PSI - Issue 7

B.M. Schönbauer et al. / Procedia Structural Integrity 7 (2017) 492–496 B.M. Schönbauer et Al./ Structural Integrity Procedia 00 (2017) 000–000

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( area b HV ⋅ +

) 6 1 (1) where the factor b is 1.43 for surface defects and 1.56 for internal defects. √ area is defined as the square root of the projection area of a defect perpendicular to the loading direction (in µm), HV is the Vickers hardness (in kgf/mm²) and σ w is in MPa. For small defects, such as non-metallic inclusions, corrosion pits, drilled holes and circumferential notches with a size smaller than √ area ≤ 80 µm, Eq. (1) is appropriate to evaluate the fatigue limit. However, larger defects with √ area < 80 µm must be considered to be comparable to long cracks, and consequently, the failure criterion can be expressed by the threshold stress intensity factor amplitude of a long crack, K th,lc : Further experiments under torsional loading (Schönbauer et al. (2017b); Schönbauer et al. (2017d)) revealed that Eq. (2) can be applied for torsional testing as well by equating τ w = σ w . However, defects with √ area ≤ 80 µm become non-detrimental since the torsional fatigue limit of smooth specimens is lower than the fatigue limit in the presence of small defects according to Eq. (1). This is demonstrated in Fig. 4, where the surface of a specimen containing a 1-hole defect with a diameter of 100 µm is shown after cyclic loading slightly above the torsional fatigue limit. As can be seen, the fatal fatigue crack nucleated at the smooth part of the specimen, although small cracks were formed at the hole. Therefore, the fatigue limit in the presence of defects with √ area ≤ 80 µm can be estimated with τ w = τ w0 . w = σ 6 th,lc w 10 − × 0.65 ⋅ ⋅ = area K π σ (2)

Fig. 4. Specimen tested at τ a = 330 MPa and N f = 1.22×10 6 cycles. The dependency of the fatigue limit on the defect size in terms of √ area is illustrated in Fig. 5. It can be seen that the fatigue limit is well estimated by Eqs. (1) and (2), with the exception of 1-hole defects with diameters d of 100 µm and 300 µm under tension-compression loading as well as 3-hole defects with a diameter of 200 µm under torsional loading (solid symbols in Fig. 5). It should be noted that for these defects, non-propagating cracks were not observed when tests were performed at the fatigue limit. In contrast, non-propagating cracks were frequently observed for all other defects (where the experimental results are in good accordance with Eqs. (1) and (2)). Therefore, it can be concluded that a fracture mechanics approach is well applicable when the threshold condition for crack propagation determines the fatigue limit. If the fatigue limit is a critical condition for crack initiation – as in the case of non-observation of self-arrested cracks – the respective defects cannot be treated as equivalent cracks and the application of fracture mechanics is not expedient. As already pointed out in Schönbauer et al. (2017c), the