PSI - Issue 71

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

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The influence of crack shielding is because of void growth near the crack tip (Hutter et al., 2012), the impact of matrix flow properties (Hutter et al., 2013), and the mode of applied loading (Roy et al., 1999; Sreedhar et al., 2024) on void interaction and crack initiation. A recent 3D cell model simulation (Gao et al., 2005), along with experimental findings from (Anderson et al., 2019), indicate that the shape and arrangement of smaller voids can significantly affect larger void coalescence and, consequently, crack propagation occurs microscopically. This study focuses on modeling the interaction of two different length scales of void ahead of the crack tip and its impact on the mechanism of voids interaction with the crack-tip. The advancement of the crack tip occurs void-by-void interaction mechanism along the crack front, it means the crack will interact with a single void at a time with lesser influence on the other voids in the crack plane. The other mechanism, in contrast, involves the simultaneous growth and interaction of multiple voids during crack growth initiation and subsequent crack advance (Tvergaard et al., 2002). A two-dimensional plane strain MBL (modified boundary layer) model, incorporating discretely modelled two-scale voids under SSY conditions, is analyzed. Secondary voids introduced explicitly in the ligament of primary voids to examine the effect of complex interactions of primary and secondary voids on the ductile fracture process under mix mode loading. The study specifically explores the effect of the shape and distribution of secondary voids, as well as the mix-mode loading, on the initiation and growth of ductile cracks. 2. Numerical Modelling All the numerical simulations are carried out by considering the elastic-plastic solid consisting discretely modelled primary and secondary voids using the finite element program (ABAQUS 2022). A plane strain 2D MBL (modified boundary layer) model, under SSY (small scale yielding) condition, is considered, see Fig. 1 a. The crack tip’s geometry is represented with a small root radius, r 0 , and the circular boundary with an initial radius of R 0 is defined far from the crack tip. The ratio, R 0 /X 0 and r 0 /X 0 is 4500 and 1/10, respectively. Where X 0 is the undeformed ligament between primary voids, See Fig. 1. Two specific configurations of the primary void distribution are considered among the various possible arrangements. The void distribution depicted in Fig. 1b, primary voids aligned across multiple planes parallel to the plane of initial crack. Which leads to the plastic flow will localization in the intervoid ligament, which allows the crack extension in the initial crack plane referred as the P-0° configuration of primary void. Whereas, in Fig. 1c, the primary voids are arranged so that the ligament between neighboring voids is distributed at a 45° angle relative to the crack plane referred as the P-45° configuration of primary void. These configurations are not intended to represent the full statistical distribution of voids in a material but rather to capture the two dominant scenarios that significantly affect crack propagation behaviour (Hutter et al., 2012; Hutter et al., 2013). The shape of secondary voids with an aspect ratio of γ 0 = a 2 /a 1 are modelled, as shown in Fig. 1d. The primary voids are assumed to be circular cylinders in the unstressed state. The initial void volume fractions of the primary are f p0 =0.016 and for secondary, it is fs 0 =0.0006. In the present work, the numerical simulations performed by applying the displacements field for mode-I and mode-II on the outer boundary. For mode I, the displacement field are defined by the following equations- 1 = 2 √2 ( 2) [3 − 4 − 1 + 2 ( 2 ) ] 1 2 = 2 √2 ( 2) [3 − 4 + 1 − 2 ( 2 ) ] 2 For mode II, the applied displacements fields are given below- 1 = 2 √2 ( 2) [3 − 4 − 1 + 2 ( 2 ) ] 3 2 =− 2 √2 ( 2) [3 − 4 + 1 − 2 ( 2 ) ] 4 Under combined loading of mode-I and mode-II J integral is calculated as