13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- The same study was also made for ceramic laminate with VATZ/VAMZ=5 - Figure 6 c), d) and here the critical loading force was estimated as F≅115N. In this case, a preferred propagation direction is starting to be a single deflection. For ratios VATZ/VAMZ<5 only a single crack deflection is predicted as preferred propagation direction. In case of volume ratio VATZ/VAMZ=2, the crack propagates almost straight, maximally with a slight deflection from the original direction (with no bifurcation phenomena). 4. Conclusions The crack path in laminates is influenced by the magnitude and location of the compressive stresses in the internal layers. A semi-analytical model based on Finite Fracture Mechanics (FFM) theory was here developed to describe and predict the crack propagation in symmetric laminates consisting of alternated tensile–compressive layers built–up in a periodic architecture. In addition to the mechanical loading under flexural bending, a thermal loading associated with the thermal mismatch of the layers during sintering was also taken into account in the model. The fracture criterion was based on the calculation of the change of the potential energy δΠ for a finite crack increment length, starting from the tip of the original crack and advancing in several possible propagation directions (angle of crack propagation). From all theoretically possible crack paths, the change of the potential energy between unperturbed and perturbed state was evaluated. Direction and/or type of propagation were selected such that the change of δΠ would attain a maximum value. In case of the low volume ratios (i.e. V1/V2= 1/1 – 4/1) single crack deflection (and in some cases straight crack propagation) is preferred with an angle lower than 20° (measured from the straight propagation). On the other hand, for relative high volume ratios, (i.e. V1/V2= 6/1 – 8/1), corresponding to high compressive residual stresses, crack bifurcation (i.e crack propagating simultaneously in two directions) is predicted by the model. Such behaviour is also in correspondence with the experimental observations. Acknowledgements The authors gratefully acknowledge a financial support through the project CZ.1.07/2.3.00/30.0005 of Brno University of Technology. A financial support by the Austrian Federal Government (in particular from the Bundesministerium für Verkehr, Innovation und Technologie and the Bundesministerium für Wirtschaft und Arbeit) and the Styrian Provincial Government, represented by Österreichische Forschungsförderungs- gesellschaft mbH and by Steirische Wirtschaftsförderungsgesellschaft mbH, within the research activities of the K2 Competence Centre on “Integrated Research in Materials, Processing and Product Engineering”, operated by the Materials Center Leoben Forschung GmbH in the framework of the Austrian COMET Competence Centre Programme, is gratefully acknowledged as well. References [1] W.J. Clegg, K. Kendall, N.M. Alford, T.W. Button, J.D. Birchall, A Simple Way to Make Tough Ceramics. Nature, 347 (1990) 455-457. [2] O. Prakash, P. Sarkar, P.S. Nicholson, Crack Deflection in Ceramic/Ceramic Laminates with Strong Interfaces. Journal of the American Ceramic Society, 78 (1995) 1125-1127.
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