Metal Foams: A Design Guide

100 Metal Foams: A Design Guide
ductile, with a notched tensile strength 1 given by equation (8.2). Alternatively,
for D greater than Dt the behavior is brittle, with 1 given by (8.4).
A simple micro-mechanical model of failure assumes that the plasticity and
tearing of the foam adjacent to the hole can be mimicked by a crack with a
constant tensile bridging stress of magnitude pl across its flanks, as illustrated
in Figure 8.9. This approach follows recent ideas on ‘large-scale bridging’
of composites, see, for example, the recent review by Bao and Suo (1992).
Assume that this bridging stress drops to zero when the crack flanks separate
by a critical value υ0. Measurementsofυ0 using deeply notched specimens
reveal that υ0 is approximately equal to the cell size ℓ for Alporas foam, and
we shall make this assumption. This physical picture of the tensile failure of
the notched panel is consistent with the notion that the foam has a long-crack
toughness of
Jc ³ plυ0 ⊲8.5⊳
and a tensile strength of pl. The transition size of hole, Dt, atwhichthe
notched strength drops smoothly from pl to a value of pl/3 is given by
Dt ³ Eℓ
⊲8.6⊳
Bridged
crack
pl
D
∆σ
σ pl
Figure 8.9 A bridge crack model for yielding and cracking adjacent to an
open hole
The transition hole size is plotted as a function of relative density for a
large number of aluminum foams in Figure 8.10. We note that Dt is large,
of the order of 1 m. This implies that, for practical problems, the net section
stress criterion suffices for notched tensile failure.
The effect of a notch on the tension–tension fatigue strength has not yet
been fully resolved. Experiments to date suggest that the net section stress