The condition of shakedown is examined for torispherical heads. The reason for using plastic analysis is to account for the strengthening that heads experience when subjected to internal pressure. Cyclic pressures are considered up to an allowable burst pressure that is based on the membrane stresses of the spherical part of the head. To simulate a proof test before service cycling, cases when the applied pressure is higher for the first cycle are also included. A definition of shakedown is used that places the limit of twice the yield strength on a fatigue stress parameter range that is defined in the paper. The equivalent stress and plastic strain ranges are calculated for ten head thickness-to-spherical radius ratios. From these data, shakedown pressures are obtained as fractions of the allowable burst pressure. By giving bounds for isotropic and kinematic strain-hardening models, the results are made independent from specific cyclic material behavior. It is also shown that if an elastic, geometrically linear algorithm is used, which is unable to account for the strengthening, the fatigue stress parameter range is overestimated for the thinner heads.

1.
ASME B&PV Code, 1995, American Society of Mechanical Engineers, New York, NY.
2.
ASME Criteria, 1969, “Criteria of the ASME Boiler and Pressure Vessel Code for Design by Analysis in Sections III and VIII, Division 2,” American Society of Mechanical Engineers, New York, NY.
3.
Findlay, G. E., and Spence, J., 1968, “Applying the Shakedown Concept to Pressure Vessel Design,” The Engineer, July 12, pp. 63–65.
4.
Findlay
G. E.
,
Moffat
D. G.
, and
Stanley
P.
,
1971
, “
Torispherical Drumheads: A Limit-Pressure and Shakedown Analysis
,”
Journal of Strain Analysis
, Vol.
6
, pp.
147
166
.
5.
Kalnins
A.
, and
Updike
D. P.
,
1996
, “
Analysis of Failure of a Torispherical Head Under Internal Pressure
,”
ASME PVP
-Vol.
338
-
1
, pp.
265
271
.
6.
Kalnins, A., and Rana, M. D., 1996, “A New Design Criterion Based on Pressure Testing of Torispherical Heads,” WRC Bulletin No. 414, Welding Research Council, New York, NY.
7.
Kalnins
A.
, and
Updike
D. P.
,
1997
, “
Effect of Hydrostatic Proof Test on Shakedown of Torispherical Heads Under Internal Pressure
,”
ASME PVP
-Vol.
353
, pp.
217
224
.
8.
Langer, B. F., 1962, “Design of Pressure Vessels for Low-Cycle Fatigue,” ASME Journal of Basic Engineering, Sept., pp. 389–402.
9.
Moreton
D. N.
, and
Moffat
D. G.
,
1991
, “
The Effect of Proof Testing on the Behavior of Two Stainless Steel Pressure Vessel Drumheads
,”
International Journal of Pressure Vessels & Piping
, Vol.
48
, pp.
321
330
.
10.
Updike, D. P., and Kalnins, A., 1991, “Elastic-Plastic Analysis of Shells of Revolution Under Axisymmetric Loading,” WRC Bulletin No. 364, pp. 47–56, Welding Research Council, New York, NY.
11.
Updike
D. P.
, and
Kalnins
A.
,
1994
, “
Burst by Tensile Plastic Instability of Vessels With Torispherical Heads
,”
ASME PVP
-Vol.
277
, pp.
89
94
.
12.
Swift
H. W.
,
1952
, “
Plastic Instability Under Plane Stress
,”
Journal of Mechanics and Physics of Solids
, Vol.
1
, p.
1
1
.
13.
Ziegler
H.
,
1959
, “
A Modification of Prager’s Hardening Rule
,”
Quarterly of Applied Mathematics
, Vol.
17
, pp.
55
60
.
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