PSI - Issue 7

Hiroshige Masuo et al. / Procedia Structural Integrity 7 (2017) 19–26 Hiroshige Masuo et Al./ Structural Integrity Procedia 00 (2017) 000–000

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Since defects have various shapes, we need to define the relevant rule for estimating the effect of defects. In this regard, the representative dimension of a defect can be expressed with √ area in terms of fracture mechanics concept (Murakami, Y. 2002, and Murakami, Y. and Endo, M., 1994). Figure 12 illustrates various possible configurations of defects for which we need to consider the effective defect size √ area eff different from the real defect size. The initial fatigue crack growth for irregularly shaped cracks and defects as shown in Fig. 12 starts from the deepest concave corner point due to the extremely high stress intensity factor at that point (Murakami, Y. 2002 and Murakami, Y., Nemat-Nasser, S. 1983). However, as the crack grows and the shape of the crack front becomes round, the stress intensity factor once decreases and the crack continues growing to failure if the value of ∆ K exceeds the threshold stress intensity factor range ∆ K th . If the value of ∆ K is lower than ∆ K th , the crack stops growing and becomes nonpropagating crack. Therefore, if defects have configurations such as the examples of Fig. 12, we must consider the effective size of defect √ area eff rather than the real size of defect. In this regard, when we apply the statistics of extremes analysis to fatigue design of AM materials, we need to consider the modification of defect size.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

EBM Surface polish without HIP DMLS Surface polish without HIP

σ a / σ w

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

N f （ cycles ）

Fig. 13 Normalized S - N curve: σ a / σ w - N f

Based on the values of the effective defect size √ area eff at fracture origin and the Vickers hardness HV , the normalized S - N data were made as in Fig. 13 where the applied stress σ a is normalized by the estimated fatigue limit σ w . It can be seen that the value of σ a / σ w for failed specimens are mostly larger than ~0.9 and the estimation based on the √area parameter model (Eq. (2)) works well.

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

(2)

Where, the units are σ w : MPa, HV : kgf/mm eff : µ m. However, Fig. 13 shows failures of some EBM specimens at σ / σ w < 1.0. The larger particle size in EBM specimens than in DMLS may be the reason. In EBM specimens the effective defect size √ area eff with large irregularity might not be correctly identified due to larger particle size than DMLS as seen in Fig. 9. It may be necessary to investigate more in detail the possible heterogeneous microstructure surrounding defects produced by lack of fusion. Thus, since the fatigue limit of AM specimens is influenced by the size of defects contained in individual specimens, it must be noted that we cannot define the definite fatigue limit for a material in question from the usual S-N data. Although the definition of the effective defect size is not evident, in case of Figs. 14 and 15 the effective defect size √ area eff must be estimated by the equivalent elliptical area, because in case of adjacent defects within the critical distance fatigue cracks emanating from one defect are likely to be connected with neighbour defects (Murakami, Y. 2002. and Aman, M. et al, 2017.). Therefore, when we apply the statistics of extremes to fatigue design of AM 2 , √ area