PSI - Issue 71

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

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initial width of the ith ligament, respectively. The crack extension is calculated as calculated by Hutter et. al. (2012), which is based on the geometric softening of voids ligament. ∆ = 0 ∑ =1 (1− ) 8 3. Results and discussion The result section consists of two sub-sections, in the first sub-section the simulations are performed by considering only the primary voids and in the second section effect of shape and distribution of secondary voids accounted by placing them in the ligament of primary voids. The crack growth is measured in terms of an active softening zone as defined by Hutter et. al. (2012). Which is based on the geometric softening of ligament in the crack path. Node release technique is not a suitable method for crack growth in the plane of = 45° . 3.1. Primary voids Initially, we focused on the configuration of primary voids alone in front of crack tip for the different value of β =0 (pure mode I), 0.25 and 0.5. Two different configurations P 0° and P 45° of primary voids are modelled here are similar to the configuration analysed by Hutter [12, 13], for the case of pure opening mode of loading.

Fig. 2 (a) and (c) Normalized fracture toughness J/(σ0X0) versus crack extension for P -0° and P-45° void configuration, respectively. (b) and (d) showing the ligament reduction between the crack tip and the first primary void . The plot of ductile fracture resistance J/(σ 0 X 0 ) against the crack growth ∆a/X 0 , calculated in the initial crack plane, is shown in Fig. 2 a and Fig. 2 c, for P 0° and P 45° voids configuration, respectively. Here, σ 0 and X 0 represents the material yield strength and the length of initial ligament between the crack tip and the neighboring primary void with which the interaction of crack tip occurs. Under pure mode I (β = 0) loading, P 0° configuration, the ductile fracture occurs via multiple void interaction. The geometric softening of the ligament occurs in the plane of = 0° . Whereas, P 45° configuration, the mechanism of ductile failure occurs via void-by-void interaction mechanism. The plastic flow localization occurs in a = 45° plane. The different mechanism of voids interaction, leads to the flat fracture resistance curve for P 0° arrangement of voids, see Fig. 2a. Whereas, for P-45° configuration, the material resistance