Experimental Study,Multi-scale Analysis And Crashworthiness Design Of Graded Cellular Metals

Graded cellular metals inherit excellent mechanical properties from uniform cellular metals,such as the abilities of impact resistance and energy absorption.Their high performance of design,which due to the variability of density distribution of material,has made them more popular.Graded cellular metals can be divided into continuous density graded cellular metals and layer density graded cellular metals.However,due to fabrication restriction,layer density graded cellular metals have been used in most of the experimental researches which could not describe the mechanical behavior of gradient cellular metals accurately.The researchers turn to theoretical analysis or finite element simulation,such as the theoretical solution based on the shock wave model and finite element simulation based on the Voronoi model.In addition,the researchers also do the crashworthiness design of graded cellular metals,but mostly choose the best performance of the crashworthiness in a range which means the potential of the design ability is not developed.In this paper,the three-dimensional finite element model is developed based on the Voronoi technique and used to perform the finite element simulation of the graded cellular metals more accurately.Finally,the reverse design of the graded cellular metals based on the shock model is firstly proposed to guide the crashworthiness design which try to change the using of energy absorption material from passive choice to active design.Experiment research is carried out to investigate the fundamental mechanical properties.Since closed-continuous graded cellular metal with a specific density distribution is difficult to fabricate,the density of the graded aluminum foams used in this paper is measured indirectly and then fitted with a linear equation.Quasi-static compressive experiments are performed with these specimens,and it is found that the collapse appears from the end with larger cell and develops to the other end.Based on this phenomenon,the relationship between the reaction force and the displacement is derived,and the stress-strain relationship of the material is simulated by the R-PP-L model.Then the experimental data are fitted to calculate the mechanical parameters of the R-PP-L model.Afterwards,a modified Hopkinson pressure bar is used to carry out dynamic experiment of graded aluminum foams,combining with the "double gauge"method,the reaction force at the distal end is calculated.The velocity history curve of bullet speed is obtained by using high-speed camera and digital image correlation,the results agree well.Based on the stress wave theory,the shock model of a graded cellular rod impinged by a mass is established.A series of graded cellular metal rods which have the same average density,different density gradient and linear density distribution are considered.The differential equations of impact velocity and wave front position are derived and calculated by using the classical Runge-Kutta method with the material parameters of R-PP-L model.The results show that density gradient has great influence on the mechanical response of graded cellular metals.It is also found that the oscillation of the deceleration curve can be very small with the maximum deceleration being minimal.Combined with the experimental results,it shows that the theoretical and experimental results agree well in the early stage.Then the reaction force at the support end obtained by experiment is much larger than that of the theoretical derivation,and the velocity of the mass decreases faster than the theoretical deduction with the decrease of the impact speed.The main reason is that the R-PP-L model is simplified,which not considering the material strain hardening.and the densification strain in the model is fixed for specific density.A meso-model is developed based on the Voronoi technique and used to perform the finite element simulation of the graded cellular metals.A varying cell-size method based on Voronoi technique is extended to construct a series of 3D graded cellular models with a same average density,different density gradient and linear density distribution.The mechanical behaviors of graded cellular structures under quasi-static compression and dynamic impact are investigated with finite element code ABAQUS/Explicit.Different from the plateau stage of uniform cellular material,graded cellular specimen has a stage which stress increases continually with the increasing of the strain.Collapse propagates from the end with big-size cell to another.Results of dynamic impact show that graded cellular materials have better performance as energy absorbers.Graded cellular structures with large density near the distal end can protect strikers,and those with low density near the distal end can protect structures at the distal end.It is concluded that graded cellular materials with suitable design may have excellent performance in crashworthiness.A reverse design of density gradient of graded cellular materials is proposed to achieve the specific crashworthiness.Based on the history curve of the impact force,a nonlinear plastic shock model is employed to derive the expression of the graded cellular rod's density distribution.Three cases of design strategy with a constant impact force,linearly increasing and linearly decreasing respectively are analyzed and the density distribution are obtained.According to these three density distribution,the three-dimension finite element models are generated and analyzed.The results reveal that the design strategy is reliable when the impact-force history is constant or increasing linearly.For the case with a linear decreasing impact force,collapses of cells occur at both end which is different from the assumption in the theoretical analysis,leading to the disagreement between the theoretical analysis and the numerical simulation.It is also noticed that a portion of the graded cellular rods close to the distal end is not fully compacted.A scheme with restricting the shock strain not less than a specific value is proposed to shorten the graded cellular rods.Therefore,the desirable crashworthiness of graded cellular materials can be obtained by designing the density distribution of graded cellular materials.