Metal Foams: A Design Guide

138 Metal Foams: A Design Guide
Weight index, Y
1
0.1
0.002
Π = 10−4 εf = 0.007
Y
0.001
Inaccessible
domains
A
Face
yield
Global weight minimum
A
Core
yield
0.01
Stiffness index, X
Weight/stiffness
Y = 3.19 X 3/5
Figure 10.14 The relationship between X and Y showing the region
bounded by core and face yield
For specific conditions, the equality of (10.38) corresponds to a point on
the curve of weight versus stiffness (Figure 10.14) below which the elastic
predictions are no longer valid. For values of the stiffness index below this
point, weights in excess of the global minimum would be needed to ensure that
the beam remains elastic. Logarithmic axes have been used in Figure 10.14
to highlight the inadmissible range.
Analogous conditions exist for core yielding (equation 10.24(c)). The coefficient
B4 is defined such that the maximum shear stress in the core is P/⊲B4bc⊳,
and thus yielding occurs when
P>B4bc c y
0.1
⊲10.39⊳
This condition can also be written in terms of X for the case of the globally
optimized beams. Core yielding invalidates the results based on the elastic
optimization if
X � 1
48
� 1
�
B1
B4 ˛2B2
� 1/2 � P
bℓ c y
�� 5
Elastic wrinkling of the face sheets may also occur (equation (10.24b)).
⊲10.40⊳