Elastic Strain-Concentration Factor of Notched Bars under Combined Loading of Static Tension and Pure Bending
The effect of notch depth on the elastic new strainconcentration
factor (SNCF) of rectangular bars with single edge Unotch
under combined loading is studied here. The finite element
method (FEM) and super position technique are used in the current
study. This new SNCF under combined loading of static tension and
pure bending has been defined under triaxial stress state. The
employed specimens have constant gross thickness of 16.7 mm and
net section thickness varied to give net-to-gross thickness ratio ho/Ho
from 0.2 to 0.95. The results indicated that the elastic SNCF for
combined loading increases with increasing notch depth up to ho/Ho =
0.7 and sharply decreases with increasing notch depth. It is also
indicated that the elastic SNCF of combined loading is greater than
that of pure bending and less than that of the static tension for 0.2 ≤
ho/Ho ≤ 0.7. However, the elastic SNCF of combined loading is the
elastic SNCF for static tension and less than that of pure bending for
shallow notches (i.e. 0.8 ≤ ho/Ho ≤ 0.95).
[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,
"Strain-concentration factor of circumferentially V-notched cylindrical
bars under static tension". Journal of Mechanics, vol. 24 (4), 419-427,
2008.
[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,
"Strain-concentration factor of circumferentially V-notched cylindrical
bars under static tension". Journal of Mechanics, vol. 24 (4), 419-427,
2008.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:57362", author = "Hitham M. Tlilan", title = "Elastic Strain-Concentration Factor of Notched Bars under Combined Loading of Static Tension and Pure Bending", abstract = "The effect of notch depth on the elastic new strainconcentration
factor (SNCF) of rectangular bars with single edge Unotch
under combined loading is studied here. The finite element
method (FEM) and super position technique are used in the current
study. This new SNCF under combined loading of static tension and
pure bending has been defined under triaxial stress state. The
employed specimens have constant gross thickness of 16.7 mm and
net section thickness varied to give net-to-gross thickness ratio ho/Ho
from 0.2 to 0.95. The results indicated that the elastic SNCF for
combined loading increases with increasing notch depth up to ho/Ho =
0.7 and sharply decreases with increasing notch depth. It is also
indicated that the elastic SNCF of combined loading is greater than
that of pure bending and less than that of the static tension for 0.2 ≤
ho/Ho ≤ 0.7. However, the elastic SNCF of combined loading is the
elastic SNCF for static tension and less than that of pure bending for
shallow notches (i.e. 0.8 ≤ ho/Ho ≤ 0.95).", keywords = "Bar, notch, strain, tension, bending", volume = "6", number = "4", pages = "820-4", }
