36 Multiaxial testing of metal foams

A brief description of an established test procedure used to measure the multiaxial properties of metal foams is given below. Details are given in Deshpande and Fleck (2000) and Gioux et al. (2000).


A high-pressure triaxial system is used to measure the axisymmetric compres-sive stress-strain curves and to probe the yield surface. It consists of a pressure cell and a piston rod for the application of axial force, pressurized with hydraulic fluid. A pressure p igives compressive axial and radial stresses of magnitude p. Additional axial load is applied by the piston rod, driven by a screw-driven test frame, such that the total axial stress is p C o. The axial load is measured using a load cell internal to the triaxial cell, and the axial displacement is measured with a LVDT on the test machine cross-head and recorded using a computerized data logger. The cylindrical test samples must be large enough to ensure that the specimens have at least seven cells in each direction. The specimens are wrapped in aluminum shim (25 |im thick), encased in a rubber membrane and then sealed using a wedge arrangement as shown in Figure 3.6. This elaborate arrangement is required in order to achieve satisfactory sealing at pressures in excess of 5 MPa.

With this arrangement, the mean stress om ,^nd the von Mises effective stress oe follow as respectively. Note that the magnitude of the radial Cauchy stress on the specimen equals the fluid pressure pi^hile the contribution oxjto the axial Cauchy stress is evaluated from the applied axial force and the current cross-sectional area of the specimen.

^ 3B mm foam specimen rubber membrane female wedge

^ 3B mm foam specimen rubber membrane female wedge

Figure 3.6 Specimen assembly for multiaxial testing The stress-strain curves

70 mm i-insulating tape

Al shim male wedge caphead screw

Figure 3.6 Specimen assembly for multiaxial testing The stress-strain curves

Three types of stress versus strain curves are measured as follows:

• Uniaxial compression tests are performed using a standard screw-driven test machine. The load is measured by the load cell of the test machine and the machine platen displacement is used to define the axial strain in the specimen. The loading platens are lubricated with PTFE spray to reduce friction. In order to determine the plastic Poisson's ratio, an essential measurement in establishing the constitutive law for the foam (Chapter 7), the specimens are deformed in increments of approximately 5% axial plastic strain and the diameter is measured at three points along the length of the specimen using a micrometer. The plastic Poisson's ratio is defined as the negative ratio of the transverse to the axial logarithmic strain increment.

• Hydrostatic compression tests are performed increasing the pressure in increments of 0.1 MPa and recording the corresponding volumetric strain, deduced from the axial displacement. The volumetric strain is assumed to be three times the axial strain. A posteriori checks of specimen deformation must be performed to confirm that the foams deform in an isotropic manner.

• Proportional axisymmetric stress paths are explored in the following way. The direction of stressing is defined by the relation — r\oe, with the parameter taking values over the range 77 # | (for uniaxial compression) to (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 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

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 number of levels of axial strain from a single specimen. The evolution of the yield surface under hydrostatic loading is measured in a similar manner. Data for the failure of metallic foams under multiaxial loading are described in Chapter 7.

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