Issue34

L. Náhlík et alii, Frattura ed Integrità Strutturale, 34 (2015) 116-124; DOI: 10.3221/IGF-ESIS.34.12 118 Figure 2 : Scheme of studied ceramic laminate with typical crack path (dimensions in [mm]) and orientation of residual stresses in composite layers. The magnitude of residual stresses in the case of crack absence in the layered composite can be estimated from forces balance in individual layers. This leads to following expressions [33]:   0 , 1 1 1 ' ' 1 sf T AMZ ATZ T res ATZ ATZ AMZ dT N E E N             , , , 1 1 res AMZ res ATZ N N          , (1) where: ATZ AMZ t t   , ' 1 AMZ AMZ AMZ E E    , ' 1 ATZ ATZ ATZ E E    , T sf [°C] is stress free temperature, T 0 [°C] room temperature, α [10 -6 K -1 ] coefficient of thermal expansion, N [-] number of layers, t [mm] thickness of layer, E [MPa] Young´s modulus and ν [-] Poisson´s ratio. Calculated values of residual stresses for studied configurations are shown in the Tab. 2. t ATZ : t AMZ t ATZ [mm] t AMZ [mm] σ res , ATZ [MPa] σ res , AMZ [MPa] 2 : 1 0.4288 0.2140 236.6 -592.6 5 : 1 0.5170 0.1038 109.8 -683.6 7 : 1 0.5384 0.0770 80.6 -704.6 10 : 1 0.5556 0.0556 57.7 -721.0 Table 2 : Residual stresses calculated for different ratio of layer thicknesses ( t ATZ : t AMZ ) by Eq. 1. It is evident from the Tab. 2 that the compressive residual stresses in the AMZ layers are circa six hundred megapascals and higher for all considered cases. These stresses are responsible for typical stepwise crack propagation like is shown in the scheme in Fig. 2. M ODEL OF CRACK PROPAGATION Estimation of crack propagation direction ih´s criterion [34,35] based on strain energy density factor S was used for the determination of crack propagation direction due to brittle nature of the composite. The criterion was implemented in finite element system Ansys [36] to perform calculations with small crack increments automatically: 2 2 11 12 22 2 I I II II S a K a K K a K    , (2) where K I and K II are stress intensity factors corresponding to mode I and II respectively, S