Dynamic Crushing Models And Rate-sensitivity Analysis Of Metallic Foams

Compared with traditional metal materials, metallic foams have super light, excellent energy absorption capacity, electromagnetic shielding and novel thermal properties because of the variability of their meso-structures. The irregularity and defects of the metallic foam meso-structures maybe have large influence on the mechanical properties of metallic foams. It is difficult to determine the influence of the irregularity and defects on the mechanical properties of metallic foams in experiment. However, the numerical simulation method can depict the problem conveniently. The relation between the irregularity/defects and the mechanical properties of metallic foams can give theoretical guidance for the application of metallic foams and their composite structures. Under dynamic impact condition, local inertia effects and the definition of the relevant parameters associated with the dynamic response are usually coupled together, and it is hard to decouple them using SHPB experimental equipment because of the deformation localization of the metallic foams. In this paper, using the shock wave theory, we analyse the dynamic impact behaviour of metallic foams. Then, based on the local strain calculation method, the dynamic stress strain states of metallic foams under dynamic impact can be obtained.Based on the3D Voronoi technique, we construct a3D open-cell metallic foam model and a3D closed-cell metallic foam. The relations between the irregularity of metallic foams and the cell volume distribution are also obtained. In order to guarantee the validity of the finite element models, we analyse the convergence of the characteristic length of the finite elements. The simulation results show that the plateau stress of open-cell/closed-cell metallic foams increases with the increase of the metallic foam cell number, when the number of metallic foam cells is small; then the plateau stress trends to a fixed value. This means that the size effect of the metallic foams is negligible, when the number of cells reaches a certain level. We also use the simulation method to explore the relation between the irregularity of open-cell/closed-cell metallic foams and the mechanical properties of metallic foams. The results show that influence of the irregularity of metallic foams on the mechanical properties of metallic foams is unapparent.In this thesis, we investigate the micro-inertia effect and dynamic plastic Poisson’s ratio of closed-cell/open-cell metallic foams. The simulation results indicate that the plastic Poisson’s ratio varies with the nominal strain, its peak value decreases as the impact velocity increases and the Poisson’s ratio increases with the relative density increasing. The micro-inertia effect plays little role in enhancing the plateau stress of metallic foams. A significantly decreasing influence of lateral constraint on the crushing stress with increasing loading rates has been found for a closed-cell metallic foam. This interesting phenomenon can be interpreted by the micro-inertia effect and the decrease of Poisson’s ratio in dynamic compression.In this thesis, we also explore the relation between the inner gas pressure of closed-cell metallic foams and theirs mechanical properties in quasi-static crushing condition. The simulation results show that the stress increment affected by the inner gas pressure is obviously in low-density closed-cell metallic foams. The stress increment also increases with the increase of the nominal strain. When the inner gas pressure reaches a high level, the gas pressure can affect the Poisson’s ratio of the metallic foams. Finally, we give the estimated formula between the inner gas pressure and the stress increment from the simulation results.Two models are developed for describing the dynamic crushing of metallic foams striking a rigid wall:a one-dimensional shock model and a3D cell-based finite element model. The shock model is proposed by using the continuum-based stress wave theory and assuming the rigid-nonlinear hardening plastic constitutive relation of foam, and then an implicit expression for determining the relation between local strain behind the shock front and the impact time is obtained. The dynamic crushing process of cell-based finite element model is simulated by using the ABAQUS/Explicit software. The local strain field is obtained by using the least squares method to calculate the deformation gradient and local strain. By comparing with the simulation results, the shock model presents good predictions of the stress and the strain behind the shock front.We also explore rate sensitivity of metallic foams under dynamic impact. Current experimental techniques make it difficult to obtain the dynamic constitutive relations of cellular metals since local inertia effects are not easily decoupled from the definition of the relevant parameters associated with the dynamic response. In order to study this effect, a cell-based metallic foam is considered in which the foam specimen impinges normally with an initial velocity, Vo, on a stationary rigid wall. Using the local engineering strain calculation method, we can obtain the local strain distribution of the metallic foam under dynamic impact. The simulation results show that the dynamic densification strain increases with the increase of impact velocity and is larger than the quasi-static densification strain used in the R-P-P-L shock model. According to the shock wave theory, the stress ahead of the shock front can be obtained, which is found to be larger than the initial crush stress in the quasi-static compression. Finally, it is found that the dynamic stress-strain states are obviously below the quasi-static stress-strain relation. This difference is explained by analysing the deformation modes at the cell level. The present results reveal that the difference of deformation modes is the main reason of the loading-rate sensitivity of metallic foams.