Metal Foams: A Design Guide

0.5
10−1 t
c
t
c
10 −2
0.5
10 −1
10 −2
a
10−2 10−1 0.5
c/
b
10 −2
1×10 −4
3×10−5
Face
yield
3×10 −4
Face
−5
F = 1×10 yield
3×10 −3
1×10 −3
Core
shear
Core shear
#1
1×10 −2
#2
Indentation
a a
= 0.005
= 0.1
Indentation
10−1 0.5
c/
Sandwich structures 121
Figure 10.6 (a) Collapse mechanism map for three-point bending, with
flat-bottom indenters. Contours of non-dimensional collapse load
F F/bℓ f
Y are plotted, with c/ℓ and t/c as axes. The map is drawn for the
c selected values Y / f
Y D 0.005 and a/ℓ D 0.1. (b) The effect of the size of the
indenter a/ℓ upon the relative dominance of the collapse mechanisms for
three-point bending
by plotting a non-dimensional measure of the collapse load F D F/bℓ f y on
a diagram with the non-dimensional axes c/ℓ and t/c, for selected values
c of a/ℓ and y / f y . An example is given in Figure 10.6(a) for the case of
c three-point bending, with a/ℓ D 0.1 and y / f y D 0.005. It is assumed that
the overhang H exceeds the transition value Ht so that core shear is by mode
B, as depicted in Figure 10.4. The regimes of dominance for each collapse
mechanism are marked: for example, it is clear that failure is by face yield for
thin face-sheets (small t/c) and long beams (small c/ℓ). The boundaries of the
indentation regime are sensitive to the value taken for a/ℓ: with diminishing
a/ℓ the magnitude of the indentation load drops and this regime enlarges
on the map, as illustrated in Figure 10.6(b). It is striking that the boundary
between the core shear and the indentation regimes has a large curvature,