PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 103–114 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

110

8

configuration in Fig. 1 is derived as

2 1 

da M dC 2

G

,

(51)

b

where the compliance, C , is written as

 

C

M (52) In formula (52),  is the angle of rotation of the free end of the upper crack arm. By applying the integrals of Maxwell-Mohr, one obtains the following expression for the angle of rotation: x dx l xdx l dx l a a a              1 1 1 3 2 0 1 0     , (53) where 1  , 2  and 3  are the curvatures of the upper and lower crack arms, and the un-cracked beam portion, a x l   , respectively. .

Fig. 4. Variation of the strain energy release rate with time (curve 1 – at / 1  S T T

0.2

/ 1  S T T

0.4

, curve 2 – at

and curve 3 – at

/ 1  S T T

0.6

).

The curvature, 1  , and the coordinate of the neutral axis are determined from the following equations of equilibrium of the elementary forces in the cross-section of the upper crack arm:

h

1

2

h  

N b 

dz

,

(54)

1

1



2