Issue 52

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

2 T EU  a

(4)

f 

1  

2



N

1

0

where E - Young's modulus. The fatigue damage accumulation rate can be obtained from the equation (3)

1 d dN N N N         ln N f f

f  

(5)





 

f

f

F ATIGUE CRACK GROWTH RATE

F

c W can be obtained from true

or Ramberg-Osgood hardening law [26] the critical value of a strain energy density

stress-strain diagram:

p       n y    

   







f

y

0 

     





W

d

(6)

c

E E

where  - is the strain hardening coefficient, p n - is the strain hardening exponent,

y  - is the yield stress,

f  - ultimate

tensile stress. According to the classical Hutchinson-Rosengren-Rice model in the zone where fully plastic singularity is dominated the strain energy density W can be found from following expression [14]:

2 y E r  

n

2 (1 ) 

1     p n

n

1

p





W

K

(7)

p

p

e



n

1

p

/ r r a  - crack tip distance, a - crack length, e   - dimensionless equivalent Mises stresses

where  - is Poisson's ratio,

  max 1 

which depend only on a polar coordinate  and normalized by P K in small-scale and extensive yielding conditions in Eqn.(7) can be expressed directly using Rice’s J -integral [15]. That is e    . The plastic stress intensity factor

1



   



p n

1

J E

(8)

 

K

P

2 I L   p y p

 

where

2 y







r



1 2 





P 

n

1

  

  





n

2

2

1

e 



e 

d  









J

cos

kk



E

n

3

6

1





















u

u

u

u

  

  

  

  









r

r





d    







r 



r 

d  

r

cos

sin

(9)





y

rr

y

rr













r

r









In Eqns. (8-9) , i u are crack tip dimensionless displacement components, L is cracked body characteristic size, in our case is the crack length L a  , and p I is the numerical constant of the crack-tip stress–strain field, which should be

301