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.

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
.
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