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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Table 1. Mechanical properties of AA6061-T6.

Young’s modulus

Poisson ratio

Density

Yield stress

Ultimate tensile stress

Total elongation

= 69 3 ( ) = 0.33 = 2.7 −9 ( 3 ⁄ ) 0.2 = 297.6 ( ) = 333.8 ( ) = 12.3 % After DIC system calibration, the experimental test was performed and the output data was reserved in the DIC computer station. To analyse the captured data, in the DIC processing software, the subset grids were formed on the problem domain considering a subset size of 43 pixels. To visualize and evaluate the displacement field, an intended region must be chosen. In this study, the central section was considered (where the final failure occurred) and two individual points with the following coordinates, 1 = (12.18, 31.62) and 2 = (12.18, 6.40) were thus identified. The vertical displacement field was therefore determined on the selected points identified as 2 and 1 . The domain coordinates and the position of selected points are shown in Fig. 2-a. Hence, the reaction force response received from load cell in terms of the corresponding vertical displacement variation ( 21 = 2 − 1 ) was correlated as demonstrated in Fig. 2-b. Besides, the failure evolution was captured by the experimental DIC test for different stress triaxiality stages. Fig. 3-b illustrates the failure modes from the initiation till the end of the test when the material collapsed. 3. GTN model Based on an analysis of a void in a rigid – plastic matrix, (Gurson 1977) established a model of porous plastic material. The void volume fraction (VVF) introduced in the model permits to model the material softening. In the same way, micro-structural criterion of ductile materials is one of the important tasks for material degradation analysis. As a widely used coupled model, the GTN model was proposed by (Gurson 1977). With the work of (Tvergaard & Needleman 1984; Tvergaard 1982b), new parameters were introduced and the model was refined. Based on some suppositions supported by experimental and numerical results, the GTN constitutive model can simulate the ductile damage through the following equation: = ( 0 ) 2 + 2 1 ℎ ( 3 2 2 0 ) − (1 + 3 2 ) (1) where is the plastic potential and 1 , 2 and 3 present the material coefficients taking into account of the effect of micro-voids. Several researches have indicated that in many cases 1 × 2 ≅ 1.5 , simultaneously, 3 = 12 (Abendroth & Kuna 2006; Benseddiq & Imad 2008). In this work, the corresponding parameters were adopted as reported in (Tvergaard 1981). In Equation (1), the equivalent von Mises stress, the hydrostatic stress and the current flow stress of the material matrix are identified as , and 0 , respectively. Besides, the void volume fraction, is a parameter which considers the damage evolution caused by voids expressed as follows: = { ≤ + ∗ − − ( − ) > (2) In which is the current void volume fraction; is the void volume fraction at failure and represents the critical void volume fraction at the onset of voids coalescence when initiates to deviate from ; ∗ is the value of at the fracture stage. The value of and depend on the initial void volume fraction (Benseddiq & Imad 2008; Zhang et al. 2000). In order to complete the constitutive model, the void volume fraction should be established as a function of time. Hence, the growth of existing voids ̇ ℎ and the nucleation of the new voids ̇ lead to the increase in