Rebound behaviour of spheres for plastic impacts

This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity V_i to the yield velocity V_y which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Young's Modulus E^* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(V_i/V_y)/(E^*/Y)]^−1/2.     

Particle sizing by quantitative acoustic emission

Two methods of particle sizing using an acoustic method are presented. The technique relies on the detection and measurement of elastic waves arising from impact of the particles with a small target plate. The acoustic impact signal, as measured from a high fidelity piezoelectric transducer, is characterised by the first wave arrival (compression wave) amplitude and risetime. A theoretical approach, based upon Hertzian impact theory and elastic wave propagation theory, is developed and used to determine the relationship between the impact dynamics of the particle and the acoustic signal. The first method of particle sizing relies upon amplitude measurements alone but requires accurate system calibration and full knowledge of the particle impact velocity, incident angle and coefficient of restitution. The velocity measurements were determined using a laser Doppler technique. The second approach for particle sizing incorporates risetime measurement and only depends very weakly upon the compression wave amplitude, thus minimizing the need for accurate absolute calibration. Knowledge of the impact velocity, incident angle, and coefficient of restitution were not required.Spherical particles of glass in the size range 35 to 140 µm diameter were dropped onto an aluminium target plate at an incident velocity of 8.1 m/s and angle to the surface normal of 0°, 40°, and 61°. The two acoustic methods were used to size the particles, and the results were compared to the particle size distributions obtained from video microscope measurements. The first sizing method undersized the smaller particles by 20% to 30% and oversized the larger ones by 5% to 10%. However, the second approach gave much smaller errors and consistently undersized all sizes of particle by just a few percent. This undersizing was understood in terms of some plasticity in the target that occurred during particle impact.     

The normal and oblique impact of three types of wet granules

Impact tests against a hardened steel plate have been carried out to obtain the coefficient of restitution of three types of spherical granules. The dominant elastic γ-Al₂O₃, the elastic-plastic zeolite 4A and the dominant plastic sodium benzoate have been chosen as granule samples. An electromagnetic canon has been constructed to accelerate the granules and to measure the normal coefficient of restitution. The moisture content of the granules has been varied so that the pore saturation ranges between of S = 0–1. Thereby, the influence of the moisture content on the normal coefficient of restitution could be determined. A free fall apparatus, on which the impact angle is changeable in the range of Θ_A = 0–80°, has been used to investigate the tangential coefficient of restitution. A high speed digital camera has been used to record the events of impact and rebound. The record frequency of the camera has been varied between 4,000 and 8,000 frames per second.     

Low-velocity collisions of particles with a dry or wet wall

Plastic and metal spheres were impacted at low velocities in the range 0.02–0.30 m/s with a quartz plate that was dry or covered with a thin oil layer. Collisions were performed with a specially designed device in the low-gravity environment provided by a KC-135 aircraft. A pendulum-based experimental set-up was also used to perform low-velocity collisions under normal gravity. The dry restitution coefficient (ratio of the rebound velocity and impact velocity) is found to decrease weakly with increasing approach velocity, as is the general case with materials exhibiting inelastic deformation. The wet restitution coefficient is zero below a critical velocity and then increases with the impact velocity before evening out to form a plateau. A simple model for the wet restitution coefficient, e_wet=e_dry(1−St_c/St), was found to adequately predict the restitution coefficient, as has been reported in earlier studies at higher impact velocities, where e_dry is the dry restitution coefficient, St is the Stokes number and St_c is the critical Stokes number below which no rebound occurs. Surface asperities are seen to cause more scatter in the data at low velocities than at high velocities. The data from pendulum experiments coincide with those collected in low gravity, thereby affirming their applicability for performing low-velocity collisions.     

冲击荷载下花岗岩残积土的滞回曲线特征与损伤定量评价

为评价冲击荷载下花岗岩残积土的损伤发展规律,基于不同振幅(A = 100 ～400 kPa)、频率(f=3 ～15 Hz)和围压(σ'3 =50 ～500 kPa)下室内循环冲击试验得到滞回曲线的形态特征,提出4个反映试样在冲击荷载下的能量消耗、损伤程度、刚度衰减和塑性应变发展特性的定量结构损伤参数:累积耗散能量EN、...     

A linear model of elasto-plastic and adhesive contact deformation

Rigorous non-linear models of elasto-plastic contact deformation are time-consuming in numerical calculations for the distinct element method (DEM) and quite often unnecessary to represent the actual contact deformation of common particulate systems. In this work a simple linear elasto-plastic and adhesive contact model for spherical particles is proposed. Plastic deformation of contacts during loading and elastic unloading, accompanied by adhesion are considered, for which the pull-off force increases with plastic deformation. Considering the collision of a spherical cohesive body with a rigid flat target, the critical sticking velocity and coefficient of restitution in the proposed model are found to be very similar to those of Thornton and Ning’s model. Sensitivity analyses of the model parameters such as plastic, elastic, plastic-adhesive stiffnesses and pull-off force on work of compaction are carried out. It is found that by increasing the ratio of elastic to plastic stiffness, the plastic component of the total work increases and the elastic component decreases. By increasing the interface energy, the plastic work increases, but the elastic work does not change. The model can be used to efficiently represent the force-displacement of a wide range of particles, thus enabling fast numerical simulations of particle assemblies by the DEM.     

铝合金梁受低速撞击动态响应的试验研究

梁受横向撞击时,其撞击力、局部变形和整体变形等动态响应受到撞击体质量、撞击速度、撞击位置以及梁刚度特性等因素的影响,研究这些参数对动力响应以及对撞击局部效应和整体效应的影响规律,是合理提出抗撞击防护手段的基础。该文利用低速落锤冲击试验装置进行了铝合金梁横向撞击试验,着重研究不同撞击速度、撞击位置和试件刚度等因素对铝合金梁所受撞击力、整体与局部变形、应变与能量等的影响规律。实验结果表明:随着撞击速度的增加,试件吸收能量的速率增大,撞击力幅值不断增加,撞击荷载主峰值段的持续时间减小;试件的整体变形和局部变形都明显增大,但局部效应相对增加更为显著;随着试件刚度（厚度）的增加,试件受相同速度撞击的吸收能量速率增大,撞击力荷载峰值显著增加;试件整体变形减小,而局部变形增加,说明试件刚度越大,其撞击整体效应减弱,而局部效应增强;试件受撞击后整体变形与撞击力相比明显具有滞后性,表明整体效应滞后于局部效应。     

Analysis of densification mechanisms of dry granulated materials

Dry granulation by roll compaction is a continuum manufacturing process to produce granules with improved flowability which can further be easily used in tableting process. However, the granules are non-homogeneous in density and have non-spherical shapes which impact their densification behaviour during die-compaction. The aim of this study was to investigate both the densification mechanism and the failure strength of granules of microcrystalline cellulose (MCC) and mannitol using Cooper-Eaton and Adams models. For both materials, the Cooper-Eaton approach led to the quantification of fractional volume compaction by particle rearrangement and by plastic deformation respectively to explain the difference in densification behaviour of raw material and granules. Moreover, the model showed its ability to capture the effect of granule density and granule sizes and to differentiate the densification mechanisms of MCC as a plastic material and mannitol as a brittle material. The Adams model was used to compute the failure strength of single granule from in-die compression data. The obtained results of the granules were in the range [0.6–1.43 MPa]. However, regarding the effect of granule density, the model showed mixed results indicating that the model is not representative of the studied granules which are not spherical and have a relatively wide range of sizes, nevertheless, the model was derived for near spherical particles with a narrow size distribution.     

Nanoindentation characterised plastic deformation of a Al0.5CoCrFeNi high entropy alloy

Abstract

The plastic deformation of a high entropy alloy Al_0.5CoCrFeNi was investigated by instrumented nanoindentation over a broad range of strain rates at room temperature. Results show that the creep behaviour depends on the strain rate remarkably. In situ scanning images showed a significant pile up around the indents, demonstrating that a highly localised plastic deformation occurred in the process of nanoindentation. Under different strain rates, contact stiffness and elastic modulus basically remain unchanged. However, the hardness decreases as indentation depth increases due to indentation size effect. For the same maximum load, serrations became less prominent as the loading rate of indentation increased. Similar serrations have been observed in the current alloy upon quasi-static compression.     

Characteristics of force chains in frictional interface during abrasive flow machining based on discrete element method

Abrading is a very important sub-technology of the surface treatment technology with vast applications in the industry. This study aims at analyzing the inherent laws of friction systems during abrading. In particle flow code modeling, the abrading process can be simplified to the movement of particles in a parallel-plate shear friction system. In this study, the PFC2D software is used to construct the particle flow friction system with the set of parallel plates and the model parameters according to the abrading processing equipment and processing materials, control the simulation of a single variable, and compare the output data to estimate the impact of change of parameters on the force chain. The simulation results show that the shear dilatancy can be divided into three stages:plastic strain, macroscopic failure, and granular recombination stages. The distribution and load rates of the weak force chains depend on the load, velocity, friction coefficient between granules, granular diameter, and number of granular layers. The number of granular layers and the load increase cause the direction of the force chain to be oriented with the vertical direction, and the force chains move toward the horizontal direction as the velocity increases. The increase in load does not cause the shear dilatancy stage to occur; the velocity, friction coefficient between granules, and granular diameter increase cause the shear dilatancy to occur gradually.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-018-0236-7     

地震时桥梁碰撞分析的等效Kelvin撞击模型

建立地震时桥梁碰撞分析的Kelvin撞击模型的参数确定方法。基于Hertz接触理论,考虑波动效应,按照最大撞击力与最大撞击变形的比值,确定Kelvin撞击模型的碰撞刚度;数值分析了影响Kelvin撞击模型阻尼系数取值的邻梁碰撞恢复系数。结果表明:Kelvin撞击模型的碰撞刚度随Hertz接触刚度、撞击速度以及短梁与长梁的长度比的增大而增大;波动效应对碰撞刚度的影响明显,不能忽略;邻梁碰撞恢复系数随撞击速度增大而减小,随短梁与长梁的长度比减小而减小;确定Kelvin撞击模型的碰撞刚度和邻梁碰撞恢复系数对城市桥梁的合理取值范围应分别为3×105kN/m―6×105kN/m和0.7―0.95。     

Hydrodynamics of granular gases of viscoelastic particles

Our study examines the long-time behaviour of a force-free granular gas of viscoelastic particles, for which the coefficient of restitution depends on the impact velocity, as it follows from the solution of the impact problem for viscoelastic spheres. Starting from the Boltzmann equation, we derived the hydrodynamic equations and obtained microscopic expressions for the transport coefficients in terms of the elastic and dissipative parameters of the particle material. We performed the stability analysis of the linearized set of equations and found that any inhomogeneities and vortices vanish after a long time and the system approaches the flow-free stage of homogeneous density. This behaviour is in contrast to that of a gas consisting of particles which interact via a (non-realistic) constant coefficient of restitution, for which inhomogeneities (clusters) and vortex patterns have been proven to arise and to continuously develop.     

Oblique impact simulations of high strength agglomerates

Different types of particle compounds like concrete particles can be considered as a model material of high strength agglomerates. It is necessary to investigate and understand fracture behaviour of these agglomerates in order to avoid breakage during storage, handling and transportation. The aim of the research is to examine the comminution behaviour of high strength agglomerates during oblique impact loadings.A two dimensional finite element analysis has been carried out to understand stress pattern distributions before crack initiation. Then a two dimensional discrete element method has been applied to study the fragmentation behaviour of the agglomerates. Concrete particles of B35 strength category have been chosen to represent the high strength agglomerates.Analysis is done with oblique impact loadings at different velocities from 7.7 to 180 m/s. The stressing conditions comprise low flow rate transportation and handling to high speed impacts during fall down in bunker, stock piles, ship loading or stressing in crushers and mill operations. Particle size distributions and new surface generation have also been evaluated in the paper.It is shown that at higher velocities, particle size distributions are identical to each other regardless of impact angle. Increasing impact velocity does not necessarily produce more new surfaces after certain velocity limit.     

Investigation on the impact and compression behavior of wet \upgamma -\hbox {Al}_{2}\mathrm{O}_{3} granules

The material behavior of dominant elastic–plastic \(\upgamma \) - \(\hbox {Al}_{2}\mathrm{O}_{3}\) granules has been experimentally studied by means of quasi static compression tests and dynamic impact tests until fracture. The obtained distributions of breakage velocity and specific breakage energy are compared. Thus, velocity dependent influences at stressing like viscous behavior can be derived. Additionally, the influences of particle size and moisture content on the material behavior are investigated.     

Cyclic surface deformation behaviour of ZrH2-purified iron: Effects of solute carbon,strain amplitude,strain rate and environment

The surface deformation behaviour in ZrH₂-purified interstitial-free iron was studied during fatigue in the push-pull plastic strain control mode under various combinations of plastic strain amplitude (5×10^–4, 5×10^–3), strain rate (5×10^–4, 3× 10^–2s^–1) and environment (ultrahigh vacuum, oxygen). Comparative tests of vacuum-melted commercially pure iron (CPI) containing 170 p.p.m. C were also conducted to investigate the effect of interstitials. At a plastic strain amplitude of 5×10^–4, the environmental effect is clearly exhibited regardless of the strain rate and the presence of interstitials. Fatigue in ultrahigh vacuum produces very fine slip lines not only in interstitial-free iron but also in vacuum-melted CPI. In the presence of oxygen, fatigue produces prominent slip lines, but those developed in CPI are more intense and coarser than those developed in interstitial-free iron. At the higher plastic strain amplitude of 5×10^–3, the gaseous environmental effect on the cyclic surface deformation is insignificant. The surface deformation behaviour is discussed in terms of the environmental effect and the basic mechanisms that govern the cyclic plasticity of iron.     

Measurements of the coefficient of restitution for particle collisions with ductile surfaces in a liquid

This paper presents the approach and rebound of a particle colliding with a deformable surface in a viscous liquid. The complex interaction between the fluid and the solid phases is coupled through the dynamics of the flow as well as the deformation process. For the experiments, steel particles impacted ductile aluminum alloys samples immersed in an aqueous mixture of glycerol and water. The experiments involved particle Stokes number from 5 to 10⁵ and deformation parameters from 10⁻² to 10². From the experiments, the coefficient of restitution is shown to depend on both these parameters. The coefficient of restitution is closest to unity when the deformation parameter is less than one and the Stokes number is greater than 10³. The coefficient of restitution decreases as the deformation parameter increases and when the Stokes number decreases.     

Design and construction of a micro‐indenter for tribological investigations

Characterisation of erosion contact conditions remains a challenge due to the chaotic morphology of eroded surfaces. The present work presents details on the design and construction of a low load micro‐indenter to investigate the initial stages of particle impact. Spherical ZrO₂ particles and angular SiC particles have been fitted onto stainless steel indenter tips to simulate contact between eroding particles on an aluminium surface. Contact loads between 50 and 1800 mN were utilised to elucidate the effects of load and indentation depth. Indented craters were subsequently imaged by the scanning electron microscope (SEM), revealing its particle dependent morphology. Crater area and depths from both types of particles were also quantified and subsequently correlated to the indentation load. It was demonstrated that contact pressure generated by angular particles are 1.5 times higher than those from spherical particles, resulting in greater plastic deformation and larger crater area at high loads. The work carried out during indentations were also calculated, it was shown that indentation experiments can be utilised for simulating dynamic erosion experiments under a large velocity range.     

Polymeric foam deformation under dynamic loading by the use of the microtomographic technique

The mechanical behaviour of polymeric foams depends on several parameters such as temperature, material density and strain rate. This last point implies that compression tests on conventional testing machines are not sufficient. Study of the behaviour in practical situations requires special apparatus like fly wheels, drop towers or Hopkinson bars, allowing high compression speeds. The polypropylene foams studied are multi-scale materials; agglomerated beads (2–3 mm in diameter), visible to the naked eye, are composed of microscopic closed cells (a few tens of microns). The response of the material to a shock consists of three regions: an elastic phase, a plastic phase and densification. The plastic phase is of prime interest since a great part of the shock energy is dissipated there. Microtomography was used in order to better understand damage mechanisms during the stress plateau of the plastic phase. The final objective of this work is to determine the strain field of porous materials at several levels of shock. As tomography is not fast enough to directly follow the impact deformation, interrupted impact tests were carried out by controlling the levels of sample deformation. Between each impact step, a microtomographic analysis offers insight on the progressive deformation of the sample. The results of these impact tests completed by a microtomographic visualisation in 2D are presented and commented in this paper.     

Transient Current Behaviour for Iron in 3.5%NaCl and 3.5%NaCl+ 1%NaNO_2 Solutions during Corrosion Fatigue

The transient current behaviour for Iron in 3.5%NaCl and 3.5%NaCl +1%NaNO2 solutions during corrosion fatigue (CF) process has been investigated at different given strain amplitudes and strain rates. The results show that elastic strain has little contribution to material dissolution. The elastic tension strain results in the decrease in the transient current, while the elastic compression strain increases the transient current. Compared to the elastic deformation, plastic deformation affects material dissolution evidently For iron in 3.5%NaCl solution, the strain amplitude plays a dominant role in the dissolution process accelerated by the plastic strain, while in 3.5%NaCl+1%NaNO2 solution, both the strain amplitude and strain rate play an important role in this process. In this paper, the effect of the elastic deformation on the material dissolution and the relation between the tension and compression current peak values under the plastic cycle deformation are discussed