Metal Foams: A Design Guide

106 Metal Foams: A Design Guide
The primary creep regime is short. The extended period of secondary creep is
followed by tertiary creep, terminated by rupture. In compression, the behavior
is somewhat different. At the end of secondary creep, the strain rate initially
increases, but then subsequently decreases; the increase corresponds to localized
collapse of a layer of cells. Once complete, the remaining cells, which
have not yet reached the tertiary stage, continue to respond by secondary creep
at a rate intermediate to the initial secondary and tertiary rates.
For tensile specimens, the time to failure is defined as the time at which
catastrophic rupture occurs. For compression loading, the time to failure is
defined as the time at which the instantaneous strain rate is five times that for
secondary creep.
9.3 Models for the steady-state 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, Pε, ofafoamof
Ł relative density, / s, under a uniaxial stress, ,is:
Pε
Pε0
D 0.6
⊲n C 2⊳
� 1.7⊲2n C 1⊳
n
Ł
0
� n � s
Ł
� ⊲3nC1⊳/2
⊲9.3⊳
where Pε0, nand 0 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 D 1 and using appropriate values of Pε0 and 0 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 , the secondary, steady-state creep strain rate
of a closed-cell foam is given by:
⎧
⎫
⎪⎨
Pε
D
Pε0 ⎪⎩
1
1.7
� �1/n �
nC2 n
0.6 2nC1
Ł
/ 0
�� Ł �⊲3nC1⊳/2n s
C 2
⊲1 ⊳
3
Ł
s
⎪⎬
⎪⎭
n
⊲9.4⊳
When all the solid is in the edges ⊲ D1⊳ the equation reduces to equation (9.3).
But when the faces are flat and of uniform thickness ⊲ D 0⊳, it reduces