Metal Foams: A Design Guide

Chapter 8
Design for fatigue with metal foams
In structural applications for metallic foams, such as in sandwich panels, it is
necessary to take into account the degradation of strength with cyclic loading.
A major cause of this degradation is the nucleation and growth of cracks
within the foams. In a closed-cell foam, the cell faces are subject to membrane
stresses while the cell edges bend predominantly. Consequently, crack initiation
and growth occurs first in the cell faces and then progresses into the
cell edges for a closed-cell foam. There is accumulating evidence that an
additional fatigue mechanism operates in the cyclic deformation of foams:
cyclic creep, also known as ratcheting, under a non-zero mean stress. When a
metallic alloy is subjected to cyclic loading with an accompanying non-zero
mean stress, the material progressively lengthens under a tensile mean stress,
and progressively shortens under a compressive mean stress. Consequently,
for a metallic foam, the cell walls progressively bend under a compressive
mean stress and progressively straighten under a tensile mean stress. This
leads to a high macroscopic ductility in compression, and to brittle fracture in
tension.
We shall show later in this chapter that a characteristic feature of metallic
foams is their high damage tolerance: the degradation in strength due to the
presence of a hole or crack in a foam is usually minor, and there is no need to
adopt a fracture mechanics approach. Instead, a design based on net section
stress usually suffices. A word of caution, however. It is expected that there
should be a critical crack size at which a transition from ductile to brittle
behavior occurs for tensile loading and tension–tension fatigue of a notched
panel. The precise value of the notch size for which the behavior switches has
not yet been determined, but is expected to be large.
8.1 Definition of fatigue terms
First, we need to define some standard fatigue terms. Consider a cylindrical
specimen loaded uniaxially by a stress, , which varies from a minimum
absolute value min to a maximum absolute value max, as shown in Figure 8.1.
For example, for a fatigue cycle ranging from 1MPa to 10 MPa, we take