PSI - Issue 2_A

Hide-aki Nishikawa et al. / Procedia Structural Integrity 2 (2016) 3002–3009 Author name / Structural Integrity Procedia 00 (2016) 000–000

3006

5

Figure 5 shows small fatigue crack growth rate versus ε eq n a parameter calculated from SWT equation. Used materials constants c for ε eq described in Eq. (1) was same as Fig. 2 (b). As described in Fig. 5, all fatigue data including tensile mean stress condition were uniformly evaluated by modified small fatigue crack growth law which using ε eq n a parameter. It is clarified that ε eq n a parameter is effective to estimate the mean stress dependency of small fatigue crack growth rate as a simple parameter. As mentioned in Fig. 3, considering crack opening behavior is important to evaluate fatigue crack growth rate. It is possible that SWT ε eq is indirectly including the effect of crack opening behavior. To clarify the relationship between crack opening behavior and SWT equivalent strain, direct measurement for the crack opening point were carried out by DIC technique. DIC analysis were conducted for microscope images which successively obtained during loading-unloading process and vertical direction strain were analyzed. Figure 6 shows small fatigue crack opening behavior observed with DIC technique. Fig. 6 (a) is reference image obtained at minimum load. Fig. 6 (b)~(f) are contour image of successively analyzed vertical strain for loading process. Strain distribution related to fatigue crack is not detected in Fig. 6 (b). In Fig. 6 (c), higher strain distribution is observed around the fatigue crack. After that this strain distribution becomes bigger as applied load becomes bigger. 3.3. Direct measurement for crack opening-closing behavior with DIC technique

1.E-06

1.E-06 10 -6

1.E-06 10 -6

10 10 10 10 -9

Material C (0.15C, 30 ℃ /s)

b

c

a

Material B (0.07C, 20 ℃ /s)

Material A (0.07C, 1 ℃ /s)

Typical long crack data (SM50B welding, NRIM (1980))

Typical long crack data (SM50B welding, NRIM (1980))

Typical long crack data (SM50B welding, NRIM (1980))

l 0.2 ≲ l ≲ 1 mm

1.E-07

1.E-07 10 -7

1.E-07 10 -7

l 0.2 ≲ l ≲ 1 mm

1.E-10 Fatigue crack growth rate d a /d N (m/cycle) 10 -10 1.E-09 1.E-08

1.E-10 Fatigue crack growth rate d a /d N (m/cycle) 10 -8 10 -9 10 -10 1.E-09 1.E-08

1.E-10 Fatigue crack growth rate d a /d N (m/cycle) Crack coalescence 10 -8 10 -9 10 -10 1.E-09 1.E-08

l 0.2 ≲ l ≲ 1 mm

a

a

a= 0.5 l

a= 0.5 l

a

a= 0.5 l

σ a [MPa]

σ m [MPa]

σ a [MPa]

σ m [MPa]

280 240 210

0 0

340 320 280

0 0

σ a [MPa]

σ m [MPa]

0 240 100 210 130

0 280 120 280 120

480 420

0

0 400 300

1

10

100

1

10

100

1

10

100

∆ K (MPa √ m)

∆ K (MPa √ m)

∆ K (MPa √ m)

Fig. 3. Small fatigue crack growth rate versus stress intensity factor.

10 -6

10 -6

10 -6

Material C (0.15C, 30 ℃ /s)

b

c

a

Material B (0.07C, 20 ℃ /s)

Material A (0.07C, 1 ℃ /s)

10 -7

10 -7

10 -7

Fatigue crack growth rate d a /d N (mm/cycle) ε a l a= 0.5 l 10 -8 10 -9 10 -10 10 -11 10 -10 10 -9

Fatigue crack growth rate d a /d N (mm/cycle) l a= 0.5 l 10 -8 10 -9 10 -10 10 -11

Fatigue crack growth rate d a /d N (mm/cycle) l a= 0.5 l 10 -8 10 -9 10 -10 10 -11

Crack coalescence

σ a [MPa] 0.2 ≲ l ≲ 1 mm

σ a [MPa] 0.2 ≲ l ≲ 1 mm σ m [MPa]

σ a [MPa] 0.2 ≲ l ≲ 1 mm σ m [MPa]

σ m [MPa]

340 320 280

0 0

280 240 210

0 0

0 280 120 280 120

480 420

0

0 240 100 210 130

0 400 300

a

a

a

10 -28

10 -27

10 -26

10 -25

10 -24

10 -8

10 -7

10 -6

10 -25

10 -24

10 -23

10 -22

10 -21

1.49 ･ a (mm)

ε a 6.62 ･ a (mm)

ε a 7.91 ･ a (mm)

n a parameter.

Fig. 4. Small fatigue crack growth rate versus ε a