PSI - Issue 33

7

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 416–427 Author name / Structural Integrity Procedia 00 (2019) 000–000

422

n z 1

1 

where

is the curvature,

is the coordinate of the neutral axis (the neutral axis shifts from the centroid since

1 z

the material is inhomogeneous in both thickness and length directions),

is the vertical centroidal axis of cross

section of the lower crack arm.

/ 0.2  a l

/ 0.4  a l



Fig. 4. The strain energy release rate in non-dimensional form plotted against

(curve 1 - at

, curve 2 – at

/ 0.6  a l

and curve 3 – at

).

The curvature and the coordinate of neutral axis are determined from the following equations for equilibrium:

A ( ) 1    1    0 A ( )

N

dA

,

(26)

1

M

z dA

,

(27)

1

0 1

1 N

1 M

where

and

are the axial force and the bending moment in the lower crack arm. It is obvious that (Fig. 1)

0

1  N

,

(28)

1 M 

Fl

.

(29)

1

0 

By using (1) and (25),

is found as





E z z   1 1 1



 0

1

n e

.

(30)



 



 t

1

1

 





