In pressure vessel technology or nuclear power plants, some of the mechanical components are often subjected to rapid heating. If the temperature gradient during such process is high enough, thermoelastoplastic stresses may be developed in the components. These plastic deformations are permanent and may result in the incremental deformation of the structure in the long term. Accordingly, determination of thermoelastoplastic stresses during this process is an important factor in design. In this paper, a thick-walled cylinder of nonlinear strain hardening is considered for the thermoelastoplastic analysis. The properties of the material are assumed to be temperature dependent. The cylinder is subject to rapid heating of the inside surface while the outside surface is kept at the room temperature. A quasi-static and uncoupled thermoelastoplastic analysis based on incremental theory of plasticity is developed and a numerical procedure for successive elastic approximation is presented. The thermoelastoplastic stresses developed during this process are also presented. The effect of strain hardening and temperature dependency of material on the results are investigated.

1.
Boyer
J. C.
, and
Boivin
M.
, “
Numerical Calculations of Relaxation in Quenched Plates
,”
Material Science and Technology
, October
1985
, Vol.
1
, pp.
786
792
.
2.
Bonder
S. R.
, and
Partom
Y.
, “
A Large Deformation Elastic-Viscoplastic Analysis of Thick-Walled Spherical Shell
,”
ASME Journal of Applied Mechanics
, Vol.
39
,
1972
, pp.
751
757
.
3.
Chu
S.
, “
A Numerical Thermoelastoplastic Solution of a Thick-Walled Tube
,”
AIAA Journal
, Vol.
12
, No.
2
,
1974
, pp.
176
179
.
4.
Carslaw, H. S., and Jeager, J. C., Conduction of Heat In Solids, Second Edition, 1980, Oxford University Press.
5.
Dastidar
D. G.
, and
Ghosh
P.
, “
A Transient Thermal Problem: A Hollow Sphere of Strain Hardening Material With Temperature Dependent Properties
,”
International Journal of Mechanical Science
, Vol.
16
, pp.
359
371
,
1974
.
6.
Fletcher, A. J., and Lewis, C., “Effect of Free Edge on Thermal Stresses in Quenched Steel Plates,” Material Science and Technology, Oct 1985, pp. 750–752.
7.
Grossmann, M. A., Element of Hardenability, 1952, American Society for Metals, Cleveland, Ohio.
8.
Hwang, C., “Thermal Stresses in an Elastic, Work-Hardening Sphere,” ASME Journal of Applied Mechanics, Dec 1960, pp. 629–634.
9.
Gachkevich
A. R.
, and
Ya Boinchuck
V.
, “
Thermal Stress of A Long Cylinder Heated By Thermal Radiation
,”
Soviet Applied Mechanics
, Vol.
23
, No.
4
, Apr.
1987
, pp.
328
332
.
10.
Ishikawa
H.
, “
Transient Thermoelastoplastic Stress Analysis for a Hollow Sphere Using Incremental Theory of Plasticity
,”
International Journal of Solids and Structures
, Vol.
13
, pp.
645
655
,
1977
.
11.
Ishikawa
H.
, “
A Thermoelastoplastic Solution for a Circular Solid Cylinder—Subjected to Heating and Cooling
,”
Journal of Thermal Stresses
, Vol.
1
, pp.
211
222
,
1978
.
12.
Ishikawa
H.
, and
Hata
K.
, “
Thermoelastoplastic Creep Stress Analysis For A Thick-Walled Tube
,”
International Journal of Solid and Structures
, Vol.
16
, pp.
291
299
,
1980
.
13.
Ishikwa
H.
,
Sugawara
Y.
, and
Hata
K.
, “
Thermoelastoplastic Stress Analysis During Phase Transformation
,”
Journal of Thermal Stresses
, Vol.
6
, pp.
365
377
,
1983
.
14.
Jahanian
S.
, and
Sabbaghian
M.
, “
Thermoelastoplastic and Residual Stresses in a Hollow Cylinder with Temperature-Dependent Properties
,”
Journal of Pressure Vessel Technology
, Feb.
1990
, Vol.
112
, pp.
85
91
.
15.
Jahanian
S.
, and
Sabbaghian
M.
, “
Residual Stress in a Hollow Cylinder Due to Rapid Cooling of Casting
,”
Design and Analysis of Piping, Pressure Vessels, and Components
, PVP-Vol.
120
,
1986
, pp.
155
164
.
16.
Jahanian
S.
, “
Plastic Deformation of a Thick-Walled Circular Cylinder With Temperature Dependent Properties Under Transient Heating and Combined Axial and Torsion Load
,”
Reliability, Stress Analysis, and Failure Prevention Aspects of Composite And Active Materials
DE-Vol.
79
,
1994
, pp.
55
62
.
17.
Jahanian
S.
, “
Determination of Residual Stress Distribution in Sensitive and Insensitive Materials
,”
Reliability, Stress Analysis, and Failure Prevention
, DE-Vol.
55
1993
, pp.
179
183
.
18.
Jeanmart
P.
, and
Bouvaist
J.
, “
Finite Element Calculation and Measurement of Thermal Stresses in Quenched Plates of High-Strength 7075 Aluminum Alloy
,”
Material Science and Technology
, October
1985
, Vol.
1
, pp.
765
769
.
19.
Kabasko
N. I.
, “
Increasing The Service Life of Machine Parts and Tools By Intensification of Cooling of Them in Quenching
,”
Metal Science and Heat Treatment
, Vol.
28
, No.
9/10
, Sept/Oct
1986
, pp.
758
764
.
20.
Kim
K. T.
, “
Thermoelastoplastic Expansion of a Strain Hardening Hollow Sphere
,”
Journal of Thermal Stresses
, Vol.
12
, pp.
107
123
,
1989
.
21.
Landu
H. G.
, and
Weiner
J. H.
, “
Stresses in an Elastic-Plastic Cylinder Due to a Dialatational Phase Transformation
,”
ASME Journal of Applied Mechanics
, Ser E.
31
,
1964
, pp.
148
150
.
22.
Landu, H. G., and Zwicky, E. E., Jr “Transient and Residual Thermal Stress in an Elastic-Plastic Cylinder,” ASME Journal of Applied Mechanics, Sept 1960, pp. 481–488.
23.
Li
Y. Y.
, and
Chen
Y.
, “
Modeling Quenching to Predict Residual Stress and Microstructure Distribution
,”
ASME Journal of Engineering Materials and Technology
, Oct
88
, Vol.
110
, pp.
372
379
.
24.
Mendelson, A., Plasticity: Theory and Application, McMillan Company, 1968.
25.
Mitter
M.
,
Rammerstorfer
F. G.
, and
Grundler
O.
, “
Discrepancies Between Calculated and Measured Residual Stresses in Quenched Pure Iron Cylinder
,”
Material Science and Technology
, October
1985
, Vol.
1
, pp.
793
797
.
26.
Ramberg, W., and Osgood, W. R., Description of Stress-Strain Curves by Three Parameters, NACA TN902, 1943.
27.
Rammerstorfer
F. G.
,
Fischer
D. F.
,
Mitter
W.
,
Bathe
K. J.
, and
Snyder
M. D.
, “
On Thermoelastoplastic Analysis of Heat Treatment Process Including Creep and Phase Transformation
,”
Computer & Structure
, Vol.
13
, pp.
771
779
,
1981
.
28.
Sachs
G.
, “
Der Nachweis Inneres Spannungen in Stangen Und Rohren
,”
Z. Metallkde
, Vol.
19
,
1927
, p.
352
352
.
29.
Sagar
V.
, and
Payne
D. J.
, “
Elasto-plastic Deformations of Thickwalled Circular Cylinders Under Transient Heating And Combined Axial Tension and Torsion Loads
,”
J. Mech. and Physics of Solids
,
1974
Vol.
22
, pp.
47
59
.
30.
Shevchenko
Y. N.
, and
Merzlyakov
V. A.
, “
Thermoelastoplastic Nonaxisymetric Deformation of Shells of Revolution
,”
Soviet Applied Mechanics
, Vol.
24
, No.
5
, Nov
1988
, pp.
469
477
.
31.
Shevchenko
Y. N.
,
Novikov
S. V.
, and
Galishin
A. Z.
, “
Determination of the Thermoelastoplastic Stress-Strain State of Cylinder Tubes With Corrugated Inserts
,”
Soviet Applied Mechanics
, Vol.
27
, No.
8
, Feb
1992
pp.
785
793
.
32.
Thomas
J. R.
,
Singh
J. P.
,
Tawil
H.
, and
Powers
L.
, “
Thermal Stresses in A Long Circular Cylinder Subjected To Sudden Cooling During Transient Convection Heating
,”
Journal of Thermal Stresses
, Vol.
8
,
1985
, pp.
249
260
.
33.
Tien
H. R.
, and
Richmond
O.
, “
Theory of Maximum Tensile Stresses in the Solidifying Shell of a Constrained Rectangular Casting
,”
ASME Journal of Applied. Mechanics
, Vol.
49
pp.
481
486
,
1982
.
34.
Weiner
J. H.
, and
Huddleston
J. V.
, “
Transient and Residual Stresses in Heat-Treated Cylinders
,”
ASME Journal of Applied Mechanics
, Vol.
26
March
1959
, pp.
31
39
.
35.
Weirzbinski
S.
, “
The Strain Hardening of Copper Carbon After Rapid Continuous Heating
,”
Physics of Metals and Metalography
, Vol.
59
, No.
6
,
1985
, pp.
148
153
.
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