PSI - Issue 28

Alexey N. Fedorenko et al. / Procedia Structural Integrity 28 (2020) 804–810 Fedorenko A., Fedulov B., Lomakin E. / Structural Integrity Procedia / Structural Integrity Procedia 00 (2019) 000–000

807

4

impact diagrams. The most common experimental method of high strain rate properties characterization is split Hopkinson pressure bar (Koerber et al., 2010; Koerber et al., 2011). For example, using impact stress-strain diagram data at time t with constant strain rate v for compression in fiber direction, the following equation can be written:

  

   

X N

  

 

1  1 / ( ) X A B t  X C C

 

  

( ) t

1  

(7)

0

1  ( ) vt t E

1

,

C   



0

1  

11

X

 

0

where 1 11 ( ) t E  represents Young modulus of damaged material in fiber placement direction at time t . In fact, on the right-hand side the quantity 0 1 11 ( ) vt t E  is a current longitudinal for composite material stress value at time t of impact load, and vt is a current corresponding strain value. Therefore, mentioned quantities should agree to experimental ones. Equation (7) is considered as ordinary differential equation for 1 ( ) t  with initial condition 1 (0) 1   . It can be solved numerically at first with trial constants, and a series of subsequent runs allows to find constants for a good agreement with experimental curves. 4. Numerical simulation The model presented in previous section was implemented to Abaqus finite-element software via user subroutines. Test problem of impact to a tubular specimen of typical geometry (Fig. 1) is considered for numerical simulation. The specimen is made of fiber-reinforced layered carbon-epoxy IM6G/3501-6 composite. Lay-up configuration includes two outer layers with reinforcement oriented in the circumferential direction, and the inner layers are oriented in the direction along the specimen. One edge of the specimen has a chamfer inclined to 30°, which plays the role of failure trigger. Another edge is freely set to supporting surface. Impactor weight is 200 kg and initial velocity is 4m/s. Material characteristics, including impact stress-strain diagrams, are taken from Hsiao and Daniel, 1999. Elastic static constants are presented in Table 1.

Table 1. IM6G/3501-6 elastic properties

E 22 (GPa)

E 33 (GPa)

G 13 (GPa)

G 23 (GPa)

G 12 (GPa)

E 11 (GPa)

 12

 13

 23

171

13.5

13.5

0.31

0.31

0.31

7.5

7.5

7.5

Fig. 1. Specimen geometry and configuration