Abstract
Analytical solutions are developed for the stress fields induced by circumferential U- and blunt V-shaped notches in axisymmetric shafts under torsion, with a finite value of the notch root radius. The boundary value problem is formulated by using complex potential functions and the real boundary notch shape. Shear stress components are then written as a function of the maximum shear stress evaluated at the notch tip. Considering different global and local geometries the obtained equations are compared with a large bulk of finite element results, showing a very good agreement. Due to their reduced complexity, such equations turn out to be particularly useful in practice.
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References
Atzori B, Lazzarin P, Tovo R (1997) Stress distributions for V-shaped notches under tensile and bending loading. Fatigue Fract Eng Mater Struct 20: 1083–1092
Atzori B, Filippi S, Lazzarin P, Berto F (2005) Stress distributions in notched structural components under pure bending and combined traction and bending. Fatigue Fract Eng Mater Struct 28: 13–23
Berto F, Lazzarin P (2007) Relationships between J-integral and the strain energy evaluated in a finite volume surrounding the tip of sharp and blunt V-notches. Int J Solids Struct 44: 4621–4645
Bowie OL (1966) Analysis of edge notches in semi-infinite region. J Math Phys 45: 356–366
Creager M, Paris PC (1967) Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int J Fract Mech 3: 247–252
Dunn ML, Suwito W, Cunningham S (1997) Stress intensities at notch singularities. Eng Fract Mech 57: 417–430
Filippi S, Lazzarin P (2004) Distributions of the elastic principal stress due to notches in finite size plates and rounded bars uniaxially loaded. Int J Fatigue 26: 377–391
Filippi S, Lazzarin P, Tovo R (2002) Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int J Solids Struct 39: 4543–4565
Fu XL, Wang GF, Feng XQ (2008) Surface effects on the near-tip stress fields of a mode-II crack. Int J Fract 151: 95–106
Glinka G, Newport A (1987) Universal features of elastic notch-tip stress fields. Int J Fatigue 9: 143–150
Howland RJ (1930) On the stresses in the neighbourhood of a circular. Hole in a strip under tension. Philos Trans R Soc Lond Ser A 229: 49–86
Kullmer G (1992) Elastic stress fields in the vicinity of a narrow notch with circular root. Reliability and structural integrity of advanced materials. In: Proceedings of the 9th Biennial European conference on fracture (ECF 9), vol II. Varna, Bulgary, pp 905–910
Kullmer G, Richard HA (2006) Influence of the root radius of crack-like notches on the fracture load of brittle components. Arch Appl Mech 76: 711–723
Lazzarin P, Tovo R (1996) A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches. Int J Fract 78: 3–19
Lazzarin P, Berto F (2005) Some expressions for the strain energy in a finite volume surrounding the root of blunt V-notches. Int J Fract 135: 161–185
Lazzarin P, Filippi S (2006) A generalised stress intensity factor to be applied to rounded V-shaped notches. Int J Solids Struct 43: 2461–2478
Lazzarin P, Zappalorto M (2008) Plastic notch stress intensity factors for pointed V-notches under antiplane shear loading. Int J Fract 152: 1–25
Lazzarin P, Zappalorto M, Yates JR (2007) Analytical study of stress distributions due to semi-elliptic notches in shafts under torsion loading. Int J Eng Sci 45: 308–328
Ling CB (1947) Stresses in a notched strip under tension. J Appl Mech 14: A-275–280
Neuber H (1958) Theory of notch stresses. Springer, Berlin
Neuber H (1961) Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. J Appl Mech 28: 544–550
Neuber H (1968) A physically nonlinear notch and crack model. J Mech Phys Solids 16: 289–294
Qian J, Hasebe N (1997) Property of eigenvalues and eigenfunctions for an interface V-notch in antiplane elasticity. Eng Fract Mech 56: 729–734
Rice JR (1967) Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear. J Appl Mech 34: 287–298
Savruk MP, Kazberuk A (2006) Relationship between the stress intensity and stress concentration factors for sharp and rounded notches. Mater Sci 42: 725–738
Savruk MP, Kazberuk A (2010) Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches. Int J Fract 161: 79–95
Seika M (1960) Stresses in a semi-infinite plate containing a U-type notch under uniform tension. Ing Arch 27: 285–294
Seweryn A, Molski K (1996) Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary condition. Eng Fract Mech 55: 529–556
Smith E (2004) The elastic stress distribution near the root of an elliptically cylindrical notch subjected to mode III loadings. Int J Eng Sci 42: 1831–1839
Sokolnikoff IS (1956) Mathematical theory of elasticity, 2nd edn. McGraw-Hill, New York
Yang Z (2009) The stress and strain concentrations of an elliptical hole in an elastic plate of finite thickness subjected to tensile stress. Int J Fract 155: 43–54
Zappalorto M, Lazzarin P (2007) Analytical study of the elastic-plastic stress fields ahead of parabolic notches under antiplane shear loading. Int J Fract 148: 139–154
Zappalorto M, Lazzarin P (2009) A new version of the Neuber rule accounting for the influence of the notch opening angle for out-of-plane shear loads. Int J Solids Struct 46: 1901–1910
Zappalorto M, Lazzarin P (2010) A unified approach to the analysis of nonlinear stress and strain fields ahead of mode III-loaded notches and cracks. Int J Solids Struct 47: 851–864
Zappalorto M, Lazzarin P, Yates JR (2008) Elastic stress distributions resulting from hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings. Int J Solids Struct 45: 4879–4901
Zappalorto M, Lazzarin P, Berto F (2009) Elastic notch stress intensity factors for sharply V-notched rounded bars under torsion. Eng Fract Mech 76: 439–453
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Zappalorto, M., Lazzarin, P. & Filippi, S. Stress field equations for U and blunt V-shaped notches in axisymmetric shafts under torsion. Int J Fract 164, 253–269 (2010). https://doi.org/10.1007/s10704-010-9493-6
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DOI: https://doi.org/10.1007/s10704-010-9493-6