Issue34

L. Náhlík et alii, Frattura ed Integrità Strutturale, 34 (2015) 116-124; DOI: 10.3221/IGF-ESIS.34.12 120 increment was chosen 1  m to describe crack path precisely and model was remeshed after each step. Stress intensity factors were calculated by author’s routine from displacements close to the crack tip in each step. New crack propagation direction was determined on the base of author´s Ansys macros based on Eqs. 2 and 3 after each step. Hundreds of calculations were performed to obtained realistic crack path in compressive AMZ layer during each simulation. PC based workstations were used for extensive numerical calculations. R ESULTS AND DISCUSSION ifferent material layers create regions with different material properties. It was shown in the former work of authors [7] that suitable selection of materials with different elastic properties can lead to the higher values of applied load for crack propagation through interface. This value of applied load can be higher than the one for crack propagation in the individual composite constituents. The effect of crack retardation is stronger in the studied case due to acting of residual stresses developed in the layers during sintering process. These residual stresses have pronounced influence on the crack behaviour in the composite, damage mechanism of the composite and consequently on the value of apparent fracture toughness of the composite body. In the numerical FE studies four different ratios of layer thicknesses were considered (see Tab. 2). The calculations performed were focused on the description of mechanism leading to the higher apparent fracture toughness of ceramic laminate with strongly bonded interfaces. Sih’s criterion (Eq. 3) was applied in each step of the simulations. The crack started to strongly deflect in certain depth a´ under the first ATZ/AMZ interface due to acting of compressive stresses in all simulations. In this moment an additional external load was necessary for the crack propagation. The depth of deflection and values of external force P are shown in the Tab. 3. t ATZ : t AMZ a’ [mm] P max [N] 2 :1 0.046 16.2 5 : 1 0.020 24.8 7 : 1 0.017 34.6 10 : 1 0.024 48.0 Table 3 : The depth a´ in AMZ layer under the first ATZ/AMZ interface, where the crack changes mode of propagation and values of the force P acting in the moment of crack deflection. Hundreds of calculations (steps) were performed in each simulation to obtain crack path in the AMZ layer. Results of simulations are shown in the Fig. 4. On the base of results obtained the crack behaviour in the compressive layer can be divided to four stages, see Fig. 5 for the explanation: 1) After passing perpendicularly through the ATZ/AMZ interface the crack is retarded (the stress intensity factor and the strain energy density factors decrease). An external load is necessary for further crack propagation. The compressive stresses don’t allow further direct crack propagation under mode I like in tensile loaded ATZ layer. 2) In the depth a ´ under the interface the character (mode) of crack propagation changes from mode I to mode II. The stress distribution around the crack tip in the depth a ´ enables crack deflection or bifurcation. Further crack propagation is controlled by compressive stresses. The crack propagates parallel or nearly parallel to the material interfaces. 3) When the crack tip is close to the next AMZ/ATZ interface the presence of tensile stresses in the ATZ layer growths in importance and the controlling mode of crack propagation starts to be again mode I and the crack deflect to the direction (nearly) perpendicular to AMZ/ATZ interface. 4) The crack passing through (nearly) perpendicularly the AMZ/ATZ interface. The resistance to the crack propagation is the highest between stages 3 and 4. Behaviour of the crack at the stage 4 was studied in [28]. D