The displacement field at the minimum cross section of an axisymmetrical notched tensile bar is analytically related to the notch root radius for large geometry changes of the notch profile. This relationship is used to complete Bridgman’s formula for the tensile load of a tensile necking in order to predict the entire load-minimum diameter curve of an axisymmetrical blunt notched bar under tension. A particular case is solved by a finite element modeling to check the theoretical results derived at different stages of the analysis.
Issue Section:
Technical Papers
1.
Bridgman
, P. W.
, 1944
, “The Stress Distribution at the Neck of a Tension Specimen
,” Trans. ASME
, 32
, pp. 553
–574
.2.
Bridgman, P. W., 1964, Studies in Large Plastic Flow and Fracture, Harvard University Press, Cambridge, MA.
3.
Davidenkov
, N. N.
, and Spiridonova
, N. I.
, 1946
, “Analysis of Tensile Stress in the Neck of an Elongated Test Specimen
,” Proc. A. S. T. M.
46
, pp. 1147
–1158
.4.
Kaplan
, A. M.
, 1973
, “The Stress and Deformation in Mild Steel During Axisymmetric Necking
,” ASME J. Appl. Mech.
, 40
, pp. 271
–276
.5.
Jones
, S. E.
, Gillis
, P. P.
, and Shalaby
, A. H.
, 1979
, “Stress Distributions in the Vicinity of a Neck
,” J. Appl. Phys.
, 50
, No. 5
, pp. 3168
–3173
.6.
Eisenberg
, M. A.
, and Yen
, C. F.
, 1983
, “An Anisotropic Generalization of the Bridgman Analysis of Tensile Necking
,” J. Eng. Mater. Technol.
, 105
, pp. 264
–267
.7.
Hancock
, J. W.
, and Mackenzie
, A. C.
, 1976
, “On the Mechanisms of Ductile Fracture in High Strength Steels Subjected to Multiaxial Stress States
,” J. Mech. Phys. Solids
, 24
, pp. 147
–169
.8.
Mackenzie
, A. C.
, Hancock
, J. W.
, and Brown
, D. K.
, 1977
, “On the Influence of State of Stress on Ductile Failure Initiation in High Strength Steels
,” Eng. Fract. Mech.
, 9
, pp. 167
–188
.9.
Ritchie
, R. O.
, Server
, W. L.
, and Wullaert
, R. A.
, 1979
, “Critical Fracture Stress and Fracture Strain Models for the Prediction of Lower and Upper Shelf Toughness in Nuclear Pressure Vessels Steels
,” Met. Trans.
, 10A
, pp. 1557
–1570
.10.
Chaouadi
, R.
, De Meester
, P.
, and Vandermeulen
, W.
, 1994
, “Damage Work as Ductile Fracture Criterion
,” Int. J. Fract.
, 66
, pp. 155
–164
.11.
Amar
, E.
, and Pineau
, A.
, 1985
, “An Interpretation of Ductile Fracture Toughness Temperature Dependence of a Low Strength Steel in Terms of a Local Approach
,” Eng. Fract. Mech.
, 22
, pp. 1061
–1071
.12.
Fontaine, A., and Jeunehomme, S., 1989, “Numerical Study and Local Approach of Fracture in a Perlitic Steel,” Advances in Fracture Research (ICF7), Pergamon Press, Oxford, UK, pp. 3865–3871.
13.
Moran
, B.
, and Norris
, M. D.
, 1978
, “Computer Simulation of the Round Notched Tension Test of Cox and Low
,” Met. Trans.
, 9A
, pp. 1685
–1687
.14.
Hancock
, J. W.
, and Brown
, D. K.
, 1983
, “On the Role of Strain and Stress State in Ductile Failure
,” J. Mech. Phys. Solids
, 31
, pp. 1
–24
.15.
Valiente
, A.
, and Lapen˜a
, J.
, 1996
, “Measurement of the Yield and Tensile Strength of Neutron Irradiated and Post-Irradiation Recovered Vessel Steels With Notched Specimens
,” Nucl. Eng. Des.
, 167
, pp. 11
–22
.Copyright © 2001
by ASME
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