Issue 48

O. Plekhov et alii, Frattura ed Integrità Strutturale, 48 (2019) 451-458; DOI: 10.3221/IGF-ESIS.48.43



ec

, p c e r r f 

.

(10)



fr

The energy increment in cyclic plastic zone can be written as

cyc



dU

, oct c d d rdrd   el oct

 

 

1 1

p

 

.

2



  





3

(11)

ec

el

dN G G

dN d



s

oct

S

0

cyc p

dU

The integration of Eqn. (5) gives . dN  . . It means that dissipation in cyclic plastic zone doesn’t depend on the crack advance but it is fully determined by the applied load. The energy dissipation in monotonic plastic zone can be estimated as 0

3 2

.

mon p



 

U

(12)

e p

Energy increment per one cycle can be written as

mon



dU

el

 

 

d d dl rdrd  

1 1

p

 

oct

oct

e 







  

(13)

3

oct

el

dN G G

dl dN d



s

oct

S

0

1

dr

p

Solution of (13) for the case of da  gives linear relationship between energy increment and crack rate. Finally, the Eqns. (11) and (13) allow us to propose the following approximation for energy of plastic deformation at the fatigue crack tip     2 2 2 2 1 2 1 2 , , tot p p p dU dl dl W A r W A r a A a A dN dN dN         , (14) where A  – applied stress amplitude which determines the diameter of yield surface. 0

Figure 4: Energy dissipation histories during the biaxial test carried at constant stress amplitude (Solid line – experimental results, dotted line –approximation (14)).

456