Metal Foams: A Design Guide

the net section stress criterion reads
Design for fatigue with metal foams 99
max,n D ⊲1 ⊲D/W⊳⊳ max,un ⊲8.3⊳
where the subscript n refers to notched, for a hole of diameter D, andthe
subscript un refers to un-notched specimens. It is reasonable to expect that
the net section stress criterion holds in compression–compression fatigue
since metal foams progressively shorten under compressive fatigue loading, as
Figure 8.4 showed. Notched fatigue data confirm this expectation, as shown
in Figure 8.8: aluminum foams are notch-insensitive, and the endurance limit
follows the net section stress criterion, given by equation (8.3).
Strength ratio, σmax,n/σmax,un [Notched/Unnotched]
1.2
1.0
0.8
0.6
0.4
0.2
Alporas, (11%) : W = 70 mm
Alulight, (24−42%) : W = 10 mm
Notch sensitive
0
0 0.2 0.4 0.6
D/W
Notch insensitive
W
D
∆σ
∆σ
0.8 1 1.2
Figure 8.8 Compression–compression notch fatigue strength of foams, at
infinite life; R D 0.1
Now consider a notched metallic foam under monotonic tension. Two types
of failure mechanism can be envisaged: ductile behavior, whereby plasticity in
the vicinity of the hole is sufficient to diffuse the elastic stress concentration
and lead to failure by a net section stress criterion, as given by equation (8.2).
Alternatively, a brittle crack can develop from the edge of the hole when the
local stress equals the tensile strength of the foam f ³ pl. In this case, a
notch-sensitive response is expected, and upon assuming a stress concentration
KT for the hole, we expect brittle failure to occur when the remote stress 1
satisfies
1 D pl/KT ⊲8.4⊳
The following fracture mechanics argument suggests that a transition hole
size Dt exists for the foam: for hole diameters D less than Dt the behavior is