Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the microstructural support factor for different failure hypotheses: Part II: Microstructural support analysis

Abstract

On the basis of the comprehensive and accurate stress field equations for sharp rounded V-notches derived in Part I of this contribution, the microstructural support factor of these notches is determined which quantifies the fictitious notch radius in Neuber’s elastic microstructural support concept. By means of Filippi’s equations and considering different failure criteria (Rankine, von Mises and Beltrami) the fictitious notch radius is evaluated for different notch opening angles as a function of the actual notch radius and the microstructural support length. Plane stress and, alternatively, plane strain conditions are introduced. Once the fictitious radius has been found, the support factor s is derived from the expression: fictitious notch radius minus actual notch radius divided by microstructural support length. The support factor s is found to be very sensitive to the notch opening angle, but constant ‘plateau values’ are determined for an actual radius greater than the microstructural support length. The dependence of s on the failure criterion and the multiaxiality conditions (plane stress or plane strain) is also investigated. Various numerical analyses using the FE method have been carried out to compare the theoretical stress concentration factor to the effective stress concentration factor, the former obtained by considering fictitiously rounded notches under tension loading using the plateau values of s, the latter obtained by integrating the relevant stress over the microstructural support length along the bisector of the pointed V-notch. Finally, dealing with out-of-plane shear loading, Neuber’s corresponding solution valid for sharp rounded notches is re-evaluated and the numerical analysis described above is extended to this loading case. All the comparisons above are preceded by elementary solutions for pointed notches in general. It is shown that the plateau values of s are well suited for engineering usage in structural strength assessments.