69 Creep

(a) Isotropic solids

Materials creep when loaded at temperatures above 1/3 Tm (where Tm is the absolute melting point). It is convenient to characterize the creep of a material by its behavior under a tensile stress a, at a temperature Tm. Under these conditions the tensile strain-rate s is often found to vary as a power of the stress and exponentially with temperature:

where Q is an activation energy and R the gas constant. At constant temperature this becomes where ¿oCs-1), a0(N/m2) and n are creep constants.

The behavior of creeping components is summarized in Figure 6.8 which gives the deflection rate of a beam, the displacement rate of an indenter and the change in relative density of cylindrical and spherical pressure vessels in terms of the tensile creep constants.

(b) Metal foams

When foams are loaded in tension or compression the cell edges bend. When this dominates (as it usually does) the creep rate can be derived from the equation in the second box in Figure 6.8, with appropriate allowance for cell-edge geometry (see Chapter 9 for details). The resulting axial strain rate is given in the bottom box. The analogy between this and the equation in the top box suggests that the creep behavior of beams, plates tubes (and other structures) made of foam can be found from standard solutions for dense solids by replacing a0 by n + 2\1/n (

which, for large n(n > 3), is well approximated by






) Area A

Constitutive law

« - « o



V "S>

y." i


u -

Figure 6.8 Creep




Foam constitutive law

â 0.6

[1.7 (2"+1) si


âo (n+2)

t n soJ

Figure 6.8 Creep

This is correct for simple tension and compression, and a reasonable approximation for bending and torsion, but it breaks down for indentation and hydrostatic compression because volumetric creep-compression of the foam has been neglected.

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