Sliding-induced adhesion of stiff polymer microfibre arrays. II. Microscale behaviour.

The adhesive pads of geckos provide control of normal adhesive force by controlling the applied shear force. This frictional adhesion effect is one of the key principles used for rapid detachment in animals running up vertical surfaces. We developed polypropylene microfibre arrays composed of vertical, 0.3 microm radius fibres with elastic modulus of 1 GPa which show this effect for the first time using a stiff polymer. In the absence of shear forces, these fibres show minimal normal adhesion. However, sliding parallel to the substrate with a spherical probe produces a frictional adhesion effect which is not seen in the flat control. A cantilever model for the fibres and the spherical probe indicates a strong dependence on the initial fibre angle. A novel feature of the microfibre arrays is that adhesion improves with use. Repeated shearing of fibres temporarily increases maximum shear and pull-off forces.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

The contact properties of naturally occurring geologic materials: experimental observations

The discrete element method (DEM) is seeing widespread use in geotechnical applications and it is generally acknowledged that the validity of DEM simulations involving this class of materials depends critically on employing realistic contact laws. To support the development of such contact laws for common naturally occurring materials, we have conducted grain-to-grain contact experiments on several quartz sands, magnesite (limestone), crushed and ball-milled gneiss and ooids (precipitated calcium carbonate spheroids) and two reference materials (glass beads and the synthetic Delrin). Here we present the results of normal and shear contact experiments on these materials, with emphasis on the range of behavior encountered and aspects of behavior that deviate from current thinking on the topic. The development of contact laws based on the results presented herein, macroscopic frictional sliding and the implementation of the contact laws in DEM simulations are addressed in separate publications. The present experiments primarily examined the cyclic loading response, which allowed for a precise determination of normal and shear contact stiffness and loss compliances. Deformation generally consisted of elastic, anelastic and permanent components and the latter could be observed in shear prior to macroscopic sliding. Normal and shear stiffness ranged from 0.2–2.0 to 0.1–\(1.0\,\hbox {MN\,m}^{-1}\), respectively although the ratio of shear to normal stiffness for specific materials varied from 0.3 to \({\approx }1\). Frictional loss was observed to varying degrees in all of the contacts examined and internal friction in shear was found to be constant prior to the onset of permanent deformation. Internal friction ranged from barely perceptible to 0.1 for normal contacts and from 0.02 to 0.3 in shear. The modeling implications of the findings are examined as well.     

Grain-scale mechanics of geologic materials and lunar simulants under normal loading

A realistic characterization of contact behavior is crucially important to the development of discrete element models of naturally occurring granular media. Although contact behavior can be inferred by adjusting the numerical simulations to agree with results from geotechnical laboratory tests, it is preferable to establish the contact laws directly with grain-scale experiments. Moreover, such an approach provides an objective way to establish the influence of characteristics such as mineralogy, microstructure, hardness, grain size, shape and surface roughness on contact behavior, and thus opens the door to a more fundamental understanding of granular media mechanics. With this motivation, we are conducting an integrated experimental/DEM modeling program with a focus on naturally occurring geologic materials. The goals of this work are to improve the physical basis of this powerful numerical modeling method, and to develop a broader understanding of the contact behavior of naturally occurring materials of interest to the geotechnical engineering community. This paper describes equipment and methods that we have developed to conduct normal contact experiments on pairs of unbonded grains of crushed and ball-milled gneiss, Ottawa sand, and lunar simulants. Contact curvatures ranged from 0.05 to 8.2 mm for the grains examined. The computer-controlled testing system applied normal forces ranging up to 10 N, and both monotonically increasing (ramp) and cyclic loading waveforms were employed. A laser proximity gauge with 100 μm resolution provided direct grain-to-grain deformation readings. The resulting force–displacement relationships showed that Hertzian behavior emerged above a normal force threshold ranging from several tenths of a Newton to several Newtons, depending on surface roughness, and approximately linear behavior was observed below the threshold for Hertzian behavior. Normal contact stiffness ranged from 0.2 to over 2 MN m⁻¹ for forces up to 10 N, and depended on material type, local radius of curvature and surface roughness. Hysteresis was generally observed under cyclic loading and calculated values of the apparent internal friction ranged from 0.01 to 0.16, depending on material type, contact geometry and force level. The test system was capable of inducing damage in some contacts with a low radius of curvature, and it was observed that minor levels of damage typically increased stiffness and frictional loss of the contact. Engineer Research and Development Center U.S. Army Corps of Engineers.     

A frictional spring and cohesive contact model for accurate simulation of contact forces in numerical manifold method

“Open-close iteration” is a crucial algorithm for handling complex contacts in numerical manifold method (NMM) and discontinuous deformation analysis (DDA). This algorithm has proved to be robust and efficient for decades. However, as some researchers have pointed out, the original open-close iteration may involve errors in sliding tests, especially in critical sliding tests with cohesive contacts. In this study, two major problems in the original algorithm are found to be nonconvergent contact force and early removed cohesive strength. The modifications are the following: (a) a frictional spring. By avoiding the trail value of normal contact force, we added a new frictional spring to the iteration scheme. This spring can apply accurate friction and can help ensure the convergence of contact forces. (b) A cohesive contact model. The original scheme can encounter an “early failure” in cohesive contacts. After investigating how contacts provide shear resistance, we found the cause and then provided a simple correction of the cohesive issue. The new algorithms in this article are essential for accurately simulating contacts by NMM/DDA.     

Shear properties of organic films adsorbed on silica fibres

Contact adhesion and sliding friction of octadecylamine and silane molecules adsorbed on silica fibre were measured with orthogonally crossed silica fibres using an electronic microbalance. Interfacial shear strengths, τ, as a function of contact pressure, P, between organic films were deduced from the adhesional model of friction using the measured frictional force and the calculated real area of contact. The pressure dependence of the interfacial shear strength was then interpreted in terms of the molecular interaction of adsorbates with solvent and the surface energetics of molecules adsorbed on the silica fibre. This revised version was published online in November 2006 with corrections to the Cover Date.     

Contact and frictional behavior of rough surfaces using molecular dynamics combined with fractal theory

The microcontact behavior of a copper asperity on a diamond plate was carried out using a molecular dynamics (MD) simulation with the parallel algorithms atom decomposition method. The results show that the dynamic frictional force had an oscillated behavior when the flat diamond plane slipped through the copper asperity. The contact load, contact area, dynamic frictional force, and dynamic frictional coefficient increased as the contact interference increased at a constant loading velocity. The dynamic frictional force and dynamic frictional coefficient increased as the sliding velocity increased. Furthermore, the microcontact behavior can be evaluated between a rigid smooth flat plane and a rigid smooth hemisphere to a deformable rough flat plane by combining the deformed behavior of the asperity obtained from MD results and the fractal and statistic parameters.     

Experimental studies on shear failure of freeze-bonds in saline ice:: Part II: Ice-ice friction after failure and failure energy

This paper is the second of two papers that present and discusses the results from experiments where artificially created freeze-bonds made from saline ice were tested on direct shear with the freeze-bond oriented horizontally. It discusses the friction forces after freeze-bond failure and the failure energy.The friction force showed increasing linear trends with a non-zero intercept when plotted against the normal force. It shows that for low confinements Amonton's law is insufficient. For larger confinements the values of friction coefficient were in the range of previously reported measurements in ice-ice friction. A slightly decreasing trend of the frictional forces was found when the initial ice temperature increased.A Mohr-Coulomb type of model was proposed to model the ice-ice frictional stresses as function of the normal stresses. An empirical model was obtained to describe freeze-bond failure and subsequent deformation by introducing softening of the cohesion and angle of internal friction.The failure energy had similar trends to those observed for the freeze-bond shear strength when plotted against normal confinement, initial ice temperature and submersion time. Quadratic fitting to the data of failure energy as a function of freeze-bond shear strength allowed the estimation of the elastic shear modulus of the freeze-bond by applying a simple rheological model. The values found were between 2 kPa and 6 kPa which are very low compared with the shear elastic modulus for the ice blocks.     

Modelling dilation in an idealised asphalt mixture using discrete element modelling

This paper investigates the use of discrete element modelling (DEM) to simulate the behaviour of a highly idealised bituminous mixture under uniaxial and triaxial compressive creep tests. The idealised mixture comprises single-sized spherical (sand-sized) particles mixed with bitumen and was chosen so that the packing characteristics are known (dense random packing) and the behaviour of the mixture will be dominated by the bitumen and complex aggregate interlock effects will be minimised. In this type of approach the effect of the bitumen is represented as shear and normal contact stiffnesses. A numerical sample preparation procedure has been developed to ensure that the final specimen is isotropic and has the correct volumetrics. Elastic contact properties have been used to investigate the effect of the shear and normal contact stiffnesses on bulk material properties. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poisson’s ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. An elastic contact has been assumed for the compressive normal contact stiffness and a viscoelastic contact for shear and tensile normal contact stiffness to represent the contact behaviour in idealised mixture. The idealised mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on the rate of dilation with shear strain for the sand asphalt. The numerical results have been validated with experimental data.     

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.     

A solution method for planar and axisymmetric contact problems

A solution procedure for the analysis of planar and axisymmetric-contact- problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure are the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.     

基于接触分析的转定子系统整周碰摩故障模拟

以一个单跨双盘柔性转子系统为研究对象,建立转子系统的有限元模型,基于接触动力学理论,将转子和定子简化为一个点-点接触单元,通过转定子间的圆形间隙变化来模拟转定子的分离及整周接触,并通过碰摩力耦合转定子模型,采用增广的拉格朗日方法处理接触约束条件,用库仑摩擦模型模拟转定子之间摩擦,考虑不同转速、转定子间隙、转定子法向接触刚度、阻尼和摩擦系数对转子系统动力学特性的影响。研究结果表明：转速和转定子法向接触刚度对系统响应影响最大,转定子法向接触阻尼和摩擦系数次之,转定子间隙影响最小。     

Frictional contact of flexible and rigid bodies

 This paper is about planar frictional contact problems of both flexible and rigid bodies. For the flexible case a nonlinear finite element formulation is presented, which is based on a modified Coulomb friction law. Stick-slip motion is incorporated into the formulation through a radial return mapping scheme. Linearly interpolating four node elements and three node contact elements are utilized for the finite element discretization. The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented. In the rigid body case the contact problem is divided into impact and continual contact, which are mathematically described by linear complementarity problems. The impact in normal direction is modeled by a modified Poisson hypothesis, which is adapted to allow multiple impacts. The formulation of the tangential impact is grounded on Coulombs law of friction. The normal contact forces of the continual contact are such that colliding bodies are prevented from penetration and the corresponding tangential forces are expressed by Coulombs law of friction. Examples and comparisions between the different methods are presented. Received: 10 January 2001     

Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy

Indentation of a piezoelectric half-space by a flat circular indenter accompanied by frictional sliding is considered. Full-field electroelastic solutions in elementary functions are obtained. The solution is based on the correspondence principle between elastic and piezoelectric problems. Stiffness relations between applied load and resulting displacement are given in elementary functions. In conjunction with the conical and spherical solutions, given previously by Makagon et al. [A. Makagon, M. Kachanov, S.V. Kalinin, E. Karapetian, Indentation and frictional sliding of spherical and conical punches into piezoelectric half-space, Physical Review B 76 (2007) 064115 (14)], this work completes the set of limiting cases of tip geometries utilized in lateral force microscopy (LFM) technology. Implications for quantitative interpretation of scanning probe microscopy (SPM) data and tribological data are analyzed.     

Effect of frictional force and nose shape on axisymmetric deformations of a thick thermoviscoplastic target

Summary We study thermomechanical deformations of a thermally softening viscoplastic thick target impacted at normal incidence by a cylindrical rod made of a material considerably harder than the target material. Thus we regard the penetrator to be rigid and analyze the effect of the penetrator nose shape and the frictional force at the target/penetrator interface on target's deformations. In the postulated expression for the frictional force, the coefficient of friction, defined as the ratio of the tangential force at a point to the normal force there, is a function of the relative speed of sliding between the two bodies. The computed depth of penetration is found to match very well with that observed in experiments by Forrestal et al. For each nose shape studied, the consideration of frictional forces reduces significantly the computed penetration depth. For the same kinetic energy of the penetrator, the penetrator with a sharp nose gives higher values of the penetration depth as compared to that obtained with a blunt nose.     

Bridging micromechanisms of Z-pin in mixed mode delamination

A numerical model for analyzing the bridging mechanisms of Z-pining in composite laminates is presented. Main failure modes of the Z-pin are: debonding between the Z-pin and matrix, split and rupture of the Z-pin material; these have been taken into account here. The cohesive zone model was utilized to simulate splitting and rupturing within the Z-pin. The interfacial contact between the Z-pin and matrix was assumed to be initially bonded, followed by debonding and frictional sliding. The present model is validated by mode I experiments; the mode II simulation is verified by similar Z-pin shear tests. It is observed that the shear bridging force component increases with the mode II ratio, while the mode I bridging response decreases slightly with the mode II ratio. An enhanced frictional zone is located near the delamination surface. The mode II bridging force in cross-ply laminates is higher than that in UD laminates, while the Z-pin is more likely to rupture in cross-ply laminates when the mode II ratio is relatively high. The presented model can be used to evaluate the Z-pin bridging response. The calculated bridging force is suitable for analyzing the mechanical performance of Z-pinned structures.     

Study of friction and wear mechanisms at high sliding speed

The aim of this work is to propose an analysis of mechanisms inducing surface interaction by friction during high sliding speed. Specific devices including a ballistic setup were used to reproduce extreme sliding conditions combining high speed and high pressure. The titanium alloy/tantalum tribo-pair is chosen to investigate the frictional and material transfer mechanisms. The tangential force measurement is used to follow the evolution of the friction coefficient at a macroscopic scale. The evolution of the sliding surface was analyzed by confocal 3D microscope to evaluate material transfer and real contact surface area. Numerical modeling of micro-contact at the asperities scale is presented to illustrate the scenarii involved during friction. The energy needed to shear a junction is estimated and analyzed for several types of interaction. Different behaviors have been taken into account in order to investigate the global forces generated by the contact including strong and weak contacts. The analysis of energy is available to predict the global friction force in a large range of velocities. Correlations between experimental measurements and numerical predictions are used to validate the proposed approach. The results can be interpreted as following: (1) at lower velocity the main mechanism dominating the interaction between asperities becomes ploughing with large volume of plastic deformation (2) at higher velocity the main mechanism is shear localization requiring less energy and force for shearing the junctions.     

Plastic deformation of silicon during contact sliding at ambient temperature

Evidence of plastic deformation during contact sliding of silicon under relatively low loads at room temperature is presented. Sapphire spheres were slid against Si (1 0 0) under various normal loads at temperatures above and below the critical temperature. Upon chemical etching, pits that are attributed to dislocations developed along the sliding track for all experiments. This suggests that plastic deformation can readily take place in covalent solids, such as silicon, even at temperatures far below the critical temperature. The results of this work support the view that frictional force and energy dissipation are largely caused by plastic deformation of the materials near the sliding contact even under relatively low loads.     

Friction and adhesion of silica fibres in liquid media

Contact adhesion and sliding friction between orthgonally configured silica fibres were measured in water, hexadecane, and cyclohexane. In the adhesion model of friction, the friction is interpreted in terms of shearing the junction and the shear strength () can simply be represented by =F/A whereFis frictional force andA is the real area of contact. While this model works well for the frictional behaviour of silica fibre in air, this was not the case in liquid media. The influence of liquid on the force required to break the adhesive junction cannot simply be interpreted in terms of the reduction in adhesional forces between two fibres; but the interpretations have to also include the nature of the liquids.     

On the contact force distributions of granular mixtures under 1D-compression

We investigate the distribution of the inter-particle contact forces inside granular mixtures of a sand-particle-size material and of a finer-particle-size material using the Discrete Element Method for frictional spherical grains. The numerical granular samples were compressed vertically with no lateral expansion following a common stress path in soil mechanics; the material states varied from jammed states towards highly jammed states with increasing solid fraction. The inter-particle contacts were categorized depending on the particle sizes of the two contacting entities. The force distributions of the contact networks were calculated depending on the contact types. It was found that different contact networks possess a similar shape of the probability distribution function of the contact forces when the populations of the respective particle sizes are involved in the percolation of the strong forces in the systems. For systems of a small percentage of the fine particles, the fine particles do not actively participate in the strong force transmission and the related contact force distributions reflect the characteristic of an unjammed state for the subsystem consisted of these particles.