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Creep and Creep Fracture

Publisher Summary

Many structures—particularly those that are associated with energy conversion (e.g., turbines, reactors, steam, and chemical plant)—operate at much higher temperatures. At room temperature, most metals and ceramics deform in a way that depends on stress but which, for practical purposes, is independent of time. As the temperature is raised, loads that give no permanent deformation at room temperature cause materials to creep. Creep is slow, continuous deformation with time: the strain, instead of depending only on the stress, then depends on temperature and time as well. Most metals and ceramics have high melting points and, because of this, they start to creep only at temperatures well above room temperature. In design against creep, those materials and the shape are selected that will carry the design loads, without failure, for the design life at the design temperature. The meaning of “failure” depends on the application. Creep tests require careful temperature control. The chapter concludes with a discussion of creep-resistant materials.

21.1 Introduction

So far we have concentrated on mechanical properties at room temperature. Many structures—particularly those that are associated with energy conversion (e.g., turbines, reactors, steam, and chemical plant)—operate at much higher temperatures.

At room temperature, most metals and ceramics deform in a way that depends on stress but which, for practical purposes, is independent of time:

ɛ=f(σ)elastic/plastic solid

As the temperature is raised, loads that give no permanent deformation at room temperature cause materials to creep. Creep is slow, continuous deformation with time: the strain, instead of depending only on the stress, now depends on temperature and time as well:

ɛ=f(σ,t,T)creeping solid

It is common to refer to the former behavior as “low-temperature” behavior, and the latter as “high temperature.” But what is a “low” temperature and what is a “high” temperature? Tungsten, used for lamp filaments, has a very high melting point—well over 3000°C. Room temperature, for tungsten, is a very low temperature. If made hot enough, however, tungsten will creep—that is the reason that lamps ultimately burn out. Tungsten lamps run at about 2000°C—this, for tungsten, is a high temperature. If you examine a lamp filament that has failed, you will see that it has sagged under its own weight until the turns of the coil have touched—that is, it has deformed by creep. Figure 21.1 shows a typical example of a sagging filament.

f21-01-9780081020517 — Figure 21.1 A tungsten lamp filament which has sagged under its own weight owing to creep.

Figure 21.2 and Table 21.1 give melting points for metals and ceramics and softening temperatures for polymers. Most metals and ceramics have high melting points and, because of this, they start to creep only at temperatures well above room temperature—this is why creep is a less familiar phenomenon than elastic or plastic deformation. But the metal lead, for instance, has a melting point of 600 K; room temperature, 300 K, is exactly half its absolute melting point. Room temperature for lead is a high temperature, and it creeps—as Figure 21.3 shows. And the ceramic ice melts at 0°C. Temperate glaciers (those close to 0°C) are at a temperature at which ice creeps rapidly—that is why glaciers move. Even the thickness of the Antarctic ice cap, which controls the levels of the earth’s oceans, is determined by the creep spreading of the ice at about –30°C.

f21-02-9780081020517 — Figure 21.2 Melting or softening temperature.

Table 21.1

Melting or Softening^(S) Temperature
Material	T(K)	Material	T(K)
Diamond, graphite	4000	Gold	1336
Tungsten alloys	3500–3683	Silver	1234
Tantalum alloys	2950–3269	Silica glass	1100^(S)
Silicon carbide, SiC	3110	Aluminum alloys	750–933
Magnesia, MgO	3073	Magnesium alloys	730–923
Molybdenum alloys	2750–2890	Soda glass	700–900^(S)
Niobium alloys	2650–2741	Zinc alloys	620–692
Beryllia, BeO	2700	Polyimides	580–630^(S)
Iridium	2682–2684	Lead alloys	450–601
Alumina, Al₂O₃	2323	Tin alloys	400–504
Silicon nitride, Si₃N₄	2173	Melamines	400–480^(S)
Chromium	2148	Polyesters	450–480^(S)
Zirconium alloys	2050–2125	Polycarbonates	400^(S)
Platinum	2042	Polyethylene, high-density	300^(S)
Titanium alloys	1770–1935	Polyethylene, low-density	360^(S)
Iron	1809	Foamed plastics, rigid	300–380^(S)
Carbon steels	1570–1800	Epoxy, general purpose	340–380^(S)
Cobalt alloys	1650–1768	Polystyrenes	370–380^(S)
Nickel alloys	1550–1726	Nylons	340–380^(S)
Cermets	1700	Polyurethane	365^(S)
Stainless steels	1660–1690	Acrylic	350^(S)
Silicon	1683	GFRP	340^(S)
Alkali halides	800–1600	CFRP	340^(S)
Beryllium alloys	1540–1551	Polypropylene	330^(S)
Uranium	1405	Ice	273
Copper alloys	1120–1356	Mercury	235

f21-03-9780081020517 — Figure 21.3 Lead pipes often creep noticeably over the years. (Source: M.F. Ashby.)

The point, then, is that the temperature at which materials start to creep depends on their melting point. As a general rule, it is found that creep starts when

T>0.3to0.4TMfor metalsT>0.4to0.5TMfor ceramics

where T_M is the melting temperature in degrees kelvin. However, special alloying procedures can raise the temperature at which creep becomes a problem.

Polymers, too, creep—many of them do so at room temperature. As we said in Chapter 5, most common polymers are not crystalline and have no well-defined melting point. For them, the important temperature is the glass temperature, T_G, at which the Van der Waals bonds solidify. Above this temperature, the polymer is in a leathery or rubbery state and creeps rapidly under load. Below, it becomes hard (and sometimes brittle) and, for practical purposes, no longer creeps. T_G is near room temperature for most polymers, so creep is a problem.

In design against creep, we select the material and the shape that will carry the design loads, without failure, for the design life at the design temperature. The meaning of “failure” depends on the application. We distinguish four types of failure, illustrated in Figure 21.4.

1. Displacement-limited applications, in which precise dimensions or small clearances must be maintained (as in the discs and blades of gas turbines).
2. Rupture-limited applications, in which dimensional tolerance is relatively unimportant, but fracture must be avoided (as in pressure-piping).
3. Stress relaxation-limited applications in which an initial tension relaxes with time (as in the pretensioning of bolts).
4. Buckling-limited applications, in which slender columns or panels carry compressive loads (as in structural steelwork exposed to a fire).

f21-04-9780081020517 — Figure 21.4 Creep is important in four classes of design: (a) displacement-limited, (b) failure-limited, (c) relaxation-limited, and (d) buckling-limited.

To analyze these we need constitutive equations which relate the strain-rate ɛ˙ or time-to-failure t_f to the stress σ and temperature T.

21.2 Creep Testing and Creep Curves

Creep tests require careful temperature control. Typically, a specimen is loaded in tension, usually at constant load, inside a furnace maintained at a constant temperature, T. The extension is measured as a function of time. Figure 21.5 shows a typical set of results from such a test. Metals, polymers, and ceramics all show creep curves of this shape.

f21-05-9780081020517 — Figure 21.5 Creep testing and creep curves.

Although the initial elastic and the primary creep strain cannot be neglected, they occur quickly, and they can be treated in much the way that elastic deflection is allowed for in a structure. But thereafter, the material enters steady state, or secondary creep, and the strain increases steadily with time. In designing against creep, it is usually this steady accumulation of strain with time that concerns us most.

By plotting the log of the steady creep rate, ɛ˙ss, against log σ at constant T, as shown in Figure 21.6, we can establish that