Metal Foams: A Design Guide

90 Metal Foams: A Design Guide
steels have an S–N curve with a sharp knee below which life is infinite; the
corresponding stress range is designated the fatigue limit. This knee is less
pronounced for aluminum alloys, and it is usual to assume that ‘infinite life’
corresponds to a fatigue life of 10 7 cycles, and to refer to the associated stress
range 1 as the endurance limit, 1 e. For conventional structural metals, a
superimposed tensile mean stress lowers the fatigue strength, and the knockdown
in properties can be estimated conservatively by a Goodman construction:
at any fixed life, the reduction in cyclic strength is taken to be proportional to
the mean stress of the fatigue cycle normalized by the ultimate tensile strength
of the alloy (see any modern text on metal fatigue such as Suresh, 1991, Fuchs
and Stephens, 1980 or a general reference such as Ashby and Jones, 1997).
This chapter addresses the following questions:
1. What is the nature of fatigue failure in aluminum alloy foams, under
tension–tension loading and compression–compression loading?
2. How does the S–N curve for foams depend upon the mean stress of the
fatigue cycle and upon the relative density of the foam?
3. What is the effect of a notch or a circular hole on the monotonic tensile
and compressive strength?
4. By how much does a hole degrade the static and fatigue properties of a
foam for tension–tension and compression–compression loading?
The chapter concludes with a simple estimate of the size of initial flaw
(hole or sharp crack) for which the design procedure should switch from a
ductile, net section stress criterion to a brittle, elastic approach. This transition
flaw size is predicted to be large (of the order of 1 m) for monotonic
loading, implying that for most static design procedures a fracture mechanics
approach is not needed and a ductile, net section stress criterion suffices. In
fatigue, the transition flaw size is expected to be significantly less than that
for monotonic loading, and a brittle design methodology may be necessary for
tension–tension cyclic loading of notched geometries.
8.2 Fatigue phenomena in metal foams
When a metallic foam is subjected to tension–tension loading, the foam
progressively lengthens to a plastic strain of about 0.5%, due to cyclic ratcheting.
A single macroscopic fatigue crack then develops at the weakest section,
and progresses across the section with negligible additional plastic deformation.
Typical plots of the progressive lengthening are given in Figure 8.2.
Shear fatigure also leads to cracking after 2% shear strain.
In compression–compression fatigue the behavior is strikingly different.
After an induction period, large plastic strains, of magnitude up to 0.6 (nominal
strain measure), gradually develop and the material behaves in a quasi-ductile