## 91 Introduction the creep of solid metals

Under constant load, at temperatures T above about one third of the melting temperature Tm, the deformation of metals increases with time t; the material is said to creep. The tensile response for a solid metal is shown schematically in Figure 9.1. There are three regimes: primary creep, secondary or steady-state creep and tertiary creep, corresponding, respectively, to decreasing, constant and increasing strain rate. The total creep strain accumulated during the primary regime is usually small compared with that of secondary creep; creep deflections are generally taken as the product of the secondary, steady-state strain rate and the time of loading. In the tertiary creep regime the creep rate accelerates, leading to tensile rupture; the time to failure is taken as the time at which rupture occurs. Engineering design may be limited by either excessive creep deflection or by the time to rupture.

The creep of a metallic foam depends on its relative density and on the creep properties of the solid from which it is made. The dominant mechanism of creep depends on stress and temperature. At low stresses and high temperatures (T/Tm > 0.8) diffusional flow along the grain boundaries (at low temperatures) or within the grains (at higher temperatures) can become the dominant mechanism; in this case the steady-state secondary creep rate varies linearly with the applied stress. At higher stresses and more modest temperatures (0.3 < T/Tm, < 0.8), climb-controled power-law creep becomes

Elastic

Figure 9.1 Schematic of creep strain response of a metal under constant load

Secondary

Elastic

Figure 9.1 Schematic of creep strain response of a metal under constant load dominant; the secondary creep rate, ¿, then depends on the stress, a, raised to a power n > 1:

Here n, a0 and Q are properties of the material (a0 is a reference stress and Q is the activation energy for the kinetic process controlling the rate of creep), A has the dimensions 1/second and R is the ideal gas constant (8.314 J/moleK). Typical values for n, a0 and Q for power-law creep of several solid metals are listed in Table 9.1.

The time to rupture for a solid metal can be found by assuming that failure is associated with a constant critical strain in the material so that the product

Table 9.1 Power law creep parameters for solid metals

Aluminum 4.4 0.12 142

Nickel 4.6 0.5 284

316 Stainless steel 7.9 33.5 270

where of the time to rupture and the secondary strain rate is a constant. The time to rupture, tr, would then be inversely proportional to the secondary strain rate. In practice, it is found that trSm » C

where C is a constant and m is an exponent with a value slightly less than one. Rearranging this expression gives the Monkman-Grant relationship:

Monkman and Grant found that 0.77 < m < 0.93 and -0.48 < log(C) < -1.3 for a number of alloys based on aluminum, copper, titanium, iron and nickel (Hertzberg, 1989).

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