17.1 Introduction

17.2 Case Study 1: Fast Fracture of an Ammonia Tank

Figure 17.1 shows part of a steel tank which came from a road tank vehicle. The tank consisted of a cylindrical shell about 6 m long. A hemispherical cap was welded to each end of the shell with a circumferential weld. The tank was used to transport liquid ammonia. In order to contain the liquid ammonia the pressure had to be equal to the saturation pressure (the pressure at which a mixture of liquid and vapor is in equilibrium). The saturation pressure increases rapidly with temperature: at 20°C the absolute pressure is 8.57 bar; at 50°C it is 20.33 bar. The gauge pressure at 50°C is 19.33 bar, or 1.9MN m^-2. Because of this the tank had to function as a pressure vessel. The maximum operating pressure was 2.07MN m^-2 gauge. This allowed the tank to be used safely to 50°C, above the maximum temperature expected in even a hot climate.

While liquid was being unloaded from the tank a fast fracture occurred in one of the circumferential welds and the cap was blown off the end of the shell. In order to decant the liquid the space above the liquid had been pressurized with ammonia gas using a compressor. The normal operating pressure of the compressor was 1.83MN m^-2; the maximum pressure (set by a safety valve) was 2.07MN m^-2. One can imagine the effect on nearby people of this explosive discharge of a large volume of highly toxic vapor.

Details of the failure

The geometry of the failure is shown in Figure 17.2. The initial crack, 2.5 mm deep, had formed in the heat-affected zone between the shell and the circumferential weld. The defect went some way around the circumference of the vessel. The cracking was intergranular, and had occurred by a process called stress corrosion cracking (see Chapter 27). The final fast fracture occurred by transgranular cleavage (see Chapter 15). This indicates that the heat-affected zone must have had a very low fracture toughness. In this case study we predict the critical crack size for fast fracture using the fast fracture equation.

Calculation of critical stress for fast fracture

The longitudinal stress σ in the wall of a cylindrical pressure vessel containing gas at pressure p is given by

σ=pr2t

provided that the wall is thin (t ≪ r) (see Example 7.5). p = 1.83 MN m^-2, r = 1067 mm, and t = 7 mm, so σ = 140 MN m^-2. The fast fracture equation is

Yσπa=Kc

Figure 17.3 shows that Y = 1.92 for our crack. The critical stress for fast fracture is given by

σ=KcYπa=391.92π×0.0025=229MNm–2

The critical stress is 64% greater than the longitudinal stress. However, the change in section from a cylinder to a sphere produces something akin to a stress concentration; when this is taken into account the failure is accurately predicted.

17.3 Case Study 2: Explosion of a Perspex Pressure Window during Hydrostatic Testing

Figure 17.4 shows the general arrangement drawing for an experimental rig, which is designed for studying the propagation of buckling in externally pressurized tubes. A long open-ended tubular specimen is placed on the horizontal axis of the rig with the ends emerging through pressure seals. The rig is partially filled with water and the space above the water is filled with nitrogen. The nitrogen is pressurized until buckling propagates along the length of the specimen.

The volumes of water and nitrogen in the rig can be adjusted to give stable buckling propagation. Halfway along the rig is a flanged perspex connector which allows the propagation of the buckle to be observed directly using a high-speed camera. Unfortunately, this perspex window exploded during the first hydrostatic test at a pressure of only one-half of the specified hydrostatic test pressure.

Failure analysis

Figure 17.5 is a photograph of the perspex connector taken after the explosion. Detailed visual inspection of the fracture surface indicated that the fracture initiated as a hoop stress tensile failure in the cylindrical portion and subsequently propagated toward each flange.

The hoop stress σ in the cylindrical portion can be calculated from the standard result for thick-walled tubes

σ=pbr2a2+r2a2–b2

where p is the internal gauge pressure and r is the radius at which the stress is calculated. The hoop stress is a maximum at the bore of the tube, with r = b and

σ=pa2+b2a2–b2=2.13p

The hoop stress is a minimum at the external surface of the tube, with r = a and

σ=p2b2a2–b2=1.13p.

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We can see that the most probable site for failure initiation is the bore of the tube: the hoop stress here is calculated to be 10 MN m^-2 at the failure pressure. This is only one-sixth of the minimum tensile strength. Using the fast fracture equation

Kc=Yσπa,Y≈1

with a fracture toughness of 1 MN m^-3/2 and a hoop stress of 10 MN m^-2 gives a critical defect size a of 3.2 mm at the failure pressure. At the operating pressure the critical defect size would only be 1.5 mm. A defect of this size would be difficult to find under production conditions in such a large volume. In addition, it would be easy to introduce longitudinal scratches in the bore of the connector during routine handling and use.

17.4 Case Study 3: Cracking of a Foam Jacket on a Liquid Methane Tank

Figure 17.6 is a schematic half-section through a tank used for storing liquid methane at atmospheric pressure. Because methane boils at –162°C, the tank is made from an aluminum alloy in order to avoid any risk of brittle failure. Even so, it is necessary to have a second line of defense should the tank spring a leak. This is achieved by placing the tank into a mild-steel jacket, and inserting a layer of thermal insulation into the space between the two. The jacket is thereby protected from the cooling effect of the methane, and the temperature of the steel is kept above the ductile-to-brittle transition temperature. But what happens if the tank does spring a leak? If the insulation is porous (e.g., fiberglass matting) then the liquid methane will flow through the insulation to the wall of the jacket and will boil off.