《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Effects of residual stresses on the fracture properties

Availableonlineatwww.sciencedirect.com ScienceDirect E噩≈RS ELSEVIER Journal of the European Ceramic Society 27(2007)351-356 www.elsevier.com/locate/jeurceramsoc Effects of residual stresses on the fracture properties of non-oxide laminated composites S Guicciardi a, c M. Nagliatia, c C. Melandri a, c G. Pezzotti b, c.D. Scitia,C, CNR-/STEC, Institute of Science and Technology for Ceramics, Via Granarolo 64. 1-48018 Faenza, lte, yoto, Japan b Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Research Institute for Nanoscience(RIN), Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan Received 16 November 2005; received in revised form 26 April 2006: accepted 29 April 2006 Available online 16 june 2006 A layered ceramic composite in the AIN-SiC-MoSi2 system was prepared with the outer layers under residual compressive stress. The mechanical properties of the constituent layers and of the laminated composite were measured. Due to the residual compressive stress, the fracture strength of the laminated composite was higher than the strength of the outer layer material. The fracture toughness of the laminar composite was evaluated by SEVNB. The resulting values were compared with a fracture mechanics model and a good agreement was found between the experimental measurements and the calculated apparent fracture toughness profile 2006 Elsevier Ltd. All rights reserved. Keyword: Composites: Mechanical properties: Laminates; AIN; SiC; MoSiz Introduction was obtained by alternating layers with two different com positions in the AIN-SiC-MoSiz system and with a stack The design of ceramic laminates has been proved to be a ing sequence that left the outer layers under compression viable strategy to obtain significant increases of the fracture AIN-SiC-MoSiz ceramic composites were previously shown to resistance of ceramic materials. 1-7 The basic idea is to cou- couple good mechanical properties to electro-conductivity. 2-14 ple material layers with different thermal expansion coefficients In similar compositions and architecture, these composites are CTE)so that residual stresses arise during cooling from the currently employed in industrial applications such as heaters sintering temperature. The relative thickness of adjacent layers, and igniters. It is therefore mandatory from the engineering their Youngs modulus and CTEs affect these residual stresses point of view to understand the effects of the residual stresses whose sign and magnitude can be adjusted through the compo- on the mechanical properties of the layered architecture, with sition, the stacking sequence and the layer thicknesses particular emphasis on the fracture properties. To this purpose, Compressive layers placed within a laminate have been in the present paper mechanical properties of the constituent proved to be able to arrest cracks and this phenomenon can materials and of the layered composite were measured and produce composites with a threshold strength in which failure analysed does not occur until a critical stress is applied. Also the fra ture toughness benefits from the presence of compressive lay- 2. Experimental ers across laminated composites. Moreover, residual surface compressive stresses have been shown to improve the tribolog- 2.1. Materials preparation ical properties. In this work, a non-oxide ceramic multilayer was pro Two different layers with the following compositions(in duced by the tape casting technique. The layered composite vol %)were prepared Corresponding author. Tel. +39 699 748: fax: +39 0546 4638 55aIN +15SiC+30MoSi, labelled as C: E-mailaddress:dile@@istec.cnr.it(D.Sciti) 80aIN+10Sic+10MoSiz labelled as i 0955-2219/S-see front matter o 2006 Elsevier Ltd. All rights reserved. doi: 10.1016/j-jeurceramsoc200604. 173

Journal of the European Ceramic Society 27 (2007) 351–356 Effects of residual stresses on the fracture properties of non-oxide laminated composites S. Guicciardi a,c, M. Nagliati a,c, C. Melandri a,c, G. Pezzotti b,c, D. Sciti a,c,∗ a CNR-ISTEC, Institute of Science and Technology for Ceramics, Via Granarolo 64, I-48018 Faenza, Italy b Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan c Research Institute for Nanoscience (RIN), Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8585 Kyoto, Japan Received 16 November 2005; received in revised form 26 April 2006; accepted 29 April 2006 Available online 16 June 2006 Abstract A layered ceramic composite in the AlN–SiC–MoSi2 system was prepared with the outer layers under residual compressive stress. The mechanical properties of the constituent layers and of the laminated composite were measured. Due to the residual compressive stress, the fracture strength of the laminated composite was higher than the strength of the outer layer material. The fracture toughness of the laminar composite was evaluated by SEVNB. The resulting values were compared with a fracture mechanics model and a good agreement was found between the experimental measurements and the calculated apparent fracture toughness profile. © 2006 Elsevier Ltd. All rights reserved. Keyword: Composites; Mechanical properties; Laminates; AlN; SiC; MoSi2 1. Introduction The design of ceramic laminates has been proved to be a viable strategy to obtain significant increases of the fracture resistance of ceramic materials.1–7 The basic idea is to cou￾ple material layers with different thermal expansion coefficients (CTE) so that residual stresses arise during cooling from the sintering temperature. The relative thickness of adjacent layers, their Young’s modulus and CTEs affect these residual stresses whose sign and magnitude can be adjusted through the compo￾sition, the stacking sequence and the layer thicknesses. Compressive layers placed within a laminate have been proved to be able to arrest cracks and this phenomenon can produce composites with a threshold strength in which failure does not occur until a critical stress is applied.8 Also the frac￾ture toughness benefits from the presence of compressive lay￾ers across laminated composites.9,10 Moreover, residual surface compressive stresses have been shown to improve the tribolog￾ical properties.11 In this work, a non-oxide ceramic multilayer was pro￾duced by the tape casting technique. The layered composite ∗ Corresponding author. Tel.: +39 0546 699 748; fax: +39 0546 46381. E-mail address: dile@istec.cnr.it (D. Sciti). was obtained by alternating layers with two different com￾positions in the AlN–SiC–MoSi2 system and with a stack￾ing sequence that left the outer layers under compression. AlN–SiC–MoSi2 ceramic composites were previously shown to couple good mechanical properties to electro-conductivity.12–14 In similar compositions and architecture, these composites are currently employed in industrial applications such as heaters and igniters. It is therefore mandatory from the engineering point of view to understand the effects of the residual stresses on the mechanical properties of the layered architecture, with particular emphasis on the fracture properties. To this purpose, in the present paper mechanical properties of the constituent materials and of the layered composite were measured and analysed. 2. Experimental 2.1. Materials preparation Two different layers with the following compositions (in vol.%) were prepared: • 55AlN + 15SiC + 30MoSi2, labelled as C; • 80AlN + 10SiC + 10MoSi2, labelled as I. 0955-2219/$ – see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2006.04.173

S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007)351-356 Fig. 1.(a) Schematic diagram of the multilayer preparation and (b) bars preparation. Circular samples with thickness of 250 um and diameter of fracture toughness, Kle, was calculated according to the SenB 40 mm were punched out from the as-cast green tapes. Both formula: 7 monolithic and layered samples were produced. Monolithic PS amples were prepared by individually stacking I or C layers. KI Bw3/2/(a) The layered samples were produced by stacking 21 layers with quence I//C/l. /C//l. A schematic diagram is presented were warm-pressed at 75C for 15 min with an applied pressure f(a) 3a1/(1.99-a(1-a)(2.15-3.93a +2. Fig. 1. All the laminate materials, composite and monolithic, of 17 MPa, and then heated at 80C for 15 min without pres 2(1+2a)(1-a)2 sure. The burnout stage(150 C/h from 25 to 600oC, 30 min Pc is the critical load at fracture, S the span, B the width of holding time) was followed by sintering in a graphite furnace the bar, W the thickness of the bar and a the ratio between notch processing are reported in Refs. s trogen. More details of the length(a) and bar thickness w. nin) under lowing n The relative densities of the sintered samples were measured 3. Results and discussion by Archimede's method. On the polished cross section of the samples, the microstructure was analysed by scanning elec- 3. 1. Microstructure of the materials tron microscopy(SEM, Cambridge S360)and energy dispersive microanalysis(EDS, INCA Energy 300, Oxford instruments, The relative density of the laminate composite after sinter UK). The linear thermal expansion coefficient(CTE) of the ing was about 98%. A very good adhesion was found between monolithic materials was measured with dilatometric tests(Net- the layers as visible delamination or large structural defects at zsch Geraetebau Dil E 402, Germany)up to 1400C in air, the interface were not found. A polished cross section of the vith a heating rate of 5C/min. The Youngs modulus(E)of the monolithic materials was measured by the resonance fre quency method on 28 mm x 8 mm x 0.8 mm specimens using an H&P gain-phase analyzer. The flexural strength(o) of the monolithic materials and the laminated composite was mea- ured on a 4-pt bending fixture(outer span: 20 mm, inner span O mm)with a crosshead speed of 0.5 mm/min using chamfered bars 25 mm x 2.50mm x 1.75 mm, length x width x thickness respectively. The fracture toughness of the monolithic materials and laminated composite was measured by Single Edge V- Notched Beam(SE VNB). From the laminated composite, bars of about25mm×4mm×3 mm(length× thickness x width) were cut with the bar thickness corresponding to the thick ness of the sintered disc, as shown in Fig. lb. A notch was first introduced at the centre of the bending bar with a 500 um thick diamond saw, then this notch was sharpened using a razor blade sprinkled with 3 um diamond paste. Care was taken in 200um positioning the notch tip well within a tensile or compressive yer,Fig. 2. The notched bars were fractured in a 3-pt bend- Fig. 2. Optical micrograph showing an example of the notch introduced in the ing device with a crosshead of 0.5 mm/min and the appa 21-layers bars

352 S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007) 351–356 Fig. 1. (a) Schematic diagram of the multilayer preparation and (b) bars preparation. Circular samples with thickness of 250 m and diameter of 40 mm were punched out from the as-cast green tapes. Both monolithic and layered samples were produced. Monolithic samples were prepared by individually stacking I or C layers. The layered samples were produced by stacking 21 layers with sequence I/I/C/I...I/C/I/I. A schematic diagram is presented in Fig. 1. All the laminate materials, composite and monolithic, were warm-pressed at 75 ◦C for 15 min with an applied pressure of 17 MPa, and then heated at 80 ◦C for 15 min without pres￾sure. The burnout stage (150 ◦C/h from 25 to 600 ◦C, 30 min holding time) was followed by sintering in a graphite furnace (1850 ◦C/30 min) under flowing nitrogen. More details of the processing are reported in Refs.15,16 The relative densities of the sintered samples were measured by Archimede’s method. On the polished cross section of the samples, the microstructure was analysed by scanning elec￾tron microscopy (SEM, Cambridge S360) and energy dispersive microanalysis (EDS, INCA Energy 300, Oxford instruments, UK). The linear thermal expansion coefficient (CTE) of the monolithic materials was measured with dilatometric tests (Net￾zsch Geraetebau Dil E 402, Germany) up to 1400 ◦C in air, with a heating rate of 5 ◦C/min. The Young’s modulus (E) of the monolithic materials was measured by the resonance fre￾quency method on 28 mm × 8 mm × 0.8 mm specimens using an H&P gain-phase analyzer. The flexural strength (σ) of the monolithic materials and the laminated composite was mea￾sured on a 4-pt bending fixture (outer span: 20 mm, inner span: 10 mm) with a crosshead speed of 0.5 mm/min using chamfered bars 25 mm × 2.50 mm × 1.75 mm, length × width × thickness, respectively. The fracture toughness of the monolithic materials and laminated composite was measured by Single Edge V￾Notched Beam (SEVNB). From the laminated composite, bars of about 25 mm × 4 mm × 3 mm (length × thickness × width) were cut with the bar thickness corresponding to the thick￾ness of the sintered disc, as shown in Fig. 1b. A notch was first introduced at the centre of the bending bar with a 500m￾thick diamond saw, then this notch was sharpened using a razor blade sprinkled with 3m diamond paste. Care was taken in positioning the notch tip well within a tensile or compressive layer, Fig. 2. The notched bars were fractured in a 3-pt bend￾ing device with a crosshead of 0.5 mm/min and the apparent fracture toughness, KIc, was calculated according to the SENB formula:17 KIc = PcS BW3/2 f (α) (1) where f (α) = 3α1/2[1.99 − α(1 − α)(2.15 − 3.93α + 2.7α2)] 2(1 + 2α)(1 − α) 3/2 (2) Pc is the critical load at fracture, S the span, B the width of the bar, W the thickness of the bar and α the ratio between notch length (a) and bar thickness W. 3. Results and discussion 3.1. Microstructure of the materials The relative density of the laminate composite after sinter￾ing was about 98%. A very good adhesion was found between the layers as visible delamination or large structural defects at the interface were not found. A polished cross section of the Fig. 2. Optical micrograph showing an example of the notch introduced in the 21-layers bars.

S Guicciardi et al. /Journal of the European Ceramic Sociery 27(2007)351-356 multilayer composite is shown in Fig 3a. The layers'thickness was in the range of 170-200 um. Small variations in thickness were unavoidable since the discs were produced from differ ent tapes with the same compositions. In Fig. 3b and c, detailed views of the single layers are reported. A small amount of poros- ty was found in both layers(1-2%). Further details on the microstructure are reported elsewhere. The monolithic mate rials presented similar microstructural features. No trace of the junction between the stacked layers was found, such that these pecimens resembled bulk materials 3. 2. Properties of the monolithic materials Some properties of the monolithic materials are reported in 100um Table 1. The CTEs were linear function of the temperature in the measured range. The Cte of material C was higher than that of material l, due to the higher content of MoSi,, which is the phase with the highest CTE. Typical values reported in the literature for the pure phases are: 8 AIN: 5.59 x 10-6oC-I iC:5.12×10-6°C-1,MoSi2:9.1×10-6°C-1 The higher value of Youngs modulus of material C is mainly e to the higher amount of MoSi2 and Sic, which are very stiff phases(440 GPa). The fracture toughness of material C was higher than that of material I(Table 1), very likely as a result of the higher content of MoSi,. Due to its high value of Cte, the higher content of moSi, increased the residual stress in the alN-Sic matrix which acted as a toughening mechanism. I The fexural strength of both materials was relatively high 10 um with a low dispersion around the mean value, see Table 1. Mate rial I was slightly stronger than material C. 3.3. Calculation of the residual stresses in the laminated The residual stresses in the various rigidly bonded layers can be estimated according to the lamination theory G+a1△T= constant E o;;=0 where Ei is the elastic residual deformation and oi the stress developed in the layer of thickness t Respectively, ai, Ei and vi are the thermal expansion coefficient, the Youngs modulus and Fig. 3. SEM micrographs of the microstructure of the multilayer saI the Poissons ratio of layer i. AT is the temperature-range over Panoramic view of the layered material. (b)Detailed view of the I layer, and(c) which elastic stress develops due to thermal strain mismatch. of the C layer. The MoSi2 phase is visible as bright contrast grains di the AlN-Sic matrix Table 1 Compositions and properties of the constituent materials Material Composition(vol %) E(GPa) CTE(25-1000°)(×10-6°C Kle(MPam.S) a(MPa) 80AIN +10SiC+10MoSi 27 620 2.1±0.1 571士25 55AIN +15SiC+30MoSiz 23 2.8±0.4 513±23 Apparent fracture toughness and flexural strength of the laminated composite material. E= Youngs modulus, v=Poissons ratio(calculated), CTE=linear thermal expansion coefficient, Kle-fracture toughness, a=4-pt bending strength

S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007) 351–356 353 multilayer composite is shown in Fig. 3a. The layers’ thickness was in the range of 170–200m. Small variations in thickness were unavoidable since the discs were produced from differ￾ent tapes with the same compositions. In Fig. 3b and c, detailed views of the single layers are reported. A small amount of poros￾ity was found in both layers (∼1–2%). Further details on the microstructure are reported elsewhere.16 The monolithic mate￾rials presented similar microstructural features. No trace of the junction between the stacked layers was found, such that these specimens resembled bulk materials. 3.2. Properties of the monolithic materials Some properties of the monolithic materials are reported in Table 1. The CTEs were linear function of the temperature in the measured range. The CTE of material C was higher than that of material I, due to the higher content of MoSi2, which is the phase with the highest CTE. Typical values reported in the literature for the pure phases are:18 AlN: 5.59 × 10−6 ◦C−1, SiC: 5.12 × 10−6 ◦C−1, MoSi2: 9.1 × 10−6 ◦C−1. The higher value of Young’s modulus of material C is mainly due to the higher amount of MoSi2 and SiC, which are very stiff phases (∼440 GPa18). The fracture toughness of material C was higher than that of material I (Table 1), very likely as a result of the higher content of MoSi2. Due to its high value of CTE, the higher content of MoSi2 increased the residual stress in the AlN–SiC matrix, which acted as a toughening mechanism.19 The flexural strength of both materials was relatively high with a low dispersion around the mean value, see Table 1. Mate￾rial I was slightly stronger than material C. 3.3. Calculation of the residual stresses in the laminated composite The residual stresses in the various rigidly bonded layers can be estimated according to the lamination theory:3 εi = 1 − νi Ei σi + αiT = constant (3) i σiti = 0 (4) where εi is the elastic residual deformation and σi the stress developed in the layer of thickness ti. Respectively, αi, Ei and νi are the thermal expansion coefficient, the Young’s modulus and the Poisson’s ratio of layer i. T is the temperature-range over which elastic stress develops due to thermal strain mismatch. Fig. 3. SEM micrographs of the microstructure of the multilayer samples. (a) Panoramic view of the layered material. (b) Detailed view of the I layer, and (c) of the C layer. The MoSi2 phase is visible as bright contrast grains dispersed in the AlN–SiC matrix. Table 1 Compositions and properties of the constituent materials Material Composition (vol.%) E (GPa) ν CTE (25–1000 ◦C) (×10−6/ ◦C) KIc (MPa m0.5) σ (MPa) I 80AlN + 10SiC + 10MoSi2 325 0.27 6.20 2.1 ± 0.1 571 ± 25 C 55AlN + 15SiC + 30MoSi2 348 0.23 6.87 2.8 ± 0.4 513 ± 23 Apparent fracture toughness and flexural strength of the laminated composite material. E = Young’s modulus, ν = Poisson’s ratio (calculated), CTE = linear thermal expansion coefficient, KIc = fracture toughness, σ = 4-pt bending strength.

S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007)351-356 For the calculations, the Poisson's ratios of the different lay ers were determined with the rule of mixture on the basis of the starting compositions and are 0.27 and 0.25 for the I and Cmate- rials, respectively, while the ai, and Ei values were taken as those experimentally determined (Table 1). A crucial parameter for the calculation with theoretical models is the stress-free temper- ature, i.e. the temperature below which stresses are accumulated elastically. This stress-free temperature is difficult to determine experimentally and is usually taken to be somewhat lower than the sintering temperature, with 1200C being a quite common choice. In a recent study temperatures as low as 675C were lected in order to get a good agreement with theoretical and experimental results. However, in the present case, the tempera- ture was selected a priori considering that each individual layer 100m contains MoSi, for which a brittle-to-ductile transition occurs at about 1000C.Taking 1000C as stress-free temperature, the calculated residual stresses were -123 MPa(compressive) in the insulating I layers and +146 MPa( tensile)in the conduc- tive C layers for the 21-layers specimens produced for toughness measurements 3.4. Properties of the laminated composite 3.4.1. Flexural strength The flexural strength of the laminated composite lated on seven specimens, was 622+41 MPa with minimum and maximum values of 574 and 694 MPa, respectively. No evidence of stable crack growth was observed in any of the load-displacement curves. The values of flexural strength were calculated considering the stress field across the section of the bending bar with a stepwise Youngs modulus profile,i.e P(Sout"Dinn/E(x) E-EIx Fig 4. Examples of fracture origins of the laminated bars(SEM micrographs). (5) (a) An inhomogeneity located in the external layer, flexural strength=694 MPa E3-EIE (b) Large microcrack at the interface between the second and the third layer where P is the applied load, Sout and Sinn the outer and inner fiexural strength=574MPa plains spectively, B the width of the bar and E(x)the in-depth of this material in the laminated composite was about 50MPa rain variation of the Youngs modulus across the section This value is of the same order of magnitude of the compres- of the laminated bar. The expressions of E1, E2 and E3 are the sive residual stress calculated by the lamination theory even if lower. The non-perfect match between these two values is due E(x)da (6) to the fact that in some fractured bars the fracture origins were not located in the external layer. An example of this situation is shown in Fig. 4a and b 3.4.2. Fracture toughness The apparent fracture toughness of the laminated composite E rE()dx (8) was in the range of 3. 8-5.6 MPa.5. During the tests, neither pop-in phenomena or stable crack propagation were detected For the construction of the Youngs modulus profile, the thick- when the notch tip was located either in the compressive layer ness of each individual layer was measured in every single bar. or in the tensile layer. The apparent fracture toughness values Since in bending the highest tensile stress is located at the ten- were therefore calculated considering the crack length a as the sile external surfaces, the strength of the laminated composite initial notch depth. Even if not particularly large, the data disper is mainly dictated by the outer layer strength. The outer layer sion of the apparent fracture toughness is the main outcome of of the laminated composite was made of material I which, in the different stress profiles, which exists along the notches with its stress-free state, had a mean flexural strength of 571 MPa different depths. In fact, the measured apparent fracture tough (Table 1). Therefore, due to the residual compressive stress orig- ness is the result of the superposition of the externally applied inating from the lamination processing, the increase in strength flexural stress and the residual stress profile inside the laminate

354 S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007) 351–356 For the calculations, the Poisson’s ratios of the different lay￾ers were determined with the rule of mixture on the basis of the starting compositions and are 0.27 and 0.25 for the I and C mate￾rials, respectively, while the αi, and Ei values were taken as those experimentally determined (Table 1). A crucial parameter for the calculation with theoretical models is the stress-free temper￾ature, i.e. the temperature below which stresses are accumulated elastically. This stress-free temperature is difficult to determine experimentally and is usually taken to be somewhat lower than the sintering temperature, with 1200 ◦C being a quite common choice. In a recent study10 temperatures as low as 675 ◦C were selected in order to get a good agreement with theoretical and experimental results. However, in the present case, the tempera￾ture was selected a priori considering that each individual layer contains MoSi2 for which a brittle-to-ductile transition occurs at about 1000 ◦C.20 Taking 1000 ◦C as stress-free temperature, the calculated residual stresses were −123 MPa (compressive) in the insulating I layers and +146 MPa (tensile) in the conduc￾tive C layers for the 21-layers specimens produced for toughness measurements. 3.4. Properties of the laminated composite 3.4.1. Flexural strength The flexural strength of the laminated composite, calcu￾lated on seven specimens, was 622 ± 41 MPa with minimum and maximum values of 574 and 694 MPa, respectively. No evidence of stable crack growth was observed in any of the load–displacement curves. The values of flexural strength were calculated considering the stress field across the section of the bending bar with a stepwise Young’s modulus profile, i.e.:21,22 σflex(x) = P(Sout − Sinn) 4B E (x) E2 − E1x E2 2 − E1E3 (5) where P is the applied load, Sout and Sinn the outer and inner span, respectively, B the width of the bar and E (x) the in-depth plain strain variation of the Young’s modulus across the section of the laminated bar. The expressions of E1, E2 and E3 are the following: E1 = W 0 E (x) dx (6) E2 = W 0 xE (x) dx (7) E3 = W 0 x2E (x) dx (8) For the construction of the Young’s modulus profile, the thick￾ness of each individual layer was measured in every single bar. Since in bending the highest tensile stress is located at the ten￾sile external surfaces, the strength of the laminated composite is mainly dictated by the outer layer strength. The outer layer of the laminated composite was made of material I which, in its stress-free state, had a mean flexural strength of 571 MPa (Table 1). Therefore, due to the residual compressive stress orig￾inating from the lamination processing, the increase in strength Fig. 4. Examples of fracture origins of the laminated bars (SEM micrographs). (a) An inhomogeneity located in the external layer, flexural strength = 694 MPa. (b) Large microcrack at the interface between the second and the third layer, flexural strength = 574 MPa. of this material in the laminated composite was about 50 MPa. This value is of the same order of magnitude of the compres￾sive residual stress calculated by the lamination theory even if lower. The non-perfect match between these two values is due to the fact that in some fractured bars the fracture origins were not located in the external layer. An example of this situation is shown in Fig. 4a and b. 3.4.2. Fracture toughness The apparent fracture toughness of the laminated composite was in the range of 3.8–5.6 MPa m0.5. During the tests, neither pop-in phenomena or stable crack propagation were detected when the notch tip was located either in the compressive layer or in the tensile layer. The apparent fracture toughness values were therefore calculated considering the crack length a as the initial notch depth. Even if not particularly large, the data disper￾sion of the apparent fracture toughness is the main outcome of the different stress profiles, which exists along the notches with different depths. In fact, the measured apparent fracture tough￾ness is the result of the superposition of the externally applied flexural stress and the residual stress profile inside the laminate

S Guicciardi et al. /Journal of the European Ceramic Sociery 27(2007)351-356 structure. By fracture mechanics analysis, the effects of the stress field superposition can be estimated by considering that the stress-intensity factor, KI, of a crack of length a due to an E arbitrary distribution of crack-line stress o(x)is KI= h(-,a o(r)dx where h(x/a, a)is a weight function given by 3 {-+4(-)-0 and a is the crack length normalized for the bar thickness(alW). Fig. 5. Apparent fracture toughness profile and superimposition of experimental ness W and width B subjected to 3-pt bending over a span of s is given by2I 4. Conclusions a(x)=Flex(x)+or(x) (11) A layered ceramic composite in the AIN-SiC-MoSiz system where o flex(x)is given by Eq (5)and or (x)is the residual stress was prepared by tape-casting. The composite was prepared by at point x given by alternatively stacking electrical insulating and conductive lami- o,(x)=o for x corresponding to the I layers nae. The stacking was such that the outer layers were underresid ual compressive stress. The magnitude of the residual stresses (123 MPa, in the present case) was estimated through the lamination theory. The mechanical 02 for x corresponding to the c layers properties of the constituent materials ite were measured. with respect to the stress-free outer material, (+146 MPa, in the present case) the fracture strength of the laminated composite increased by an amount comparable to the compressive residual stress calcu For the calculations of the apparent fracture toughness pI lated by the lamination theory. The apparent fracture toughness file, the coefficients A in Eq (6)were taken from Ref.,which of the laminated composite was estimated by an analytical frac- considered the case of a flexural bar made of a homogeneous ture mechanics model and a good agreement was found betweer material without variation of Youngs modulus across its sec- experimental values and the predictions of fracture mechanics tion. However, as shown in Ref, even with a strong gradient the section of the bar the dif- References ference in the calculated stress intensity factor remains <10% The apparent fracture toughness profile of the laminated com- 1. Marshall, D B. Ratto, J.J. and Lange, F E, Enhanced fracture toughness posite was calculated as follows. For any crack length a, a in layered microcomposites of Ce-ZrO and Al2O3. J. Am. Ceram. So corresponding critical bending load, Pc, was calculated so that, 2. Sathy amoorthy, R, Virkar, A. V. and Cutler, R. A, Damage-resistant integrating Eq (9)with the stress distribution given by Eq (11), SiC-AIN layered composites with surface compressive stresses. J. Am. the intrinsic (i.e. stress-free) Klc for the material containing Ceran.Soe,1992,75,1136-1141. the tip of the crack a was obtained. This couple(a, Pc) was 3. Chartier, T, Merle, D and Besson, J.L. Laminar ceramic composites. J. then inserted in Eqs. (1)and (2)to find out the corresponding 4. saijgalik, P, Lences, Z and Dusza, J, Layered Si NA composites with apparent fracture toughness. By varying the crack length and the corresponding Pc, the apparent fracture toughness profile as 5.Rao, M P, Sanchez-Herencia, A.I. Beltz, G.E., McMeeking, R.Mand a function of crack length a can be drawn. In order to obtain a Lange, F. F, Laminar ceramics that exhibit a threshold strength. Science, unique Kle profile, the thickness of the layers were in this case averaged. This apparent KIc profile is shown in Fig. 5 along with 6. Kovar, D, Thouless, M D. and Halloran, J. w, Crack deflection and propa- the experimental data points. As can be seen, the apparent KI 1998,81,1004-1012. is an increasing function of the crack length in the compressive 7. Cai, PZ, Green, D.J. and Messing, GL, Mechanical layer and a decreasing function of the crack length in the tensile Al2O3/ZrO2 hybrid laminates. J. Eur Ceram Soc., 1998, 5, 2025-2034 layer with values ranging from 0.9 to 7.2 MPam.Recognis- 8.Rao, M. P and Lange, E F, Factors affecting threshold strength in laminar ing all the approximations involved in the calculation of the 1222-1228 apparent fracture toughness, the agreement between the theoret 9. Blattner. A. J. Lakshmina ical curve and the experimental points can be considered quite layered ceramic composites with residual surface compression: effects of yer thickness. Eng. fract. Mech, 2001, 68, 1-7

S. Guicciardi et al. / Journal of the European Ceramic Society 27 (2007) 351–356 355 structure.23 By fracture mechanics analysis, the effects of the stress field superposition can be estimated by considering that the stress-intensity factor, KI, of a crack of length a due to an arbitrary distribution of crack-line stress σ(x) is KI = a 0 h x a , α σ(x) dx (9) where h(x/a, α) is a weight function given by23 h x a , α =  2 πa 1 (1 − (x/a))1/2(1 − α) 3/2 ×  (1 − α) 3/2 +Aij 1 − x a i+1 αj  (10) and α is the crack length normalized for the bar thickness (a/W). The in-depth stress distribution σ(x) in a laminated bar of thick￾ness W and width B subjected to 3-pt bending over a span of S is given by21 σ(x) = σflex(x) + σr(x) (11) where σflex(x) is given by Eq. (5) and σr(x) is the residual stress at point x given by σr(x) = σ1 for x corresponding to the I layers (−123 MPa, in the present case) = σ2 for x corresponding to the C layers (+146 MPa, in the present case) For the calculations of the apparent fracture toughness pro- file, the coefficients Aij in Eq. (6) were taken from Ref.24, which considered the case of a flexural bar made of a homogeneous material without variation of Young’s modulus across its sec￾tion. However, as shown in Ref.,25 even with a strong gradient profile of Young’s modulus across the section of the bar, the dif￾ference in the calculated stress intensity factor remains <10%. The apparent fracture toughness profile of the laminated com￾posite was calculated as follows.23 For any crack length a, a corresponding critical bending load, Pc, was calculated so that, integrating Eq. (9) with the stress distribution given by Eq. (11), the intrinsic (i.e. stress-free) KIc for the material containing the tip of the crack a was obtained. This couple (a, Pc) was then inserted in Eqs. (1) and (2) to find out the corresponding apparent fracture toughness. By varying the crack length and the corresponding Pc, the apparent fracture toughness profile as a function of crack length a can be drawn. In order to obtain a unique KIc profile, the thickness of the layers were in this case averaged. This apparent KIc profile is shown in Fig. 5 along with the experimental data points. As can be seen, the apparent KIc is an increasing function of the crack length in the compressive layer and a decreasing function of the crack length in the tensile layer with values ranging from 0.9 to 7.2 MPa m0.5. Recognis￾ing all the approximations involved in the calculation of the apparent fracture toughness, the agreement between the theoret￾ical curve and the experimental points can be considered quite good. Fig. 5. Apparent fracture toughness profile and superimposition of experimental data points. 4. Conclusions A layered ceramic composite in the AlN–SiC–MoSi2 system was prepared by tape-casting. The composite was prepared by alternatively stacking electrical insulating and conductive lami￾nae. The stacking was such that the outer layers were under resid￾ual compressive stress. The magnitude of the residual stresses was estimated through the lamination theory. The mechanical properties of the constituent materials and the layered compos￾ite were measured. With respect to the stress-free outer material, the fracture strength of the laminated composite increased by an amount comparable to the compressive residual stress calcu￾lated by the lamination theory. The apparent fracture toughness of the laminated composite was estimated by an analytical frac￾ture mechanics model and a good agreement was found between experimental values and the predictions of fracture mechanics. References 1. 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