A differential form of Neuber’s rule, originally proposed by M. Chaudonneret, has been formulated for a generic viscoplastic notch problem, making extensive use of suitably normalised stress, strain and time. It has been shown that the stress-strain history at the root of a notch in a viscoplastic body can be determined directly from the elastic response, provided far-field viscoplastic strains can be neglected. Neuber’s rule has also been applied to the more general cases of stress and strain concentration at notches under (i) nominal creep conditions (constant nominal stress) and (ii) stress relaxation (constant nominal strain). Predictions are in good agreement with results from finite element analyses. Stress and strain concentration factors have been observed to approach stationary values after long-time loading. The stationary stress concentration factor under stress relaxation falls below that under nominal creep conditions.

1.
Chaudonneret, M., “Calcul de concentrations de contrainte en elastoviscoplasticite´,” Thesis, ONERA Publication No. 78.1. (English translation ESA-TT 547.)
2.
Chaudonneret
M.
, and
Culie
J. P.
,
1985
, “
Adaptation of Neuber’s Theory to Stress Concentration in Viscoplasticity
,”
Rech. Ae´rosp.
Vol.
4
, pp.
33
40
.
3.
Ha¨rkega˚rd, G., and Stubstad, S., 1993, “Simplified Analysis of Elastic-Plastic Strain Concentration in Notched Components Under Cyclic Loading,” Fatigue Design, ESIS 16, Solin, J. et al., eds., Mechanical Engineering Publications, London, pp. 171–186.
4.
Hoffman
M.
, and
Seeger
T.
,
1985
, “
A Generalized Method for Estimating Multiaxial Elastic-Plastic Notch Stresses and Strains, Part 1: Theory, Part 2: Application and General Discussion
,”
ASME JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY
, Vol.
107
, Oct., pp. 250–254,
255
260
.
5.
Kurath, P., 1984, “Extension of the Local Strain Fatigue Analysis Concepts to Incorporate Time Dependent Deformation in Ti-6A1-4V at Room Temperature,” Diss., Dept. of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign.
6.
Kuwabara
K.
,
Nitta
A.
, and
Kitamura
T.
,
1985
, “
Crack Initiation Life at Notch Root Under the Transition of Creep Condition
,”
Engineering Fracture Mechanics
, Vol.
21
, No.
2
, pp.
229
237
.
7.
Moftakhar, A. A., 1992, “Localized Time-Independent and Time-Dependent Plasticity at Notches,” Diss., Dept. of Mechanical Engineering, University of Waterloo.
8.
Moftakhar, A., and Glinka, G., 1992, “Elastic-Plastic Stress-Strain Analysis Methods for Notched Bodies,” Theoretical Concepts and Numerical Analysis of Fatigue, Blom, A. J., and Beevers, C. J., eds., EMAS, Warley, U.K., 327–342.
9.
Moftakhar, A. A., Glinka, G., Scarth, D., and Kawa, D., 1994, “Multiaxial Stress-Strain Creep Analysis for Notches,” ASTM STP 1184, pp. 230–243.
10.
Neuber
H.
,
1961
, “
Theory of Stress Concentration for Shear Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law
,”
ASME Journal of Applied Mechanics
, Vol.
28
, Dec., pp.
544
550
.
11.
Nguyen, U. L., 1986, “The Determination of Strain Concentration Factors Under the Influence of Plasticity and Creep by Neuber’s Method,” Designing with High Temperature Materials, York, UK.
12.
Sharpe
W. N.
,
Yang
C. H.
, and
Tregoning
R. L.
,
1992
, “
An Evaluation of the Neuber and Glinka Relations for Monotonic Loading
,”
ASME Journal of Applied Mechanics
, Vol.
59
, June, pp.
S50–S60
S50–S60
.
13.
So̸rbo̸, S., and Ha¨rkega˚rd, G., 1994, “Evaluation of Approximate Methods for Elastic-Plastic Analysis of Notched Bodies,” Localized Damage III, Aliabadi, M. H., et al., eds., Computational Mechanics Publications, Southampton, pp. 471–478.
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