The problem of providing an experimental basis for an isothermal theory of plasticity of metals at elevated temperatures has been examined. The key objectives are considered to be the establishment of a steady‐state function and the discovery of a nonsteady deformation law. Constant stress and constant strain rate are judged the best loading conditions for both of these tasks since they provide paths, under the simplest thermomechanical histories, to the steady‐state deformation. The use of plots of strain rate and its time derivative for constant stress tests and plots of stress and its time derivative for constant strain rate tests is advocated as a means of best displaying the transient nonsteady behavior. It is even suggested that the functions represented by such plots may be independent of the loading history prior to the period of constant stress or constant strain rate applications. Constant stress and constant strain rate tests are limited in the early (nonsteady) period by lack of control of structure on initial loading, and generally in the later period by the nonuniformity of deformation. It is suggested that the former difficulty may be overcome by employing loading rates sufficiently rapid to permit sensible constancy of structure. Nonuniformity of deformation imposes a severe restriction on the examination of steady‐state deformation.

1.
E. N. da C.
Andrade
,
Proc. Roy. Soc.
A84
,
1
(
1910
).
2.
C. W.
MacGregor
and
J. C.
Fisher
,
J. Appl. Mech.
12
,
A217
(
1945
).
3.
J.
Weertman
,
J. Mech. Phys. Solids
4
,
230
(
1956
).
4.
Although constant stress and constant strain rate appear to be the only isothermal conditions which lead to steady states, a test where both the stress and the strain rate are maintained constant by controlling the temperature is a nonisothermal possibility.
5.
F. Garofalo, O. Richmond, W. F. Domis, and F. v. Gemmingen, Proc. Joint Intern. Conf. Creep, Inst. Mech. Engrs. 1–31 (1963).
6.
J. F. Wilson and O. Richmond, Edgar C. Bain Laboratory PR 190.
7.
O. D.
Sherby
,
R.
Frenkel
,
J.
Nadeau
, and
J. E.
Dorn
,
Trans. AIME
200
,
275
(
1954
).
8.
In such a test the relationship between stress and strain rate would be established for a given structure. The coefficients in this relationship would then be macroscopic coefficients representing the structure, just as a measured yield stress can be said to represent the structure in simple strain hardening behavior or a measured viscosity can be said to represent the structure in simple viscous behavior.
9.
P.
Feltham
and
J. D.
Meakin
,
Acta Met.
7
,
614
(
1959
).
10.
F.
Garofalo
,
W. F.
Domis
, and
F. v.
Gemmingen
,
Trans. AIME
230
,
1460
(
1964
).
11.
E. N. da C.
Andrade
and
W. J. D.
Jones
,
Proc. Roy. Soc.
A269
,
1
(
1962
).
12.
J. T.
Barnby
,
JISI
204
,
23
(
1966
).
13.
P. W.
Bridgman
,
Trans. ASM
32
,
553
(
1944
).
14.
A. J.
Kennedy
,
Proc. Phys. Soc.
62B
,
501
(
1949
).
15.
T.
Hazlett
and
R. D.
Hansen
,
Trans. ASM
47
,
508
(
1955
).
16.
A material obeying a constitutive relation f(σ,σ̇ε̇,ε̈) = 0 evidently would give both a unique ε̇, ε̈ curve in constant stress tests independent of initial loading and a unique σ, σ̇ curve in constant strain rate tests. In a separate study at this laboratory, Dr. E. J. Appleby has shown that such a constitutive relation is one of the simplest possible models for elevated temperature behavior.
17.
D. G.
McVetty
,
Mech. Eng.
56
,
149
(
1934
).
18.
J. C. M.
Li
,
Acta Met.
11
,
1269
(
1963
).
19.
F.
Garofalo
,
Trans. AIME.
227
,
351
(
1963
).
20.
J.
Weertman
,
Trans. AIME
,
227
,
1476
(
1963
).
21.
C. R.
Barrett
and
W. D.
Nix
,
Acta Met.
13
,
1247
(
1965
).
22.
G. I.
Taylor
and
H.
Quinney
,
Proc. Roy. Soc.
A143
,
307
(
1934
).
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