By Dieter Radaj, Michael Vormwald
In 5 chapters, this quantity provides contemporary advancements in fatigue overview. within the first bankruptcy, a generalized Neuber suggestion of fictitious notch rounding is gifted the place the microstructural aid elements rely on the notch commencing perspective in addition to the loading mode. the second one bankruptcy specifies the notch tension issue together with the tension power density and J-integral thought whereas the SED technique is utilized to universal fillet welded joints and to thin-sheet lap welded joints within the 3rd bankruptcy. The forth bankruptcy analyses elastic-plastic deformations within the close to crack tip region and discusses driver parameters. The final bankruptcy discusses thermomechanical fatigue, tension, and pressure ranges.
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28. A power series expansion of the stress field is performed, neglecting the higher order terms. The resulting equations for in-plane shear loading (mode 2) read as follows: 8 8 9 9 8 9 sin 3h=2 > sin h=2½2 þ cos h=2 cos 3h=2 > > > > < < rx > = = < = KII KII q ry ¼ pﬃﬃﬃﬃﬃﬃﬃﬃ sin h=2 cos h=2 cos 3h=2 À sin 3h=2 þ pﬃﬃﬃﬃﬃﬃﬃﬃ > > > 2pr > 2pr 2r > : : > ; : ; ; sxy À cos 3h=2 cos h=2½1 À sin h=2 sin 3h=2 ð1:59Þ 8 8 9 9 8 9 > > À5 sin h=2 þ 3 sin 3h=2 > < À sin h=2 > < rr > = = K q> = KII < II ð1:60Þ sin h=2 rh ¼ pﬃﬃﬃﬃﬃﬃﬃﬃ À3 sin h=2 À 3 sin 3h=2 þ pﬃﬃﬃﬃﬃﬃﬃﬃ > > > 2pr 2r > : : > ; : ; ; 4 2pr > À cos h=2 cos h=2 þ 3 cos 3h=2 srh The shear stress in the bisector plane (h = 0°) follows from Eq.
The fictitious notch rounding concept is applied in the following to pointed V-notches (q = 0) with different notch opening angles and analysed by the FE method (Berto et al. 2009). The geometry and dimensions of the specimen are shown in Fig. 9, whereas the concept applied to sharp notches is demonstrated in Fig. 1. By evaluating the integral of the theoretical (equivalent) stress rth along the distance qÃ , it is possible to define an effective stress concentration factor K t (corresponding to the theoretical fatigue notch factor Kf) for a sharp notch as follows: 20 1 Generalised Neuber Concept of Fictitious Notch Rounding Fig.
The analytical frame for out-of-plane shear stress fields at notches is less complicated than for in-plane stress fields. The former stress fields are governed by potential functions, the latter by bipotential functions (real functions according to Airy or complex functions according to Kolosov and Muskhelishvili). In consequence, closed form solutions can be derived to a larger extent and approximation formulae are easier to gain. On the basis of Neuber’s stress field equations for sharply rounded V-notches in out-of-plane shear loading, the microstructural support factor s of these notches is determined which quantifies the fictitious notch radius in Neuber’s microstructural support concept.