Dynamic Mechanical Behavior And Multi-functional Optimal Design Of Graded Cellular Metals

Cellular metals have considerable excellent properties of energy absorption and shock resistance. They are widely used as energy absorbers and crashworthiness structures in the automotive, high-speed trains and aerospace industries. Recently, a novel class of cellular metals with a gradual change in mechanical properties of its constituent phases, namely a graded cellular metal (GCM), has attracted considerable research interests. Researchers have shown good properties of GCMs, and introducing a density gradient to cellular metals can help to improve their energy absorption capacity, shock resistance and other properties. However, the GCMs studied in the literature were limited to stepwise, discontinuous density gradients formed by joining different uniform-density layers. The excellent dynamic mechanical properties of GCMs have not been explored, but the energy absorption and deformation mechanisms of GCMs are not clear. GCMs with stepwise and discontinuous density gradients are uncontrollable and they are difficult to explore the energy absorption and deformation mechanisms. In order to explore the energy absorption and deformation mechanisms of GCMs, we conduct some numerical tests of GCMs with continuous density gradients to study their dynamic impact responses. For a deep understanding of the energy absorption and deformation mechanisms, shock wave models corresponding to two impact scenarios are presented to explore shock wave propagation mechanisms of GCMs.A varying cell-size distribution method is newly developed to construct GCMs via using the Voronoi technique. The characteristic of the relation between the relative density and the distance between any two adjacent nuclei of a regular honeycomb when the cell-wall thickness is fixed enlightens us to design GCMs via changing cell-size distribution to change density distribution. To evaluate the varying cell-size distribution method, we compare the mesostructure parameters of constructed GCMs with that of the designed. Results show that they are fitted well.Numerical simulations are performed to study the dynamic mechanical behaviors of GCMs under mass impact, and the dynamic responses of GCMs under constant-velocity are investigated to explore their deformation mechanisms. The results show that GCMs exhibit superior energy absorption characteristics than the equivalent uniform cellular metals under a not high initial velocity impact, but this superiority becomes indistinct with the increase of initial impact velocity. For a not high initial velocity impact, the reaction force at the support end of a negative gradient and that at the impact end of a positive gradient are much smooth. At a high initial velocity, GCMs with a positive gradient can mitigate effectively the peak impact stress. Deformation patterns, local strain distributions and load histories under constant-velocity impact have provided some insight to understand the energy absorption and deformation mechanisms of GCMs. A new deformation pattern named double "I"-shaped pattern is found. Two critical impact velocities of mode transitions are quantitatively determined by using the stress uniformity index and the deformation localization index. The deformation mechanisms well explain the energy absorption characteristics of GCMs. During the mass impact, a GCM may experience one or more deformation modes with the decrease of impact velocity. The total energy absorbed by the GCM is determined by the competition between different deformation mechanisms.One-dimensional shock wave model is extended to GCMs for further understanding the energy absorption and deformation mechanisms of GCMs. Consider two shock wave propagation models of GCMs under constant-velocity impact:a shock wave is generated at the impact end and two shock waves are generated at the two ends simultaneously. Under mass impact, we also consider two shock models, namely single shock model and double shock model. Single shock model is suitable for the density increases gradually from the impact end to the support end and double shock model is suitable for the inverse density distribution. In the double shock model, there maybe exist two stages:stage1, two shock waves generated at the two ends simultaneously and propagate to the opposite directions; stage2, only one shock wave propagates from the support end to the impact end. Numerical verifications are carried out and the results are compared well with the predictions by shock models.Dynamic mechanical behaviors of GCMs in a temperature field are also studied by finite element method. Numerical simulations of the steady heat conduction in GCMs are performed firstly and then a temperature-dependent constitutive of the cell-wall material of GCMs is discussed. Density and temperature distributions in GCMs may significantly affect the mechanisms of deformation and stress wave propagation, because the local strength of a graded cellular metal depends not only on the local relative density but also on the local temperature. The energy absorption of GCMs in a temperature field experiences three characteristic segments similar to that in room temperature. One-dimensional shock wave model is extended to study these shock wave propagations in GCMs in a temperature field. Here, single shock model is suitable for the material strength increases gradually along impact direction and double shock model is suitable for the inverse material strength distribution. Cell-based finite element models of GCMs are employed to verify the predictions of the shock models.Based on the excellent mechanical properties and heat properties of GCMs, we design their crashworthiness and thermal insulation properties. In the crashworthiness design, energy absorption and impact resistance are two design objectives. The results show that a good choice of positive density gradient not only improves the energy absorption but also reduces the initial impact stress. Thus, there is an optimal value for the density-gradient parameter to meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress for an input kinetic energy. The analysis of the thermal insulation parameter of GCMs gives that changing the density distribution of cellular metals can improve their thermal insulation properties.