PSI - Issue 14

Dipankar Bora et al. / Procedia Structural Integrity 14 (2019) 537–543 Author name / Structural Integrity Procedia 00 (2018) 000–000

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axisymmetric, a 3-D solid finite element model is built rather than an axisymmetric model (Gautam and Dixit (2012)). Eight-noded brick element - C3D8RT - with linear approximation for the displacement and temperature fields is used along with the reduced integration and hourglass control. The finite element mesh consists of 50000 elements and 56100 nodes. The rigid wall is modeled as a discrete rigid shell in Abaqus/Explicit. The time step is chosen automatically within the solution algorithm by Abaqus considering the stability of the simulation. It is observed that the time step is generally less than 0.01 μ sec. A cutoff value of the stress triaxiality equal to -1/3, below which the fracture never occurs, is used (see Bao and Wierzbicki (2002)). As pointed out by Experimental results show that fracture in the impact of thin-walled tubes is not axisymmetric (Wang and Lu (2002)). This non axisymmetric fracture occurs due to material imperfection, imperfect rod geometry, non-perpendicular impact etc. To simulate the non-axisymmetric fracture mode, the material imperfection, in the form of some small initial damage and equivalent plastic stain, is introduced at some locations. The material imperfection is introduced along three radial lines selected randomly. An initial damage value of 0.09 is assumed for these elements. Table 1. Material properties of Armco iron (Johnson and Cook (1985, Xue (2007), Echávarri (2012)) E   K n m � T m k (GPa) (kg/m 3 ) (MPa) (MPa) ( 0 C) 207 0.29 7890 175 380 0.32 0.55 1.0 1811 73 c  T ref C D 1 D 2 D 3 D 4 D 5  F (W/m 0 C) (J/kg 0 C) ( 0 C) 452 0.000032 25 0.06 -2.2 5.43 -0.47 0.016 0.63 0.6

Fig. 1. Initial geometry of the tube (Gautam and Dixit (2012))

3.1. Ductile fracture on thin walled cylindrical tubes considering Lode angle effect In this section, the growth of equivalent plastic strain, triaxiality and damage is studied at the impacted end for the impact velocity of V = 350m/s. Figure 2 shows the deformed configurations of the tube at various time steps. For the sake of clarity, only the zoomed view of impacted end is shown. As can be seen from the figure, till t = 10μ sec, the deformation consists of the mushrooming of the impacted end. At around t = 6μ sec, the in-plane velocity of the inner surface at the impacted end (i.e., at point A of Fig. 1) becomes positive (Fig. 3(a)). Thereafter, the outer surface starts bulging more than the inner surface. Damage and triaxiality variations are shown in Fig. 3(c) and 3(d) respectively. Also, around t = 1μ sec, the inner surface at the impacted end starts to lift (Fig. 3(b)) leading to unloading of the material points in this region. Additionally, the initiation of buckling is also observed. It can be seen clearly in the deformed configurations that at times t = 10 μ sec material failure starts. As the deformation progresses, more and more damage growth and fracture is observed (t = 50μ sec).