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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3.3. Effect of secondary voids cluster

Figure 7: Effect of clustering of circular secondary voids on (a) 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. The initial volume fraction of primary and secondary voids is 1.6% and 0.06%, respectively. In this section, the effect of clustering of circular secondary voids on the crack driving force is analyzed. The clusters of secondary voids are modelled as two small voids lying in the matrix in the vicinity of the large primary voids at Ɵ=0 and Ɵ=45 from the initial crack plane. The initial size of the secondary voids are adjusted so that the initial volume fraction remains the same as in Section 3.2. As expected, the lowest crack driving force is observed when the two circular secondary voids are placed at Ɵ=0 , see Fig. 7 (a). For the case of initially circular secondary voids lying at an angle Ɵ=45 , the crack driving force and the reduction in the ligament ahead of the crack tip is almost the same as for primary voids alone. Irrespective of the orientation of secondary voids cluster, the ligament between the crack-tip and the nearest primary void decreases with imposed deformation, see Fig. 7(b). For the idealized cluster of circular secondary voids lying at Ɵ=45 , a zig-zag pattern of crack growth, in the direction of initial crack plane, is observed and is similar to that shown in Fig. 6(c). 3.4. Combined effect of initial shape and clustering of secondary voids We finally present some numerical results analyzing the combined effect of initial shape and clustering of secondary voids on the crack driving force and details of c rack propagation. Clusters of secondary voids lying at θ=0° lead to lower crack driving force and for this orientation the effect of initial void shape is rather insignificant, see Fig. 8 (a). Note that results for the case of initially circular secondary voids, already presented in Section 3.3, are retained for comparison purpose. Clusters of initially elliptical ( =6) secondary voids lying at Ɵ=45 lead to interesting results. The strong interaction between the secondary voids at Ɵ=45 and the crack tip promotes strain localization in the plane containing these small voids and eventually link the crack tip with a large primary void located initially at Ɵ=45 , thus, leading to crack branching, see Fig. 10(a-d). As a consequence, the driving force required for crack propagation, see Fig. 8(a) is much higher compared to the cases where crack growth is coplanar. For the same orientation Ɵ=45 , clusters of initially circular secondary voids, as reported in Section 3.3, lead to a zig-zag pattern of crack growth, in the direction of initial crack plane.