Issue 53

A. Zakharov et alii, Frattura ed Integrità Strutturale, 53 (2020) 223-235; DOI: 10.3221/IGF-ESIS.53.19

P LASTIC STRESS INTENSITY FACTOR FOR SMALL - AND LARGE - SCALE YIELDING

Small scale yielding t the small scale yielding the plastic SIF K P in pure Mode I (or pure Mode II) can be expressed directly in terms of a corresponding elastic stress intensity factor using Rice’s J -integral [12]. For an infinite plate with a centred line crack subjected to mixed-mode loading, the plastic SIF K P and the J- integral are related by the Shih’s relation [2]:   2 2 1 0 1 n n p K J I K E E     (2) where the components of the J- integral are defined in terms of elastic stress intensity factors K 1 and K 2 by:      2 2 1 2 1 1 4 x J K K E       (3)    1 2 2 1 1 4 y J K K E       (4) Where E is the Young’s modulus, ν is the Poisson’s ratio, k = 3-4 ν . Substituting Eqs. (3) and (4) into Eqn. (2) leads to the following expression: A

1 



    

 



n

1

2





2

2 K K

2  

K K

4

  1 1 4      n I w



1

2

1 2

 

K

(5)

P

2



 

0

The elastic SIF for a finite size cracked specimen under mixed mode loading conditions can be expressed as:

a  

a



  







1 (1 )cos 2     



1 Y T w    , ,

K

(6)

1

2

a  

a



  





(1 )sin 2  



2 Y T w    , ,



K

(7)

2

2

where a is the crack length, β is the crack angle,  n is the nominal applied stress,  0 is the yield stress, η is the load biaxiality ratio, w is the specimen width, T is the nonsingular stress, Y i (a/w, β ,T) are the geometry dependent correction factors. The governing parameter of the crack-tip elastic–plastic stress–strain field in the form of the I n -integral in Eqn.2 and Eqn.5 is a function of the material strain hardening exponent n and the angular stress/displacement distributions. Shlyannikov and Tumanov [3] suggested the numerical procedure for calculating I n - integral for the different cracked bodies by means of the elastic–plastic FE-analysis of the near crack-tip stress-strain fields: [2]:





n

  1 n e   





FEM

 



FEM

, 







I

, , M n a w

cos

n

p



n

1





   

   

FEM

FEM

  

  

  

  

du 

du 

FEM FEM

FEM FEM



r

 

r  













u 

u 

(8)

sin





rr

r





d

d

1 





FEM FEM FEM FEM rr r r u u         

cos . 



n

1

226