Quasi-static And Dynamic Mechanical Behavior And Deformation Mechanism Of Granular Materials And Chain Structures

Granular material refers to a large number of discrete solid particles with particle sizes greater than 1 ?m,which can also be called granular matter.According to different stacking methods,granular materials can be stacked randomly or orderly.Random stacked granular materials are widely concerned in the field of powder metallurgy.In the process of powder metallurgy,the particle compression stage plays a key role in the mechanical properties of the final product.However,due to the complex physical properties of the granular materials,there are still some deficiencies in understanding the mechanical behavior in the compression stage:1)particle rearrangement and plastic deformation are involved in the compression densification process of granular metal materials,but a simple and convenient physical compaction model is lacking to describe them;2)the meso-configuration of granular materials is random,the meso-structure is complex and there are many meso-parameters.The relationship between the macro mechanical response and the meso-parameters is not clear;3)the mechanical response of granular metal materials under dynamic and quasi-static loading is different,and the understanding of rate-sensitivity mechanism and behavior characterization of granular metal materials under dynamic loading are still lacking.Different from the random stacked granular materials,the ordered arranged granular structures are valued in waveform control.For example,the propagation of stress waves in a one-dimensional granular chain structure is highly adjustable,which can be linear,weakly nonlinear and strongly nonlinear.However,there are some shortcomings in understanding the propagation behavior and regulation mechanism of stress wave in the granular chain structure:1)cylindrical shell chains can regulate waveform,but the understanding of the stress wave propagation law and dispersion mechanism in the cylindrical shell chains are not clear;2)the stress wave propagation behavior in the granular chain structure is affected by the microstructure of particles,so it is urgent to study the meso-structure effect and its characterization of stress wave propagation;3)the discreteness of the granular chain structure makes the experimental test very difficult,and there is no experimental verification of the effect of the meso-structure of the cylindrical shell chain.These deficiencies make the quality improvement of PM-products and the design of waveform control limited.Therefore,it is necessary to understand the mechanical behavior and complex stress wave propagation process of granular materials and structures under dynamic and static compression.In view of the above shortcomings,the meso-finite element models of ordered and random packed granular materials were established to study their mechanical behavior under compression.The mechanical behavior of randomly packed granular metal materials under quasi-static single closed die compression was studied.Based on the mechanism of particle rearrangement and deformation during compression,a strain-activated statistical compression model is established by introducing the Weibull distribution of the activation strain of particle clusters.The expression of the compaction model(compaction equation)is explicit and only contains four parameters,namely hardening parameter C,maximum strain ?m,shape parameter ka and scale parameter ?a.The validity of the compression model is verified by multi-particle finite element simulation results and experimental data.The results show that the model can well characterize the nominal compression stress-strain relationship of two-dimensional and three-dimensional granular materials with different initial relative densities.The stress increases slowly at first and then increases sharply with the increase of the strain.Besides,the influence of initial relative density on the four parameters in the compaction equation was analyzed,and the corresponding quantitative statistical relationship was determined.The results show that the hardening parameter C has a power-law relationship with the initial relative density,the proportional parameter ?a decreases linearly with the increase of the initial relative density,and the shape parameter ?a and the maximum strain ?m decrease exponentially with the increase of the initial relative density.For two-dimensional and three-dimensional granular materials,the expression of the statistical relationship is the same,but there are quantitative differences.Compared with the existing experimental data of Al powder,it is found that the results of the three-dimensional multi-particle finite element model agree well with the experimental results.Based on the study of a single particle,the densification process of random stacked composite particles under quasi-static single closed die compaction was further simulated.The macro and micro mechanical behaviors during the deformation process were analyzed.The influences of initial relative density and uniformity of Cu-W composite powders on the relationship between compaction pressure and relative density were discussed.The results show that the relative density increases with the increase of the initial relative density or the uniformity of the composite powders under the same compression pressure.By introducing the average rotation angle and average equivalent strain of the powder,the rearrangement and deformation of particles are quantitatively characterized.It is found that the pore filling process can be divided into three stages.In the first stage,the average rotation degree of W and Cu particles increases rapidly,the average equivalent strain of W and Cu powder is almost zero,and the pores are filled by particle rearrangement.In the second stage,the particles reach the locked state,the rearrangement of particles is limited,and the rotation degree of particles increases slowly.Then Cu particles deform to fill the adjacent pores,while W particles hardly deform.In the third stage,the deformation of W particles increases,which further extrudes Cu particles,causing more rotation of Cu particles.However,in this stage,due to the high yield stress of W particles and the constraint of adjacent particles,the increase of relative density is not obvious.In addition,we find that the small pores in the powder with high initial relative density are easily filled by the deformation of neighboring particles during compression.The strong chain formed by the contact of W particles seriously hinders the compression and makes the distribution of residual pores uneven.Granular materials may show different characteristics under dynamic compression from those under quasi-static compression.The mechanical behavior of randomly stacked granular metal materials under dynamic compression was further studied,and the propagation characteristics of shock waves in the granular metal materials were analyzed.The numerical results show that a highly localized deformation band is observed under the high-velocity impact(175?300 m/s),and the deformation band propagates in the form of a plane wave.The velocity field calculation method is used to analyze the particle velocity distribution and the position of the plastic shock front.It is found that the position of the front is approximately linear with time,and then the propagation velocity of the shock wave is determined.The shock wave speeds of Al powders with different relative densities(0.45?0.65)have a linear relationship with their particle velocities.According to the characteristics of particle deformation after wavefront,a strain locked shock wave model was proposed.The model can predict the mechanical response of copper powder under dynamic compression,but it is only suitable for high-speed compression or matrix materials with low yield stress.Furthermore,based on the plastic shock wave model and the quasi-static statistical compression model,the strain-hardening shock wave model of granular materials was established.The model is used to characterize the dynamic compression behavior of granular materials,and the predicted stress and shock wave speed are in good agreement with the finite element results.Finally,the difference of densification mechanism between dynamic compression and quasi-static compression was revealed.Under quasi-static compression,arch bridge structure and stable long force chain in granular material hinder compression,so dynamic compression makes powders denser than quasi-static compression.Diferent from randomly stacked discrete particles,orderly arranged particle chain structures are applied to waveform control.By establishing the equivalent continuum model of orderly stacked cylindrical shell chain structure,the stress wave propagation process and its geometric dispersion characteristics in the cylindrical shell chain under mass impact were analyzed.Based on the Rayleigh-Love wave equation with lateral inertia correction,the influence of geometric dispersion on stress wave propagation was analyzed,and the dimensionless governing equation of the cylindrical shell chains under the mass impact with an initial velocity is established.Based on the Laplace transform and its inverse transform,the analytical solution of the governing equation is obtained.The predicted force and displacement history curves,strain and velocity distributions are in good agreement with the mesoscopic finite element results,and are applicable for cylindrical shell chains with different wall thicknesses.The effects of Poisson's ratio,radius of gyration,impact mass and velocity on wave dispersion in the cylindrical shell chain under mass impact were studied.The results show that the peak strain,the amplitude of wave oscillation,the width of wave front and the wave velocity at the maximum strain position are mainly related to the Poisson's ratio and inertia radius.The larger the Poisson's ratio and the radius of gyration of the cylindrical shell chain,the smaller the peak strain,the stronger the oscillation of the strain waveform,the wider the width of the waveform front,and the smaller the wave velocity at the maximum strain position.The simplified model of elastic wave propagation in the cylindrical shell chain under mass impact is of great significance to reveal the dispersion mechanism of the cylindrical shell chain.Cylindrical shell chain can disperse waveform.If shape gradient(asymmetry)is introduced,pulse transmission may be controlled in a wider range.In view of this,a new structure,i.e.variable aspect ratio cylindrical shell chain,was proposed.In the case of mass impact,a stress wave propagation model of gradient cylindrical shell chain was established,and the analytical solutions of the displacement field,velocity field and strain field were derived by using the Laplace transform method.The wave propagation in the chain with a positive aspect ratio gradient(aspect ratio increasing along the loading direction)was investigated.It is found that the force is amplified with the wave propagation due to the dramatic increase of the apparent elastic modulus along the impact direction,whereas the chain with a negative aspect ratio gradient shows the opposite.The features of wave acceleration or deceleration and shock attenuation or amplification depend on whether the apparent elastic modulus applied to the chain is positive or negative gradient.The mechanism of impact amplification and attenuation is that for linear aspect ratio gradient chains,the change of elastic modulus along the loading direction is more dramatic than that of strain.Compared with the density gradient chain,the aspect ratio gradient chain can control the transmission pulse in a wider range due to its different structure.And,a unique energy redistribution mechanism in the positive aspect ratio gradient chains was revealed.With the wave propagation,the peak strain energy increases in the positive aspect ratio gradient chain,while it decreases in the positive density gradient chain.This unique energy redistribution mechanism of the positive aspect ratio gradient chain can be used to develop new energy storage systems.In addition,the results of parameter analysis based on the theoretical model show that in the linear aspect ratio gradient chain,the transmitted peak force increases with the increase of the aspect ratio distribution parameters.The cylindrical shell chains with different aspect ratio distributions were prepared by 3D printing technology,and the dynamic impact tests of the 3D printed samples were carried out.The results of the experiment and numerical simulation confirm the validity of the theoretical analysis.The research can be used to manipulate the waveform effectively,i.e.to amplify or attenuate the impact pulse,and can be used to guide the optimal design of the waveform controller.