Elastic Strain-Concentration Factor of Cylindrical Bars with Circumferential Flat-Bottom Groove under Static Tension

Authors: Hitham M. Tlilan

Abstract:

Using finite element method (FEM), the elastic new strain-concentration factor (SNCF) of cylindrical bars with circumferential flat-bottom groove is studied. This new SNCF has been defined under triaxial stress state. The employed specimens have constant groove depth with net section and gross diameters of 10.0 and 16.7 mm, respectively. The length of flatness ao has been varied form 0.0 ~12.5 mm to study the elastic SNCF of this type of geometrical irregularities. The results that the elastic new SNCF rapidly drops from its elastic value of the groove with ao = 0.0, i.e. circumferential U-notch, and reaches minimum value at ao = 2 mm. After that the elastic new SNCF becomes nearly constant with increasing flatness length (ao). The value of tensile load at yielding at the groove root increases with increasing ao. The current results show that severity of the notch decreases with increasing flatness length ao.

Keywords: Bar, groove, strain, tension

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331497

References:

[1] K. Nishida, Stress Concentration (in Japanese). Morikita Shuppan, Tokyo, 1974.
[2] W.D. Pilkey, Peterson-s Stress Concentration Factors. Wiley, New York, 1997.
[3] H. F. Hardrath and L. Ohman, "A study of elastic and plastic stress concentration factors due to notches and fillets in flat plates,". NACA Report 1117, National Advisory Committee Aeronautics, 1953.
[4] H. Neuber, "Theory of stress concentration factor for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law," J. Appl. Mechanics, vol. 28, pp. 544-550, 1961.
[5] M. M. Leven and M. M. Frocht, "Stress-concentration factors for single notch in flat bar in pure and central bending,". J. Appl. Mechanics, vol. 74, pp. 560-561. 1952.
[6] A. Kato, "Design equation for stress concentration factors of notched strips and grooved shafts," J. strain analysis, vol. 26, pp. 21-28, 1991.
[7] N. -A. Noda, M. Sera, and Y. Takase, "Stress concentration factors for round and flat test specimens with notches," Int. J. Fatigue, vol. 17 (3), pp. 163-178,1995.
[8] P.S. Theocaris, "Experimental solution of elastic-plastic plane stress problems," J. Appl. Mechanics, vol. 29, pp. 735-743, 1962.
[9] P.S. Theocaris and E. Marketos, "Elastic-plastic strain and stress distribution in notched plates under plane stress," J. Mech. Phys. Solids, vol. 11, pp. 411-428, 1963.
[10] A.J. Durelli and C.A. Sciammarella, "Elastoplastic stress and strain distribution in a finite plate with a circular hole subjected to unidimensional load," J. Appl. Mechanics, vol. 30, pp. 115-121, 1963.
[11] P.S. Theocaris, "The effect of plasticity on the stress-distribution of thin notched plates in tension," J. Franklin Inst., vol. 279, pp. 22-38, 1965.
[12] K. Ogura, N. Miki, and K. Ohji, "Finite element analysis of elasticplastic stress and strain concentration factors under plane strain and axisymmetric conditions (in Japanese)," Trans. Japan Soc. Mech. Engrs., vol. 47, pp. 55-62, 1981.
[13] S.J. Hardy and M.K. Pipelzadeh, "An assessment of the notch stressstrain conversion rules for short flat bars with projections subjected to axial and shear loading," J. Strain Analysis, vol. 31 (2), pp. 91-110, 1996.
[14] T. Majima, "Strain-concentration factor of circumferentially notched cylindrical bars under static tension," J. Strain Analysis, vol. 34 (5), pp. 347-360, 1999.
[15] H. M. Tlilan, N. Sakai, and T. Majima, "Strain-concentration factor of a single-edge notch under pure bending". (In Japanese) Yamanashi District Conference, No. 040-4, Japan, 2004
[16] H. M. Tlilan, N. Sakai, and T. Majima, "Strain-concentration factor of rectangular bars with a single-edge notch under pure bending". (In Japanese), Journal of the Society of Materials Science, vol. 54 (7), 2005.
[17] H. M. Tlilan, S. Yousuke, and T. Majima, "Effect of notch depth on strain-concentration factor of notched cylindrical bars under static tension", European Journal of Mechanics A / Solids, vol. 24 (3), 406- 416, 2005.
[18] H. M. Tlilan, N. Sakai, and T. Majima, "Effect of notch depth on strainconcentration factor of rectangular bars with a single-edge notch under pure bending", International Journal of Solids and Structures, vol. 43, 459-474, 2006.
[19] H. M. Tlilan, A. S. Al-Shyyab, T. Darabseh, and T.Majima," Strain- Concentration Factor of Notched Cylindrical Austenitic stainless Steel Bar with Double Slant Circumferential U- Notches Under Static Tension". Jordan Journal of Mechanical and Industrial Engineering, vol. 1(2), 105-111, 2007.
[20] H. M. Tlilan, A. S. Al-Shyyab, A. M. Jawarneh, A. K. Ababneh, "Strainconcentration factor of circumferentially V-notched cylindrical bars under static tension". Journal of Mechanics, vol. 24 (4), 419-427, 2008.