PSI - Issue 41

Jesús Toribio et al. / Procedia Structural Integrity 41 (2022) 728–735 Jesús Toribio / Procedia Structural Integrity 00 (2022) 000–000

730

3

where the enlargement ∆L CT of the local reference length is twice the displacement of each end (local displacement v CT ) and the local reference length L CT is two times the axial coordinate of its end (z CT ). The hypothesis of small strains is included in definition (1), which will be used throughout this paper. The center of the local reference length L CT is always at the plane of the crack, although it can be placed at a variable radial distance r (always small) from the crack tip (Fig. 1).

Fig. 1. Local displacements (v CT ) in the vicinity of a crack tip. The CTSR can be obtained by time-derivation of the expression (1) as d  CT /dt, and it has been shown previously (Toribio and Elices, 1992) that the space-time average of the CTSR , << d  CT /dt >> is representative in HAC tests: << d  CT /dt >> = <  CT,C > t c  (2) <  CT,C > being the space average of the critical crack tip strain (CTS), 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 r c from the crack tip marks the middle of such a domain  CT,C (r c ) With the local strain (1) and placing the local reference length L CT just at a distance r c from the crack tip:  CT,C (r c ) = v CT,C r c tg   (3) where v CT,C is the critical local displacement in the vicinity of the crack tip (obtained at the fracture situation) and  is the local polar angle defined in Fig.1. Under planes strain and on the basis of linear elastic fracture mechanics (LEFM) principles the local distributions of stress, strain and displacement can be used (Hartranft and Sih, 1977), and  CT,C (r c ) is:

K c G

1 2  r c

 CT,C (r c ) =

 (  ) 

(4)

where K c is the critical stress intensity factor (at the end of the HAC process), G=E/2/(1+  ), E and  are the elastic constants, and  (  ) is a dimensionless function of the angular coordinate   given by:  (  ) = sin(  /2) tg  [2–2  –cos 2 (  (5)