Issue34

O.Ševeček et alii, Frattura ed Integrità Strutturale, 34 (2015) 362-370; DOI: 10.3221/IGF-ESIS.34.40 364 and extension of such edge cracks in the compressive layers is still lacking. In this work, a 2D parametric finite element model has been developed to predict the onset and propagation of an edge crack in ceramic laminates. The FE model utilizes the coupled stress-energy criterion [39], which considers simultaneously the necessary stress and energy conditions for the onset of the edge/tunnelling cracks and their further propagation. Several cases have been computed to show the effect of the compressive residual stresses on the onset and extension of edge cracks in ceramic laminates. E XPERIMENTAL OBSERVATIONS he ceramic laminate of study consists of 9 alternated layers combining two ceramic materials: (i) alumina with 5% tetragonal zirconia, named as ATZ, (ii) alumina with 30% monoclinic zirconia, referred to as AMZ. Fig. 2 shows a schematic of a prismatic bending bar with approx. dimensions of (LxBxH) 45mm x 4mm x 3mm. Due to the different thermal strains during cooling down from the sintering temperature, elastic strains are generated in the ATZ and AMZ layers, which lead to internal (in-plane) residual stresses. In this particular case, the ATZ layers have tensile stresses and the AMZ layers compressive stresses. For more details on the estimation of residual stresses see [26, 35]. In Fig. 2 an edge crack along the centre of the AMZ layer can be clearly seen. This is due to the tensile stress component generated at the free surface, having its maximum value at the edge, and decreasing into the material (see [34] for more details). Figure 2. Experimental observation of the edge crack phenomenon in compressive AMZ layer, and stress redistribution at the free surface of the thinner compressive layer. N UMERICAL ANALYSIS OF EDGE CRACKING IN LAMINATES FE Model he FE model prepared for the studies has been designed as a fully parametric model which enables automatic creation of any arbitrary laminate configuration with different volume ratios of particular material components (leading to different levels of residual stresses) or different thicknesses of the AMZ layer. Based on the real specimens, the considered model consists of nine layers composed by alternating ATZ and AMZ materials. The height and width of the laminate was fixed for all simulations to be H=3mm and W=4mm, respectively. The thickness of the inner AMZ layer was varied in the interval (30-350  m) and the thicknesses of the ATZ layers correspondingly tailored to reach the total thickness of 3mm. The material properties for the ATZ and AMZ layers needed for the numerical simulation are listed in Tab. 1. To simulate (i) the nucleation and (ii) the propagation of the edge crack and its dependency on the layer thickness and level of residual stress inside the layer, a 2D FE model of the laminate cross-section was created – see Fig. 3. Quadratic PLANE183 elements with generalized plane strain option were used to correctly capture the thermoelastic stress state in the laminate. FE software ANSYS 15.0 was used for this purpose. An example of the FE mesh is shown in Fig. 3. The T T Edge (surface) crack ATZ layer AMZ layer x z y  T Laminate cross-section ATZ AMZ ATZ a