Metal Foams: A Design Guide

Characterization methods 33
ž Proportional axisymmetric stress paths are explored in the following way.
The direction of stressing is defined by the relation m D e, with the
D (for uniaxial compression)
3
1
parameter taking values over the range
to D1(for hydrostatic compression). In a typical proportional loading
experiment, the hydrostatic pressure and the axial load are increased in
small increments keeping constant. The axial displacement are measured
at each load increment and are used to define the axial strain.
Yield surface measurements
The initial yield surface for the foam is determined by probing each specimen
through the stress path sketched in Figure 3.7. First, the specimen is pressurized
until the offset axial plastic strain is 0.3%. This pressure is taken as
the yield strength under hydrostatic loading. The pressure is then decreased
slightly and an axial displacement is applied until the offset axial strain has
incremented by 0.3%. The axial load is then removed and the pressure is
decreased further, and the procedure is repeated. This probing procedure is
continued until the pressure p is reduced to zero; in this limit the stress state
consists of uniaxial compressive axial stress. The locus of yield points, defined
at 0.3% offset axial strain, are plotted in mean stress-effective stress space.
In order to measure the evolution of the yield surface under uniaxial loading,
the initial yield surface is probed as described above. The specimen is then
compressed uniaxially to a desired level of axial strain and the axial load is
removed; the yield surface is then re-probed. By repetition of this technique,
the evolution of the yield surface under uniaxial loading is measured at a
σ e
8
6
3
0 7 5 4 2 1
− σ m
Uniaxial compression
Line (sm = −
1
s
3
e)
Figure 3.7 Probing of the yield surface. In the example shown, the
specimen is taken through the sequence of loading states 0,1,2,3,4,5,6,7,0,8.
The final loading segment 0 ! 8 corresponds to uniaxial compression