Numerical Analysis Of The Rate Effect And Theoretical Study On The Dynamic Behavior Of Cellular Metals

Cellular metals have considerably excellent mechanical properties and energy absorption capacity because of the specialty and variability of their micro structures. Therefore, cellular metals are widely used as advanced structural components in many engineering applications. The static and quasi-static mechanical behaviors of cellular metals have been studied substantially and systematically while the dynamic mechanical responses of them are relatively less researched. Although many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, there are some conflicting conclusions on the strain-rate effect and the inertia effect of metallic foams. In order to know the role of rate effect in this paper, we conduct some numerical tests to explore the influence of inertia effect and strain hardening, strain-rate hardening of metal matrix on the behavior of cellular metals under impact compression. Moreover, for a deep understanding of the deformation propagating behavior, two theoretical models corresponding to different deformation modes are presented to reveal the inherent mechanism of this shock wave phenomenon.Finite element model of irregular honeycomb samples is constructed using the 2D random Voronoi technique. When elastic-perfectly plastic model is adopted for the cell wall material, numerical simulations show that three types of deformation modes are observed. At a low impact velocity, the deformation of the honeycomb is macroscopically homogeneous with multiple random weak shear bands (the quasi-static mode). At a high impact velocity, the deformation mode is layer wise collapse near the impact surface (the shock or dynamic mode). A transition mode with gradual change of macroscopic strain exists for an intermediate impact velocity. It is also shown that when the density and cell-wall material properties of the honeycomb are changed, these three types of deformation modes are still happened, but the corresponding critical velocities are different.To explore the effect of inertia, the density of the wall material is artificially reduced and it is found that when the honeycomb deformed in quasi-static mode, the stress-strain curves are nearly the same, regardless of the impact velocity and the matrix density. Hence the inertia effect will not cause strain-rate sensitivity of the stress-strain relation of the honeycomb. Nevertheless, the plateau stress in transition mode and shock mode increase significantly with the increase of impact velocity. As the matrix density decreases, the critical impact velocities of mode transition increase significantly, and the increase in plateau stress under the same impact velocity for both transition mode and shock mode reduces remarkably. It will be seen form this that due to the inertial effect, the deformation becomes inhomogeneous and localized, and the plateau stress on the impact interface increases rapidly when the impact velocity is moderate or high. So the rate effect of the cellular metals exhibited under high-velocity impact is mainly because of an inertia effect, rather than the strain-rate effect. Meanwhile, the effect of micro inertia is also studied and the results show that this effect is almost neglectable.In order to further understand the mechanical behavior of cellular metals, we also study the influence of cell-wall material properties on their dynamic responses, including strain hardening effect and strain-rate hardening effect. It is found that strain-rate hardening effect of base metal has little influence to the mode transition velocities (increasing about 10%), and will cause a slight increase in the plateau stress. The relative increase in the plateau stress is less than the relative increase in yield stress of the matrix under the same strain rate. The increase in the plateau stress for different impact velocity is nearly the same, and usually decreases gradually with the increasing velocity, thus the influence at high impact velocities is neglectable, in comparison with the inertia effect. Meanwhile, the strain hardening effect of metal matrix is taken into account. In comparison with the elastic-perfectly plastic material, the relative increase in the plateau stress caused by the strain hardening effect is about 5%, so it is found that this effect has minor influence on the plateau stress under dynamic cases. Finally, the critical velocities between the three different deformation modes are discussed and we also evaluate the shock front propagation velocity during the compaction process.On the one hand, among extensive studies of the dynamic responses of cellular materials under high impact velocity, there is a common phenomenon that a zone almost only one single-layer width of cell at the compaction front exists, across which the physical quantities such as stress, strain and velocity are apparently discontinuous. In this case, the compressed part of the cellular material is progressively crushed and almost densified. On the other hand, when the impact velocity is moderate, there also exists a discontinuity at the compaction front while the nominal strain of the compressed portion of the cellular metal is gradually getting smaller. To explore the inherent mechanism of this phenomenon, two models, viz. Transition-Mode model and Shock-Mode model, based on stress wave theory with a'rigid unloading' assumption are established, and their explicit solutions are obtained by using a supplemental relationship of the continuous condition at impact interface. The theoretical results show that the initial stress at the impact end of the foam rod is proportional to the square of the impact velocity when the cellular metal is deformed in Shock Mode but increases linearly with the increasing impact velocity in Transition Mode. The critical velocity for the occurrence of Shock Mode and the transition time when the deformation mode transformed from Shock Mode to Transition Mode are presented. Finally, numerical verifications based on finite element method were carried out and the results are compared well with the theoretical predictions by both the models.