### Strain – Concentration Factor of Notched Bars under Combined Loading

^{(*)}

*Corresponding author*

**DOI's assignment:**

*the author of the article can submit here a request for assignment of a DOI number to this resource!*

**Cost of the service: euros 10,00 (for a DOI)**

#### Abstract

This paper investigates the effect of notch depth and Poisson’s ratio on the elastic new Strain-Concentration Factor (SNCF) of rectangular bars with a single edge U-notch under combined loading. The new SNCF under combined loading of static tension and pure bending have been defined under triaxial stress state. The Finite Element Method (FEM) simulation and super-position technique are used to provide favorable results. The employed specimens have constant gross thickness of 16.7 (mm). The 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 new SNCF for combined loading increases as the notch depth increases up to ho/Ho = 0.7 and then the new SNCF sharply decreased for shallow notches in the range of 0.8 ≤ ho/Ho ≤ 0.95. Also, the elastic new SNCF of combined loading is greater than that of pure bending and less than that of the static tension for 0.2 ≤ ho/Ho ≤ 0.7and vice versa for shallow notches. Significantly, it is shown that the new SNCF influenced by the Poisson’s ratio, especially in the range 0.2 ≤ ho/Ho ≤ 0.85. On the other hand, the SNCF is nearly independent of the Poisson’s ratio for shallow notches (i.e. ho/Ho ≥ 0.90). *Copyright © 2014 Praise Worthy Prize - All rights reserved.*

#### Keywords

#### Full Text:

PDF#### References

A. J. Durelli, 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.

H. F. Hardrath, L. Ohman, A study of elastic and plastic stress concentration factors due to notches and fillets in flat plates, NACA Report, National Advisory Committee Aeronautics, no. 1117, 1953.

S.J. Hardy, M.K. Pipelzadeh, An assessment of the notch stress-strain conversion rules for short flat bars with projections subjected to axial and shear loading, J. Strain Analysis, Vol. 31, n. 2, pp. 91-110, 1996.

A. Kato, Design equation for stress concentration factors of notched strips and grooved shafts, J. strain analysis, Vol. 26, pp. 21-28, 1991.

M. M. Leven, 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.

T. Majima, Strain - concentration factor of circumferentially notched cylindrical bars under static tension, J. Strain Analysis, Vol. 34, n. 5, pp. 347-360, 1999.

K. Nishida, Stress Concentration (in Japanese) (Morikita Shuppan, Tokyo, 1974).

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.

N. -A. Noda, M. Sera, and Y. Takase, Stress concentration factors for round and flat test specimens with notches, Int. J. Fatiguem Vol. 17, no. 3, pp. 163-178, 1995.

K. Ogura, N. Miki, and K. Ohji, Finite element analysis of elastic-plastic stress and strain concentration factors under plane strain and axisymmetric conditions (in Japanese), Trans. Japan Soc. Mech. Engrs., Vol. 47 , pp. 55-62, 1981.

W.D. Pilkey, Peterson’s Stress Concentration Factors (Wiley, New York, 1997).

P.S. Theocaris, Experimental solution of elastic-plastic plane stress problems, J. Appl. Mechanics, Vol. 29, pp. 735-743, 1962.

P.S. Theocaris, E. Marketos, Elastic-plastic strain and stress distribution in notched plates under plane stress, J. Mech. Phys. Solids, Vol. 11, pp. 411- 428, 1963.

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.

H. M. Tlilan, N. Sakai, T. Majima, Strain-concentration factor of a single-edge notch under pure bending. (In Japanese) Yamanashi District Conference 040, n. 4, Japan, 2004.

H. M. Tlilan, N. Sakai, 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, n. 7, pp. 724-729, 2005.

H. M. Tlilan, S. Yousuke, 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, n. 3, pp. 406-416, 2005.

H. M. Tlilan, N. Sakai, T. Majima, Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending, International Journal of Solids and Structures, Vol. 43, 459–474, 2006.

H. M. Tlilan, A. S. Al-Shyyab, T. Darabseh, T.Majima, Strain-Concentration Factor of Notched Cylindrical Austenitic stainless Steel Bar with Double Slant Circumferential U- Notches Under Static Tension, Jordan J. of Mechanical and Industrial Engg., Vol. 1, n. 2, pp. 105-111, 2007.

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, J. of Mechanics, Vol. 24, n. 4, pp. 419-427, 2008.

H.M Tlilan, A.M Jawarneh, A.S Al-Shyyab, Strain-concentration factor of cylindrical bars with double circumferential U-notches under static tension, Jordan J. of Mechanical and Industrial Engg, Vol. 3,n. 2, pp. 97-104, 2009.

H. M .Tlilan, Effect of Poisson’s ratio on the elastic strain – concentration factor of notched bars under static tension under pure bending, Jordan J. of Mechanical and Industrial Engg, Vol. 4, n. 6, pp. 757-778, 2010.

I. Morris, P. O’Donnell, P. Delassus, T. McGloughlin, Experimental assessment of stress pattern in abdominal aortic aneurysms using the photoelastic method, Strain, Vol. 40, pp. 165-172, 2001.

A. J Durelli, W. F, Riley,Introduction to photo mechanics. (Prentice-Hall, Englewood Cliffs, New Jersey, 1965).

Y. Peishi, G. Wanlin, S. Chongmin, Z. Junhua, The influence of Poisson’s ratio on thickness-dependent stress concentration at elliptic holes in elastic plates, International J. of Fatigue, Vol. 30, pp. 165–171, 2008.

N. Partaukas, J. Bareišis, Poisson’s ratios influence on strength and stiffness of cylindrical bars, Mechanika, Vol. 17, n. 2, pp. 132-138, 2011.

J. F. Shackelford, Introduction to material science for engineers, (Prentice-Hall, Englewood Cliffs, New Jersey, 1996).

R. J. Grant, M. Lorenzo. J. Smart, The effect of Poisson’s ratio on stress concentrations, J. Strain Analysis, Vol., 42, pp. 95-104, 2007.

### Refbacks

- There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com**Copyright © 2005-2024**** Praise Worthy Prize**