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
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