PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 402–415 Author name / Structural Integrity Procedia 00 (2019) 000–000

412

11

The integration in (33) is carried-out by using the MatLab computer program. It should be noted that solution (33) is time-dependent since the strain energy densities are functions of the time (refer to formulae (25) and (31)).

/ 1 3 1 1  L L E E

0.5

1 2 1 1 / L L E E (curve 1 – at

Fig. 8. The strain energy release rate in non-dimensional form plotted against

, curve 2 – at

/ 1 3 1 1  L L E E

1.0

/ 1 3 1 1  L L E E

2.0

and curve 3 – at

).

The compliance method is applied in order to verify (33). According to the compliance method, the strain energy release rate is written as

h G M 2 2 

da dC

,

(34)

where the compliance, C , is expressed as

 

C

.

(35)

M

In formulae (34) and (35), M is the bending moment at the free end of the right-hand delamination crack arm. This bending moment is obtained by considering the equilibrium of the elementary forces in the cross-section of the right-hand delamination crack arm      RH i i n i A i z dA M 1 ( ) 1  . (36) It should be mentioned that M expressed by (36) is time-dependent since i  is function of the time according to formula (16). The angle of rotation,  , is expressed as a function of a by combining of (4) and (5)

2 [

(

)]

a

l a 











.

(37)

DRH

DUN

h