| Cellular materials including foams and honeycombs have been widely used in a wide range of engineering applications including impact resistance and protective structure,due to their good energy absorption capacity,high strength/weight ratio and the outstanding designability.Also,in order to improve the mechanical property of cellular materials,many researchers pay more attention to the graded foams,in which the distribution of relative density and cell morphology can be designed to control the mechanical properties of foams,thereby withstanding varying loads in specific engineering fields.These materials possess great potential in application and important value in research.However,it is difficult to manufacture cellular material with predetermined configuration by using traditional production technique.Hence,limited experimental study on regular,uniform and graded cellular materials has been reported,the method of optimization design in cellular material is lacked.Recent development in additive manufacturing(AM)technique has led to advances in fabricating foams with desired internal structures.In this paper,a series of polylactic-acid cellular materials such as honeycomb,Kelvin foam(regularity=1.0),random foam(regularity=0.0-0.8),Voronoi uniform foam and graded foam,are produced by AM technique.Quasi-static and dynamic experiments are conducted to study the mechanical responses of these materials.Numerical and theoretical investigations are also carried out to reveal the deformation mechanism and constitutive model,thereby indicating the energy-control mechanism of lightweight multi-stage energy-absorption materials.The main conclusions are drown and listed as follows:(1)The mechanical response and deformation mode of regular cellular materials are studied.Four deformation modes are observed in experiments for Kelvin foams with different relative densities and at different compression loading rates.Further numerical results indicate the presence of a critical relative density,below which the Kelvin foams deform primarily by cell edges bending,and beyond which the cell membranes stretching dominates.It is also found that the position of the deformation bands is dominated by the loading rate.A mode classification map is proposed to clarify the effects of the relative density and loading rate on the deformation modes of Kelvin foams.In addition,the quasi-static and dynamic crushing behaviors of Kelvin foams and honeycombs under combined shear-compression are compared.The normal strengths of both honeycomb and Kelvin foam decrease while the shear strengths increase with the loading angle increasing.Moreover,honeycombs change the deformation mode from the progressive folding mode to the global rotation mode while Kelvin foams maintain the layered folding mode as the loading angle increases.Therefore,honeycombs show the normal strength decreasing more sharply than Kelvin foams.As a result,there is a cross point on the macroscopic yield envelopes of honeycomb and Kelvin foam,these yield envelopes provide design criteria for cellular materials to withstand any applied shear/compressive stress state.(2)The effects of cell regularity and geometric topology on the mechanical properties of uniform foams are revealed.Random foams have randomly-distributed localized deformations and thus can mitigate the collapse stress than Kelvin foams.Also,random foams tend to show cell-wall tearing failures,thereby causing lower plateau stress in experiments.However,the cell regularity(0.0-0.8)has no obvious effect on the mechanical properties of foams based on all experimental and numerical data.In addition,this paper proves that uniform foams with constant relative density present similar mechanical properties despite their different cell morphologies.Also,several powerlaw empirical formulae are proposed for uniform foams to describe their mechanical behaviors.(3)The constitutive model of graded foams in the homogeneous stress state is established.The cell size graded foams deform continuously from lower to higher density regions and hence possess a gradually increasing plateau stage in the stress-strain curve.The cell-wall thickness graded foams show three stepwise plateau stages because of their three layers with different cell-wall thicknesses.Also,this paper indicates the strength of each layer in a graded foam depends on its local density rather than cell morphology.In addition,it is found that graded foams exhibit successive plateau stresses of their component layers.Thus,the graded-foam property can be modeled using the mechanical properties of uniform-foam component layers.An elastic,plastic-hardening,locking model and an elastic,collapse,plastic-hardening,densification model for graded foams are built.These models can predict the mechanical properties of graded foams,and verified by our experimental data and some published results.On the basis of this model,it is possible to tailor the mechanical properties of graded foams for various engineering applications without conducting numerous experimental studies.(4)The effects of shock wave and gradient distribution on the mechanical behaviors of foams are investigated.The model of shock wave propagating in uniform and graded foams is deduced.Based on the one-dimensional shock wave theory,the physical quantities behind and ahead of the shock front are determined.Then,numerical results provide the one-dimensional velocity distribution and the shock front distribution of foams,thus obtaining the dynamic initial crushing stress σ0d and the dynamic strain-hardening parameter D.Afterwards,a dynamic constitutive model is established to describe the dynamic behavior of polylactic-acid foam.In addition,the combined effects of gradient and shock wave on the mechanical responses of foams are studied.Based on the predetermined impact-force function,the corresponding density gradient can be estimated by a theoretical model of graded foams.Five impact-force functions including constant,linear,quarter sine,triangle and half sine,are considered to verify this theoretical model. |
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