13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- and subsequent delamination of the interface. a) b) Figure 1. a) Fracture of a ceramic laminate under flexural bending; bright layers have compressive residual stresses. b) Bifurcation of a crack entering the compressive layer of the laminate. The prediction of the crack path upon loading in such layered systems should help in tailoring the design with maximal fracture energy. Methods based on energetic considerations are available which attempt to predict the behavior of a crack approaching the interface of dissimilar materials (see for instance Ref. [16]). However, the modeling of the propagation of an interface crack through layered architectures with residual stresses is still missing. A method which can be used to predict the conditions under which the crack deflects or bifurcates within the compressive layer is sought. In this work, a model based on the finite fracture mechanics approach is developed to interpret and predict the direction of propagation of a crack impinging an interface of a ceramic laminate designed with internal compressive residual stresses. The thermal strains in the layers occurring during sintering, which are responsible for the mechanical behavior of the laminate, are taken into account. 2. Model for crack path prediction in laminates 2.1. Material of study: loading configuration A Finite Element analysis of a pre-cracked ceramic laminate specimen mechanically loaded in four-point bending was carried out. The thermal loading resulting from cooling down after sintering was also considered. The multilayer consists of a symmetric and periodic architecture with nine alternating layers of different thickness. In the initial state, a crack is introduced only in the first ATZ layer and impinges the first interface between ATZ and AMZ layer as depicted in Figure 2. Such laminate is subsequently subjected to the mechanical loading (4-point bend test). All the layers made of the same material, ATZ (alumina with 5% tetragonal zirconia), or AMZ (alumina with 30% monoclinic zirconia) have the same thickness, tATZ and tAMZ, respectively. Table 1 gives the values of the constituent material properties employed in the calculations.
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