PSI - Issue 71

A.K. Dwivedi et al. / Procedia Structural Integrity 71 (2025) 142–149 147 of in-plane shear loading, which allows the crack tip to interact with the circular voids in the plane of = ±45° from the plane of initial crack and leads to the crack branching, See eq. plastic strain contours in Fig. 5 a, Fig. 5 b and Fig. 5 c. The contours for the case β=0.5 are like case =0.25, hence not shown here.

Fig. 4. Material resistance versus crack growth for (a) P-0° - initially circular secondary voids and (b) P-0° - initially elliptical (S 0 =1/6) secondary voids distributed in several planes at ±45°. (c) P-45° - initially circular secondary voids and (b) P-45° - initially elliptical (S 0 =1/6) secondary voids distributed in the initial crack plane. However, in case of elliptical secondary voids, the fracture toughness of material is varying non-monotonically with the mode mix ratio (β). For β=0.1 the lowest fracture toughness is observed and with the further increase in the β the resistance to crack growth increases, See Fig. 4b. The observed drop in material resistance when β changes from 0 to 0.1 arises from a shift in the void’s interaction mechanism, as illustrated in Fig. 5a and Fig. 5b. For β = 0, the crack propagates symmetrically with respect to the initial crack plane. This symmetric extension involves a more uniform distribution of plastic deformation, resulting in higher energy dissipation and, therefore, greater resistance to crack growth. However, when β = 0.1, the interaction mechanism be comes asymmetric due to strain localization. This localized deformation path reduces the extent of plastic dissipation needed for crack propagation, thereby lowering the material’s resistance to crack growth. The eq. plastic strain contours of the P -0° and S-45° (elliptical secondary voids) configuration of voids are shown in Fig. 5d, Fig. 5e and Fig. 5f for the β=0, 0.1 and 0.25, respectively. The contours for the case β=0.5 are like case =0.25, hence not shown here. The material resistance curve for the P 45°, S 0° distribution of circular and elliptical secondary voids with aspect ratio of γ 0 =1/6, are shown in Fig. 4 c and Fig. 4 d, respectively. For both the configuration, as mode-mixity increases from 0 to 0.25, due to the change in mechanism of void interaction from void by void to multiple void the fracture toughness of material decreases. However, the further increase in value of β offers higher resistance due to the large plastic dissipation in front of the crack tip. The eq. plastic strain contours for three loading ratio β =0, 0.25 and 0.5 and for the voids arrangement of P-45° S-0° are shown in Fig. 6a, Fig. 6b, Fig. 6c for circular secondary voids and Fig. 6e, Fig. 6e, Fig. 6f for elliptical secondary voids.