Numerical construction of axisymmetric slip-line fields for indentation of thick blocks by rigid conical indenters and friction at the tool-metal interface

A general form of axisymmetric slip-line field solutions using numerical methods is given for cases of axisymmetric smooth and partially rough conical punch indentation of a rigid-perfectly plastic ductile material of semi-infinite thickness, where the cone semi-angle α varies from 15° to 90°. The basic problem of indetermination of the field and pressures near the apex of the conical punch experienced earlier by Locket (J. Mech. Phys. Solids 11, 345 (1963), [1]) for small cone angles was overcome by treating small segments of the curvilinear slip lines as arcs of circles of varying radii and assuming a straight boundary to the deformed lip. The numerical method outlined in detail by Chitkara and Butt (Int. J. Mech. Sci. 34, 833 (1992), [2]) allows the construction of axisymmetric slip-line fields for cone indentation, with varying frictional conditions at the tool-metal interface. The computer program developed requires only the cone semi-angle α and the frictional conditions at the tool-metal interface as the data set. It includes graphical plotting subroutines to plot the calculated slip-line field on a Hewlett-Packard 7550 plotter. A computographic plot of the associated velocity field for a typical case of conical punch indentation is also included.     

A theoretical study on the application of asymmetric rolling for the estimation of friction

In this work, a method for the estimation of friction coefficient is proposed based on the asymmetric rolling operation. Asymmetry is produced by operating the lower and upper rolls at different speeds. A slab method based computer code is developed for estimating the curvature of the rolled sheet under asymmetric rolling conditions. Strain-hardening behavior of the material has been incorporated and Wanheim and Bay's friction model is employed. The developed code is used for solving the inverse problem of estimating the coefficient of friction by measuring the curvature of the rolled sheet under known operating conditions. The simulations show a good potential of the method.     

A continuum plasticity model for the constitutive and indentation behaviour of foamed metals

A yield surface is proposed that can be fitted to the plastic flow properties of a broad class of solids exhibiting plastic compressibility and different yield points in tension and compression. The yield surface is proposed to describe cellular solids, including foamed metals, and designed to be fitted to three experimental results: (1) the compressive stress–strain response (including densification), (2) the difference between the tensile and compressive yield points and (3) the degree of compressibility of the foam, as measured by the lateral expansion during a uniaxial stress compression test. The model is implemented using finite elements and used to study the effects of plastic compressibility on two problems: the compression of a doubly notched specimen and indentation by a spherical indenter. The model is then fitted to the properties of a typical closed cell aluminum foam and used to study indentation into a dense aluminum face sheet on a foam foundation. The dependence of the indentation load–displacement curve on the relevant material and geometric parameters is determined, and a single load–displacement relation is presented which approximates the behaviour of a wide range of practical designs. These results can be used to design against indentation failure of sandwich panels.     

Calculation of the deformation component of the force of friction for a standard elastoviscous base

The deformation component of the force of friction is determined for the standard elastoviscous base using the energy approach. The obtained formula served to calculate the force of friction of a punch with extreme points. It is established that the friction coefficient grows as the punch becomes rougher. When the sliding velocity of the flat punch with the left angle tends to zero, the force of friction has a nonzero limit.     

球面接触轴颈摩擦问题的探讨

通过分析球面接触时,轴承与轴颈间的相对运动关系,计算轴承对轴颈的摩擦阻力矩,得出球面接触与一般圆柱面接触的摩擦阻力计算方法的区别,为准确进行机械的力分析,平衡力的计算以及零件的设计计算打下基础.     

Mechanical analysis of the scratching of metals and polymers with conical indenters at moderate and large strains

Scratch test provides a convenient mean to study the surface mechanical properties and the tribological performances of materials. The representative strain of the material in this test increases with the attack angle β of the indenter and so for a conical indenter increases as its apical angle 2θ decreases. But the mechanical analysis of this test by analytic models is very intricate. First we perform a preliminary discussion of the various aspects of the problem by considering the plane strain scratching of materials by wedges. After we present the conditions of the numerical simulations of the scratch test with conical indenters with a three-dimensional (3D) finite element code. These simulations provide the scratch geometry (contact surface, elastic recovery), the plastic strain map and the volume average plastic strain, the scratch hardness and the force ratio, the apparent friction coefficient μ₀=F_t/W. So we compare the behaviour of polymeric and metallic materials in scratch test at low and large strain and relate their difference in scratching resistance to their rheological properties. Polymers develop more higher elastic strains than metals a phenomenon which is characterised at low strain by the yield stress to Young's modulus ratio ε_e=σ_y/E. For θ=70.3° where pure ploughing occurs we study the scratching of elastic perfectly plastic solids with various values of ε_e under zero friction. Some comparisons with the behaviour in indentation are performed and we study the influence of friction in the scratching of workhardened steel with the same cone. At high strain the main rheological difference is the workhardening behaviour: it is described by a power law for metals and an exponential law for polymers. For θ decreasing from 70.3 to 20° we compare the behaviour of a cold worked steel to the behavour of polycarbonate, a thermoplastic polymer: a transition from ploughing to ploughing–cutting occurs only for steel.     

Reduction of the sliding friction of metals by the application of longitudinal or transverse ultrasonic vibration

The influence on sliding friction of ultrasonic vibration both parallel and perpendicular to the sliding direction has been studied for samples of aluminium alloy, copper, brass and stainless steel sliding against tool steel. Experiments were performed at a mean sliding speed of 50 mm s⁻¹, and at mean contact pressures up to 0.7 MPa, with vibration amplitudes up to 10 μm at 20 kHz. Significant reduction in sliding friction was observed (up to >80%) and good agreement was found between the measured values and the predictions of two simple models for the effects of longitudinal and transverse vibrations. Longitudinal vibration produces greater reduction in friction than transverse vibration at the same amplitude and frequency. At high vibration amplitudes, the reduction in friction was less than that predicted by the models, because significant metallic transfer occurred from the softer metals to the tool steel counter surface.     

Experimental and theoretical evaluation of the deformation component of the coefficient of friction

An analytical model for the calculation of the deformation component of a friction force in sliding of a hard spherical indenter on a viscoelastic material that is modeled as a Kelvin solid is constructed. The influence of mechanical properties of a material and slip velocity of an indenter on the contact characteristics and deformation component of the coefficient of friction is studied. An experimental method for estimation of deformation loss under friction of a high-elasticity material is proposed. A comparison of the results obtained with the use of theoretical model with experimental data is performed.     

The significance and use of the friction coefficient

The quantity known as the friction coefficient (or ‘coefficient of friction’) has long been used in science and engineering. It is easy to define, but not easy to understand on a fundamental level. Conceptually defined as the ratio of two forces acting, respectively, perpendicular and parallel to an interface between two bodies under relative motion or impending relative motion, this dimensionless quantity turns out to be convenient for depicting the relative ease with which materials slide over one another under particular circumstances. Despite the fact that both static and kinetic friction coefficients can be measured with little difficulty under laboratory conditions, the time- and condition-dependent characteristics of friction coefficients associated with both clean and lubricated surfaces have proven exceedingly difficult to predict a priori from first principles.The shaky nature of friction's fundamental underpinnings, has not prevented investigators from compiling lists of friction coefficients and publishing them for general use. Problems often arise, however, when engineers attempt to use tabulated friction coefficients to solve specific problems in mechanical design or failure analysis. The systems-dependence of frictional behavior is sometimes ignored, leading to misapplication of published data. This is particularly true for applications in nano-technology and others that differ from typical laboratory size scales. This paper will review the measurement and use of static and kinetic friction coefficients, discuss their usefulness, and describe the sources of frictional resistances in terms of shear localization.     

Dual extended Kalman filter for combined estimation of vehicle state and road friction

Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute(HSRI) tire model; the dual extended Kalman filter (DEKF) technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions(high-friction, low-friction, and joint-friction). On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.     

Tunable friction behavior of oriented carbon nanotube films

Measured friction coefficients of carbon nanotubes vary widely from μ < 0.1–μ > 1.0 [1–6], while theoretical studies suggest intrinsically high friction coefficients, approaching unity [7]. Here we report that measured friction coefficients of MWNT films are strong functions of surface chemistry and temperature, but are not dependent on the presence of water vapor. We hypothesize that the origin of the temperature dependence arises from the interaction of the surface chemical groups on the nanotubes [8–12] and rubbing counterface. The friction coefficient of individual films can be easily tuned by changing the surface temperature and chemistry of either the countersurface or the nanotubes, we have demonstrated the ability to create and control high and low friction pairs through plasma treatments of the nanotube films with argon, hydrogen, nitrogen, and oxygen. This behavior is completely reversible, and when coupled with the superior strength, thermal, and electrical properties of nanotubes, provides a versatile tunable, multifunctional tribological system.     

An enriched finite element algorithm for numerical computation of contact friction problems

In this paper, the extended finite element method (XFEM) is employed to model the presence of discontinuities caused by frictional contact. The method is used in modeling strong discontinuity within a standard finite element framework. In extended finite element method (XFEM) technique, the special functions are included in standard FEM to simulate discontinuity without considering the boundary conditions in meshing the domain. In this study, the classical finite element approximation is enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. These terms, which are included for enrichment of nodal displacements, depend on the contact condition between two surfaces. The partition of unity method is applied to discretize the contact area with triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, numerical examples are presented to demonstrate the applicability of the XFEM in modeling of frictional contact behavior.     

Effect of molybdenum disulphide upon the friction and wear in ceramic–steel pair

Friction and wear tests between a stationary block and a rotating ring under lubrication with molybdenum disulphide (MoS₂) were carried out at room temperature at a sliding distance of 500 m. Silicon nitride and cemented carbide blocks were pressed against a bearing steel ring, silicon nitride-bearing steel and cemented carbide-bearing steel pairs, by a load of 1600 N. The effect of molybdenum disulphide upon the coefficient of friction and the wear of the steel ring was discussed for both pairs in comparison with mineral oil lubricants. Molybdenum disulphide was more effective in reducing the coefficient of friction and the wear of the ring than the oil lubricants. Various mechanical pretreatment for forming MoS₂ film on the ring surface prior to the sliding tests were also considered. The mechanical pretreatment enabled the sliding test with the low friction coefficient even without lubrication over the sliding distance of 500 m. In general, the coefficient of friction and wear loss of the steel ring were smaller in the silicon nitride-bearing steel pair than in the cemented carbide-bearing steel pair.     

A finite-element analysis of the indentation of an elastic-work hardening layered half-space by an elastic sphere

An elastic–plastic contact problem in elastic-work hardening layered half-space indented by an elastic sphere was solved numerically using the finite element method. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stresses and deformation fields are presented for a relatively thin elastic layer. Differences between the elastic and elastic–plastic solutions for the contact pressure distribution have been investigated for various layer thicknesses. Crack initiation and decohesion of the layer was also discussed with reference to the growth of the plastic zone.     

Indentation of ring-stiffened cylinders by wedge-shaped indenters—Part 1: An experimental and finite element investigation

This is the first of a two part account of the indentation of ring-stiffened cylinders with fully fixed ends loaded centrally at mid-span by a wedge-shaped indenter. In this paper, the results of experimental tests on three similar cylinders of 315 mm outer diameter are presented and discussed. The cylinders were stiffened internally with rectangular sectioned rings and deep frames (bulkheads). Strains and deformations were determined in the dent-affected zone particularly along the top generator and around the circumferential mid-section. The cylinders were loaded up to failure, i.e. until rupture of the shell occurred. A finite element analysis for a geometrically identical specimen is also presented and compared to the experimental results.     

On the dynamics of the friction coefficient

The paper deals with the principal wear mechanism in brake systems and introduces a new dynamical model of the friction coefficient, where necessarily both friction and wear are taken into account. This model explains many open questions on the principal functionality of brake systems.In brake systems, characteristic structures are formed in the contact area by the flow of wear particles. Modulated by the friction power the wear particles are used by the system to build up hard contact patches on the brake pad. Nearly all energetic dissipation of the system is concentrated on these patches. By wear, these contact patches are destroyed after some time.So the friction coefficient is given by the equilibrium of flow of birth and death of contact patches. The resulting dynamical model describes the dynamical behaviour of the friction coefficient and the dependence of the temperature in the friction layer.This theory explains the fading effect of brake systems as well as complex hysteretic effects in the diagram of the friction coefficient versus the velocity, known from instationary measurement procedures.The structure of this theory seems to be quite general to describe other frictional systems too.     

The repeatability of friction and wear results obtained from unlubricated reciprocating sliding tests

Laboratory tests can help in the analysis of tribological failures of elements, and improve tribo‐systems by choosing appropriate materials. In order to characterise the friction and wear behaviour of candidate materials, various different test methods have been developed in the past and are still in use. One such method is the reciprocating sliding of a ball against a disc. In the work reported here, the repeatability of friction and wear results was evaluated with ten tests under identical conditions with a steel (100Cr6) or alumina (Al₂O₃) ball against a steel (100Cr6) disc under unlubricated conditions at room temperature. The influence of ambient humidity on friction and wear behaviour was determined in three additional tests in dry and in moist air, respectively. The repeatability of friction coefficient in normal air was better than 5% for alumina/100Cr6 and 12% for 100Cr6/100Cr6, while the repeatability of volumetric wear was slightly better than 10% for alumina/steel, and slightly worse than 10% for steel/steel. For both couples the coefficient of friction is lowest in moist air and about 50% higher in dry air. The coefficient of wear is also least in moist air and higher by a factor of 3(5) in dry air for tests with a 100Cr6 (alumina) ball.     

Stress drop and contact stiffness measured from stick-slip experiments on PMMA-PMMA friction

We present results from an extensive stick-slip study on PMMA-PMMA dry friction, where we studied the influence of a wide range of normal stresses, loading velocities and roughnesses of the sliding surfaces. In this paper we focus (a) on the analysis of a residual coefficient of friction, i.e., shear stress measured at the end of the slip phase divided by the corresponding normal stress, and (b) on the contact stiffness measured by plotting the relative displacement between sample against the shear stress during the stick phase. It is shown that the residual coefficient of friction (i) decreases as normal stress increases, (ii) shows a slight increase when the roughness of the sliding surfaces increases and (iii) does not vary according to the loading velocity. The contact stiffness proved independent of loading conditions and of the roughness of the sliding surfaces. These results are interpreted in terms of asperity interlocking. This revised version was published online in July 2006 with corrections to the Cover Date.     

The evolution of the surface layers on metals in sliding friction

The methods of speckle-interferometry, electron, optic, and atom-force microscopy were used to study the structure and regularities of deformation of surface layers on metals and alloys in friction. The causes of deformation localization are analyzed. An explanation of the strong wear resistance of Hadfield steel is proposed using data on the evolution of the surface layer structure.     

Interaction between friction surfaces and lubricating materials of the 2H-MoS2 type

The paper presents an analysis of investigations concerning the concept of the molecular-mechanical origin of the friction and fatigue mechanism as applied to solid lubricants having a structure of the 2H-MoS₂ type.