PSI - Issue 14

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

539

3

tubes has been analyzed numerically using commercial finite element codes by several researchers (see Jones (1998) for details). However, there seems to be very few attempts to numerically study the dynamic ductile fracture of thin walled tubes impacting against a rigid target. Galib et al. (2006) studied the impact of square aluminum tubes at velocities of 7-15.2 m/s both experimentally as well as numerically. Wang and Lu (2002) studied the impact of aluminum and mild steel tubes against a rigid surface at velocities of 137-385 m/s experimentally. Experimental results show that, at lower impact velocities, thinner tubes buckle axisymmetrically, while thicker tubes mushroom at the impacted end before buckling. The important experimental result is that, at higher impact velocities, the tubes fracture, developing only a single through the thickness crack initially. Eventually, many such cracks develop leading to fracture. Gautam and Dixit (2012) used a continuum damage based model to study the ductile fracture in thin walled cylindrical tubes impacting against a rigid target. They were able to simulate the initial stages of the fracture of the tube 2. Plasticity model and damage growth law In the present work, the Johnson and Cook (1985) plasticity model is used to incorporate plastic hardening phenomenon. The dependence of the yield stress ( ) on the equivalent plastic strain ( �� � ), the equivalent plastic strain rate ( � ) and the temperature (T) is assumed to be governed by the following equation (see Johnson and Cook (1985)) � � � �� � � �� � � � � � � �� � �� � � � �� (3) The damage growth law used is the Johnson-Cook-Xue (Echávarri (2012)) damage model. The damage is defined as an internal state variable which is the ratio of incremental equivalent plastic strain to fracture strain.

1 t t D D D    

(4)

P eq        

D   

(5)





f

P eq   is incremental equivalent plastic strain and f  is fracture strain which is given by (Echávarri (2012))         * * * 1 2 3 4 5 6 | | exp 1 ln 1 (1 ) f F F D D D D D T                          (6)

Here,

Here, *  is the stress triaxiality, *  is � � � � , T* = � � � � m is a constant and D damage constants.

1 , D2 , D 3 , D 4 and D 5 are the

3. Result and discussion In the present work, dynamic ductile fracture of thin-walled cylindrical tube impacting against a rigid surface is simulated. The dimensions of the tube are taken from Wang and Lu (2002). The sectional front view of the tube is shown in Fig. 1. The outer diameter of the tube (D 0 ) is 12.55 mm, the thickness (t 0 ) is 0.78 mm and the length (L 0 ) is 64 mm.The material of the tube is armco iron (Johnson and Cook (1985)). The material properties and the values of the damage constants in the expression for fracture stain (given by equation 6) are given in Table 1. The mechanical properties are given in Table 5.4. The friction coefficient (μ f ) between the tube and the rigid surface is taken as 0.05. The simulation is performed for the impact velocity of 350 m/s. Since, the simulated fracture patterns are not