Metal Foams: A Design Guide

78 Metal Foams: A Design Guide
6.9 Creep
(a) Isotropic solids
Materials creep when loaded at temperatures above 1/3Tm (where Tm is the
absolute melting point). It is convenient to characterize the creep of a material
by its behavior under a tensile stress ,atatemperatureTm. Under these
conditions the tensile strain-rate Pε is often found to vary as a power of the
stress and exponentially with temperature:
� �n Pε D A exp Q
RT
0
where Q is an activation energy and R the gas constant. At constant temperature
this becomes
� �n Pε DPε0
0
where Pε0⊲s 1 ⊳, 0⊲N/m 2 ⊳ 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 celledge
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 0 by
Ł
0 D
� �1/n �
n C 2
n
��
0.6 1.7⊲2n C 1⊳
s
� ⊲3nC1/2n⊳
which, for large n⊲n > 3⊳, is well approximated by
�
Ł 1
0 ³
2
s
� 3/2
0.
0