreover, the indenter size and material used are the same for both materials. The only difference is in the apparent toughness, which equals to approximately 3.5 MPa m1/2 in the monolithic alumina and 6.0 MPa m1/2 in the laminated composite. This difference in apparent fracture toughness for the two materials implies that the ratio PY/Pc for the laminated material is approximately three times smaller than the ratio for monolithic alumina. That means that the A/AZ material has a more pronounced quasiplastic behaviour than the MA. This behaviour, as said before, is a consequence of the more extensive microcracking produced in the A/AZ material due to the Fig. 4. Scanning electron microscope pictures of the alumina layer in A/AZ composite showing: (a) damage zone underneath the indenter, where the severe microcracking produced by shear loading can be appreciated (b) undamaged microstructure of the same material away from the indentation site. Both pictures have been taken at a depth of 50 lm from the surface. L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381 379
L Ceseracciu et al International Journal of Refractory Metals& Hard Materials 23(2005)375-381 higher shear stresses suffered, because the cone cracking cycles at 500N. During polishing under the previously cannot be generated due to the higher apparent fracture described conditions, it is usual that a number of alu- toughness. This inability to generate cone cracking im- mina grains are pulled away from the surface [23] plies that build-up internal stresses cannot be relieved This tearing of grains is enhanced in the case that y the opening of the cone crack and therefore, more microcracking exists already in the material, because it microcracking will be generated for the same applied weakens the material and the cohesion between grains load as a microcrack can be considered as a gap between This enhanced microcracking in the A/AZ will imply materials In Fig. 5 it is seen how the MA produces a a weakening and loss of strength of the material under typical cone crack fracture, which is presented as an the indenter and near the surface, especially if cyclic expanding ring crack feature as the depth is increased loading is applied which results in a faster crack growth This type of cracking is the expected one for brittle [15]. Upon repetitive loading, some of the microcracking materials. However, in the A/AZ material, the fully ill coalesce and reach the surface, producing spalling of developed cone crack it is not observed, and instead material. This effect will also be enhanced by the fact in addition to a ring crack, a highly damaged zone is ob- that the indenter and the indented material are not the served after 10 um of material removal, which almost same material, which will imply a certain degree of fric- disappears after removing 50 um of material. This re- tion and lateral movement in the contact zone due to gion can be identified with the area with microcracks, their mismatch in elastic properties [22]. This lateral dis- which produces the quasi-plasticity of the material. In placement will enhance the exfoliation of parts of mate- Fig. 5 it is also seen that damage is fully localized in rial. In addition, the compressive residual stress could the first layer of material, (50 um, for a total depth of also enhance the chip-off of surface microcracks in the layer of 200 um), so, in this case, the second and subse laminated composite. It is also acknowledged that quent layers of the laminated composite do not appear the laminate may be subjected to larger strains due to to have a direct role in the response of the material the delayed cone cracking, which will, consequently After these observations, indeed, we can say that the influence the fatigue behaviour A/AZ material behaves more quasi-plastically than the In Fig. 5, the different damage evolution for both MA MA material, due to the higher apparent fracture and A/AZ is presented as a function of depth, after 10* toughness z=-10 um z=-50 um 300um in the MA and A/AZ materials as a function of the depth(=) for an applied load of 500N and 10 cycles. It can be appreciated that in the MA a cone crack is formed, whereas in the A/AZ it exist both ring crack(partially developed into cone crack) and qu plastic damaged, as it can be appreciated in 2=-10 um, where the ring crack is marked with(1)and the quasi-plastic damage is marked with(2)
higher shear stresses suffered, because the cone cracking cannot be generated due to the higher apparent fracture toughness. This inability to generate cone cracking implies that build-up internal stresses cannot be relieved by the opening of the cone crack and therefore, more microcracking will be generated for the same applied load. This enhanced microcracking in the A/AZ will imply a weakening and loss of strength of the material under the indenter and near the surface, especially if cyclic loading is applied which results in a faster crack growth [15]. Upon repetitive loading, some of the microcracking will coalesce and reach the surface, producing spalling of material. This effect will also be enhanced by the fact that the indenter and the indented material are not the same material, which will imply a certain degree of friction and lateral movement in the contact zone due to their mismatch in elastic properties [22]. This lateral displacement will enhance the exfoliation of parts of material. In addition, the compressive residual stress could also enhance the chip-off of surface microcracks in the laminated composite. It is also acknowledged that the laminate may be subjected to larger strains due to the delayed cone cracking, which will, consequently influence the fatigue behaviour. In Fig. 5, the different damage evolution for both MA and A/AZ is presented as a function of depth, after 104 cycles at 500 N. During polishing under the previously described conditions, it is usual that a number of alumina grains are pulled away from the surface [23]. This tearing of grains is enhanced in the case that microcracking exists already in the material, because it weakens the material and the cohesion between grains, as a microcrack can be considered as a gap between materials. In Fig. 5 it is seen how the MA produces a typical cone crack fracture, which is presented as an expanding ring crack feature as the depth is increased. This type of cracking is the expected one for brittle materials. However, in the A/AZ material, the fully developed cone crack it is not observed, and instead, in addition to a ring crack, a highly damaged zone is observed after 10 lm of material removal, which almost disappears after removing 50 lm of material. This region can be identified with the area with microcracks, which produces the quasi-plasticity of the material. In Fig. 5 it is also seen that damage is fully localized in the first layer of material, (50 lm, for a total depth of layer of 200 lm), so, in this case, the second and subsequent layers of the laminated composite do not appear to have a direct role in the response of the material. After these observations, indeed, we can say that the A/AZ material behaves more quasi-plastically than the MA material, due to the higher apparent fracture toughness. Fig. 5. Damage present in the MA and A/AZ materials as a function of the depth (z) for an applied load of 500 N and 104 cycles. It can be appreciated that in the MA a cone crack is formed, whereas in the A/AZ it exist both ring crack (partially developed into cone crack) and quasiplastic damaged, as it can be appreciated in z = 10 lm, where the ring crack is marked with (1) and the quasi-plastic damage is marked with (2). 380 L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381
L Ceseracciu et al. International Journal of Refractory Metals Hard Materials 23(2005)375-381 4. Conclusions References The alumina surface of Al O3/AlO3+ZrO, lami [1 Fischer-Cripps AC, Lawn BR. Stress analysis of contact nated structure exhibited an apparent fracture tough nation in quasi-plastic ceramics. J Am Ceram Soc 1996 less higher than that of monolithic alumina. Under the explored experimental conditions when this material 2]Moya JS. Layered ceramics. Adv Mater 1995: 7(2): 185-9 3] Harner MP, Chan HM, Miller GA. Unique opportunities for is subjected to cyclic loading, and the resultant surface microstructural engineering with duplex and laminar ceramic damaged produced is compared to a monolithic alumina composites. J Am Ceram Soc 1992: 75(7): 1715-28 with a similar microstructure, two different types of (4 Sanchez-Herencia AJ, James L, Lange FF. Bifurcation in alumina behaviour are observed depending on the number of cy plates produced by a phase transformation in central alumina zirconia thin layers. J Eur Ceram Soc 2000: 20(9): 1297-300 cles: At a low number of cycles, the a/AZ is more resis- 5 Chan HM. Layered ceramics: Processing and mechanical behav tant to the development of ring cracks than the MA r. Annu Rev Mater Sci 1997: 27: 249-82. At high numbers of cycles, a highly damaged surface [6] Mawdsley JR, Kovar D, Halloran JW. Fracture behaviour of appears in the A/AZ This difference is attributed to the enhanced fracture toughness of the A/AZ material, which implied [7 Marshall DB, Ratto JJ, Lange FF. Enhanced fracture toughness a higher resistance to ring and cone cracking. This layered microcomposites of Ce-ZrO2 and Al2O3. J Am Ceram enhanced apparent fracture toughness also implies a 8] Sorensen BF, Horsewell A. Crack growth along interfaces in higher tendency to shear microcracking, that is, to porous ceramic layers. J Am Ceram Soc 2001; 84(9): 2051-9 quasi-plasticity. At very high number of cycles, this [9] Requena J, Moreno R, Moya JS.Alumina and alumina/zirconia microcracking leads to material spallation at the contact 1989:72(8):151l-3 [10] Goretta KC, Gutierrez- Mora F, Picciolo JJ, Routbort JL Joining In previous works [12, 20] the difference in behaviour alumina/zirconia ceramics. Mater Sci Eng A 2003: 341: 158-62. (cone cracking vs quasi-plasticity) was studied as a fune [11]Toschi F, Melandri C, Pinasco P, Roncari E, Guicciardi S, De ion of grain size(which gives a change in toughness) Portu G. Influence of residual stress on the wear behaviour of alumina/alumina-zirconia laminated composites. J Am Ceram However in this study this difference is attributed solely Soc2003;86(9:1547-53 to the presence of residual stress, as microstructure of [12] Lee SK, Lawn BR. Contact fatigue in silicon nitride. J Am Ceram both laminates and monolithic material can be consid- Socl99982(5:128l-8. ered almost similar. This is a novel result that has to [13] Kim DK, Jung Y-G, Peterson IM, Lawn BR. Cyclic fatigue of be taken into account in designing laminated materials intrinsically brittle ceramics in contact with spheres. Acta Mater 999:47(18):4711-25 with residual stresses. Thus, although the A/az materia [14] Fett T, Keller R, Munz D, Ernst E, Thun G. Fatigue of alumina presents a better resistance to the development of dam- under contact loading. Eng Fract Mech 2003: 70: 1143-5 age at low and intermediate numbers of cycles, at high [15] Jimenez-Pique E, Ceseracciu L, Chalvet F, Anglada M, de portu numbers of cycles spallation of the material occurs, in Hertzian G. contact fatigue on alumina/alumina-zirconia lami stead of multiple cone cracking. It is then important nated composites. J Eur Ceram Soc, in press. [16] Fiori C, de Portu G. Tape casting: A technique for preparing and properly use these laminate materials in order to take studying new materials, In: Davidge RW, editor. British Ceramic dvantage in their contact resistance while avoiding sur Proccedings no. 38. Novel ceramic fabrication face chipping, specially if used in a application where tri- applications. Shelton, Stoke-on-Trent, UK, December 1986. p 213 bological and wear properties are important [17 Anstis GR, Chantikul P, Lawn BR. A critical evaluation of indentation techniques for measuring fracture toughness: I. Direct crack measurements. J Am Ceram Soc 1981: 64: 533-8. [18] Lawn BR. Indentation of ceramics with spheres: A century after Acknowledgement Hertz. J Am Ceram Soc 1998: 81(8): 1977-94. [19] Warren PD, Hills DA, Dal DN. Mechanics of Hertzian cracking. Tribol int1995;28(6):357-62. Work supported in part by the European Commu- [20] Rhee Y-W, Kim H-W, Deng Y, Lawn BR. Brittle fracture versus nity's Human Potential Programme under contract HPRN-CT-2002-00203, [SICMAC] and by the Spanish Ceram Soc200148(3):56l-5. Ministry of Science and Technology, through grant [21] Roberts sG, La Cw. Bisrat Y. Warren PD. Hills DA. MAT200200368 Determination of surface residual stresses in brittle materials by Hertzian indentation: Theory and experiment. J Am Ceram So L C. and F.C. acknowledge the financial provided through the European Communitys 2] Warren PD, Hills DA. The influence of elastic mismatch between Potential Programme under contract HPRN-C indenter and substrate on hertzian fracture. J Mater 00203 [SICMAC]. E.J.P. acknowledges the 2860-6. support provided by the Generalitat de Catalunya [23]Kara H, Roberts SG. Polishing behavior and surface quality of alumina and alumina/silicon carbide nanocomposites. JAm Grant RED-15/2002 Ceram Soc2000;83(5):1219-25
4. Conclusions The alumina surface of Al2O3/Al2O3 + ZrO2 laminated structure exhibited an apparent fracture toughness higher than that of monolithic alumina. Under the explored experimental conditions when this material is subjected to cyclic loading, and the resultant surface damaged produced is compared to a monolithic alumina with a similar microstructure, two different types of behaviour are observed depending on the number of cycles: At a low number of cycles, the A/AZ is more resistant to the development of ring cracks than the MA. At high numbers of cycles, a highly damaged surface appears in the A/AZ. This difference is attributed to the enhanced apparent fracture toughness of the A/AZ material, which implied a higher resistance to ring and cone cracking. This enhanced apparent fracture toughness also implies a higher tendency to shear microcracking, that is, to quasi-plasticity. At very high number of cycles, this microcracking leads to material spallation at the contact surface. In previous works [12,20] the difference in behaviour (cone cracking vs quasi-plasticity) was studied as a function of grain size (which gives a change in toughness). However in this study this difference is attributed solely to the presence of residual stress, as microstructure of both laminates and monolithic material can be considered almost similar. This is a novel result that has to be taken into account in designing laminated materials with residual stresses. Thus, although the A/AZ material presents a better resistance to the development of damage at low and intermediate numbers of cycles, at high numbers of cycles spallation of the material occurs, instead of multiple cone cracking. It is then important to properly use these laminate materials in order to take advantage in their contact resistance while avoiding surface chipping, specially if used in a application where tribological and wear properties are important. Acknowledgement Work supported in part by the European Communitys Human Potential Programme under contract HPRN-CT-2002-00203, [SICMAC] and by the Spanish Ministry of Science and Technology, through grant MAT-2002-00368. L.C. and F.C. acknowledge the financial support provided through the European Communitys Human Potential Programme under contract HPRN-CT-2002- 00203 [SICMAC]. E.J.P. acknowledges the financial support provided by the Generalitat de Catalunya, Grant RED-15/2002. References [1] Fischer-Cripps AC, Lawn BR. Stress analysis of contact deformation in quasi-plastic ceramics. J Am Ceram Soc 1996;79(10): 2609–18. [2] Moya JS. Layered ceramics. Adv Mater 1995;7(2):185–9. [3] Harner MP, Chan HM, Miller GA. Unique opportunities for microstructural engineering with duplex and laminar ceramic composites. J Am Ceram Soc 1992;75(7):1715–28. [4] Sa´nchez-Herencia AJ, James L, Lange FF. Bifurcation in alumina plates produced by a phase transformation in central alumina/ zirconia thin layers. J Eur Ceram Soc 2000;20(9):1297–300. [5] Chan HM. Layered ceramics: Processing and mechanical behaviour. Annu Rev Mater Sci 1997;27:249–82. [6] Mawdsley JR, Kovar D, Halloran JW. Fracture behaviour of alumina/monazite multilayer laminates. J Am Ceram Soc 2000; 83(4):802–8. [7] Marshall DB, Ratto JJ, Lange FF. Enhanced fracture toughness in layered microcomposites of Ce–ZrO2 and Al2O3. J Am Ceram Soc 1991;74(12):2979–87. [8] Sorensen BF, Horsewell A. Crack growth along interfaces in porous ceramic layers. J Am Ceram Soc 2001;84(9):2051–9. [9] Requena J, Moreno R, Moya JS. Alumina and alumina/zirconia multilayer composites obtained by slip casting. J Am Ceram Soc 1989;72(8):1511–3. [10] Goretta KC, Gutierrez-Mora F, Picciolo JJ, Routbort JL. Joining alumina/zirconia ceramics. Mater Sci Eng A 2003;341:158–62. [11] Toschi F, Melandri C, Pinasco P, Roncari E, Guicciardi S, De Portu G. Influence of residual stress on the wear behaviour of alumina/alumina–zirconia laminated composites. J Am Ceram Soc 2003;86(9):1547–53. [12] Lee SK, Lawn BR. Contact fatigue in silicon nitride. J Am Ceram Soc 1999;82(5):1281–8. [13] Kim DK, Jung Y-G, Peterson IM, Lawn BR. Cyclic fatigue of intrinsically brittle ceramics in contact with spheres. Acta Mater 1999;47(18):4711–25. [14] Fett T, Keller R, Munz D, Ernst E, Thun G. Fatigue of alumina under contact loading. Eng Fract Mech 2003;70:1143–52. [15] Jime´nez-Pique´ E, Ceseracciu L, Chalvet F, Anglada M, de Portu Hertzian G. contact fatigue on alumina/alumina-zirconia laminated composites. J Eur Ceram Soc, in press. [16] Fiori C, de Portu G. Tape casting: A technique for preparing and studying new materials., In: Davidge RW, editor. British Ceramic Proccedings no. 38, Novel ceramic fabrication processes and applications. Shelton, Stoke-on-Trent, UK, December 1986. p. 213. [17] Anstis GR, Chantikul P, Lawn BR. A critical evaluation of indentation techniques for measuring fracture toughness: I. Direct crack measurements. J Am Ceram Soc 1981;64:533–8. [18] Lawn BR. Indentation of ceramics with spheres: A century after Hertz. J Am Ceram Soc 1998;81(8):1977–94. [19] Warren PD, Hills DA, Dal DN. Mechanics of Hertzian cracking. Tribol Int 1995;28(6):357–62. [20] Rhee Y-W, Kim H-W, Deng Y, Lawn BR. Brittle fracture versus quasi plasticity in ceramics: A simple predictive index. J Am Ceram Soc 2001;48(3):561–5. [21] Roberts SG, Lawrence CW, Bisrat Y, Warren PD, Hills DA. Determination of surface residual stresses in brittle materials by Hertzian indentation: Theory and experiment. J Am Ceram Soc 1999;82(7):1809–16. [22] Warren PD, Hills DA. The influence of elastic mismatch between indenter and substrate on Hertzian fracture. J Mater Sci 1994;23: 2860–6. [23] Kara H, Roberts SG. Polishing behavior and surface quality of alumina and alumina/silicon carbide nanocomposites. J Am Ceram Soc 2000;83(5):1219–25. L. Ceseracciu et al. / International Journal of Refractory Metals & Hard Materials 23 (2005) 375–381 381