Metal Foams: A Design Guide

Normalized effective stress
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
Alporas
8%
Uniaxial compression line
Alporas
13%
Alulight
16.5%
0.2 0.4 0.6 0.8 1 1.2
Normalized mean stress
A constitutive model for metal foams 83
Alulight
18%
Figure 7.1 Yield surfaces for Alporas and Duocel foams. The surfaces are
approximately elliptical, described by equations (7.11) and (7.12)
Plastic Poissons ratio, ν p
0.5
0.4
0.3
0.2
0.1
0
−0.1
Alporas, ρ = 16 %
Duocel, ρ = 7.0%
Alporas, ρ = 8.4 %
1.4
−0.2
0 0.5 1 1.5 2 2.5
Mean stress coefficient, α
Figure 7.2 The relationship between the plastic Poisson’s ratio P and the
constant ˛
plastic Poisson’s ratio in a uniaxial compression test: the ratio of transverse
strain to axial strain P depends upon ˛, as shown in Figure 7.2. Experimental
data, available for Alporas and Duocel foams, support this, (see Figure 7.2).
The yield surface shape (equations (7.11) and (7.12)) is sufficiently simple for
an analytical expression to be derivable for P in terms of ˛, giving
1 �˛ �2 P
D 2 3
�˛ �2 1 C
3
⊲7.13⊳