Stress field equations for U and blunt V-shaped notches in axisymmetric shafts under torsion

Zappalorto, Michele; Lazzarin, P.; Filippi, Stefano

doi:10.1007/s10704-010-9493-6

Cited by 45 publications

(29 citation statements)

References 35 publications

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“…This form, which represents a particular case of the function suggested in (Zappalorto et al 2010), account for the symmetry of the problem considered here, characterised by a notch bisector normal to the symmetry axis. Then:…”

Section: The Mode III Problemmentioning

confidence: 99%

In-plane and out-of-plane stress field solutions for V-notches with end holes

Zappalorto

Lazzarin

2010

Int J Fract

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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

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Section: The Mode III Problemmentioning

confidence: 99%

In-plane and out-of-plane stress field solutions for V-notches with end holes

Zappalorto

Lazzarin

2010

Int J Fract

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“…By proceeding on parallel tracks, closed form expressions of the stress fields have been obtained for semi-elliptic notches, parabolic or hyperbolic notches, and U-or V-blunt notches under the out-of-plane mode Zappalorto et al 2008Zappalorto et al , 2010.…”

Section: Introductionmentioning

confidence: 99%

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

2011

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The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the notch radius

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“…As a consequence the notch profile can be described according to the following equation (Zappalorto et al 21 )…”

Section: Description Of the Geometry Of The Notched Tubesmentioning

confidence: 99%

“…The proposed formulas, obtained by extending to tubular specimens the solution by Zappalorto et al 21 , valid for finite size round bars weakened by circumferential notches and loaded in torsion, explicitly account for the local geometry (notch tip root radius and notch opening angle) as well as for the global geometry (inner and outer diameter of the tube).…”

Section: Introductionmentioning

confidence: 99%

Torsional stress distributions in tubes with external and internal notches

Zappalorto

Lazzarin

2012

The Journal of Strain Analysis for Engineering Design

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Practical expressions useful to assess the elastic stress distribution in a torque loaded axisymmetric tube, weakened by circumferential U- and blunt V-shaped notches, are presented. The solution is obtained as an extension of a previous analytical solution valid for axisymmetric solid shafts. It accounts for the local geometry (notch tip root radius and notch opening angle) as well as for the global geometry (inner and outer diameter of the tube). Shear stress fields are written as a function of the shear stress at the notch tip. Varying global and local geometries, the obtained equations are compared with a large bulk of finite element results, showing a good agreement

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Stress field equations for U and blunt V-shaped notches in axisymmetric shafts under torsion

Cited by 45 publications

References 35 publications

In-plane and out-of-plane stress field solutions for V-notches with end holes

In-plane and out-of-plane stress field solutions for V-notches with end holes

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

Torsional stress distributions in tubes with external and internal notches

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