## 81 Definition of fatigue terms

First, we need to define some standard fatigue terms. Consider a cylindrical specimen loaded uniaxially by a stress, a, which varies from a minimum absolute value amin to a maximum absolute value amax, as shown in Figure 8.1. For example, for a fatigue cycle ranging from — 1MPa to — 10MPa, we take

Cycles to failure, Nf

Figure 8.1 (a) Definition of fatigue loading terms; (b) Typical S-N curve for aluminum alloys, in the form of stress range Aa versus number of cycles to failure, Nf. The endurance limit, Aae, is defined, by convention, for a fatigue life of 107 cycles

Cycles to failure, Nf

Figure 8.1 (a) Definition of fatigue loading terms; (b) Typical S-N curve for aluminum alloys, in the form of stress range Aa versus number of cycles to failure, Nf. The endurance limit, Aae, is defined, by convention, for a fatigue life of 107 cycles amin = 1 MPa and amax = 10MPa. The load ratio R is defined by

amax

It is well known that the fatigue life of structural metals such as steels and aluminum alloys is insensitive to the loading frequency, under ambient conditions. This simplification does not hold in the presence of a corrosive medium, such as a hot alkaline solution, or salt water for aluminum alloys. These broad conclusions are expected to hold also for metallic foams.

In low-cycle fatigue testing, the usual strategy is to measure the number of cycles to failure, Nf, for a given constant stress range Aa = amax — amin, and then to plot the resulting pairs of values (Nf, Aa) on log-linear axes. The resulting S-N curve is used in design for finite life (Figure 8.1(b)). Many 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 107 cycles, and to refer to the associated stress range Act as the endurance limit, Aae. 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.

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