Z.Y. Gao

Stress–Strain Relationship for Metal Hollow Sphere Materials as a Function of Their Relative Density

in large strains is obtained using a simplified model for the spheres deformation within a 3D block assuming a hexagonal packing pattern. The yield strength and material strain hardening are obtained as functions of the relative density in two characteristic loading directions. The expression for the stress-strain relationship consisting of quadratic and linear terms with respect to the relative density is linked to the partitioning of the defor- mation energy during compression. The theoretical predictions are compared with limited test results on mild steel hollow sphere material and finite element simulation results obtained by our group. DOI: 10.1115/1.2712235 The properties of metallic cellular materials honeycomb, foam, hollow sphere agglomerate have been studied extensively in re- cent years 1 owing to the wider engineering applications in lightweight structures for impact energy absorption 2, acoustic wave attenuation, etc. A large number of experimental, numerical, and analytical studies on the behavior of cellular materials have been reported in the literature e.g., see Refs. 3,4. However, relatively little is published on the prediction of the properties of metal hollow sphere MHS agglomerates, especially with respect to their stress-strain behavior in large strains due to the complex- ity of the spheres deformation within a material block. Metal foams made from hollow spheres offer low density with reasonably good energy absorption and high strength to weight ratios. Sintered metal hollow sphere foams have a certain volume fraction of enclosed pore space inside the spheres, but also have interstitial porosity between the sintered spheres appearing as a mixed open/closed-cell cellular solid. The key physical attributes of the MHS material, which are relevant to their mechanical be- havior, include the characteristic sphere dimensions diameter and wall thickness, wall material properties, and the relative density, * / s. The latter is affected by both the relative density of indi- vidual spheres as well as the packing pattern of spheres in the cellular solid. Unlike foams that are processed using expansion methods or injection of molten metal, hollow sphere metal foams may be processed either as random or ordered 5, leading to isotropic or anisotropic macroscopic elastic-plastic behavior, re- spectively. In other words, it is likely that a higher control on the mechanical properties of the MHS materials can be achieved in comparison to the open or closed cell foams. Due to the particular deformation mechanism of the spheres within a material block, a stress enhancement was experimentally observed 6,7 when the deformation progresses, which is not typical for the other types of open or closed cell metal foams. Among the few studies on the characterization of MHS materials, most thorough analyses of the material properties are published in Refs. 8-11 but they are exclusively concerned with the elastic modulus and the initial yield strength despite the fact that these materials manifest a noticeable strain hardening 6,7 before den- sification. The hardening is an inherent property of the metal hol- low sphere material due to the deformation mechanism of the spheres and reflects the hardening feature of the force- displacement characteristic of a single hollow sphere under uniaxial compression 12. In this case, the assumption of a rela- tively flat stress plateau cannot adequately characterize the MHS material. The present study aims to obtain the stress-strain rela- tionship in large strains and describe the material hardening as a function of the relative density. A rigid, perfect-plastic model is assumed for the base material, which is a reasonable approxima- tion of typical mild steel in large strains.

One-Dimensional Analysis on the Dynamic Response of Cellular Chains to Pulse Loading

Abstract On the basis of our previous studies of a typical type II structure (i.e. a pair of prebent plates), a simplified one-dimensional mass-spring model is proposed to describe the uniaxial load-deformation characteristic of cellular materials and structures. When compared with the previous mass-spring model proposed by Shim et al., the present model employs fewer parameters (only two) to describe elastic-plastic behaviour, and the structural hardening/softening is represented by only one of the parameters. The model is then used to study the dynamic response of a cellular chain to a pulse loading of specified force intensity and duration. By adjusting the value of a single parameter adopted in the model, each cell of the cellular chain is identically assigned to possess either an elastic-hardening or an elastic-softening-consolidation property. The effects of material elasticity, cell compliance characteristic, cell number, and pulse intensity and duration are all examined by this model and discussed in detail. A special attention is paid to the initiation and propagation of the plastic collapse of the cells in the cellular chain so as to identify the governing parameters. Apart from the elastic wave speed, two other characteristic velocities, i.e. the particle velocity induced by the elastic wave and the plastic collapse propagation velocity, are defined and analytically evaluated. It is found that these three characteristic velocities completely govern the elastic and plastic dynamic behaviour of the cellular chains.

The Dependence of the Energy-absorption Capacity of Metal Hollow Sphere Materials on Their Relative Density

Experimental, numerical and theoretical analyses are carried out to obtain the relationship between the stress and relative density of metal hollow sphere (MHS) materials during their large plastic deformation in order to estimate the energy absorbing capacity of these materials under uniaxial compression. Based on a numerical parametric analysis empirical functions of the relative material density are proposed for the elastic modulus, yield strength and ‘plateau’ stress for FCC packing arrangement. Analytical stress-strain dependences are suggested for the yield strength and material strain hardening properties as functions of the relative density of MHS materials under uniaxial compression.