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

3005

4

stress sensitivities were deferent depends on microstructure, mean stress dependency of simulated HAZ microstructure was able to be fixed by SWT equivalent strain as shown in Fig. 2 (b). In addition, material constant value c for Eq (1) were 0.6, 0.7 and 0.35 for material A, B and C respectively. Such a conventional mean stress dependency of fatigue life is possibly related to fatigue crack growth behavior. Therefore mean stress effect for fatigue crack growth rate will be discussed below.

1000

0.00 0.01 Equivalent Strain amplitude ε eq (-) TP c value A 0.6 B 0.7 C 0.35 b

ε eq = ε a

c ( σ

max /E)

(1- c ) … eq .1

a

*

*

*

* *

*

Stress amplitude σ a (MPa)

for eq. 1 σ m =0 σ max ≂ σ y-c

TP σ m =0 σ max ≂ σ y-c A B C

* Round bar specimen

* Round bar specimen

100

10 3

10 4

10 5

10 6

10 7

10 3

10 4

10 5

10 6

10 7

Number of cycles to failure (cycles)

Number of cycles to failure (cycles)

Fig. 2. S-N diagrams represented with (a) stress amplitude and (b) SWT equivalent strain calculated by eq. 1.

3.2. Mean stress effects on small fatigue crack growth rate

Figure 3 shows small fatigue crack growth rate versus stress intensity factor. Stress Intensity factor range was calculated by Eq. (2). Stress intensity factor range was able to be approximately calculated with √ area, projected area of the crack, as shown in Eq (2) which proposed by Murakami (2002). area K π σ ∆ = ∆ 0.65 (2) ( ) ( ) > − ≤ ∆ = 0 min max σ σ σ σ σ σ Long fatigue crack growth property of welding reported by NRIM (1980) also represented in the figure. Fatigue crack growth rates were not uniformly evaluated by stress intensity factor range. In addition, fatigue crack growth rate was partly higher than that of long crack property. It is well known that evaluating crack closure effect is necessary to estimate fatigue crack growth rate as mentioned by Elber (1971). To evaluate small fatigue crack growth rate and its mean stress dependency, considering crack closure effect seems necessary also for small fatigue crack growth rate of simulated HAZ microstructure. Since quantitative estimation for crack closure effect is difficult, simple modeling is one of the useful approach for small fatigue crack growth problem. Nishitani (1981) proposed small fatigue crack growth law expressed as: da dN C l n σ = / (3) where C and n are materials constant and l is surface crack length. In this study, applicability of similar ε a n a type parameter where a is crack depth was considered. Since uniaxial loading, it is assumed that l =2 a . Figure 4 shows small fatigue crack growth rate versus ε a n a parameter. Fatigue crack growth rate under σ m = 0 conditions were uniformly evaluated by ε a n a parameter in spite of simulated HAZ microstructure. On the other hands, this model can’t estimate fatigue crack growth rate acceleration under tensile mean stress conditions. As described above, SWT equivalent strain ε eq is effective to fix the mean stress dependency for fatigue fracture life. Since large part of fatigue life is occupied by small fatigue crack growth life, ε eq may be also related to mean stress dependency of small fatigue crack growth rate. Therefore, modified crack growth equation using ε eq n a parameter expressed as Eq. 4 is considered below. da dN C a n eq ε = / (4)    0 min min max