PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 31–35 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

34 4

<  CT,C > t c

<< d  CT /dt >> =

(4)





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<  CT,C > being the space average of the critical strain in the vicinity of the crack tip, which can be computed as the critical strain at the middle of the critical region, process zone or hydrogen-assisted micro-damage region (the hydrogen-affected area), i.e., a distance rc from the crack tip marks the middle of such a domain:

 CT,C (r c ) t c

<< d  CT /dt >> =

(5)







Considering the definition of local strain (1) and placing the local reference length L CT just at a distance rc from the crack tip:

v CT,C r c tg 

 CT,C (rc) =

(6)



where v CT,C is the critical local displacement in the vicinity of the crack tip (defined at the fracture situation) and  is the local polar angle defined in Fig. 1. On assuming linear elastic fracture mechanics (LEFM) hypothesis under plane strain conditions, the well known singular solution in the vicinity of a 3D crack with an arbitrary curved front (Hartranft and Sih, 1977) can be used in a plane perpendicular to the crack front as follows:

KI

3  2 ) + o (r

 2 (1 – sin

 2 sin

1/2 )

cos

(7)

 nn =

2  r

KI

3  2 ) + o (r

 2 (1 + sin

 2 sin

1/2 )

cos

(8)

 zz =

2  r

KI

 2 + o (r

1/2 )

2  cos

(9)

 tt =

2  r

(10)

 nt = 0

KI

3  2 + o (r

 2 cos

 2 cos

1/2 )

sin

(11)

 nz =

2  r

(12)

 tz = 0

The afore-said LEFM solution allows the calculation of the critical local strain in the vicinity of the crack tip, so that the equation (6) yields:

K c G

1 2  r c

 CT,C (rc) =

 (  ) 

(13)

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