## 93 Models for the steadystate creep of foams

Open-cell foams respond to stress by bending of the cell edges. If the material of the edges obeys power-law creep, then the creep response of the foam can be related to the creep deflection rate of a beam under a constant load. The analysis is described by Gibson and Ashby (1997) and Andrews et al. (1999). The result for the secondary, steady-state creep strain rate, ¿, of a foam of relative density, p*/ps, under a uniaxial stress, a, is:

¿o (n + 2) V n oo where ¿0, n and a0 are the values for the solid metal (equation (9.1)). The creep response of the foam has the same activation energy, Q, and depends on stress to the same power, n, as the solid, although the applied stress levels are, of course, much lower. Note that the secondary strain rate is highly sensitive to the relative density of the foam. Note also that this equation can also be used to describe the response of the foam in the diffusional flow regime, by substituting n = 1 and using appropriate values of ¿0 and a0 for the solid.

Closed-cell foams are more complicated: in addition to the bending of the edges of the cells there is also stretching of the cell faces. Setting the volume fraction of solid in the edges to 0, the secondary, steady-state creep strain rate of a closed-cell foam is given by:

When all the solid is in the edges (0 = 1) the equation reduces to equation (9.3). But when the faces are flat and of uniform thickness (0 = 0), it reduces n instead to:

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