Issue34

P.O. Judt et alii, Frattura ed Integrità Strutturale, 34 (2015) 208-215; DOI: 10.3221/IGF-ESIS.34.22 212 and displacement fields differ from the isotropic case, the relation between J k -integral and SIF must be adapted. Furthermore, due to the rolling process, anisotropic fracture toughness is observed. In plates of Al-7075-T651, the crack resistance in the rolling direction (RD) is smaller than in the transverse direction (TD), RD TD c c G G  , thus depending on the global angle α. The crack resistance anisotropy is accounted for in the fracture criterion by introducing an elliptic interpolation function c ( ) G  . The ERR is the projection of the J k -vector onto the crack growth direction and thus can be written as a function of α. Finally, the maximum value of the ratio R ( ) / ( ) c G G G    provides the crack deflection angle. In rolled plates of Al-7075-T651, the anisotropy of the crack resistance is measured by standard CT tests providing RD 9.0 c G  N/mm and TD 11.4 c G  N/mm. The ratio of fracture toughness anisotropy, i.e. TD RD / 1.12 c c G G    for this material, is an important parameter of the model and must be considered for the correct prediction of crack paths [16]. C RACK PATH PREDICTION he presented model is applied for the prediction of crack paths at specimens with material interfaces. The specimen is cut from a rolled plate of aluminum alloy Al-7075-T651 (Young’s modulus E = 72000MPa, Poisson’s ratio ν = 0.3) and exhibits a circular hole. The incipient crack, exhibiting a length of a 0 = 13.5mm, is aligned parallel to the TD. A cylindrical steel core (steel 9S20K, Young’s modulus E = 210000MPa, Poisson’s ratio ν = 0.3) is grouted into the hole leading to an initial stress distribution at the interface region, see Fig. 2(b). The hole’s diameter is d = 22mm and the diameter of the steel core is slightly larger. The clamping of the steel core leads to an initial stress distribution at the interface region. The calculation procedure involves an intelligent remeshing algorithm refining the mesh at the crack faces and tip, and a repeated incremental extension of the crack. The crack extension parameter is chosen 0.5 a   mm. A numerical loading analysis is performed applying remote integration contours according to Section 2, providing the J k -integral after each crack extension step. The crack deflection angle is calculated according to Section 3. Further details are presented in [16]. Three configurations of the model with different boundary conditions at the hole are investigated in the simulation and compared with the experiment. In configuration 1 the phase B is just air, the hole representing a free boundary. The configuration 2 considers the material B to be a steel core which is perfectly bonded to the aluminum specimen. In the configuration 3 the material B also represents a steel core, which is grouted into the hole allowing for a separation of the materials A and B. To provide path independence of the J k -integral, the integration along the hole h  is considered, see Fig. 2(b). The calculated crack paths reveal that the impressed steel core, according to configuration 3 , attracts the crack even stronger than solely a hole with free surfaces (configuration 1 ). In contrast to configuration 3 a perfectly bonded steel core induces the crack to veer away from the core. Similar results as observed at configuration 2 have been reported by Patton and Santare [20], Bouchard et al. [21] and Nielsen et al. [22]. The crack path obtained from the experiment, where the boundary conditions of configuration 3 are met, is in very good agreement with the numerically predicted path. At the beginning, the crack veers away from the steel core and is then strongly attracted finally ending in the hole. (a) (b) Figure 2 : (a) Comparison of experimental and numerically predicted crack paths for three different model configurations, (b) aluminum alloy specimen with hole and cylindrical steel core, incipient crack length a 0 and loading p 0 T