PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 94–102 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

99

6

l

G I T D * 2



U

dx

=

.

(17)

4

2

2

l

a

+

1

2 U and 3 U are unknown quantities. They

The torsion moments in the two crack arms involved in formulae for

are determined by applying the theorem of Menabrea for statically undetermined structures 0 1 =   T U . Besides, the torsion moments in the two crack arm are related by the following equation of equilibrium: T T T + = 1 2 . (19) After substituting of (10) in (18), equations (18) and (19) are solved with respect to 1 T and 2 T . Then the strain energy release rate is derived by using (9) at various values of time (the strain energy release rate is function of time due to creep). (18)

 1 1 / G G ratio (curve 1 – at 

0.5 / 1 1 =     , curve 2 – at

Fig. 4. The strain energy release rate displayed as a function of

/ =     ). 2.0 1

/ =     and curve 3 – at 1.0 1

1

1

The compliance method is applied in order to verify the strain energy release rate. For this purpose, the compliance, C , of the beam is written as (20) where  is the angle of twist of the free end of the beam. By applying the integrals of Maxwell-Mohr, the angle of twist is determined as T C  = ,