82 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

Metal Foams
Figure 8.2 Progressive lengthening in tension-tension fatigue ofAlporas, at various fixed levels of stress cycle (R = 0.1; relative density 0.11; gauge length 100 mm)

manner (see Figure 8.3). The underlying mechanism is thought to be a combination of distributed cracking of cell walls and edges, and cyclic ratcheting under non-zero mean stress. Both mechanisms lead to the progressive crushing of cells. Three types of deformation pattern develop:

1. Type I behavior. Uniform strain accumulates throughout the foam, with no evidence of crush band development. This fatigue response is the analogue of uniform compressive straining in monotonic loading. Typical plots of the observed accumulation of compressive strain with cycles, at constant stress range Act, are shown in Figure 8.4(a) for the Duocel foam Al-6101-T6. Data are displayed for various values of maximum stress of the fatigue cycle amax normalized by the plateau value of the yield strength, ctp1.

2. Type II behavior. Crush bands form at random non-adjacent sites, causing strain to accumulate as sketched in Figure 8.3(b). A crush band first forms at site (1), the weakest section of the foam. The average normal strain in the band increases to a saturated value of about 30% nominal strain, and then a new crush band forms elsewhere (sites (2) and (3)), as is sometimes observed in monotonic tests. Type II behavior has been observed for Alporas of relative density 0.08 and for Alcan Al-SiC foams. A density gradient in the loading direction leads to the result that the number of crush bands formed in a test depends upon stress level: high-density regions of the material survive without crushing. Consequently the number of crush bands and the final strain developed in the material increases with increasing stress (Figure 8.4(b)) for an Alcan foam of relative density 0.057.

Cumulative strain,

Cumulative strain,

Band spreading

Log cycles, N

Cumulative strain,

Log cycles, N

Cumulative strain,

Log cycles, N

Band spreading

Sequential discrete bands

Figure 8.3 Typical behaviors in compression-compression fatigue of metallic foams at a fixed stress range. (a) Progressive shortening by broadening of a single crush band with increasing cycles; (b) sequential formation of crush bands

3. Type III behavior. A single crush band forms and broadens with increasing fatigue cycles, as sketched in Figure 8.3(a). This band broadening event is reminiscent of steady-state drawing by neck propagation in a polymer. Eventually, the crush band consumes the specimen and some additional shortening occurs in a spatially uniform manner. Type III behavior has been observed for Alulight of composition Al-1Mg-0.6Si (wt%) and of relative density 0.35, and for Alporas of relative density 0.11. Data for the Alporas are presented in Figure 8.4(c). In both materials, the normal to the crush bands is inclined at an angle of about 20° to the axial direction, as sketched in Figure 8.3(a). The strain state in the band consists of a normal strain of about 30% and a shear strain of about 30%.

A significant drop in the elastic modulus can occur in fatigue, as shown in Figure 8.4(d) for Alporas. This drop in modulus is similar to that observed in static loading, and is a result of geometric changes in the cell geometry with strain, and cracking of cell walls. The precise details remain to be quantified.

A comparison of Figures 8.4(a)-(c) shows that all three types of shortening behavior give a rather similar evolution of compressive strain with the number of load cycles. Large compressive strains are achieved in a progressive manner. We anticipate that this high ductility endows the foams with notch insensitivity in compression-compression fatigue (see Section 8.4 below).

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1 10 102 103 104 105 106 107 Number of cycles (a)

1 10 102 103 104 105 106 107 Number of cycles (a)

102 103 104 105 Number of cycles (b)

Figure 8.4 (a) Progressive shortening behavior in compression-compression fatigue for a Duocel AI-6101-T6 foam of relative density 0.08. (b) Progressive shortening behavior in compression-compression fatigue for Alcan foam (relative density 0.057; R = 0.5). (c) Progressive shortening behavior in compression-compression fatigue for Alporas foam (relative density 0.11). (d) Progressive shortening behavior in compression-compression fatigue: comparison of the progressive drop in stiffness of Alporas in a monotonic and fatigue test (relative density 0.11)

102 103 104 105 Number of cycles (b)

Figure 8.4 (a) Progressive shortening behavior in compression-compression fatigue for a Duocel AI-6101-T6 foam of relative density 0.08. (b) Progressive shortening behavior in compression-compression fatigue for Alcan foam (relative density 0.057; R = 0.5). (c) Progressive shortening behavior in compression-compression fatigue for Alporas foam (relative density 0.11). (d) Progressive shortening behavior in compression-compression fatigue: comparison of the progressive drop in stiffness of Alporas in a monotonic and fatigue test (relative density 0.11)

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Figure 8.4 (continued)

Nominal compressive strain, e (d)

Figure 8.4 (continued)

In designing with metal foams, different fatigue failure criteria are appropriate for tension-tension loading and compression-compression loading. Material separation is an appropriate failure criterion for tension-tension loading, while the initiation period for progressive shortening is appropriate for compression-compression loading. Often, a distinct knee on the curve of strain versus cycles exists at a compressive strain of 1-2%, and the associated number of cycles, NI, is taken as the fatigue life of the material.

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