PSI - Issue 2_A

Junichiro Yamabe et al. / Procedia Structural Integrity 2 (2016) 525–532 J Yamabe et al/ Structural Integrity Procedia 00 (2016) 000–000

531

7

Slop based on the normalized distance from crack tip:

p ω Dt S C Hydrogen concentration, C H Dt C G 2 S p ω = Larger G

Condition for the FCG acceleration:

D f

C

=

S p ω

C

S p ω

D f

2

G

C

G

=

=

>

S p ω

ω p : ordinary plastic zone

C

2

Dt

2

G C : critical slope for the FCG acceleration

Smaller G

Hydrogen distribution:

p ω ′ ⋅

2 x

′ = −

( ) C x C

)}

{1 erf (

H

S

Dt

Crack

Normalized distance from crack tip, x'

Fig.6. Schematic illustration of approximate gradient of hydrogen concentration around crack tip.

K

K

1

1

∆

2

2

YS max σ π )

(10).

{

}

(

p ω

=

=

(1 ) R −

3

3

π

σ

YS

For quantifying the gradient of hydrogen concentration near the crack tip in consideration of the ration of the penetration depth of hydrogen per cycle to the ordinary plastic zone in air, the following parameter, G , was defined:

C

S p ω

D f

(11).

G

C

=

=

S p ω

2

Dt

2

When the value of G in Eq. (11) exceeds the critical value, G C , an onset of the FCG acceleration occurs.

D f

D f

G C =

G C

0 p G G ω

,

(12).

= ≥

ω

2 0 S =

S p 2

C

Under the Δ K -constant tests at R = 0.1 and RT, instead of the G in Eq. (12), we can use ( p H2 ･ f ) the onset of the FCG acceleration, since C S is approximately proportional to p H2

1/2 for quantifying

1/2 . Fig. 7(a) shows the relationship

1/2 for the Δ K -constant tests at R = 0.1 and RT (cf. Fig. 3). The onset of the FCG

between the RFCGR and ( p H2 ･ f )

1/2 , revealing that the FCG acceleration occurred at ( p H2 ･ f ) 1/2 ≈

acceleration was quantified by the parameter, ( p H2 ･ f )

0.1. From ( p H2 ･ f ) 0 value for Δ K onset at pressures ranging from 0.1 to 90 MPa at RT was 1.86 mass ppm/mm; therefore, the values of G 0 and ω p for the Δ K onset in the Δ K -constant tests at RT can be obtained. The values of G 0 and ω p for the Δ K onset in the Δ P -constant tests at 363 K and 423 K can be also obtained from Fig. 5(a). These three relationships between G 0 and ω p were fitted by G 0 ω p = G C as the G C was an unknown parameter. Fig. 7(b) shows the relationship G 0 and ω p for the Δ K onset in the Δ K - constant tests at RT and the Δ P -constant tests at 363 K and 423 K. As a reference, the experimental result of the Δ P - constant test at RT, where Δ K onset is not observed in Fig. 5(a), is shown here. The relationship between G 0 and ω p for Δ K onset could be fitted by G 0 ω p = G C . These results demonstrate that the onset of the FCG acceleration in presence of hydrogen was satisfactorily quantified 1/2 = 0.1, the average G

b

10 12 14 16 18

0.1 0.7 10 45 90 ▽ ◇ △ □ ○ Hydrogen pressure, p H2 [MPa]

a

0.7-MPa H 2 , RT, f = 1 Hz, Δ P -constant

100

Δ K -constant Δ K = 30 MPa ･ m/ 1/2 R = 0.1

G 0 ･ ω p = G C

(d a /d N ) H2 / (d a /d N ) air

10

FCG acceleration ( G 0 ･ ω p > G C )

0 2 4 6 8

0.7-MPa H 2 , 363K f = 1 Hz, Δ P -constant

FCG acceleration

G 0 [mass ppm/mm]

0.7 ~ 90-MPa H 2 , RT, f = 0.001 ~ 10 Hz, Δ K -constant

1

0.7-MPa H 2 , 423K, f = 1 Hz, Δ P -constant

0.01

0.1

1

10

( p H2 ･ f )

1/2

0.4

0.6

0.8

1

0

0.2

ω p [mm]

1/2 for the Δ K -constant tests at RT; (b) Relationship between the G

Fig. 7. (a) Relationship between the RFCGR and ( P H2 ･ f )

0 and ω p

for the Δ K onset in the Δ K -constant tests at RT and the Δ P -constant tests at RT, 363 K and 423 K.