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

805

2

1. Introduction Composite materials are very effective for energy-absorbing components in automotive and aerospace industries. In particular, composite tubular structures are used in helicopters and sport cars for crash safety. Typical design process of energy-absorbing structure includes selection of material with required crashworthiness performance. Specific energy absorption (SEA) or specific crashing stress are commonly used as general characteristics to assess a crashworthiness of the material. One way of the experimental measurements of these characteristics is a mass drop to a tubular specimen edge face with the measurement of mass acceleration during crushing process. According to experimental studies, mentioned characteristics are very sensitive to numerous parameters and conditions: lay-up configuration of laminated composite, impact velocity, specimen end chamfer geometry and others. This fact is a motivation to develop modelling procedure for prediction of crashworthiness of composite material in different conditions and experiment set-up. 2. Damage model of laminated orthotropic composite The presented model is based on the use of damage parameters, originally introduced by Kachanov and Rabotnov (1986). The degradation degree of the elastic properties of an orthotropic material is defined by the damage parameters 1  and 2  , with 1 0 1    and 2 0 1    associated with fiber and matrix failure correspondingly, and values of 1 i   correspond to undamaged initial state ( i = 1, 2):

11 C E E E E E E G G G G G G                            1 11 22 2 22 33 2 33 12 2 12 13 2 13 23 2 23 1 2 12 13 1 2 13 23 1 2 23 , , , , , , , , C C C C C C C C 12

(1)

,

where C superscript denotes values for elastic constants of damaged material. Constitutive relation for damaged material can be written as proposed in Fedulov et al. (2017, 2018) and Lomakin et al. (2019):

1

 

 

    

                  

0

0

0

2 31





2 21

E

E

E



1 11  

22

33

1

 

0

0

0

2 32





2 12

11                             22 33 12 13 23       

11                   22       33 12 13 23

E

E

E



11

2 22

33

1

2 13     2 23

0

0

0



E

E

E



11

22

2 33

(2)

1

0

0

0

0

0

2 12 G



1

0

0

0

0

0 1

2 13 G



    

0

0

0

0

0

2 23 G



Maximum stress criterion is chosen as damage initiation criterion as expressed below: 11 1 ( 1), c T X X     

, Y Y         

(3)

, (

1),

Y 

Y





22

33

2

c

T

c

T

,

,

, (

1)

S

S

S















12

13

23

2

where X c – compression failure stress in fiber direction, X T – tension failure stress in fiber direction, Y c – compression