Theoretical Methods And Additive Manufacturing Verification On Crashworthiness Design Of Graded Cellular Materials

Graded cellular materials can be introduced to adjust the impact load of structure and to improve the structural crashworthiness,but in traditional studies it is difficult to directly provide rational graded cellular materials for meeting some given crashworthiness requirements.Due to the deformation localization characteristic of cellular materials under dynamic impact,the understanding of the propagation law of collapse wave front may be helpful to guide the crashworthiness design of graded cellular materials.In recent years,a backward design strategy based on a non-linear plastic shock model was proposed,and reasonable density distributions were obtained for some specific impact force requirements under mass impact.However,there are still some shortcomings in this backward design strategy:firstly,the design strategy is implicit and requires numerical solution to obtain the distribution function of relative density;secondly,the design strategy is not accurate enough,and the influence of the loading rate sensitivity of cellular materials was not considered;lastly,the design strategy has not been verified by experiments,and the traditional process cannot accurately prepare graded cellular material with the designed relative density distribution.In order to improve the simplicity,accuracy and practicability of the crashworthiness design of graded cellular materials,this paper intends to develop theoretical analysis methods and to conduct experimental verification with using additive manufacturing technology and dynamic testing method.An experimental test method to determine the relationship between dynamic material parameters and relative density of cellular materials is proposed based on the one-dimensional shock model of graded cellular materials under direct impact.The relationship between the impact velocity and time is obtained based on the one-dimensional shock model under dynamic impact of specimens with an increasing/decreasing density distribution along the impact direction.And by applying this relationship to fit the experimental data,the dependence of the dynamic material parameters on the relative density can be determined.The graded ABS closed-cell foam with a linear density distribution made by the additive manufacturing technology was taken as an example.The high-velocity impact experiments of the graded foam specimens with an increasing/decreasing density distribution along the impact direction were conducted.According to the experimental results of impact velocity,the power-law relationship between the dynamic material parameters and the relative density of the ABS closed-cell foam was determined.By combining the power-law relationship and the one-dimensional shock wave model,the shock stress in the densification region was predicted,and it is found to coincide well with those obtained from experiments.Under mass impact,the backward design strategy without considering the loading rate sensitivity of cellular material was simplified for considering the crashworthiness requirement of a constant impact force.The asymptotic solution of the relative density distribution was obtained by applying a series expansion method.It is found that the second-order approximate solutions of the relative density distribution for graded cellular materials with different meso-structures have enough accuracy to approximate the exact solutions.The cell-based finite element models of graded irregular honeycombs and graded closed-cell foams were constructed by a varying cell-size distribution method based on Voronoi technology and applied to verify the validity of the design method.The results show that the impact force keeps constant overall and meets the crashworthiness requirement.The design based on the second-order approximate solution is effective.However,whether based on the exact solution or based on the second-order approximate solution,the impact force results are slightly higher than the target values.It indicates that the backward design strategy without considering the loading rate sensitivity of cellular material has some flawsFurthermore,the backward design strategy was improved by considering the loading rate sensitivity of cellular material.The asymptotic solutions was obtained,which can directly give the relative density distribution and the specimen length.Compared to the design without considering the loading rate sensitivity of cellular materials,the design with considering the loading rate sensitivity has a lower value of the relative density distribution and a shorter value of the length of specimen,and thus a shorter and lighter specimen is needed to meet the crashworthiness requirement and the present design method meets the requirements of lightweight The numerical simulation results show that the impact force of the second-order approximate design considering the loading rate sensitivity of cellular material remains almost constant,and the average impact force is slightly lower than the tolerance value,which meets the requirements of crashworthiness.It also explained why the impact force of the backward design method without considering the loading rate sensitivity of cellular material is higher than the tolerance value.Different working conditions,i.e.different initial velocities and masses impact conditions as well as different impact force design targets,were discussed.It is found that the second-order approximate design considering the loading rate sensitivity can meet the requirements of crashworthiness very well and has good applicability.Therefore,the second-order approximate design considering the loading rate sensitivity improves the simplicity and accuracy of the crashworthiness design of graded cellular materials,which is of theoretical significance for practical engineering applications.Based on the power-law relationship between the dynamic material parameters and the relative density of ABS foam,the relative density distributions of the second-order approximate design considering the loading rate sensitivity of cellular material were determined for different initial velocity impact situations.Specimens of graded ABS closed-cell foam with specific density distributions were prepared by geometric construction and additive manufacturing.Then,the high-velocity mass impact experiment of the graded ABS closed-cell foam was carried out.The experimental results show that the impact velocity of the mass presents a linear attenuation trend,which is basically consistent with the theoretical results,and the average impact force is lower than that from the theoretical prediction.Therefore,the effectiveness of the second-order approximate design considering the rate sensitivity of cellular material is verified by the experiments.By comparing the results of the cell-based finite element simulation without considering the damage of the matrix material with the experimental results,it is found that the impact velocity history and the average impact force of the numerical simulations are in good agreement with the experimental results,but the force at the support end is slightly higher than the experimental results when the impact velocity is low.The difference may be explained by different deformation modes between the cell-based finite element simulations and the experimental tests.The graded foam collapses layer by layer in the numerical simulation making the force transferring to the support end steadily.While in the experiments,the cells of foam experience collapse and accumulation under impact,which is not conducive to the transfer of the force.The results show that the damage of matrix material only has little effect on the mechanical properties of gradient ABS foam compacted area by using the cell-based finite element model,but slightly overestimates the force at the support end when the impact velocity is low.