Issue 48

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 48 (2019) 676-692; DOI: 10.3221/IGF-ESIS.48.64 685 The values of x, y,  ,  were applied in solutions 6 and 7 to obtain Y I and Y II , respectively. Then considering experimental loads presented in Tab. 3, K I and K II were calculated. Finally, effective stress intensity factor was obtained using Eqn. 8. Fig. 9 compares the values of K v for  =60º obtained with solutions 6 and 7, and with Richard’s solution. Two different approaches were considered when applying Richard’s solution: consider x and consider crack length, a. Significant differences were found, with maximum values of -6% and -31%, as indicated in Fig. 9. Differences are significantly reduced if total crack length, a, is used in Richard’s solution instead of coordinate x. Therefore, the present solution represents a significant improvement relatively to Richard’s solution. Notice that Richard’s solution was obtained for y=0 and  =0º. N UMERICAL PREDICTION OF CRACK PATH ropagation directions were also studied numerically using the solutions developed here for Y I and Y II . Qian et al.  19  reviewed the criteria used to predict crack growth direction under mixed mode loading, which can be divided into two categories  20  . The first includes the methodologies which consider the stress, the strain or the displacement as the driving parameters, namely the Maximum Tangential Stress criterion (MTS criterion), and the vector crack tip displacement criterion (CTD criterion). The second category contains the methodologies considering the total or the dilatational elastic strain as the driving parameters, namely the minimum strain energy density criteria (S- criterion), the dilatational strain energy density criterion (T-Criterion), the minimum accumulated elastic strain energy (P-criterion) and the J-criterion. The MTS and S criteria are widely used. According S-criterion [21] the crack is assumed to grow along a direction that minimizes the strain energy density factor, S: 2 2 2 S a k 2a k k a k a k 11 1 12 1 2 22 2 33 3     (9) where a ij are coefficients relating polar angle (  ), E and  , and  k K / π i i  . S includes the dilatational and the distortional strain energy. The J-criterion uses the line integral with the same name and states that crack extends along direction of vector: ˆ ˆ J J .i J .j I II    (10) Figure 10 : (a) Crack direction predictions considering different criteria (  =60º). (b) Crack tip slopes (  ) for different crack propagation criteria (  =60º). Notice that since K solutions were defined in terms of (  ), crack propagation increments must consider a rotation of Cartesian coordinate system. In fact, J II =0 corresponds to a propagation along a direction normal to loading direction. P a) b)