轮对运动状态对轮轨滚动接触应力的影响

分析计算了锥型踏面轮对沿轨道滚动接触时轮轨接触几何参数和不同运动状态下的轮轨之间的刚性蠕滑率。根据确定的轮轨接触几何参数和轮轨接触界面之间的蠕滑率,利用非Hertz滚动接触理论分析计算了锥型轮对和钢轨滚动接触斑作用力的分布。再利用弹性力学中Bossinesq-Cerruti力/位移计算公式并借助Gauss数值积分方法,确定了轮轨滚动接触时体内的弹性位移、应变和应力随轮对运动状态变化情况。数据结果为轮轨强度设计提供了重要的参考依据。     

回转窑滚圈与托轮接触应力解析

 滚圈与托轮接触应力的计算对回转窑滚动接触疲劳寿命预测起到至关重要的作用。考虑滚圈与托轮在牵引滚动接触状态下相互之间传递法向力和切向摩擦力的综合作用,将其简化为二维平面应变问题,然后从经典Hertz理论中弹性半空间在分布法向力和切向力作用下受载区应力分量的积分表达式出发,对接触区对称平面上各点的应力进行分析与计算,得出受载区各主应力的解析表达式,并采取最优函数逼近法求得半解析解,确定了最大主剪应力及其位置,能满足工程应用的要求。     

Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials

This paper presents the results of a comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials using the discrete element method. The study used the Particle Flow Code (PFC) to simulate biaxial compression tests in granular materials. To study the effects of rolling resistance, a user-defined rolling resistance model was implemented in PFC. A series of parametric studies was performed to investigate the effects of different levels of rolling resistance on the stress–strain response and the emergence and development of shear bands in granular materials. The PFC models were also tested under a range of macro-mechanical parameters and boundary conditions. It is shown that rolling resistance affects the elastic, shear strength and dilation response of granular materials, and new relationships between rolling resistance and macroscopic elasticity, shear strength and dilation parameters are presented. It is also concluded that the rolling resistance has significant effects on the orientation, thickness and the timing of the occurrence of shear bands. The results reinforce prior conclusions by Oda et al. (Mech Mater 1:269–283, 1982) on the importance of rolling resistance in promoting shear band formation in granular materials. It is shown that increased rolling resistance results in the development of columns of particles in granular materials during strain hardening process. The buckling of these columns of particles in narrow zones then leads to the development of shear bands. High gradients of particle rotation and large voids are produced within the shear band as a result of the buckling of the columns.     

Statistical properties of a 2D granular material subjected to cyclic shear

This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, P, and the mean contact number, Z. This relationship applies to the shear stress τ, except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as P, τ and Z are strongly hysteretic functions of the strain, ε. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks.     

Distinct simulation of earth pressure against a rigid retaining wall considering inter-particle rolling resistance in sandy backfill

The focus of this paper is to analyze earth pressure against a rigid retaining wall under various wall movement modes with a contact model considering inter-particle rolling resistance implemented into the distinct element method (DEM). Firstly, a contact model considering rolling resistance in particles was generally explained and implemented into the DEM. The parameters of the contact model are determined from DEM simulation of biaxial tests on a sandy specimen. Then, the influence of inter-particle rolling resistance in the backfill is discussed by comparing the active and passive earth pressure against a rigid wall subjected to a translational displacement with and without inter-particle rolling resistance in the material. Third, the DEM model considering the rolling resistance is used to investigate active and passive earth pressures while the rigid wall moves in a more general manner such as rotation or translation. The influence of rolling resistance on the earth pressures is examined from the microscopic particle scale (e.g., shear strain field) as well as the macroscopic scale (e.g., the magnitude and action point of resultant earth pressures). Finally, the effect of the initial density and the particle size of the backfill are discussed. The results show that when rolling resistance in the particles is taken into account in the DEM simulation, the simulation results are more appropriate and are in line with practical situation. Hence, particles rolling resistance should be taken into account to get more realistic results in DEM analyses.     

多步非稳态载荷下钢轨滚动接触应力和弹塑性变形分析

采用弹塑性有限元法,分析了多步非稳态载荷下钢轨滚动接触应力和变形。多步载荷指的是钢轨同时受到机车和车辆车轮的反复作用或多趟列车通过钢轨。通过在钢轨表面重复移动Hertz法向压力分布和切向力分布来模拟车轮的反复滚动作用。材料循环塑性本构模型采用考虑材料棘轮效应的Jiang-Sehitoglu模型。分析结果表明:在非稳态载荷作用下,钢轨接触表面产生不均匀塑性变形而形成波状表面;多步载荷对钢轨残余应力影响不大;随着机车车轮通过次数的增加,钢轨残余剪应变、表面材料位移、波深和残余累积等效塑性应变将增大,在机车车轮通过之后,随着车辆车轮通过次数的增加,前三个量将减小,而残余累积等效塑性应变继续增大,但其增大的速率变小。随着机车和车辆车轮反复滚过钢轨,钢轨残余剪应变、表面材料位移和波深变化速率即棘轮率呈衰减性。     

DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials

The importance of particle rotation to the mechanical behavior of granular materials subject to quasi-static shearing has been well recognized in the literature. Although the physical source of the resistance to particle rotation is known to lie in the particle surface topography, it has been conveniently studied using the rolling resistance model installed typically on spherical particles within the DEM community. However, there has been little effort on assessing the capability of the rolling resistance model to produce more realistic particle rotation behavior as exhibited by irregular-shaped particles. This paper aims to eliminate this deficiency by making a comprehensive comparison study on the micromechanical behavior of assemblies of irregular-shaped particles and spherical particles installed with the rolling resistance model. A variety of DEM analysis techniques have been applied to elucidate the full picture of micromechanical processes occurring in the two types of granular materials with different particle-level anti-rotation mechanisms. Simulation results show that the conventional rheology-type rolling resistance models cannot reproduce the particle rotation and strain localization behavior as displayed by irregular-shaped materials, although they demonstrate clear effects on the macroscopic strength and dilatancy behavior, as have been adequately documented in the literature. More insights into the effects of particle-level anti-rotation mechanism are gained from an in-depth inter-particle energy dissipation analysis.     

Depth-dependent strain fields of articular cartilage under rolling load by the optimized digital image correlation technique

It is significant to investigate the depth-dependent mechanical behaviors of articular cartilage under rolling load since considerable rolling occurs for cartilage joint in activities of daily living. In this study, the rolling experiments of articular cartilage were conducted by applying an optimized digital image correlation (DIC) technique for the first time and the depth-dependent normal strain and shear strain of cartilage were analyzed. It is found that the normal strain and shear strain values of different layers increase firstly and then decrease with rolling time, and they increase with increasing compressive strains. The normal strain and shear strain values decrease along cartilage depth with constant compressive strain. The normal strain values of different normalized depth decrease with increasing rolling rates. The shear strain values of superficial layer and middle layer decrease; however there are no major changes for the shear strain values of deep layer with increasing rolling rates. The normal strain values with different rolling time increase with increasing rolling numbers and the 30.6% increase in initial normal strain is observed from 1st to 99th cycle. The fitting relationship of the normal strain and normalized depth was obtained considering the effects of compressive strain and rolling rate and the fitting curves agree with the experimental results for cartilage very well.     

The effect of a sliding load on strain gauges embedded under the contact surface

Strain gauges embedded in plastic models can be used in three dimensional stress analysis. When gauges are located immediately below a surface subjected to the tangential traction of a sliding load, unexpected values are recorded. This phenomenon was investigated by suitably loading a semi–infinite solid with normal and shear stresses and comparing theoretical strain values with the experimental results. The comparison showed that strain gauges embedded in epoxy can be successfully used under sliding loads provided that the gauge depth below the contact surface is greater than a critical value.     

The Effect of Friction on Wide Shear Bands

Frictional and frictionless granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasi-static deformation. Here, the differences between frictional and frictionless materials are elaborated using discrete element simulations (DEM). Several continuum fields like the density, the velocity field, the deformation gradient, and the stress are used here for comparison.

Interestingly, the shear stress intensity, i.e., the shear stress divided by the pressure, is approximately constant throughout the wide shear band, as long as the strain rate is large enough—indicating a Mohr-Coulomb type yield stress fluid. The “viscosity,” i.e., the shear stress divided by the strain rate, is proportional to the pressure, which is increasing with the contact number density. Furthermore, the viscosity is inversely proportional to the nondimensional strain rate, indicating shear softening behavior inside the wide shear bands.     

Exploring the critical state properties and major principal stress rotation of sand in direct shear test using the distinct element method

This paper provides insights into the critical state properties and major principal stress rotation of sands in direct shear tests using the distinct element method (DEM), in which a three dimensional contact model considering rolling and twisting resistances proposed by the authors was implemented. Firstly, the DEM was used to simulate a series of direct shear tests. Then the macroscopic characteristics of the DEM samples and the critical state properties within the shear band were analyzed, including the major principal stress rotation and the stress level dependency of peak strength. Finally the effect of the grain angularity was investigated. The rolling and twisting resistances were separately considered to check their individual effects. The results demonstrate the strong capability of DEM with the 3D contact model to capture the mechanical behavior of sands in direct shear tests. After a global shear strain of 15%, the shear zone reached the critical state while the whole sample did not. The major principal stress rotation angle evolved in a similar trend to that of the shear stress, and the stress level dependency of the peak strength of dense sand can be attributed to the fact that the vertical stress affects the rotation of the major principal stress. Higher shear strength, more obvious dilatancy and upward move of critical state line on the \(e\hbox {-lg}p\) plane were obtained when larger values of shape parameter (leading to greater rolling and twisting resistances) were used. And twisting resistance is much less important relatively in the presence of rolling resistance.     

The model of the residual life time estimation of tribojoint elements by formation criteria of the typical contact fatigue damages

A two-dimensional theoretical model is proposed for investigation of the fracture processes and assessing residual contact durability of solids subjected to cyclic contact. The model is based on the step-by-step calculation of fatigue crack propagation paths in the contact region which includes the criteria of local fracture of materials under complex stress–strain state, characteristics of fatigue crack growth resistance of materials and also presupposes the possible change of fracture mechanisms (transversal shear – normal opening fracture mechanisms). Within the frames of the model the peculiarities of formation of such typical contact fatigue damages like pits, spalls, squat (“dark spot”) and cracking (“checks”) in rolling bodies and edge cracks growth in the elements of fretting couples under conditions of sliding/sticking between them are investigated. Examples of assessing the life time by damages formation (pitting and spalling) in the contact region are presented.     

Surface strain measurements of fingertip skin under shearing

The temporal evolution of surface strain, resulting from a combination of normal and tangential loading forces on the fingerpad, was calculated from high-resolution images. A customized robotic device loaded the fingertip with varying normal force, tangential direction and tangential speed. We observed strain waves that propagated from the periphery to the centre of the contact area. Consequently, different regions of the contact area were subject to varying degrees of compression, stretch and shear. The spatial distribution of both the strains and the strain energy densities depended on the stimulus direction. Additionally, the strains varied with the normal force level and were substantial, e.g. peak strains of 50% with a normal force of 5 N, i.e. at force levels well within the range of common dexterous manipulation tasks. While these observations were consistent with some theoretical predictions from contact mechanics, we also observed substantial deviations as expected given the complex geometry and mechanics of fingertips. Specifically, from in-depth analyses, we conclude that some of these deviations depend on local fingerprint patterns. Our data provide useful information for models of tactile afferent responses and background for the design of novel haptic interfaces.     

Analysis of the energy and damage evolution rule for sandstone based on the particle flow method

We use the particle flow code PFC3D to simulate the triaxial compression of sandstone under various radial stresses and loading strain rates to determine the triaxial stress-strain curves, crack propagation path, and contact forces to investigate the failure process of sandstone. We analyze the energy and damage evolution during triaxial compression. The results indicate that the tension and shear-induced cracks increase with the increase of radial stress under the same loading strain rate. Both normal and tangential contact forces exhibit strong anisotropy and increase with radial stress and strain rate. The normal contact force has an approximately symmetrical distribution with respect to the horizontal plane, whereas the tangential contact force has an approximately symmetrical distribution with respect to the axis. For the characteristics of the energy evolution, the boundary energy density, strain energy density, and dissipated energy density all increase linearly with the radial stress, and the boundary energy density increases at the fastest rate, followed by the strain energy density and dissipated energy density. In the post-peak stage the primary energy consumption is the dissipated energy. After that, in the remaining stage the strain energy decreases gradually. By analyzing the evolution of the damage variables in the prepeak area we observed that the damage variable followed an exponential relationship with the axial strain. When the loading strain rate is constant, the damage variable corresponding to the same strain value decreases with increase of radial stress. The results indicate that the increase in radial stress delays the damage acceleration. In contrast, the effect of the loading strain rate on the damage variable is small. The findings reveal the internal structural evolution of rocks during deformation and failure.

     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

Simple shear in 3D DEM polyhedral particles and in a simplified 2D continuum model

We develop a discrete element model (DEM) simulation of mixed regular rounded polyhedra and spheres in simple shear with walls and periodic boundaries in 3-dimensions. The results show reasonably realistic behaviour developing shear and dilation or compaction depending on whether the initial state is dense or loose. Similarly non-coaxiality of principal stress direction and strain rate direction are shown. Polyhedra show more general realistic behaviour than spheres but take significantly longer to run. Particle forces include normal elastic, damping, and tangential friction and rolling friction. No cohesion or interstitial fluid is modelled. A separate simplified dynamic implicit finite difference Eulerian continuum model is developed and its parameters are used to fit the DEM results. This uses mass and momentum balances, a non-linear constitutive model and Mohr–Coulomb failure criterion. It runs in 2D with periodic boundaries effectively making it pseudo-1D. The model can reproduce the general trend of the DEM results and is a good basis for further development and understanding the physics.     

Examining the mechanisms of sand creep using DEM simulations

In this study, DEM simulations of triaxial creep tests on dense and loose sand samples were carried out to examine the micromechanics involved during creep. The simulated creep responses reproduce qualitatively the published experimental results. During the primary creep, the creep stress is gradually borne by the contact normal forces instead of contact tangential forces so that the columnar particle structures can be formed. This process also leads to a continuous decrease in the creep rate. The columnar structures eventually are completely formed and the creep rate reaches a minimum. However, the structures become meta-stable and susceptible to buckling. This explains why a sand packing does not show an extended period of secondary creep in the experiment. Buckling of the columnar structures also gives rise to maximum dilatancy and a sharp transition of the major fabric orientation of weak forces from horizontal to vertical. The continuous buckling process of columnar structures increases the creep rate and sliding ratios of contacts during the tertiary creep. In addition, the trend of contact tangential forces decreasing and contact normal forces increasing is reversed. Finally creep rupture occurs as the creep stress–strain line intersects the complete stress–strain curve. All the creep samples follow their original volume-change tendency to continue their dilation or contraction response during creep.     

DEM investigation on the evolution of microstructure in granular soils under shearing

The mechanical behaviors of granular soils at different initial densities and confining pressures in the drained and undrained triaxial tests are investigated micromechanically by three-dimensional discrete element method (DEM). The evolutions of the microstructure in the numerical specimen, including coordination number, contact force and anisotropies of contact normal and contact force, are monitored during the shearing. The typical shear behaviors of granular soils (e.g. strain softening, phase transformation, static liquefaction and critical state behavior) are successfully captured in the DEM simulation. It is found that the anisotropies of contact normal, normal and tangential contact forces comprise the shear resistance and show different evolution features during shearing. After large strain shearing, the microstructure of the soil will finally reach a critical state, although the evolution path depends on the soil density and loading mode. Similar to the macroscopic void ratio $e$ and deviatoric stress $q$ , the coordination number and anisotropies of contact normal and contact force at the critical state also depend on the mean normal effective stress $P^{\prime }$ at the critical state.     

基于面心立方孔洞堆砌模型的泡沫铝准静态及动态压缩模拟研究

以有限元分析软件 ANSYS 的 Workbench 为平台,以高孔隙率面心立方孔结构(Face centered cubic, FCC)的泡沫铝模型为对象,进行了准静态压缩和落锤冲击的有限元模拟。高孔隙率泡沫铝特指孔隙率(Porosity, Pr)在85%~90%之间的泡沫铝。已有的实验结果表明,孔隙率为90%的泡沫铝的准静态压缩下屈服平台应力值为3 MPa,当冲击应变速率在900 s-1以上时,其屈服平台的应力值稳定在7 MPa 左右;模拟结果与实验结果一致,并发现当应变速率达到35342 s-1后,泡沫铝的屈服平台应力值会再次大幅升高,达到14 MPa。根据泡沫铝压缩模拟的应力云图,揭示了不同应变速率下泡沫铝的吸能能力和变形模式的对应关系,并从结构变形的角度解释了泡沫铝的抗冲击吸能性能优于其准静态压缩的原因。