PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 981–988 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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porosity as; ̇ = ̇ ̇ ℎ = (1 − ) ̇ ̇ = √2 {−0.5 [ − ]} ̇̅ ℎ + ̇

(3) (4)

(5) In which, ̇̅ is the plastic strain rate where its trace is thus identified as ̇ . The volume fraction of the particles available for void nucleation is and the main void nucleation strain is . Besides, the standard deviation of the distribution is defined as . 4. FE Analysis and results Concerning the finite element analysis (FEA), the problem was simulated in an available commercial software, ABAQUS©. An explicit dynamic model was thereby considered where a 3D deformable shell model was applicable. Furthermore, 3-node linear triangular elements (S3) were used to construct a fine mesh where the element size range is between 0.5 and 1.0 millimeter with a total number of 4724 and 2559 elements and nodes, respectively, see Fig. 3 a. To secure the results accuracy, more refined elements were considered in the anticipated failure region where an intended section with a dimension of 25-by-25 millimetres was selected, referring to the dash lines in Fig. 3-a. Regarding the essential boundary condition, the points located on the upper specimen edge was clamped to satisfy the experimental conditions. Concerning the natural boundary condition, a uniform displacement imposition possessing a magnitude of = −2 [ ] was vertically enforced on the points coupled with the bottom edge, see Fig. 3-a. In FEA, the model geometrical characteristics followed the values presented in Fig. 1-a. In addition, the mechanical properties, particularly for the elastic regime, were used as shown in Table 1. The GTN parameters were adopted in accordance with the values reported by (Tvergaard 1981; Yu et al. 2014), see Table 2. The relative density in the porous model was thus set to = 0.99 . Table 2. Main parameters in GTN model adopted for Aluminium alloy AA6061-T6, FE analysis. 1 = 1.5 2 = 1 3 = 2.25 = 0.1 = 8 −4 = 0.3 = 0.013 = 0.04 As previously done in the experimental DIC procedure, two individual points were identified on the central section of the specimen to determine and visualize the vertical displacement variation. These points possess the same properties as the ones used in the experimental resolution. The reaction force response with respect to the displacement field, 21 , obtained for FEA, is plotted in Fig. 2-b. Porous metal plasticity (Tvergaard 1981) Void nucleation (Yu et al. 2014) Porous failure criteria (Yu et al. 2014)