Issue34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 42-58; DOI: 10.3221/IGF-ESIS.34.04 52   2 2 2 2 0 I II 1  8 G k k         (51) As far as the condition I II k k  holds, conditions (50) and (51) indicate that the kink angle  is given by I II 3 I II 2 2 II II I I 2 2 2 k k k k O k k k k                      (52) which gives rise to the maximum elastic energy release rate of the body. This result together with Eq. (35) in the previous section may designate equivalent crack paths by employing the conditions of local symmetry and maximum energy release rate in homogeneous materials within the second order approximation theory. Considering material inhomogeneity such as a local degradation zone, a crack may be kinked and curved due to the spatial variation of the fracture toughness. The method presented here may be effective to obtain possible crack paths in materials with inhomogeneous fracture toughness. Let us consider a crack under pure Mode-I loading condition, whose tip intersects a line degradation zone oriented at angle *  (see Fig. 8), where the critical energy release rates for the base material and the degraded material are c G and * c G , respectively. If the crack extends in the base material, Eq. (52) is applicable, which obviously leads to the straight crack extension. The stress intensity factor at the instance of fracture is calculated from Eq. (49) and given by I 8 1 c G k     (53) In contrast, if the crack extends in the degraded zone, the kink angle is *  , and the corresponding stress intensity factor at the instance of kinked propagation is also calculated by Eq. (49) as   * * I *2 8 1 1 2 c G k            (54) The crack may actually extend in the degraded zone under the condition * I I k k  . Substitution of Eqs. (53) and (54) into this inequality leads to the following relationship between the angle of inclination and the material properties; *2 * 1 2 c c G G         (55) which cannot be predicted by a conventional stress criterion. When one applies the inequality (55), the resulting inclination angle *  should be less than 30–40°, where the second order perturbation solution of the stress intensity factors is practically applicable. B RITTLE FRACTURE ALONG BUTT - WELD Morphological Aspects of Brittle Fracture along Butt-Weld ne of the most hazardous failure modes of welded steel structures is an instantaneous fracture due to crack propagation along weldment, which may lead to the catastrophic failure of the total structure. Typical crack paths along a welded joint are schematically illustrated in Fig. 9, where the applied stress a  and the welding residual stress r  acting parallel to the weldment are also sketched, Hall et al . [25], Munse [26], Wells [27]. O