Availableonlineatwww.sciencedirect.com DIRECT Part B: ELSEVIER Composites: Part B 37(2006)556-567 Laminated ceramic structures from oxide systems G. de portu c,L. micele G. pe b. c Research institute of Science and Technology for Ceramics, ISTEC-CNR, via Granarolo 64. 48018 Faenza Ceramic Physics Laboratory, Kyoto Institute of Technology, KIT, Sakyo ku, Matsugasaki, 606-8585 Kyoto, Research institute for Nano-S.science, RIN, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Ky Received 11 March 2005: received in revised form 5 August 2005; accepted 24 August 2005 Available online 19 April 2006 Abstract In this paper we present the results recently obtained in the study of laminated ceramic composites. The motivation for studying and producing laminated ceramic composites have been illustrated. Theoretical model useful to guide the design of laminated structures have been discussed and a route to prepare layered structures in the system Al2O3-ZrO2 have been suggested. The residual stresses developed in the ceramic layers have been quantified by indentation technique and piezo-spectroscopic analysis. With the latter technique also the stress distribution in the different layers has been assessed. Higher wear resistance under sliding and abrasive conditions of layered ceramics have been demonstrated. The improvement of fatigue contact damage resistance and an increase of Weibull modulus underlined. C 2006 Elsevier Ltd. All rights reserved Keywords: A. Layered structures: B. Mechanical properties; C. Residual internal stress; B. Wear 1. Introduction The interest in structural properties of such materials is not The main limit for an extensive application of ceramics as concerns the phenomena related to contact damage resistance, structural materials is their inhert brittleness and, as a tribological behaviour and machinability consequence, their poor reliability. In order to overcome this The motivation for the use of graded materials and problem three principal routes have been explored in the last laminated composites(considered as a special case of FGM) can be traced back to the observation of biological One consists in increasing the knowledges of macro-micro In those structures, the most performing parts of the materia mechanical behaviour of brittle materials. the second one deals are located in regions that experience the highest stresses. with the improvement of the preparation process of these Similarly, considering the tribological aspect, for example materials and the third one regards the design and development it has been recognized that the performances of wear-resistant of new materials and structures with improved flaw tolerance. materials are mainly related to the properties of thin surface The development of ceramic composites [1, 2], in general and functional graded materials(FGM)[3, 4] or laminated The development of laminated structures is based on the structures[5-7], in particular, incorporates the latter two tasks assumption that it is possible to design a material containing and stimulates, also, the interset in the first one, promoting the controlled residual stresses that can be used to increase refinement and progress of theoretical models able to describe the mechanical [16-23] and tribological performances of the the structural behaviour of such complex multiphase micro- system [24,25]. This goal can be achieved exploiting the structures [8-13 differences in thermal-physical properties (i.e. different sintering rates or coefficients of thermal expansion-CTE) among the laminae of dissimilar materials utilized in the process. w Corresponding author. Address. Research Institute of Science and These laminar ceramics containing large compressive Technology for Ceramics, ISTEC-CNR, via Granarolo 64. 48018 Faenza, stresses were shown to exhibit crack bifurcation [26,27 and Italy.Tel:+390546699752;fax:+39054646381 increasing strain to failure during fexural failure and a threshold strength when loaded in tension [28]. In the latter 1359-8368/- see front matter o 2006 Elsevier Ltd. All rights reserved. case, large cracks that initiate in the 'tensile layers'are stopped doi: 10.1016/j- composites. 2006.02.018 by the compressive layers at low stresses. Because the crack
Laminated ceramic structures from oxide systems G. de Portu a,c,*, L. Micele a,c, G. Pezzotti b,c a Research Institute of Science and Technology for Ceramics, ISTEC-CNR, via Granarolo 64, 48018 Faenza, Italy b Ceramic Physics Laboratory, Kyoto Institute of Technology, KIT, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan c Research Institute for Nano-Sscience, RIN, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan Received 11 March 2005; received in revised form 5 August 2005; accepted 24 August 2005 Available online 19 April 2006 Abstract In this paper we present the results recently obtained in the study of laminated ceramic composites. The motivation for studying and producing laminated ceramic composites have been illustrated. Theoretical model useful to guide the design of laminated structures have been discussed and a route to prepare layered structures in the system Al2O3-ZrO2 have been suggested. The residual stresses developed in the ceramic layers have been quantified by indentation technique and piezo-spectroscopic analysis. With the latter technique also the stress distribution in the different layers has been assessed. Higher wear resistance under sliding and abrasive conditions of layered ceramics have been demonstrated. The improvement of fatigue contact damage resistance and an increase of Weibull modulus underlined. q 2006 Elsevier Ltd. All rights reserved. Keywords: A. Layered structures; B. Mechanical properties; C. Residual internal stress; B. Wear 1. Introduction The main limit for an extensive application of ceramics as structural materials is their inhert brittleness and, as a consequence, their poor reliability. In order to overcome this problem three principal routes have been explored in the last decades. One consists in increasing the knowledges of macro–micro mechanical behaviour of brittle materials, the second one deals with the improvement of the preparation process of these materials and the third one regards the design and development of new materials and structures with improved flaw tolerance. The development of ceramic composites [1,2], in general, and functional graded materials (FGM) [3,4] or laminated structures [5–7], in particular, incorporates the latter two tasks and stimulates, also, the interset in the first one, promoting the refinement and progress of theoretical models able to describe the structural behaviour of such complex multiphase microstructures [8–13]. The interest in structural properties of such materials is not limited to the enhancement of strength and toughness but also concerns the phenomena related to contact damage resistance, tribological behaviour and machinability. The motivation for the use of graded materials and laminated composites (considered as a special case of FGM) can be traced back to the observation of biological structures. In those structures, the most performing parts of the material are located in regions that experience the highest stresses. Similarly, considering the tribological aspect, for example, it has been recognized that the performances of wear-resistant materials are mainly related to the properties of thin surface layers [14,15]. The development of laminated structures is based on the assumption that it is possible to design a material containing controlled residual stresses that can be used to increase the mechanical [16–23] and tribological performances of the system [24,25]. This goal can be achieved exploiting the differences in thermal–physical properties (i.e. different sintering rates or coefficients of thermal expansion-CTE) among the laminae of dissimilar materials utilized in the process. These laminar ceramics containing large compressive stresses were shown to exhibit crack bifurcation [26,27] and increasing strain to failure during flexural failure and a threshold strength when loaded in tension [28]. In the latter case, large cracks that initiate in the ‘tensile layers’ are stopped by the compressive layers at low stresses. Because the crack is Composites: Part B 37 (2006) 556–567 www.elsevier.com/locate/compositesb 1359-8368/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2006.02.018 * Corresponding author. Address. Research Institute of Science and Technology for Ceramics, ISTEC-CNR, via Granarolo 64, 48018 Faenza, Italy. Tel.: C39 0546 699752; fax: C39 0546 46381. E-mail address: deportu@istec.cnr.it (G. de Portu)
G de Portu et al. /Composites: Part B 37(2006)556-567 557 clampedby the compressive layers, crack extension through of large EM=(a2-a1)dT (1) stresses and catastrophic failure only occurs at a well defined, hreshold stress The increase in mechanical properties of layered architec- where, al and a2 are the thermal expansion coefficient of the tures can be also achieved through different strategies such as two materials and To is the temperature at which elastic stress introduction of weak interfaces[29,30), containment of develops due to thermal strain mismatch and T is the room martensitic transformation [31] or existence of porous layers ature [32]. However, the approach, which involves the stimulation of Considering a perfectly symmetrical architecture, far away compressive stresses [13, 33-35] is one of the most promising from the free surface, the residual stress ores depend from the one. if also contact damage phenomena are considered. Such ratio between the thickness ti and t2 of the materials I and 2, respectively structures are normally obtained by stacking alternating layers The layer with the lower thermal expansion coefficient sidual stresses can also be introduced by other means such as given by ) underg oes residual biaxial compressive stress of materials with different cte that will translate in residual stresses during cooling in the sintering stage. In some cases, phase transformation [27, 31]. In case of well bonded interface the increase in fracture toughness and fracture energy is 1+(1Eh2E) achieved through the existence of residual stresses and the crack deflection caused by the elastic mismatch between the while in the layer with greater thermal expansion coefficien dissimilar materials [8 (material 2)experiences a biaxial tensile stress given by: Some interesting reviews on laminated composites have been published in the past [6,7]. The aim of this work is to (3) illustrate the recent achievements we have got in the development and characterization of laminated ceramic and v is the Poissons ratio of the relative materials modulus In Eq( 2)E=E/(I-v), where E is the Y structures obtained from oxides system In the model, the role of thermal-physical properties in developing residual stresses appears evident. From the theoretical analysis laminated structures with proper residual 2. Theoretical background stress distribution can be designed. The experimental evidence of the type of stress associated to different layers is reported in With reference to the structural performance/reliability of Fig. I the laminated structures, different authors have emphasized As a matter of fact Eqs.(2)and ()are valid as first that several toughening mechanisms are operative in these approximation. They assume a constant value within each layer structures. Some authors have suggested the importance of and do not account for edge effects. In fact the actual situation obtaining a structure with low interface fracture energy, as this is more complicated and a correct theoretical model for the would enable the crack to be deflected along those weak prediction of the residual stress in different layers should take interfaces [29, 30]. Other authors evidenced the role played by into account the position of each layer(outer or inner),the elastic modulus mismatch, shrinkage and coefficient of thermal position in the single layers, the numbers of layers and the expansion( CTE)between different layers in generating volume fraction of the laminae of each material in the whole residual stresses in the laminated structure [36-39]. The structure(the latter requisite implies a size effect) stresses have been shown to improve both mechanical [40, 41] However, a deep discussion of the models is not in the aim and tribological properties of the composite [34] of this paper. If the observed toughening is actually related to res tresses, detailed understanding of the nature of these stresses, 3. Processing their distribution and entity are essential. Such residual stresses yield higher strength values, apparent toughness and wear Lamination of different thin ceramic layers to form thick resistance than found in monolithic materials of the same specimens is a relatively simple and inexpensive process, composition. Green et [37-39] performed theoretical which has shown interesting results and can be considered a calculations to determine the influence and magnitude of the valid alternative to more sophisticated processes [1,2,42 different thermo-physical parameters affecting residual Several processing routes have been explored for the stresses preparation of these composites including electrophoretic Several models have been proposed 18-13] to predict the deposition [43-46), sequential slip casting[11,31,47)and stress amount and distribution in laminated structures tape casting[12, 48-51] In the case of rigidly bonded layers of two different Among the ceramic laminated composites that can be naterials, the laminated structure suffer a mismatch strain produced, one of the most studied system is the alumina- represented by [9] zirconia one. As discussed in a previous paragraph, in order
‘clamped’ by the compressive layers, crack extension through the compressive layers requires the application of larger stresses and catastrophic failure only occurs at a well defined, threshold stress. The increase in mechanical properties of layered architectures can be also achieved through different strategies such as introduction of weak interfaces [29,30], containment of martensitic transformation [31] or existence of porous layers [32]. However, the approach, which involves the stimulation of compressive stresses [13,33–35] is one of the most promising one, if also contact damage phenomena are considered. Such structures are normally obtained by stacking alternating layers of materials with different CTE that will translate in residual stresses during cooling in the sintering stage. In some cases, residual stresses can also be introduced by other means such as phase transformation [27,31]. In case of well bonded interface, the increase in fracture toughness and fracture energy is achieved through the existence of residual stresses and the crack deflection caused by the elastic mismatch between the dissimilar materials [8]. Some interesting reviews on laminated composites have been published in the past [6,7]. The aim of this work is to illustrate the recent achievements we have got in the development and characterization of laminated ceramic structures obtained from oxides systems. 2. Theoretical background With reference to the structural performance/reliability of the laminated structures, different authors have emphasized that several toughening mechanisms are operative in these structures. Some authors have suggested the importance of obtaining a structure with low interface fracture energy, as this would enable the crack to be deflected along those weak interfaces [29,30]. Other authors evidenced the role played by elastic modulus mismatch, shrinkage and coefficient of thermal expansion (CTE) between different layers in generating residual stresses in the laminated structure [36–39]. These stresses have been shown to improve both mechanical [40,41] and tribological properties of the composite [34]. If the observed toughening is actually related to residual stresses, detailed understanding of the nature of these stresses, their distribution and entity are essential. Such residual stresses yield higher strength values, apparent toughness and wear resistance than found in monolithic materials of the same composition. Green et al. [37–39] performed theoretical calculations to determine the influence and magnitude of the different thermo-physical parameters affecting residual stresses. Several models have been proposed [8–13] to predict the stress amount and distribution in laminated structures. In the case of rigidly bonded layers of two different materials, the laminated structure suffer a mismatch strain represented by [9] 3M Z ð T0 T ða2Ka1ÞdT (1) where, a1 and a2 are the thermal expansion coefficient of the two materials and T0 is the temperature at which elastic stress develops due to thermal strain mismatch and T is the room temperature. Considering a perfectly symmetrical architecture, far away from the free surface, the residual stress sres depend from the ratio between the thickness t1 and t2 of the materials 1 and 2, respectively. The layer with the lower thermal expansion coefficient (material 1), undergoes residual biaxial compressive stress given by sres1 ZK 3ME0 1 1 C t1E0 1=t2E0 2 (2) while in the layer with greater thermal expansion coefficient (material 2) experiences a biaxial tensile stress given by: sres2 ZKsres1 t1 t2 (3) In Eq. (2) E0 ZE/(1Kn), where E is the Young’s modulus and n is the Poisson’s ratio of the relative materials. In the model, the role of thermal–physical properties in developing residual stresses appears evident. From the theoretical analysis laminated structures with proper residual stress distribution can be designed. The experimental evidence of the type of stress associated to different layers is reported in Fig. 1. As a matter of fact Eqs. (2) and (3) are valid as first approximation. They assume a constant value within each layer and do not account for edge effects. In fact the actual situation is more complicated and a correct theoretical model for the prediction of the residual stress in different layers should take into account the position of each layer (outer or inner), the position in the single layers, the numbers of layers and the volume fraction of the laminae of each material in the whole structure (the latter requisite implies a size effect). However, a deep discussion of the models is not in the aim of this paper. 3. Processing Lamination of different thin ceramic layers to form thick specimens is a relatively simple and inexpensive process, which has shown interesting results and can be considered a valid alternative to more sophisticated processes [1,2,42]. Several processing routes have been explored for the preparation of these composites including electrophoretic deposition [43–46], sequential slip casting [11,31,47] and tape casting [12,48–51]. Among the ceramic laminated composites that can be produced, one of the most studied system is the alumina– zirconia one. As discussed in a previous paragraph, in order G. de Portu et al. / Composites: Part B 37 (2006) 556–567 557
558 G. de Portu et al. /Composites: Part B 37(2006)556-567 35 Fig. 1. Effect of residual stresses on crack propagation in laminated structure (a) Layers containing compressive stress. Note that crack propagation perpendicular to the stress is hindered.( b) Layer containing tensile residual stress In this case, only cracks perpendicular to the interface(i.e to the direction of the stress)are visible to stimulate residual stresses in laminated structures it is In this paper, we take into consideration hybrid laminated necessary to use materials with different coefficients of composites of alternate layers of pure alumina and of a thermal expansion and shrinkage. In the range 25-1500C composite formed by 60 vol% Al2O3+40 vol% tetragonal alumina has a coefficient of thermal expansion (CTA) ZrO2 stabilized with 3 mol% Y203(3Y-TZP) fabricated by a≈9×10-6-, while zirconia has a≈11×10-6°-1. warm pressing and sintering of layers produced by tape casting In addition, alumina has different sintering rate and lower shrinkage than zirconia. On the other hand to control the 3.1. Tape casting residual stresses in the structure and avoid defects durin sintering, such as edge cracking [9, 11 tunnelling cracks This study entailed the use of a high purity (99.7%)alumina [52,53(Fig. 2)or delamination [54](Fig 3), an appropriate powder(Alcoa A16-SG, Alcoa Aluminum Co., New York, design and controlled mismatch in CTE among different USA)and a zirconia powder (TZ3Y-S, Tosoh Corp. Japan) laminae is necessary. To reach this goal usually, at least one doped with 3 mol% of Y203(usually referred to as 3Y-TZP) of the layers of the laminate is made of an alumina-zirconia both with an average particle size of 0.3 um. laminate. The reason for choosing alumina and zirconia as According to previous experiences[49,55,56],the different the constituent materials of ceramic laminates can be powders were mixed with organic binders, dispersant, generally traced back to the excellent bonding between plasticizers and solvents to obtain suitable slips for tape the layers in the absence of excessive diffusion between casting Slurry compositions were the same for both Al2O3 and omponents, their good thermo-mechanical properties and Al2O3-ZrO2 composite powders. In all slurry compositions the their relatively ease of processing organic components/inorganic powder weight ratio was fixed These characteristics make the two materials interesting at 1.6 and the binders were present at the same percentag idates for the production of ceramic multilayers. the plasticizer
to stimulate residual stresses in laminated structures it is necessary to use materials with different coefficients of thermal expansion and shrinkage. In the range 25–1500 8C alumina has a coefficient of thermal expansion (CTA) az9!10K6 8CK1 , while zirconia has az11!10K6 8CK1 . In addition, alumina has different sintering rate and lower shrinkage than zirconia. On the other hand to control the residual stresses in the structure and avoid defects during sintering, such as edge cracking [9,11], tunnelling cracks [52,53] (Fig. 2) or delamination [54] (Fig. 3), an appropriate design and controlled mismatch in CTE among different laminae is necessary. To reach this goal usually, at least one of the layers of the laminate is made of an alumina–zirconia laminate. The reason for choosing alumina and zirconia as the constituent materials of ceramic laminates can be generally traced back to the excellent bonding between the layers in the absence of excessive diffusion between components, their good thermo-mechanical properties and their relatively ease of processing. These characteristics make the two materials interesting candidates for the production of ceramic multilayers. In this paper, we take into consideration hybrid laminated composites of alternate layers of pure alumina and of a composite formed by 60 vol% Al2O3C40 vol% tetragonal ZrO2 stabilized with 3 mol% Y2O3 (3Y-TZP) fabricated by warm pressing and sintering of layers produced by tape casting. 3.1. Tape casting This study entailed the use of a high purity (99.7%) alumina powder (Alcoa A16 -SG, Alcoa Aluminum Co., New York, USA) and a zirconia powder (TZ3Y-S, Tosoh Corp. Japan) doped with 3 mol% of Y2O3 (usually referred to as 3Y-TZP) both with an average particle size of 0.3 mm. According to previous experiences [49,55,56], the different powders were mixed with organic binders, dispersant, plasticizers and solvents to obtain suitable slips for tape casting. Slurry compositions were the same for both Al2O3 and Al2O3–ZrO2 composite powders. In all slurry compositions the organic components/inorganic powder weight ratio was fixed at 1.6 and the binders were present at the same percentage of the plasticizer. Fig. 1. Effect of residual stresses on crack propagation in laminated structure. (a) Layers containing compressive stress. Note that crack propagation perpendicular to the stress is hindered. (b) Layer containing tensile residual stress. In this case, only cracks perpendicular to the interface (i.e. to the direction of the stress) are visible. 558 G. de Portu et al. / Composites: Part B 37 (2006) 556–567
G de Portu et al. /Composites: Part B 37(2006)556-567 200m ig. 2. Example of tunneling L. The slurry was ball milled for about 60 h then filtered and were obtained. The structure was designed to leave the layers acuum degassed of alumina(A)on the two surfaces(Fig. 5)in order to stimulate Tape-casting was performed with a laboratory tape-casting surface compressive stresses Due to lower thermal expansion bench with a stationary double blade system [55] coefficient and shrinkage during sintering, the external alumina As already reported [57] the types of powder used in this layers underwent residual compressive stresses. work do not lead to an evident green density gradient through To obtain a perfectly symmetrical structure, two A layers the thickness of the tapes were used on each side. This allowed one layer to be removed Sheets of pure alumina(hereinafter designated'A')and of from each side by grinding for a proper machining of the the composite alumina-zirconia with a volume ratio of 60/40 surface after sintering (hereinafter designated 'Az) were produced Final dense samples(98% of the theoretical density)were pproximately 2 mm thick, with layers approxin 3. 2. Production of the laminated structures 180 um. In order to modify the residual stress distribution in the structures the thickness of the Az layers was varied changing the thickness of the green tapes or stacking two layers c Discs with a diameter of 40 mm were cut from the different together(sequence A/2AZ/A/AZ/.). In Fig. 6, the section of The discs were put into a die, heated up to 80C then different architectures are reported To obtain a stress-free material for use as referenc pressed at 30 MPa for 30 min. The sequence and the number of laminated structures containing layers of pure alumina(here the different layers were varied according to the designed inafter referred to as'AA, )were also prepared with the same architectures procedure described before resulting in a material with surface As heating and cooling rates are crucial parameters porosity as the A/AZ one, but with zero( or very low)residual determining residual stresses in the structure [37, 38, the stresses. In addition full dense, pure monolithic alumina(MA) sintering cycle was carefully controlled. was prepared by cold isostatic pressing(pressure 150 MPa)and At the beginning a very low heating rate(3C/h)was used, sintered at 1600"C for lh in order to facilitate the binder removal. Then the heating rate was increased to 30C/h up to the sintering temperature (1550C)and hold for I h. After that the laminated samples 4. Residual stress measurements were cooled down with the same rate to 600 C. The profile of the sintering cycle is reported in Fig. 4 From the model described in paragraph 2, we Samples with a hybrid laminated structure of alumina and the magnitude of residual stresses is proportional to the CtE alumina-zirconia composite(hereinafter referred to as 'A/Az) mismatch between the materials but it also greatly depends
The slurry was ball milled for about 60 h then filtered and vacuum degassed. Tape-casting was performed with a laboratory tape-casting bench with a stationary double blade system [55]. As already reported [57] the types of powder used in this work do not lead to an evident green density gradient through the thickness of the tapes. Sheets of pure alumina (hereinafter designated ‘A’) and of the composite alumina–zirconia with a volume ratio of 60/40 (hereinafter designated ‘AZ’) were produced. 3.2. Production of the laminated structures Discs with a diameter of 40 mm were cut from the different ceramic green tapes. The discs were put into a die, heated up to 80 8C then pressed at 30 MPa for 30 min. The sequence and the number of the different layers were varied according to the designed architectures. As heating and cooling rates are crucial parameters determining residual stresses in the structure [37,38], the sintering cycle was carefully controlled. At the beginning a very low heating rate (3 8C/h) was used, in order to facilitate the binder removal. Then the heating rate was increased to 30 8C/h up to the sintering temperature (1550 8C) and hold for 1 h. After that the laminated samples were cooled down with the same rate to 600 8C. The profile of the sintering cycle is reported in Fig. 4. Samples with a hybrid laminated structure of alumina and alumina–zirconia composite (hereinafter referred to as ‘A/AZ’) were obtained. The structure was designed to leave the layers of alumina (A) on the two surfaces (Fig. 5) in order to stimulate surface compressive stresses. Due to lower thermal expansion coefficient and shrinkage during sintering, the external alumina layers underwent residual compressive stresses. To obtain a perfectly symmetrical structure, two A layers were used on each side. This allowed one layer to be removed from each side by grinding for a proper machining of the surface after sintering. Final dense samples (w98% of the theoretical density) were approximately 2 mm thick, with layers of approximately 180 mm. In order to modify the residual stress distribution in the structures the thickness of the AZ layers was varied changing the thickness of the green tapes or stacking two layers together (sequence A/2AZ/A/2AZ/.). In Fig. 6, the section of different architectures are reported. To obtain a stress-free material for use as reference, laminated structures containing layers of pure alumina (hereinafter referred to as ‘AA’) were also prepared with the same procedure described before resulting in a material with surface porosity as the A/AZ one, but with zero (or very low) residual stresses. In addition full dense, pure monolithic alumina (MA) was prepared by cold isostatic pressing (pressure 150 MPa) and sintered at 1600 8C for 1 h. 4. Residual stress measurements From the model described in paragraph 2, we have seen that the magnitude of residual stresses is proportional to the CTE mismatch between the materials but it also greatly depends on Fig. 2. Example of tunneling crack. G. de Portu et al. / Composites: Part B 37 (2006) 556–567 559
G. de Portu et al. /Composites: Part B 37(2006)556-567 I mm Fig. 3. Example of delamination among layers of dissimilar materials the geometry of the layered structure, in particular on layer 4.1. Mechanical approach thickness 19, 28 The overall stress field, affected by different shrinkage during sintering and CTE mismatch between The magnitude of surface compressive stress can be constituent phases/layers, mismatch in elastic constants estimated from the difference in indentation crack length between different phases/layers, and layers'geometry, may between a stressed surface and stress-free surface [58]. For a be rather complex and thus difficult to predict by theoretical stress-free material the fracture toughness can be related to the calculations. In order to avoid cracking and delamination, a indentation load and length of the relative cracks emanating precise control of both magnitude and distribution of residual from the comers of the impressions through the following tresses is mandatory. In multilayered ceramic components, equation the development of a reliable experimental procedure for the evaluation of residual stresses is highly desirable. The Klc=X (4) development of such a technique may also help to substantially reduce the computational time required for complete three- where dimensional finite-element calculations Few techniques are available for assessing residual stresses KIc toughness of the stress free material in ceramic materials, including X-ray diffraction, neutron x dimensionless constant (experimentally deter- diffraction, indentation method and piezo-spectroscopic and- lyses of photo-stimulated fluorescence or Raman bands. In this P indentation load paper, we focalize our attention on the latter ones Co crack length
the geometry of the layered structure, in particular on layer thickness [9,28]. The overall stress field, affected by different shrinkage during sintering and CTE mismatch between constituent phases/layers, mismatch in elastic constants between different phases/layers, and layers’ geometry, may be rather complex and thus difficult to predict by theoretical calculations. In order to avoid cracking and delamination, a precise control of both magnitude and distribution of residual stresses is mandatory. In multilayered ceramic components, the development of a reliable experimental procedure for the evaluation of residual stresses is highly desirable. The development of such a technique may also help to substantially reduce the computational time required for complete threedimensional finite-element calculations. Few techniques are available for assessing residual stresses in ceramic materials, including X-ray diffraction, neutron diffraction, indentation method and piezo-spectroscopic analyses of photo-stimulated fluorescence or Raman bands. In this paper, we focalize our attention on the latter ones. 4.1. Mechanical approach The magnitude of surface compressive stress can be estimated from the difference in indentation crack length between a stressed surface and stress-free surface [58]. For a stress-free material the fracture toughness can be related to the indentation load and length of the relative cracks emanating from the corners of the impressions through the following equation KIc Zc P c3=2 0 (4) where KIc toughness of the stress free material c dimensionless constant (experimentally determined) P indentation load c0 crack length. Fig. 3. Example of delamination among layers of dissimilar materials. 560 G. de Portu et al. / Composites: Part B 37 (2006) 556–567