PSI - Issue 60

A.K. Dwivedi et al. / Procedia Structural Integrity 60 (2024) 286–297 A.K.Dwivedi/ Structural Integrity Procedia 00 (2019) 000 – 000

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Circular

Elliptical

Elliptical

Circular

Fig. 6: Contours of equivalent plastic strain showing details of two-scale void interaction and the resulting crack growth. In (a) circular secondary voids where as in (b) elliptical secondary voids are located in the ligament between the primary voids. The contours shown in (a) and (b) are extracted at J = 0.7015σ 0 X 0 a nd J = 0.683σ o X 0 , respectively. Corresponding results for the case where the ligament between a secondary and the neighbouring primary void is at an angle of 45 0 with respect to the crack plane are shown in (c) and (d) for a circular and an elliptical secondary void, respectively. The contours shown in (c) and (d) are extracted at J = 0.924σ 0 X 0 and J = 0.892σ o X 0 , respectively. The initial volume fraction of primary and secondary voids is 1.6% and 0.06%, respectively. Effect of initial shape and spatial distribution of secondary voids on normalized crack driving force J/(σ 0 X 0 ) versus crack extension and variation of J/(σ 0 X 0 ) as a function of the reduction in the ligament between the crack tip and the nearest void is presented in Fig. 5. For a given crack extension, the pre-existing secondary voids lead to a reduction in the crack driving force. For both distributions of secondary voids modelled here, the effect of initial shape of secondary voids is, however, not significant. The secondary voids lying in the crack plane ( Ɵ=0 ) exhibits significant growth, thus, leading to a significant reduction in the crack driving force. A strong void to void interaction occurs ahead of the crack plane and, as a consequence, the crack extension is observed to be co-planar, see Fig. 6 (a) and 6 (b). When secondary voids are modelled at an angle θ =45° with respect to the initial crack plane, the crack tip interacts with the secondary void due to relatively smaller ligament. As the imposed deformation increases, the secondary voids grow and link with the nearest primary voids located in the crack plane. This complex interaction between the neighboring primary and secondary voids leads to zig-zag crack growth, see Fig. 6 (c) and 6 (d).