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Review Article

Experimental Perspective on the Buckling of Pressure Vessel Components

[+] Author and Article Information
J. Błachut

Institute of Physics,
Cracow University of Technology,
ul. Podchorążych 1,
Kraków, 30-085Poland

Manuscript received August 18, 2013; final manuscript received November 14, 2013; published online December 30, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 66(1), 010803 (Dec 30, 2013) (24 pages) Paper No: AMR-13-1061; doi: 10.1115/1.4026067 History: Received August 18, 2013; Revised November 14, 2013

This review aims to complement a milestone monograph by Singer et al. (2002, Buckling Experiments—Experimental Methods in Buckling of Thin-Walled Structures, Wiley, New York). Practical aspects of load bearing capacity are discussed under the general umbrella of “buckling.” Plastic loads and burst pressures are included in addition to bifurcation and snap-through/collapse. The review concentrates on single and combined static stability of conical shells, cylinders, and their bowed out counterpart (axial compression and/or external pressure). Closed toroidal shells and domed ends onto pressure vessels subjected to internal and/or external pressures are also discussed. Domed ends include: torispheres, toricones, spherical caps, hemispheres, and ellipsoids. Most experiments have been carried in metals (mild steel, stainless steel, aluminum); however, details about hybrids (copper-steel-copper) and shells manufactured from carbon/glass fibers are included in the review. The existing concerns about geometric imperfections, uneven wall thickness, and influence of boundary conditions feature in reviewed research. They are supplemented by topics like imperfections in axial length of cylinders, imperfect load application, or erosion of the wall thickness. The latter topic tends to be more and more relevant due to ageing of vessels. While most experimentation has taken place on laboratory models, a small number of tests on full-scale models are also referenced.

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Neto, F. L., 1991, “The Behaviour of Externally Pressurised Composite Domes,” Ph.D. thesis, The University of Liverpool, Liverpool, UK.
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Błachut, J., 2013, “Externally Pressurized Toricones—Buckling Tests,” Shell Structures: Theory and Applications, Vol. 3, W.Pietraszkiewicz and J.Górski, eds., Taylor & Francis, London, pp. 183–186.
Healey, J. J., 1965, “Exploratory Tests of Two Prolate Spheroidal Shells Under External Hydrostatic Pressure,” David Taylor Model Basin Report No. 1868.
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EN 1993-1-6/Eurocode3, 2004, Design of Steel Structures, Part 1-6: Stability of Shell Structures, CEN, Belgium.
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Błachut, J., Galletly, G. D., and Moreton, D. N., 1990, “Buckling of Near-Perfect Steel Torispherical and Hemispherical Shells Subjected to External Pressure,” AIAA J., 28, pp. 1971–1975. [CrossRef]
Błachut, J., and Smith, P., 2007, “Tabu Search Optimization of Externally Pressurized Barrels and Domes,” Eng. Optim., 39, pp. 899–918. [CrossRef]
Smith, P., and Błachut, J., 2006, “Optimization of Externally Pressurised Domes Using Tabu Search,” Proceedings of the 6th ASMO-UK/ISSMO Internatioanl Conference on Engineering Design Optimization, Oxford, UK, July 3–4, pp. 111–119.
Smeltzer, S. S., and Bowman, L. M., 2002, “Buckling Design Studies of Inverted, Oblate Bulkheads for a Propellant Tank,” Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, April 22–25, Paper No. AIAA-2002-1525.
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Galletly, G. D., and Błachut, J., 1995, “Stability of Complete Circular and Non-Circular Toroidal Shells,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 209, pp. 245–255. [CrossRef]
Błachut, J., and Jaiswal, O. R., 1998, “Buckling of Imperfect Ellipsoids and Closed Toroids Subjected to External Pressure” PVP Vol. 368, Analysis and Design of Composite, Process, and Power Piping and Vessels, D. K.Williams, ed., ASME, New York, pp. 121–128.
Błachut, J., and Jaiswal, O. R., 1998, “Buckling Under External Pressure of Closed Toroids With Circular and Elliptical Cross Sections,” Advances in Civil and Structural Engineering Computing Practice, B. H. V.Topping, ed., Civil-Comp Press, Edinburgh, UK, pp. 323–334.
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Błachut, J., and Jaiswal, O. R., 2000, “On Buckling of Toroidal Shells Under External Pressure,” Comput. Struct., 77, pp. 233–251. [CrossRef]
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Błachut, J., 2002, “Collapse Tests on Externally Pressurised Toroids,” PVP Vol. 439, Pressure Vessel and Piping Codes and Standards, M. D.Rana, ed., ASME, New York, pp. 65–72.
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Aylward, R. W., and Galletly, G. D., 1979, “Elastic Buckling of, and, First Yielding, in Thin Torispherical Shells Subjected to Internal Pressure,” Int. J. Pressure Vessels Piping, 7, pp. 321–336. [CrossRef]
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Galletly, G. D., Błachut, J., and Moreton, D. N., 1990, “Internally Pressurized Machined Domed Ends—A Comparison of the Plastic Buckling Predictions of the Deformation and Flow Theories,” Proc. Inst. Mech. Eng., 204, pp. 169–186. [CrossRef]
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Figures

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Fig. 1

Cylinders with uneven length at the top end

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Fig. 2

Buckling response for axially compressed cylinders with various waviness of length

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Fig. 3

Combined stability plot for cylindrical shell (axial compression, F, versus external pressure, p) [67]

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Fig. 4

Load carrying capacity of equivalent barrels as a function of barrelling, Δ/Ro. Photographs of tested models at a, b, c, and d.

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Fig. 5

The magnitude of failure pressure for a shell generator described by generalized ellipse [76]. View of barrel's shape at bifurcation corresponding to pmax.

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Fig. 6

Plot of the cost function versus design vector components n1 = n2. Also, photograph of two tested barrels E1 and E1a [76].

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Fig. 7

Buckling strength of two-segment vessel versus the flange thickness [67]

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Fig. 8

Collapsed four-segment vessel [67]

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Fig. 9

Comparison of buckling loads with Bosor5 predictions [93]

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Fig. 10

View of machined cones: (a) β = 26 deg, (b) β = 14 deg, and (c) arrangement for combined loading. Adapted from Ref. [103].

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Fig. 11

Combined stability plots for β = 26 deg cones [106]. Loading paths shown in Fig. 11(a) while configurations given by the current Design Codes are superimposed in Fig. 11(b).

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Fig. 12

Combined stability plot for ten, β = 14 deg, cones [110]

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Fig. 13

Photographs of collapsed cones by external hydrostatic pressure (β = 26 deg for C6 model, β = 14 deg for CS6 model)

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Fig. 14

Geometry of inward, axisymmetric dimple imperfection [116]

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Fig. 15

The worst interactive stability plots for different imperfection profiles (a). Collapsed shapes at points a, b, and c [116].

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Fig. 16

Plot of buckling load versus shallowness parameter, λ. Also, view of collapsed cap and joining arrangements between the cap and integral base flange (adapted from Ref. [123]).

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Fig. 17

Safe and unsafe domains in PD 5500 code. Models 1A and 1C fall outside admissible geometry stipulated by PD 5500 (a). Test data for ten machined and two spun torispheres is plotted in (b) (pe=1.21Et2/Rs2 and pyss=2σypt/Rs) adapted from Ref. [138].

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Fig. 18

Various stages of manufacturing of a hemisphere to be externally pressurised ((a) and (b)). View of collapsed hemisphere (c).

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Fig. 19

Photographs of collapsed petal-welded and plain, nominally identical, torispheres

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Fig. 20

Female molding tool after the first ply being draped. Also, view of hemisphere after the collapse test.

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Fig. 21

Pattern of distorted fibers after draping (a). One quarter of draped fabric superimposed on the FE grid (b) [151].

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Fig. 22

View of cone T4 as machined (a), and after collapse (b). Buckled toricones T2 and T2a are seen in (c) and (d). External pressure in all cases.

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Fig. 23

View of collapsed ellipsoidal shells (adapted from Ref. [159]). External pressure.

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Fig. 24

Currently allowed and proposed ellipsoids (a), prolate and oblate geometries sketched in (b), (c), and view of three pairs of elliptical domes after tests (d)

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Fig. 25

Failure pressures of optimized generalized ellipsoids. Also shown is the failure of standard ellipsoids (ν1 = ν2 = 2.0). Points a, b, c, and d denote experiments (two tests per point) [166].

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Fig. 26

Bifurcation and collapse pressures for toroidal shell with circular cross-section and r/t = 18.74 [177]

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Fig. 27

Two spun halves prior to welding into TS1. Toroids TS1 and TS2 after collapse [177].

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Fig. 28

View of stainless steel toroidal shell, TE1 being lowered to pressure tank for testing (a), and the model after collapse (b) [177]

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Fig. 29

Comparison of computed plastic load pC1 with experimental values. Also, plot of experimental burst pressures. View of burst models K1, K2, and K6, adapted from Ref. [201].

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Fig. 30

History of plastic strains growth versus number of pressure cycles in steel torisphere T8 (a). Also views of burst oblate ellipsoidal models: (b) mild steel, and (c) aluminum (adapted from Ref. [206,207]).

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