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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voids nucleating early in the deformation history are often referred to as the primary voids. When void growth is substantial, plastic flow localizes in the ligament between neighboring voids. Beyond this stage, a second population of much smaller secondary voids nucleate at small carbides in steels and dispersoids or coarse precipitates in aluminium alloys (Garrison87). The small secondary voids are typically around 0.1 to 0.01 times the size of the primary voids (Fabrègue & Pardoen, 2008). The nucleation and growth of these sub-microscopic voids in the ligament between large voids accelerate the damage process and voids coalescence either by internal necking or by localized shearing between the well-separated voids (Cox & Low, 1974). Additionally, a third type of void coalescence is also observed, mostly in steels containing MnS inclusions along the rolling direction, called necklace coalescence (Noell et al., 2018). Understanding the interplay between the two-scale voids and the ductile fracture process is of paramount importance for enhancing the reliability and safety of engineering components made from structural alloys. Ductile damage in metals and alloys has been modelled computationally using different approaches, see (Pineau et al., 2016). Notable among them is the cell model technique pioneered by Needleman and co-workers (Koplik & Needleman, 1988; Needleman, 1972; Viggo Tvergaard, 1981). In cell model calculations, a representative volume element containing voids of various shapes and sizes is analyzed. This approach facilitates the study of different void configurations, material anisotropy and stress states, thus, providing valuable insights into the material's failure behavior (Benzerga & Besson, 2001; Gao & Kim, 2006; Keralavarma et al., 2020; Gulivindala et al., 2023; Keralavarma & Chockalingam, 2016; Koplik & Needleman, 1988; Pardoen & Hutchinson, 2000; Tekoglu, 2014). While most of the cell models studies have focused mainly on primary voids, a few analyzing the influence of small secondary voids on the mode of coalescence and mesoscopic ductility have also been reported, see for e.g. (Dwivedi et al., 2022, 2023; Khan & Bhasin, 2017; Morin & Michel, 2018) among others. Another computational scheme that has been widely employed to study the ductile fracture process models the interaction between the crack-tip and the voids lying ahead of crack in the process zone. Here, the focus is on analyzing the ductile fracture behavior under small-scale yielding. Based on explicit modelling of voids lying ahead of crack tip, fracture initiation and crack propagation behavior has been studied extensively (Aravas & McMeeking, 1985; Gao et al., 2005; V. Tvergaard & Niordson, 2008). Later studies have focused on multiple rows of voids and the effect of initial void shape has also been modelled (Kim et al., 2003; Mostafavi et al., 2011; Petti & Dodds, 2005; Viggo Tvergaard, 2007) (Hütter et al., 2012, 2014, 2015). The effect of mixed mode of loading on ductile crack growth has also been reported (Andersen et al., 2019). Numerical studies modelling the influence of primary void distribution on ductile fracture toughness, the distribution being controlled by the frequency and amplitude of void nucleating particles, were reported by (Srivastava et al., 2017). Studies analyzing the influence of a second population of small voids, distributed homogenously in a ductile matrix, through a non-local GTN model have also been performed. Here, the size of the secondary voids is controlled by the length scale parameter in the non-local GTN model, and its effect on the material's resistance to crack growth is analyzed, see (Hütter et al., 2014). Besides these computational studies, the in-situ experimental observations also suggest that the ductile crack growth is not solely controlled by the large primary voids; instead, its path may be influenced by the distribution of secondary voids (Buljac et al., 2018). The present work models the interaction between the two populations of pre-existing voids lying ahead of crack tip. A plane-strain two-dimensional modified boundary layer (MBL) model, under small-scale yielding condition, subjected to remote mode-I loading is considered. Numerical investigations are performed on an elastic-plastic solid containing periodic spatial arrangements of large size primary voids. Small secondary voids are then introduced explicitly in the matrix surrounding the large voids and the influence of complex two-scale void interaction on ductile crack path is analyzed numerically. In the absence of secondary voids, as expected, the crack path is controlled by the distribution of primary voids. Secondary void attributes, in particular, the shape and distribution of secondary voids, however, may influence ductile crack propagation and, hence, the crack driving force . Numerically computed driving force versus crack extension (J- Δ a) curves and some details of crack propagation are also presented. 2. Numerical Formulation The mechanism of ductile crack propagation in an elastic-plastic solid containing two populations of pre-existing voids is modelled numerically. The focus here is on modelling the complex interaction between the two-scale voids and its influence on ductile crack path. A modified boundary layer (MBL) model with a semi-infinite crack (Larson