PSI - Issue 71

A.K. Dwivedi et al. / Procedia Structural Integrity 71 (2025) 142–149

146

curve is rising, see Fig. 2c. As the mode mix ratio “β” increases, the resistance to crack growth in the P -0° configuration of primary voids increases monotonically. This happens because the mechanism of voids interaction and the path of crack is same as the case of pure mode I loading. Conversely, in the P-45° configuration, the interaction mechanism changes from void-by-void to interactions multiple voids interaction which reduces the resistance provided by the material to crack grow as shown in Fig. 2 c. The plots of material resistance versus the ratio of X/X 0 ( (X = current ligament, X 0 = initial ligament) are shown in Fig. 2b and Fig. 2d for P 0° and P 45° arrangement of voids, respectively. In the P 0° arrangement of void, the ligament ratio reduces to 0.5, which indicates the crack growth in the direction of = 0° plane. Whereas the P-45° arrangement of voids, as loading increases, the criteria of half reduction of ligament ratio does not meet. This indicates that the crack extension is not in the plane of = 0°.

Fig. 3. Contours of eq. plastic strain depicting the active softening zone for the primary void configuration (a), (b) and (c) for P -0° corresponding to β =0, 0.25 and 0.5.Whereas, (d), (e) and (f) for P -45° corresponding to β =0, 0.25 and 0.5.

The eq. plastic strain contours are showing the active softening zone for the arrangement of void P 0° and P 45° in Fig. 3 a (β = 0, pure mode I), Fig. 3 b (β = 0.25, mix mode), Fig. 3 c (β = 0.5, mix mode) and Fig. 3 d (β = 0, pure mode I), Fig. 3 e (β = 0.25, mix mode), Fig. 3 f (β = 0.50, mix mode), respectively. The P 0° arrangement of voids, leads to multiple void interaction for all three cases of loading. Whereas the P 45° configuration of voids, leads to crack growth of crack via the mechanism of void-by-void interaction f or the β = 0, pure mode I case of loading, see Fig. 3 d. As “β” increases to 0.25 the tendency of shear localization in P-45° configuration increases. Which leads to the change in interaction mechanism from voids by voids to multiple voids interaction, see Fig. 3 e. Consequently, the resistance offered by material to crack growth is reduces drastically, 2c. 3.2. Role of secondary voids In this sub section the effect of mix mode loading on the crack path as well as on the material fracture toughness is analysed in the presence of two scale of voids in the matrix. Here, two different shape of secondary void is analyzed, one is circular, and another is of elliptical shape. The cluster of secondary voids are distributed in two different planes of = 0° and = 45° with respect to initial crack plane, represented by S 0° and S 45° distribution, respectively. For P 0° configuration of primary voids, the secondary voids are distributed in the plane of = ±45° . This arrangement is represented by P 0°, S 45°. However, For P 45° configuration of primary voids, the secondary voids are placed in the plane of = 0° . This arrangement is represented by P 45°, S 0°. The material resistance curve for the P 0°, S 45° distribution of circular and elliptical secondary voids with aspect ratio of γ 0 =1/6, are shown in Fig. 4 a and Fig. 4 b, respectively. For the circular cylindrical secondary voids, the fracture toughness, for β= 0.1 and 0.25 loading, is almost comparable to the pure mode I loading, see Fig. 4 a. Whereas for β= 0.5, the rising curve can be seen due to the change in crack path. The increase in mode-mixity increases the contribution