Mechanical relations for porous metal foams under several typical loads of shearing, torsion and bending

Porous metal foams with isotropic three-dimensional reticulated structure are excellent engineering materials with dual attributes of structural and functional characteristics, and they may bear shearing or torsional or bending loads when they are used as engineering components in various cases. With the octahedral model, the mechanical behavior is investigated for the component of these materials under shearing loads, the loading state of struts within the porous body is analyzed for these materials under torsion, and the mechanical performance is further discussed for these materials under bending moment based on their properties of uniaxial tension and compression. Using the simple manner of segregating analysis, the relevant mechanical relationships are respectively derived from the corresponding mathematical deduction for these materials under those loads. The results show that, when the porous body endures the fracture resulting from shearing loads or from torsion, the maximum nominal shearing stress or the nominal torque for the porous component can be described with the porosity and the inherent characteristic parameters of the metal foam itself. Also, the applicable maximum nominal bending moment can be expressed as a function of the porosity for the metal foams under bending moment. This mathematical relationship may be regarded as the extension of the expression about the relationship between the maximum nominal stress and the porosity for these materials under uniaxial tensile and compressive loads. From these mathematical relations, the loading criterions may be directly and conveniently achieved for these materials under the corresponding loads, respectively.