Metal Foams: A Design Guide

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70 Metal Foams: A Design Guide
Plasticity
Crack
F
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F
F
F
F
t
Plastic hinge
F
F
F
C
1
1
2
4
8
8
16
Figure 6.3 Failure of beams and panels
Mf = ( σ∗ I
y
) (Onset)
m
M f = Hσ y (Full plasticity)
I σ
y )
m
∗
Ff = C ( (Onset)
CHs y
F f = (Full plasticity)
Mf = Failure moment (Nm)
Ff = Force at failure (N)
= Length (m)
t = Depth (m)
b = Width (m)
I = See Figure 6.1 (m4 )
I = See Figure 6.1 (m3 )
ym H = See Figure 6.1 (m3 )
sy = Yield strength (N/m2 )
sf = Modulus of rupture (N/m2 )
s∗ = σy (Plastic material)
= σf (Brittle material)
6.5 Buckling of columns, panels and shells
(a) Isotropic solids
If sufficiently slender, an elastic column, loaded in compression, fails by elastic
buckling at a critical load, Fcrit. This load is determined by the end constraints,
of which four extreme cases are illustrated in Figure 6.4: an end may be
constrained in a position and direction; it may be free to rotate but not translate
(or ‘sway’); it may sway without rotation; and it may both sway and rotate.
Pairs of these constraints applied to the ends of column lead to the cases shown
in the figure. Each is characterized by a value of the constant, n, whichis
equal to the number of half-wavelengths of the buckled shape.