V.M. Sglavo, M. Bertoldi/Composites: Part B 37 (2006)481-489 be evaluated by Eq (11)if elastic constants, thermal expansion coefficient and thickness of each layer are known. Since, the stress level in Eq (11)does not depend on stacking order the sequence of laminae can be still changed provided the symmetry condition is maintained to tailor the T-curve and promote stable growth of defects. Once the stress profile is defined, the apparent fracture toughness can be estimated by Eq(9)and strength and fracture behavior are directly defined. By changing the stacking order and composition of the layers, i.e. the laminate architecture, it is therefore possible to produce a material with unique and predefined failure stress. As examples, ceramic laminates composed of layers mullite or zirconia content (vol %o) belonging to the alumina/zirconia and alumina/mullite systems Fig. 7. Thermal expansion coefficient for AZ and AM composites have been designed. The thermal expansion coefficient required for the development of the residual stress profile was tailored by ratioequal to 229 GPa and 0.27, respectively, were considered for changing the composition of the single laminae. The architecture pure mullite. The elastic modulus for pure alumina and zirconia notation,'AZwly'or'AMwly', A stays for alumina, Z for The difference between the elastic modulus bounds is lower than zirconia, M for mullite, w corresponds to the volume percent 7 and 10%o, respectively for mullite and zirconia content below content of zirconia or mullite and y to the layer thickness in 40%. For the Poisson's ratios the difference is lower than 1.5% microns. The composition and thickness of the layers and their Therefore, the average of the values reported in Table I has been stacking order were selected to produce ceramic laminates with a used for the evaluation of Eqs. (11)and(12), thus accepting an constant strength, oF, equal l to =500 and =400 MPa in the az error equal to =5% at the highest for E. The thermal expansion and AM system, respectively. The apparent fracture toughness coefficient and fracture toughness for AM and AZ composites curve and corresponding residual stress profile were also tailored were measured on monolithic samples as reported in a previou in order to promote the stable growth of surface defects as deep as work [27] =150 and 180 um in the Az and AM system, respectively The residual stress profile and the Kc; curve for the AZ-I and On the basis of the aforementioned analysis, once the Young AM-1 engineered laminates are shown in Figs. 8 and modulus, Poissons ratio, thermal expansion coefficient and fracture toughness for each layer are determined, the residual X(um) stress distribution and the corresponding apparent fracture 0100200 toughness curve for each laminate can be estimated. In this study room temperature equal to 25C and stress-free tempera- ture equal to 1200C were established as indicated in previous works [23-25]. The properties of the materials required for the calculation are summarized in Table 1 and in Fig. 7. Youn modulus and Poissons ratio values for AM and AZ composites shown in Table 1 correspond to Voigt-Reuss bounds [17] according to previous results[26], Young modulus and Poisson's T Materials properties used to estimate the stress distribution and the apparent E(GPa) 100200 400 AMaZe 3.600.2) 0.23 AMIO 378÷368 3.300.2) 0.234÷0.233 61÷344 3.100.3) 0.238÷0.237 345÷324 6(0.2) 0.242÷0.241 328÷306 2400.2) 3.50.3 0.236÷0.235 Az20 56÷332 0.242÷0.240 Az40 3.900.3) 248÷0.245 318÷287 4.50.3) 0.254÷0.25 204(8) 400 Numbers rentheses correspond to the standard deviation. Elastic modulus pond to calculated Voigt-Reuss bounds for AM10-AM40 and Az10. Fig. 8. Residual stress profile of the AZl (a) and AM-1 (b) engineered Ret.[26]be evaluated by Eq. (11) if elastic constants, thermal expansion coefficient and thickness of each layer are known. Since, the stress level in Eq. (11) does not depend on stacking order, the sequence of laminae can be still changed provided the symmetry condition is maintained to tailor the T-curve and promote stable growth of defects. Once the stress profile is defined, the apparent fracture toughness can be estimated by Eq. (9) and strength and fracture behavior are directly defined. By changing the stacking order and composition of the layers, i.e. the laminate architecture, it is therefore possible to produce a material with unique and predefined failure stress. As examples, ceramic laminates composed of layers belonging to the alumina/zirconia and alumina/mullite systems have been designed. The thermal expansion coefficient required for the development of the residual stress profile was tailored by changing the composition of the single laminae. The architecture of the engineered laminates is reported in Fig. 6. In the used notation, ‘AZw/y’ or ‘AMw/y’, A stays for alumina, Z for zirconia, M for mullite, w corresponds to the volume percent content of zirconia or mullite and y to the layer thickness in microns. The composition and thickness of the layers and their stacking order were selected to produce ceramic laminates with a ‘constant’ strength, sF, equal to z500 and z400 MPa in the AZ and AM system, respectively. The apparent fracture toughness curve and corresponding residual stress profile were also tailored in order to promote the stable growth of surface defects as deep as z150 and z180 mm in the AZ and AM system, respectively. On the basis of the aforementioned analysis, once the Young modulus, Poisson’s ratio, thermal expansion coefficient and fracture toughness for each layer are determined, the residual stress distribution and the corresponding apparent fracture toughness curve for each laminate can be estimated. In this study room temperature equal to 25 8C and stress-free tempera￾ture equal to 1200 8C were established as indicated in previous works [23–25]. The properties of the materials required for the calculation are summarized in Table 1 and in Fig. 7. Young modulus and Poisson’s ratio values for AM and AZ composites shown in Table 1 correspond to Voigt-Reuss bounds [17]; according to previous results[26], Young modulus and Poisson’s ratio equal to 229 GPa and 0.27, respectively, were considered for pure mullite. The elastic modulus for pure alumina and zirconia was measured on monolithic samples as reported elsewhere [27]. The difference between the elastic modulus bounds is lower than 7 and 10%, respectively for mullite and zirconia content below 40%. For the Poisson’s ratios the difference is lower than 1.5%. Therefore, the average of the values reported in Table 1 has been used for the evaluation of Eqs. (11) and (12), thus accepting an error equal to z5% at the highest for E* . The thermal expansion coefficient and fracture toughness for AM and AZ composites were measured on monolithic samples as reported in a previous work [27]. The residual stress profile and the K
C;i curve for the AZ-1 and AM-1 engineered laminates are shown in Figs. 8 and 9, Table 1 Materials properties used to estimate the stress distribution and the apparent fracture toughness Material E (GPa) KC (MPam0.5) n AM0/AZ0 394 (14) 3.6 (0.2) 0.23a AM10 378O368 3.3 (0.2) 0.234O0.233 AM20 361O344 3.1 (0.3) 0.238O0.237 AM30 345O324 2.6 (0.2) 0.242O0.241 AM40 328O306 2.4 (0.2) 0.246O0.244 AZ10 375O360 3.5 (0.3) 0.236O0.235 AZ20 356O332 3.6 (0.2) 0.242O0.240 AZ30 337O308 3.9 (0.3) 0.248O0.245 AZ40 318O287 4.5 (0.3) 0.254O0.251 AZ100 204 (8) – 0.29a Numbers between parentheses correspond to the standard deviation. Elastic modulus values correspond to calculated Voigt-Reuss bounds for AM10-AM40 and AZ10-AZ40 composites. a Ref. [26]. Fig. 7. Thermal expansion coefficient for AZ and AM composites. Fig. 8. Residual stress profile of the AZ-1 (a) and AM-1 (b) engineered laminates. 486 V.M. Sglavo, M. Bertoldi / Composites: Part B 37 (2006) 481–489