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

3007

6

1.E-06 10 -6

1.E-06 10 -6

1.E-06 10 -6

Material C (0.15C, 30 ℃ /s)

b

c

a

Material B (0.07C, 20 ℃ /s)

Material A (0.07C, 1 ℃ /s)

1.E-07 10 -7

1.E-07 10 -7

1.E-07 10 -7

1.E-11 Fatigue crack growth rate d a /d N (m/cycle) l a= 0.5 l c = 0.7 ε eq = ε a c ( σ 10 -8 10 -9 10 -10 10 -11 1.E-10 1.E-09 1.E-08

max /E)

1.E-11 Fatigue crack growth rate d a /d N (m/cycle) l a= 0.5 l c = 0.6 ε eq = ε a c ( σ 1 -8 10 -9 10 -10 10 -11 1.E-10 1.E-09 1.E-08

1.E-11 Fatigue crack growth rate d a /d N (m/cycle) Crack coalescence l a= 0.5 l c = 0.35 ε eq = ε a c ( σ 1 -8 10 -9 10 -10 10 -11 1.E-10 1.E-09 1.E-08

(1- c )

max /E)

max /E)

(1- c )

(1- c )

σ a [MPa] 0.2 ≲ l ≲ 1 mm σ m [MPa]

σ a [MPa] 0.2 ≲ l ≲ 1 mm σ m [MPa]

σ a [MPa] 0.2 ≲ l ≲ 1 mm σ m [MPa]

340 320 280

0 0

280 240 210

0 0

0 280 120 280 120

0 240 100 210 130

480 420

0

0 400 300

a

a

a

10 -19

10 -18

10 -17

10 -16

10 -15

10 -28

10 -27

10 -26

10 -25

10 -24

10 -31

10 -30

10 -29

10 -28

10 -27

1E-28 1E-27 1E-26 1E-25 1E-24

1E-31 1E-30 1E-29 1E-28 1E-27

1E-19 1E-18 1E-17 1E-16 1E-15

7.48 ･ a (mm)

4.81 ･ a (mm)

8.95 ･ a (mm)

ε eq

ε eq

ε eq

n a parameter calculated from SWT equation.

Fig. 5. Small fatigue crack growth rate versus ε eq

Such a strain distribution around the fatigue crack is mainly related to Crack Opening Displacement (COD) during loading cycle. Conventionally, macroscopic COD is effective for measuring crack opening point for long crack such as CT specimen. Therefore, strain analyzed by DIC which related to microscopic COD is possibly effective to detect the crack opening point even for small fatigue crack. Figure 7 shows the example of the relationship between stress and crack opening strain measured with DIC technique for crack length of (a) 0.3 mm and (b) 0.8 mm. Crack opening strain is measured on the fatigue crack where a few tens of µ m behind from the crack tip as described in the figures. Figures also includes the strain measured by strain gage. Although, for long crack, crack opening point is able to be detected by strain gage conventionally, strain gage data of Fig. 7 is approximately linier and crack opening point is not able to be detected. On the other hand, crack opening point is clearly appeared in the strain measured by DIC as shown in Fig. 7 even for 0.3 mm length fatigue crack. Rabblini et al. (2015) reported DIC technique applicability for crack closure measurement for relatively larger crack of length more than 1 mm. It is clarified that DIC technique is effective to detect the crack opening point even for early stage small fatigue crack of length less than 0.3 mm which naturally initiated on the material surface. Then, relationship between effective strain range and SWT equivalent strain is confirmed below. Effective strain ε eff calculated from ε op which is correspond to σ op obtained by DIC is expressed as Eq. (5). op eff ε ε ε = − max (5) Figure 8 shows relationship between ε eq and ε eff measured with DIC technique. As shown in the figure, ε eq is approximately proportional to ε eff . This results indicates that since SWT ε eq is indirectly including the effect of crack opening behavior, it is also effective to evaluate the mean stress effect on small fatigue crack growth rate. As described above, SWT equivalent strain is able to be obtained without crack growth test. Therefore, modified small fatigue crack growth law described in Eq. (4) is effective to evaluate the mean stress effect for small crack as a simple approach. Figure 9 shows relationship between small fatigue crack growth rate and ∆ K eff evaluated with DIC technique. Micro structure dependency of fatigue crack growth rate is not clear. This results indicates fatigue life difference related to microstructure seems subjected to crack closure effect. Since quantitative crack closure evaluation is difficult, modified small crack growth law proposed above which implicitly includes crack closure effect is seems effective to evaluate small fatigue crack growth rate. To estimate the fatigue life of welding, it is also necessary to considering stress concentration. Small fatigue crack growth behavior under the stress concentration and fatigue life estimation method based on small fatigue crack growth property for actual weld joint will be investigated in future.