Issue34

L. Náhlík et alii, Frattura ed Integrità Strutturale, 34 (2015) 116-124; DOI: 10.3221/IGF-ESIS.34.12 119    11 1 1 cos cos 16 a k           ,   12 1 sin 2cos 1 16 a k           ,       22 1 1 1 cos 1 cos 3cos 1 16 a k               , constant 3 4 k    for plane strain or 3 1 k      for plane stress,   2 1 E     is shear modulus,  is polar coordinate originating from the crack tip. The criterion postulates that the crack will propagate in the direction where factor S is the minimum. The angle of next crack propagation direction  0 can be determined from the conditions: 0 0 2 2 0  0 S S                            (3) The crack will propagate under angle  0 if the value of S will reach its critical value S cr , i.e. for S = S cr . In special case (pure mode I) can be the critical value S cr related to fracture toughness K Ic :   2 1 2 4 IC cr K S     for plane strain condition. (4) Fracture toughness of AMZ layer is 2.6 MPa.m 0.5 . Corresponding value of S cr = 825.10 -8 MPa.m. Figure 3 : Detail of fine mesh around the crack tip. Numerical model For the numerical modelling finite element (FE) method was chosen. Numerical models were developed in commercial system Ansys. Models contained circa 100 000 elements PLANE 183. Boundary conditions corresponding to 4PB, i.e. vertical displacements on the lower side in the locations of rigid supports were equal to zero and the loading forces P/2 on the upper side of the models were applied, see Fig. 2 for details. Thermal load by change of temperature from 1200°C to 20°C was applied together with mechanical loading to generate residual stresses in the layers. Material characteristics written in the Tab. 1 were used. All calculations were performed under condition of plane strain. Very fine mesh was used around the crack tip to well describe the stress distribution there (see Fig. 3), which is of crucial importance for determination of crack behavior. The size of smallest elements was circa 1.10 -5 mm. On the base of former experience [28] the crack propagation was modelled from first ATZ/AMZ interface through the AMZ layer. The initial crack