No abstract

No abstract

No abstract

No abstract

Closed form expressions of stress distributions for V-notches with end holes and varying opening angles are presented. The solution for the elastic plane problem is obtained by means of the Kolosov-Muskhelishvili approach by using a reduced number of complex terms. The exponents of the potential functions are simple combinations of Williams' eigenvalues for pointed V-notches in mode I and mode II. The degree of accuracy of the new solution, which is approximate, is found to be very satisfactory for engineering applications. When the V-notch opening angle is equal to zero, the solution matches the keyhole notch solutions already reported in the literature by Neuber (for mode I) and by Kullmer and Radaj (mode I and mode II) and based on the Airy stress function. In parallel, the out-of-plane problem is solved by means of an holomorphic function H(z) where the exponent is still linked to the leading order eigenvalue of the pointed V-notch in mode III. For this loading mode the solution is exact. When the notch opening angle is equal to zero and also the notch root radius tends to zero the solution matches Kullmer's keyhole notch solution

By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three-dimensional governing equations lead to a system where a bi-harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out-of-plane shear notch problem. The system can be applied not only to pointed three-dimensional V-notches but also to sharply radiused V-notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models

Closed-form Solutions are developed for the stress fields induced by circumferential hyperbolic and parabolic notches in axisymmetric shafts under torsion and uniform antiplane shear loading. The boundary Value problem is formulated by using complex potential functions and two different coordinate systems, providing two classes Of solutions. It is also demonstrated that some Solutions of linear elastic fracture and notch mechanics reported ill the literature can be derived as special cases of the general solutions proposed herein. Finally the analytical frame is Used to link the Mode III notch stress intensity factor to the maximum shear stress at the notch tip, as well as to give closed-form expressions for the strain energy averaged over a finite size volume surrounding the notch root

The paper deals with a work-hardening, elastic-plastic, stress analysis of pointed V-notches under antiplane shear deformation loading both under small and large scale yielding. Stress and strain field intensities are expressed in terms of plastic Notch Stress Intensity Factors, which are analytically linked to the corresponding linear elastic ones under small scale yielding. The near tip stress and strain fields are then used to give closed-form expressions for the Strain Energy Density over a circular sector surrounding the notch tip, and for the J-integral parameter, both as a function of the relevant plastic NSIFs, these expressions being valid both under small and large scale yielding