Issue 52

A.V. Tumanov et alii, Frattura ed Integrità Strutturale, 52 (2020) 299-309; DOI: 10.3221/IGF-ESIS.52.23

determined for the cracked body with a finite size. In the case of full three-dimensional cracked body, the p I -factor in Eqn. (8) changes not only with the strain hardening exponent n p but also with the position along the crack front. In Eqn. (9), the stress tensor and invariant are both normalized by the yield stress: and ij ij y kk kk y         . More detail in determining the p I factor for different elastic-plastic cracked body configurations are given by Refs. [15-18]. In a first approximation the crack growth as a static cracks sequence is considered. Thus, the path independent J-integral can be obtained from:

2 2 1 (1 ) K J E  



(10)

Substitution Eqns. (6) and (8) into (7) give a possibility to obtain the critical distance where the strain energy density reaches a critical value:

2 y E W  

2 (1 ) 

n

1     p n

n

1





r

K

(11)

p

f

p

e



n

1

c

The fatigue crack growth rate can be calculated by substitution Eqns. (5) and (11) into (1) directly, it leads to the following relationship:

    

     

2



n

1

r

2 2   

2 p



n

r

K

2 (1 )  

p

f

da   

1   n

n

1

p

y e f

0 

2    y e

f  

(12)

dr a 



K

1

p

p

dN    

p



ln( EW N N N  )(

n

EU

1 2 

)

fatigue

p

t

c

f

f

0

C REEP DAMAGE ACCUMULATION

I

n this study the classical Kachanov-Rabotnov power law is used for the creep damage accumulation description. According to this model, the strain rate during creep is [1-2]:

n

  

  

cr

e 

(13)





e 

B



cr 

1

and the creep damage accumulation rate is:

m





cr 

e 

d

D   

cr 

(14)

  

cr 

dt

1

where B and cr n are material constants of the Norton power law constitutive equation, D and m – are material properties. The damage variable  indicate the measure of creep damage with 0   denoting the undamaged state and 1   the fully damaged state. The creep damage increment cr   at time t  can be obtained by integrating the expression (14):

1



 



 

1  . m  

(15)

.

1 m D t       

cr 



C m

1

3

where 3 C - is integration constant. This constant can be determined from the initial state.

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