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 laminate354 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