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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The ligament assumed to fail when the current ligament between the voids is reduced to some critical value, which is arbitrarily taken as 0.5 times the ligament in the undeformed state (Andersen et al., 2019). For voids distribution where the ligament between the secondary voids and the neighbouring primary voids is at some angle (say θ=45° ) with respect to the initial crack plane, the crack extension may be non-coplanar. In such cases, the crack growth is calculated using the following relation (Hutter, 2015), ∆a = √ 1 2 0 ∑ 1−χ 1− 0 ⁄ =1 (7) Where, is the remaining ligament in the crack plane between the primary voids, see in Fig. 6. 3.1. Primary voids We first present numerical results for the case where only primary voids exist ahead of the crack tip. The initial configuration of primary voids modelled here is similar to that of (Hütter et al., 2012,2013). The plot of normalized crack driving force J/( σ 0 X 0 ) versus normalized crack extension ( Δ a/X 0 ) is shown in Fig. 3a. Here, σ 0 and X 0 denotes the yield strength of the elastic-plastic matrix and the initial ligament between the crack tip and the nearest primary void, respectively. The plot of normalized crack driving force versus the reduction in the ligament ( / ) is shown in Fig. 3b. As the intensity of far-field loading, characterized by J , increases the current value of the ligament W i reduces to half of its original length, thus, indicating the initiation of crack growth. With further deformation, the interaction between the crack tip and the neighboring voids becomes more pronounced and crack extension is observed to occur in the plane containing the initial crack. The contours of equivalent plastic strain depicting the details of crack extension are shown in Fig. 4.

Fig.3:- (a) Plot of normalized crack driving force J/ ( σ 0 X 0 ) versus crack extension, (b) variation of J/ ( σ 0 X 0 ) as a function of the reduction in the ligament between the crack tip and the nearest void. Only primary voids are modelled ahead of the crack tip and the initial volume fraction ( ) is around 1.6%