Issue 53

R.R. Yarullin et alii, Frattura ed Integrità Strutturale, 53 (2020) 210-222; DOI: 10.3221/IGF-ESIS.53.18 218 the cross section of the real compressor disk and the conditions of the mixed mode crack growth. Each imitation model was tested with the same loading conditions. (a) (b) (c) Figure 7: Typical (a, b) FE meshes and (c) equivalent stress distributions for imitation model II with surface crack. The description of the elastic and plastic fracture mechanical parameters will be given in terms of the elastic equivalent mixed mode SIF K eqv and the plastic SIF P M K defined by Eqn. (4) and Eqn. (10), respectively. All parameters are determined at the crack tip distance range r/a=0.0025-0.01, where the numerical solution provides a stabilized result. To compare the parameter distributions along the corner surface and through-thickness crack tip, it is convenient to introduce dimensionless coordinates in the following form:   0 0 0 0 0 0 cos , sin , cos , sin , cos , sin , , , c c c c i i i i i c c x y x y x y                                    (11) 0 0 0 0 , , i i i i c c x x y y X Y x x y y         2 2 1 , 0,1 2 i i i R X Y R    (12) where  0 is the angle determining the position of the initial point of the crack tip, and  c is the angle corresponding to the last point of the crack tip. In the following representation of the numerical results, the authors will use the variable R in the 0 to 1. R =0 indicates the exterior free surface of the imitation model, while R =1 indicates the slot surface (Fig. 5b). In the case of through-thickness cracks, R =1 indicates the second free surface of the imitation models (Fig. 3a, b). The distributions of the elastic SIF K eqv along the surface and through-thickness cracks in the imitation model I are shown in Fig. 8a. Looking at this figure, it can be noted that the elastic SIFs K eqv for the imitation model I are changed by a moderate amount in the range of 38-60 MPa·m 1/2 . The maximum value of the elastic SIFs K eqv for each considered crack front is in the range of 0<R<1, which correspond to the deepest points of crack front. This behavior is observed for conditions of plane strain due to the free-surface effect. Contrary to this, the distributions of the elastic SIF K eqv in the imitation model II significantly changes in the range of 50- 170 MPa·m 1/2 (Fig. 8b), and the maximum values are observed at the free surfaces of the crack fronts when R=0 or 1. This behavior is characteristic of the plane stress conditions due to the reduction of the cross section of imitation model II that coincides with the real compressor disk geometry. The behaviors of the elastic SIFs K eqv along the free and slot surfaces of the imitation models under biaxial loading conditions are shown in Fig. 9a and b. In these figures, the crack length a and crack depth c are normalized by the imitation model thickness t=15 mm . It should be noted that at the same ranges of crack length and crack depth, the elastic SIFs K eqv are significantly changed for the imitation model II, and they have increasing trends. Looking at these figures and considering changes in the SIFs along the crack front of imitation model II undergoing biaxial loading, differences in the crack growth rate along the external free surface and on the key slot surface are evaluated. It is clear that the imitation model II is more suitable for the experimental determination of durability in the stage of the crack growth, and to predict