Semianalytical solution for the stress distribution in notched tubes

The aim of this paper is to present an alternative solution to the finite element method for the determination of the elastic stress field for an axi-symmetric notched tube under tension and bending loadings. The proposed solution is an extension of the work of Filippi and Lazzarin (2004) [8] to tubular specimens. It provides the stress field distribution along the notch bisector. A good agreement was found between the solution proposed in the present paper and the results from a finite element analysis. A sensitivity analysis is performed to establish the domain of validity of the solution with respect to the dimensions of the notched tube.

[1]  Daniel Averbuch,et al.  A computational approach for the fatigue design of threaded connections , 2011 .

[2]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[3]  Filippo Berto,et al.  Stress distributions in notched structural components under pure bending and combined traction and bending , 2005 .

[4]  A. S. Milyayev.  The action of a concentrated force inside an elastic half-plane with a step , 2002 .

[5]  K. Tanaka,et al.  Engineering formulae for fatigue strength reduction due to crack-like notches , 1983 .

[6]  G. Bertolino,et al.  A multiscale approach of fatigue and shakedown for notched structures , 2007 .

[7]  Vassilis P. Panoskaltsis,et al.  INVARIANT FORMULATION OF A GRADIENT DEPENDENT MULTIAXIAL HIGH-CYCLE FATIGUE CRITERION , 1996 .

[8]  Paul C. Paris,et al.  Elastic field equations for blunt cracks with reference to stress corrosion cracking , 1967 .

[9]  G. Pluvinage.  Fatigue and fracture emanating from notch; the use of the notch stress intensity factor , 1998 .

[10]  T. Topper,et al.  An Analysis of Notch-Size Effects at the Fatigue Limit , 1988 .

[11]  Grzegorz Glinka,et al.  Universal features of elastic notch-tip stress fields , 1987 .

[12]  Daniel Kujawski,et al.  Estimations of stress intensity factors for small cracks at notches , 1991 .

[13]  H. Bui,et al.  Solutions exactes de fissure d'interface sous contact frottant avec un milieu indéformable , 2004 .

[14]  J. Schijve.  Stress gradients around notches , 1980 .

[15]  Roberto Tovo,et al.  Fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity , 1997 .

[16]  David Taylor,et al.  Geometrical effects in fatigue: a unifying theoretical model , 1999 .

[17]  Thierry Palin-Luc,et al.  A non‐local theory applied to high cycle multiaxial fatigue , 2002 .

[18]  H. Neuber.  Theory of notch stresses : principles for exact calculation of strength with reference to structural form and material , 1958 .

[19]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity : fundamental equations, plane theory of elasticity, torsion, and bending , 1953 .

[20]  Andrei Constantinescu,et al.  NUMERICAL EXPLORATION OF THE DANG VAN HIGH CYCLE FATIGUE CRITERION: APPLICATION TO GRADIENT EFFECTS , 2009 .

[21]  Paolo Lazzarin,et al.  A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches , 1996 .

[22]  A. Constantinescu,et al.  A Multiscale Discussion of Fatigue and Shakedown for Notched Structures , 2010 .

[23]  Guriĭ Nikolaevich Savin,et al.  Stress concentration around holes , 1961 .

[24]  Paolo Lazzarin,et al.  Distributions of the elastic principal stress due to notches in finite size plates and rounded bars uniaxially loaded , 2004 .

[25]  M. Williams,et al.  Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension , 1952 .

[26]  Tim Topper,et al.  PRACTICAL STRESS EXPRESSIONS FOR STRESS CONCENTRATION REGIONS , 2007 .

[27]  N. Frost,et al.  Non-Propagating Cracks in Vee- Notched Specimens Subject to Fatigue Loading , 1957 .

[28]  J. Jäger,et al.  Half-planes without coupling under contact loading , 1997 .

[29]  Roberto Tovo,et al.  Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates , 2002 .