Metal Foams: A Design Guide

122 Metal Foams: A Design Guide
with the indentation mechanism operating at a large values of t/c as well as
at small values. This is a consequence of plastic hinge formation within the
face sheets in the core shear collapse modes: the collapse load for core shear
increases quadratically with increasing t/c due to the contribution from face
sheet bending, as seen by examining the first term on the right-hand side of
relations (10.17) and (10.18). The contours of collapse load in Figure 10.6(b)
show that the load increases along the leading diagonal of the map, with
increasing c/ℓ and t/c.
A similar map can be constructed for four-point bending; this is illustrated
in Figure 10.7, for the same values a/ℓ D 0.1 and c y / f y
D 0.005 as for three-
point bending, but with the added parameter s/ℓ D 0.5. A comparison with the
map of Figure 10.6(a) reveals that the domain of face yield shrinks slightly for
four-point bending, and indentation almost disappears as a viable mechanism.
Core shear dominates the map for the values of parameters selected.
t
c
0.5
10 −1
3×10 −4
1×10 −3
1×10 −2
3×10 −3
2×10
Indentation
−2
10−2 10−1 10
0.5
−2
1×10
Face
Core
shear
yield
−4
F = 3×10−5 c/
Indentation
Figure 10.7 Collapse mechanism map for four-point bending, with
flat-bottom indenters. Contours of non-dimensional collapse load
F F/bℓ f y are plotted for the selected values c
y / f and s/ℓ D 0.5
y D 0.005, a/ℓ D 0.1
Now, some words of caution. The collapse mechanisms described neglect
elastic deformation and assume perfectly plastic behavior. Alternative failure
modes are expected when the face sheets are made of a monolithic ceramic
or composite layers, and behave in an elastic–brittle manner. Then, collapse
is dictated by fracture of the face sheets, as analysed by Shuaeib and Soden
(1997) and Soden (1996). The above treatment has been limited to the case
of flat-bottomed indenters. An alternative practical case is the loading of
sandwich beams by rollers, of radius R. This case is more complex because