Limited Life of Shells of Revolution Subjected to Severe Local Bending

Abstract

Tests were performed on axially loaded expansion bellows in order to obtain the relationship between maximum strain, load and deflection in the plastic region. A numerical method, previously proposed by the authors, was also used to investigate the behaviour of the bellows. The experimental and calculated results were found to be in reasonable agreement.

The strains measured at collapse did not exceed three and a half times the strain at first yield while the strains after collapse were of a higher order of magnitude.

The bellows were finally tested to failure in the low-cycle regime. The results agreed with fatigue tests on the parent material.

A simple model based on the behaviour of the bending of a beam is proposed for predicting the strains in a shell of revolution with severe local bending. This model is used to classify the types of loading which lead to different modes of failure in the plastic region. The proposed design procedures are then used in case studies of the limited-life design of bellows and pipe bends, and comparison made with the observed fatigue lives.

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References

Benham

P. P.

‘Fatigue of metals caused by a relatively few cycles of high load or strain amplitude’, Metallurgical Reviews 1958 3 (No. 11), 203.

Yao

J. T. P.

Munse

W. H.

‘Low cycle fatigue of metals—literature review’, Welding Research Supplement 1962 41 (No. 4), 182S.

Gross

M. R.

‘Low-cycle fatigue of materials for submarine construction’, Soc. automot. Engrs 1963, 690B.

Gross

J. H.

Gucer

D. E.

Stout

R. D.

‘The plastic fatigue strength of pressure vessel steels’, Weld J. 1954 33, 31S.

Kooistra

L. F.

‘Effect of plastic fatigue on pressure vessel materials and design’, Weld. J. 1957 36, 120S.

Langer

B. F.

‘Design of pressure vessels for low cycle fatigue’, Trans. Amer. Soc. mech. Engrs 1962 84D, 389.

Mendelson

Manson

S. S.

‘Practical solution of plastic deformation problems in elastic-plastic range’, Nat. aero. space Admin. R-28, 1959.

Marcal

P. V.

Turner

C. E.

‘Numerical analysis of the elastic-plastic behaviour of axisymmetrically loaded shells of revolution’, J. mech. Engng Sci. 1963 5 (No. 3), 232.

Kooistra

L. F.

Lemcoe

M. M.

‘Low cycle fatigue research on full-size pressure vessels’, Weld. J. 1962, 297S.

10.

Kooistra

L. F.

Lange

E. A.

Pickett

A. G.

‘Full size pressure vessel testing and its application to design’, J. Eng. Power 1964 (October), 419.

11.

Samans

Blumberg

‘Endurance testing of expansion joints’, Amer. Soc. mech Engrs paper 54/A/103, 1954.

12.

Lane

P. H. R.

‘Fatigue tests on seamless mild-steel pipe bends’, Proc. Int. Conf. Fatigue of Metals 1956, 687 (Institution of Mechanical Engineers, London).

13.

Markl

A. R. C.

‘Fatigue tests of welding elbows and comparable double-mitre bends’, Trans. Amer. Soc. mech. Engrs 1947 69, 869.

14.

Markl

A. R. C.

‘Fatigue tests of piping components’, Trans. Amer. Soc. mech. Engrs 1952 74, 287.

15.

Turner

E. C.

Ford

‘Stress and deflection studies of pipeline expansion bellows’, Proc. Instn mech. Engrs, Lond. 1957 171, 526 (see also Ph.D. thesis, C. E. Turner, 1954, University of London).

16.

Turner

C. E.

‘Stress and deflection studies of flat-plate and toroidal expansion bellows, subjected to axial, eccentric or internal pressure loading’, J. mech. Engng Sci. 1959 1 (No. 2), 130.

17.

Morgan

Bizon

‘Experimental evaluation of theoretical elastic stress distribution for cylinder to hemisphere and cone to sphere junction in pressurized shell structures’, Nat. aero, space Admin. Tech. Note D-1565, February 1963.

18.

Turner

C. E.

‘Study of the symmetrical elastic loading of some shells of revolution, with special reference to toroidal elements’, J. mech. Engng Sci. 1959 1 (No. 2), 113.

19.

Gross

Ford

‘Flexibility of short-radius pipe-bends’, Proc. Instn mech. Engrs, Lond. 1952–53 1B (No. 10), 480.

20.

Edmunds

H. G.

Beer

F. J.

‘Notes on incremental collapse in pressure vessels’, J. mech. Engng Sci. 1961 3 (No. 3), 187.

21.

Coffin

L. F.

‘A study of the effects of cyclic thermal stresses in ductile metals’, Trans. Amer. Soc. mech. Engrs 1954 76, 931.

22.

Benham

P. P.

Ford

‘Low endurance fatigue of a mild steel and an aluminium alloy’, J. mech. Engng Sci. 1961 3 (No. 2), 119 (see also Ph.D. thesis, P. P. Benham, 1960, University of London).