582 P Vena et al/ mechanics research communications 35(2008)576-582 The calculated laminate strength is consistent with the experimental results taken from the literature. Moreover, the en- rgy analysis evidenced the existence of a threshold lower limit on the external applied load below which the fracture will not occur except for very long cracks, which have no practical interest. This particular aspect cannot be obtained through mechanical laboratory tests unless a large number of specimens are considered. Indeed, the experimental tests presented in Sglavo and Bertoldi (2006)did not exhibit such threshold behavior. The micromechanical analyses have shown that the ceramic AMz laminate, because of the presence of residual stresses, does not exhibit a typical Weibull statistics behavior. The Weibull modulus is stress-dependent and a threshold stress below which Weibull statistic does not hold can be identified The AMZ laminate can be described using a modified Weibull approach, where additional parameters are needed. There- fore, further theoretical developments are required for a refined formulation of the Weibull statistics for materials with esidual stresses Acknowledgement The financial support of the Italian Ministry of University and research is kindly acknowledged. References Beremin, F.M., 1983. A local criterion for cleavage fracture of a nuclear pressure vessel steel Metallurgical Transactions A 14A, 2277-2287 Bertoldi, M. Paternoster, M, Sglavo, V M, 2003. Production of multilayer ceramic laminates with improved mechanical properties. Ceramic Transactions R, Pascual, ], Fischer, FD, Kolednik, O, Danzer, R, 2007. Prediction of the fracture toughness of a ceramic multilayer composite -modelling and ments. Acta Materialia 55. 409-42 ramics- Weibu Fracture Mechanics 74. 2919-29 posito, L Gentile, D, Bonora, N, 2007. Investigation on the Weibull parameters identification for local approach application in the ductile to brittle Gre od Cai, P Z, Messing, G L, 1999. Residual stresses in alumina-zirconia laminates. Journal of the European Ceramic Society 19. 2511-2517 Hilden, J, Bowman, K Trumble, KP, Rodel. ]- 2002. R-curve behavior in alumina-zirconia composites with repeating graded layers. Engineering Fracture Mechanics 69. 1647-1665 ett, T, 1999. Ceramics. Springer, Berlin. ty80.1633-1638 V M, Bertoldi, M., 2006. Design and production of ceramic laminates with high mechanical resistance and reliabilit Sglavo, VM Larentis, L, Green, JL, 2001. Flaw insensitive ion-exchanged glass: 1. Theoretical aspects. Journal of America Ceramic Society 84, 1827-1831 Vena, P, 2005. Thermal residual stresses in graded ceramic composites: a microscopic computational model versus homogenized models. Meccanica 40, Vena, P, Gastaldi, D, Contro, R, 2005. Effects of the thermal residual stress field on the crack propagation in graded alumina-zirconia ceramics Material Science Forum 492-493. 177-182.The calculated laminate strength is consistent with the experimental results taken from the literature. Moreover, the en￾ergy analysis evidenced the existence of a threshold lower limit on the external applied load below which the fracture will not occur except for very long cracks, which have no practical interest. This particular aspect cannot be obtained through mechanical laboratory tests unless a large number of specimens are considered. Indeed, the experimental tests presented in Sglavo and Bertoldi (2006) did not exhibit such threshold behavior. The micromechanical analyses have shown that the ceramic AMZ laminate, because of the presence of residual stresses, does not exhibit a typical Weibull statistics behavior. The Weibull modulus is stress-dependent and a threshold stress below which Weibull statistic does not hold can be identified. The AMZ laminate can be described using a modified Weibull approach, where additional parameters are needed. There￾fore, further theoretical developments are required for a refined formulation of the Weibull statistics for materials with residual stresses. Acknowledgement The financial support of the Italian Ministry of University and Research is kindly acknowledged. References Beremin, F.M., 1983. A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metallurgical Transactions A 14A, 2277–2287. Bertarelli, E., 2007. Master’s Thesis, Politecnico di Milano (in Italian). Bertoldi, M., Paternoster, M., Sglavo, V.M., 2003. Production of multilayer ceramic laminates with improved mechanical properties. Ceramic Transactions 153, 89–102. Chen, C.R., Pascual, J., Fischer, F.D., Kolednik, O., Danzer, R., 2007. Prediction of the fracture toughness of a ceramic multilayer composite – modelling and experiments. Acta Materialia 55, 409–421. Danzer, R., Suspancic, P., Pascual, J., Lube, T., 2007. Fracture statistics of ceramics – Weibull statistics and deviations from Weibull statistics. Engineering Fracture Mechanics 74, 2919–2932. Esposito, L., Gentile, D., Bonora, N., 2007. Investigation on the Weibull parameters identification for local approach application in the ductile to brittle transition regime. Engineering Fracture Mechanics 74, 549–562. Green, D.J., Cai, P.Z., Messing, G.L., 1999. Residual stresses in alumina–zirconia laminates. Journal of the European Ceramic Society 19, 2511–2517. Lei, Y., O’Dowd, N.P., Busso, E.P., Webster, G.A., 1998. Weibull stress solutions for 2D cracks in elastic and elastic–plastic materials. International Journal of Fracture 89, 245–268. Moon, R.J., Hoffman, M., Hilden, J., Bowman, K.J., Trumble, K.P., Rödel, J., 2002. R-curve behavior in alumina–zirconia composites with repeating graded layers. Engineering Fracture Mechanics 69, 1647–1665. Munz, D., Fett, T., 1999. Ceramics. Springer, Berlin. Sergo, V., Lipkin, M., De Portu, G., Clarke, D.R., 1997. Edge stresses in alumina–zirconia laminates. Journal of American Ceramic Society 80, 1633–1638. Sglavo, V.M., Bertoldi, M., 2006. Design and production of ceramic laminates with high mechanical resistance and reliability. Acta Materialia 54, 4929–4937. Sglavo, V.M., Larentis, L., Green, J.L., 2001. Flaw insensitive ion-exchanged glass: I. Theoretical aspects. Journal of America Ceramic Society 84, 1827–1831. Vena, P., 2005. Thermal residual stresses in graded ceramic composites: a microscopic computational model versus homogenized models. Meccanica 40, 163–179. Vena, P., Gastaldi, D., Contro, R., 2005. Effects of the thermal residual stress field on the crack propagation in graded alumina–zirconia ceramics. Material Science Forum 492–493, 177–182. 582 P. 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