PSI - Issue 39

D. Fedotova et al. / Procedia Structural Integrity 39 (2022) 419–431 Author name / Structural Integrity Procedia 00 (2019) 000–000

425

7

Pure mode I

Initial pure mode II

b

a

Mixed Mode Point 2

Mixed Mode Point 7

d

c

Fig. 3. (a,b) distribution of normalized effective stresses in pure mode I and pure mode II and (c, d) figures represent point 2, which corresponds to an increase in the crack length by 1 mm after the crack is inflected, and point 7 corresponds to the state before the final destruction. Several interesting features can be inferred from the results shown in Table 3. First, the singularity indexes are in all modes larger than the classical linear elastic result. Thus, SGP models based on Taylor’s dislocation theory appear to predict a stronger singularity than linear elastic solids under mode I /II and mixed modes loading conditions. Shi et al. (2001) also found a higher stress singularity than that of linear elasticity in the case of the higher-order MSG plasticity model under mode I conditions; they concluded that the stresses scale as in the vicinity of the crack tip. Second, the magnitude of the stress singularity exhibits some sensitivity to the intrinsic material length parameter l , with differences becoming more noticeable for larger strain hardening values. Third, the values of the singularity indexes in pure mode I and mode II are different, and the values in mixed modes repeat the scenario in pseudo mode I. This trend is also observed for steel 34X and Al-alloy. A clear demonstration of the redistribution processes of nonlinear deformations is provided by the local contours of plastic zones at the crack tip, which are shown on Fig. 4, as example, for steel P2M and Ti-6Al-4V alloy. The plots are shown for the applied mode I and mode II and the material length parameter l = 5 mm. It can be noted that for pure mode I the plasticity zone is symmetric with respect to the plane of the initial crack, while for pure mode II this zone is asymmetric. For pure mode II loading conditions, it can be observed that one side of the crack tip is dominated by tensile stresses and blunts, while the other side is dominated by shear strains and sharpens. At point 2 of the crack path, after the formation of a kinked crack, plasticity zones with small asymmetry are observed, and they are indicated by the mixed-mode fracture. However, the degree of asymmetry is not large, and it