PSI - Issue 54

Victor Rizov et al. / Procedia Structural Integrity 54 (2024) 475–481 Victor Rizov/ Structural Integrity Procedia 00 (2019) 000 – 000

479 5

i m 1 ( ) *      i

u dV * 0 i

U

,

(16)

V

i

i i      1 ( ) A i m i

where * 0 i u is the CSE density in an arbitrary layer, i V is the layer volume. Equations,

N

dA



and

i i      1 ( ) A i m i

M

zdA



, are used to find-out the curvature and the neutral axis coordinate.

An examination of the SERR is done by the J -integral (Broek (1986)). The contour, L , shown in Fig. 1 is used. The J -integral values are equal to the SERR which proves the correctness of the analysis performed. 3. Numerical results To illustrate the effects of the mobile force on the delamination, a beam structure with three layers is considered where each layer is of thickness, 0 h . The numerical results presented here are derived by using the following data: 0.012  b m, 0.006 0  h m, 0.018  h m, 0.400  l m, 0.050 1  l m, 3  F N, 5 3 10    F v m/s, 0.7  i n , 0.8  i p , 0.5  i  and 0.6  i  .

5 1 10   

5 2 10   

1 / le re

F v

F v

 

Fig. 4. Normalized SERR –

ratio plots (curve 1 – at

m/s, curve 2 – at

m/s and curve 3 – at

1

5 3 10   

F v

m/s).

The change of the SERR with time is studied first. The results are displayed in Fig. 3. It is seen from the plots in Fig. 3 that the SERR continuously grows. This behaviour is provoked by two factors. The first one is the increase of the moment in the delamination-tip cross-section of the beam. The second one is the viscoelastic response of the beam. The ascendency of F v and 1 1 / le re   over the SERR are studied too. The corresponding plots are displayed in Fig. 4. Looking at the plots of the SERR in Fig. 4, the generalization observed is that growth of F v and 1 1 / le re  