PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 115–124 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

122

8

z

       i i n n 2 1 1 1 i

  x p u xi

  x p v yi

  

    ds

  

  

i cos 02

u







z

2

i

z

i i     1 1 i n 

x p u xi  

x p v yi  

  

  

  

  

3 1

i cos 03

u

ds









.

(50)

z

3

i

The integration in (50) is performed by the MatLab computer program. The fact that the J -integral value is equal to the strain energy release rate found by (30) proves the correctness of the delamination analysis. 3. Numerical results The numerical results presented in this section of the paper are obtained by using the following data: 0.010  b m, 0.015  h m, 0.300  l m, 3  n , 4  m , 0.7  ij r , 0.7  ij s , 5 0.6 10    F v N/s and 5 0.4 10    M v Nm/s.

11 12 / E E ratio (curve 1 – at

/

0.5    , curve 2 – at

Fig. 5. Variation of the non-dimensional strain energy release rate with

13

11

/

1.5 11    and curve 3 – at

/

2.5    ). 11

13

13

The variation of the strain energy release rate with time is depicted in Fig. 3. The strain energy release rate and time in Fig. 3 are expressed in non-dimensional form by using formulae   G G E b N 11 /  and 11 11 /  t tE N  , respectively. The strain energy release rate is found also for the case when the multilayered beam is statically determinate structure (it is assumed that the beam is clamped in its right-hand end, while the left-hand end of the beam is free). The variation of the strain energy release rate with time in the statically determined beam is depicted also in Fig. 3. It can be observed that the strain energy release rate in statically undetermined beam is lower (Fig. 3). The variation of the strain energy release rate with 11 12 /   ratio is illustrated in Fig. 4. The strain energy release rate is found also assuming linear viscoelastic behaviour of the beam. For this purpose, 1  ij r and 1  ij s are substituted in the non-linear solution (30). The strain energy release rate at linear viscoelastic behaviour is shown