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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and Carlson, 1974) under plane strain condition is analyzed numerically. In many structural alloys, small second phase particles nucleating the secondary voids are randomly distributed (Fabregue, 2008). In the present work, the random distributions of second phase particles are idealized as linear clusters lying at different orientations with respect to the plane containing an initial semi-infinite crack. Since the primary voids nucleate quite early, their nucleation is not modeled. Also, it is assumed that at some stage in the deformation history, the second phase particles have nucleated the secondary voids prior to the onset of flow localization in the ligament of larger voids. Thus, in our numerical calculations the two populations of voids are considered as pre-existing and are modeled discretely. Although our framework doesn't account for the stage of void nucleation, it permits us to model the effect of the inhomogeneous stress state that develops around the voids, the effect of initial void shape and orientation of clusters of secondary voids on ductile crack propagation in a detailed manner. In general, the spatial distributions of large size inclusions are also arbitrary. Thus, it will be more realistic to study the interaction of two-scale voids that are more or less randomly distributed. However, to reduce the computational efforts, numerical studies are performed on a model material comprising periodic arrangements of the two-scale voids, lying ahead of the crack tip, see Fig. 1a. In the undeformed state, all the voids belonging to each family are assumed to have identical shape and size. All the calculations are performed on idealized two-dimensional (2D) voids. The configuration of primary voids analyzed in this study is shown in Fig. 1a. To consider the shielding effect of voids on the crack tip (Hütter et al., 2013), four layers each containing ten primary voids are modeled above and below the initial crack plane. The primary voids are assumed initially to be circular cylinders extending infinitely in the X 3 direction. The initial shape of the secondary voids is assumed to be elliptical defined by = ⁄ . Here, the semi major-axis " c " is parallel to the initial crack plane, and the semi minor-axis is normal to it, see Fig. 1b. The initial volume fraction of the primary voids is defined as, = ( 0 0 ) 2 (1) Here, R 0 is the initial radius of the circular cylindrical primary voids and X 0 describes the initial spacing between the two neighbouring primary voids. The initial volume fraction of the secondary ( ) voids is defined in a similar manner. For the case where one secondary void modelled at the vicinity of primary void For circular shape = ( s0 0 ) 2 , for elliptical = ( 2 ) (2) Where, is the initial radius of the circular secondary void. In our numerical calculations, the initial volume fractions of the primary and secondary voids are assumed as 0.016 and 0.0006, respectively.