PSI - Issue 7

Yoichi Yamashita et al. / Procedia Structural Integrity 7 (2017) 11–18 Yoichi Yamashita et Al./ Structural Integrity Procedia 00 (2017) 000–000

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in contact with specimen surface? We can explain the reason as follows. The initial fatigue crack growth for irregularly shaped cracks and defects as shown in Fig. 9 (Murakami, Y. 2002) starts from the deepest concave corner point due to the extremely high stress intensity factor at that point. However, as the crack grows and the shape of the crack becomes round, the stress intensity factor once decreases and continues growing to failure if the value of ∆ K is higher than ∆ K th . If the value of ∆ K is lower than ∆ K th , the crack stops growth and becomes nonpropagating crack. Therefore, if a defect exists at or near specimen surface, we must consider the effective size of defect which is larger than the real size of defect. Thus, in case of Fig. 8 the effective equivalent crack size √ area eff must be estimated by the dotted line.

√ area eff

(a)

(b)

d 2

e

d 1

(a)

(b)

(d) e

√ area eff

√ area eff

d

e

(c) e < d → √ area eff (e) √ area eff = Dotted area Fig. 9 Effective size (dotted line) of irregularly shaped defect

Fig. 8 Inclined defect in contact with specimen surface and the effective defect size (dotted line).

The effective maximum value of the stress intensity factor K for this kind of inclined defect is attained at the angle between defect and specimen surface with 45deg. Therefore, when we apply the statistics of extremes to fatigue design of AM materials, we need to consider the modification of defect size based on this fact. As shown in Fig.4, the specimen A1 which ran out N =2x10 7 and B1, B2 and C1 which ran out N =10 7 were tested again at higher stress to identify the fatal defect. The data tested at higher stress are denoted by A2, B2, B3 and C2 in Fig.4. Similar tests were carried out for specimens a 1 , b 1 , a 2 and b 2 of Material B in Fig. 6. Based on the values of the effective defect size √ area eff and the Vickers hardness HV , the fatigue limit σ w can be estimated by the following equation of the √ area parameter model.

σ w = 1.43( HV +120)/( √ area eff ) 1/6

(2)

Where, the units are σ w : MPa, HV :kgf/mm eff : µ m. The normalized S-N data were made as in Fig. 10 (a) and (b) where the applied stress σ is normalized by the estimated fatigue limit σ w . It can be seen that the value of σ / σ w for failed specimens are mostly larger than ~0.9 and the estimation based on the √area parameter model works well . However, some specimens of Material B failed at 2 , √ area

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

○ ： Material B （ direction - L ） ● ： Material B （ direction - T ）

□ ： Material A （ direction - L ） ■ ： Material A （ direction - T ）

b2

σ a /σ w

A2

a2

σ a /σ w

C2

C1

B3

A1

B2

b1

B1

a1

Runout

Runout

1.E+04 10 4

1.E+04 10 4

1.E+05

1.E+06

1.E+07 10 7

1.E+08 10 8

1.E+05 10 5

1.E+06

1.E+07 10 7

1.E+08 10 8

10 6

10 5

10 6

Cycles to Failure N f [cycles]

Cycles to Failure N f [cycles]

(a) Material A

(b) Material B

Fig. 10 Normalized S-N curve: σ / σ w - N f