Issue34

O.Ševeček et alii, Frattura ed Integrità Strutturale, 34 (2015) 362-370; DOI: 10.3221/IGF-ESIS.34.40 366 available to create a crack, and the second condition stipulates that the tensile stress is greater than the tensile strength all along the new presumed crack path. To predict the onset of such an edge crack, the coupled criterion [39, 41] allows getting rid of any assumption on the existence of flaws able to trigger cracking [36, 37]. There is no adjustable parameter in the coupled criterion, whereas in the other case the flaw size is selected so as to fit with the experimental measures. This choice is somewhat arbitrary because it does not rely on micrographic observations. Moreover the flaw approach analyses the early stage of the edge cracking and assumes a further crack growth in depth and along the specimen faces (channelling) to reach the observable state. On the other hand, with the coupled criterion we make the assumption that the crack appears almost simultaneously all around the specimen and then grows in depth. Application to ceramic laminates For demonstration, let us consider our laminate of study, where the thickness of the AMZ layer is selected as 0.150mm. After the sintering process the laminate is cooled down from the reference (sintering) temperature - lying between 1200- 1500°C - to room temperature which results in origination of compressive residual stresses inside the AMZ layer (and tensile stresses in ATZ layer). In case that the difference to the reference temperature is relatively low (e.g. ≈ 700°C), the magnitude of compressive residual stresses will be relatively low (in this particular case ≈-400MPa) and no edge crack can be initiated, because at no point both energy and stress criterion is fulfilled (  yy≥  c  and G inc ( a )≥ G c (AMZ) ) – see Fig. 4a). If the specimen is further cooled down until a value of residual stress  res (AMZ) =-432MPa inside the AMZ layer, then a first point of satisfaction of both criteria is reached (namely G inc ( a )= G c (AMZ) ) and the edge crack is originated with a sudden jump from zero length to length a 1 =0.059mm as depicted in the Fig. 4b). After continuation of the cooling down process, the residual stresses inside the AMZ layer become yet lower and can theoretically reach values around -700MPa. This state is demonstrated in the Fig. 4c). Once the crack is nucleated, then it propagates through the AMZ layer as long as the ERR at the crack tip G ( a ) is greater than G c (AMZ) . The final crack length after the cooling down process is thus determined by point 3 in the Fig. 4c) and reaches a value of a 3 . If the curve of G ( a ) become higher than G c (AMZ) at all points along the possible edge crack path, then the AMZ layer should break totally in the whole plane of the specimen. This can thus indicate not suitable laminate configurations for which the processing of the specimens would become problematic. R ESULTS ith the introduced model a parametric study involving an influence of the AMZ layer thickness and level of residual stress inside this layer on the origination and propagation of the edge crack has been carried out. The aim was to understand how the mentioned parameters influence the edge cracking phenomenon. A large number of different laminate configurations were calculated in order to obtain general insight into the problem. Let us consider now several laminate configurations with different thicknesses of the AMZ layer, ranging from 50 to 350  m. If the total height of the laminate is kept constant, then these configurations will result in different volume ratios of ATZ and AMZ components and thus also in different levels of residual stresses (upon the assumption of a complete cooling down process from 1300°C to room temperature). In order to enable a comparative study for a given level of residual stress, a corresponding  T has to be first calculated for each laminate configuration. Then a further set of simulations is performed by introducing an edge crack with a length between 0  m and 400  m (with a step of 1  m), enabling the estimation of G , G inc and  yy (along the prospective crack path) as a function of the edge crack length a . Consider now a level of residual stress in the AMZ layer to be  res (AMZ) =-200MPa. The dimensionless ERR and tangential stress  yy ahead the crack tip are plotted together in Fig. 5a. This plot clearly shows that no edge cracking is possible. If the level of compressive stress is increased to the value  res (AMZ) =-300MPa as shown in Fig. 5b, we can clearly see that for AMZ layers thicker or equal to 285  m edge cracking can be predicted, since both conditions  yy ≥  c  and G inc ( a )≥ G c (AMZ) are fulfilled simultaneously to certain length of the edge crack indicated by point 1 in the referred graph. Once the edge crack is created, it propagates until ERR at the crack tip is higher than the fracture toughness of the material G ( a ) ≥ G c (AMZ) . Again for layer thicknesses lower than 285  m no edge cracking is to be expected. W