PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 90–97 Jesús Toribio / Procedia Structural Integrit y 00 (2024) 000 – 000

93

4

ao

(5)

K O = Y O  O

where Y O is the dimensionless SIF for the geometry under consideration – fatigue pre-crack in air environment ( without TTS extension) – , a O is the fatigue pre-crack and their values, taken from studies previous, are shown in Table 3. In this paper, only the more realistic eletrochemical conditions of pre-stressing steel eutectoid wire in life in service was considered (E = – 1200 mV SCE, pH = 12.5 pH). For the fracture instant, K O represents the fracture toughness of the material in air given in Table 2 and the remote stress in this case:

 O = 4F O /  D 2

(6)

where F O is the fracture load in air. From eqs. (3) and (5), it yields

K K

Y Y

a a

 

H

H

H

H







(7)

O

O

O

O

and, in terms of the critical load F H and TTS depth x TTS (Table 3),

x

K K

Y Y

F F

1

H

H

H

TTS









(8)

a

O

O

O

O

Now it is interesting to check to what extent this relationship is near unity or, accordingly, to what extent the critical SIF in hydrogen ( K H ) is close to the fracture toughness of the material in air ( K O ). To calculate the relationship (8) it is necessary to know the dimensionless SIFs Y O and Y H for the geometry and loading mode under consideration: a cylinder subjected to tension with a part-through crack (assumed to be semi-elliptical) perpendicular to the tensile loading direction. With regard to the real crack depth obtained in the experiments, Fig. 1 shows the typical shape of the HAMD region (TTS zone) of increasing depth near the external surface.

Table 3. Critical SIF in hydrogen pH E (mV SCE)

a O (mm)

x TTS (  m)

K max /K O

F FAH /F O

3.62 3.78 4.18 3.93

170 110

0.28 0.45 0.60 0.80

0.55 0.62 0.70 0.81

12.5

– 1200

80

8

According to a recent critical review on the SIF in cylinder with elliptical surface cracks (Toribio et al. 2009) Shin and Cai (2004) provided the most adequate K -solution for cases such as those analyzed in this study, where three parameters such as the relative crack depth ( a /D), the crack aspect ratio ( a /b) and the position at the crack front (x/h) are required (Fig. 2). So, the three dimensionless SIF considered in this paper, in hydrogen environment ( Y H ) and in inert environment ( Y O ), are respectively

i

j

k

  

  

b a

a

h x

  

  

  

  

2

7

2

    0 0 0 i j k

Y

M

H

H



(9)

H

ijk

D

H