PSI - Issue 59

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

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5. Definition and evaluation of the local strain rate at a crack tip ( crack tip strain rate CTSR) The local strain at the crack tip  CT is defined as the strain associated with the local reference length L CT (small enough to guarantee the convergence of the method, although greater than the material grain size) at the crack tip or its vicinity (Fig. 1):

∆ L CT L CT

v CT z CT

 CT =

=

(1)

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 local strain rate at the crack tip ( crack tip strain rate CTSR) is obtained by time-derivation of the eq. (1):

i+1 – v z CT ∆t

i

v CT

CT

d  CT /dt =

(2)

where superscripts i and i+1 mean a loading step and the next one, respectively. The value  t represents the time interval between two loading steps, which can be constant or variable between one step and another. 6. Estimation of the crack tip strain rate (CTSR) It has been shown previously (Toribio and Elices, 1992) that the space-time average of the local strain rate is representative in hydrogen embrittlement tests. It can be defined as:

1 t c  0 t c

< d  CT /dt > dt

<< d  CT /dt >> =

(3)



where tc is the time to failure and < d  CT /dt > is the space average (over the hydrogen affected area) of the local strain rate in the vicinity of the crack tip. Expression (3) can be approximated by: