Issue 42

P. Raposo et alii, Frattura ed Integrità Strutturale, 42 (2017) 105-118; DOI: 10.3221/IGF-ESIS.42.12

Crack Propagation Data  and  UniGrow Model 

Elementary material block size  a = a i =  * 

Δσ applied

 , R 

Linear‐elastic Stress Analysis  (cracked geometry)  FEM 

Elastoplastic Stress Analysis  (cracked geometry)  FEM 

Weight Function    a u K    

Residual Stress, σ r

H a,xm y

I

Residual Stress Intensity Factor 

Stress Intensity Factor  (J‐Integral method)   K applied and K max,applied 

a  0

    dx a,xmx 

K

 

r

r

K

K

K





tot max,

applied max,

r

applied K K K  





ε‐N exp. data

tot

r

Actual elastoplastic stresses and strains  (σ max and  ε/2)  Neuber’s Approach 

p‐ε‐N or p‐SWT‐N  Weibull fields

YES 

< K c 

a = a +  * 

p‐S‐N p

‐R fields 

K max,applied

NO 

END

Figure 3 . Procedure for the estimation of the probabilistic fatigue crack propagation fields for the notched geometries. In this study, sub-steps a), b) and c) were replaced by an elastoplastic finite element analysis in order to allow the direct computation of the residual stress fields to be performed. iii) The residual stress distribution computed ahead of the crack tip is assumed to be applied on the crack faces, behind the crack tip, in a symmetric way with respect to the crack tip. The residual stress intensity factor, K r , is then computed using the weight function method according to the following general expression [13]:

a

    . , x m x a dx 

 

K

(1)

r

r

0

To this purpose, the weight function m ( x , a ) was computed for the cracked detail under consideration using the following expression [10]:

. K a  

y uH m x a

  ,



(2)

1

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