Plastic deformation in rough surface line contacts—a finite element study

The paper describes an elastic-plastic finite element (EPFE) analysis of line contact between a cylinder and rigid plane using commercial software. The range of loading demonstrates the transition from purely elastic to fully plastic contact behaviour, revealing the residual deformations and stress fields upon unloading. A multiple contact configuration was analysed in the form of sinusoidal roughness. Results obtained under elastic conditions were validated by comparison with theoretical solutions. This model was extended by replacing the sinusoidal surface with a real roughness profile. Modelling multiple contacts indicates the influence of adjacent surface “asperities” on contact pressure and residual stress distributions.     

A simplified elliptic model of rough surface contact

Nayak's analysis of isotropic surface roughness as a random field has been extended to show that most summits are only mildly ell, the most common ratio of principal summit curvatures being near 2:1. Also from Nayak's theory, the distribution of the geometric-mean summit curvature with height has been obtained. By using an approximate solution for elliptical Hertzian contacts based on the geometric-mean summit curvature, the full elliptical solution of Bush, Gibson and Thomas can be reproduced more conveniently. Their values for the area of contact are accurately reproduced, and it is argued that the present values for load and contact pressure are more plausible: unlike the original numerical values, the present values converge smoothly to the BGT asymptote . Once again, it is found that elastic contact models can explain the proportionality between contact area and load, although at realistic loads the proportionality is merely very good, not exact. The model shows that a plasticity index ψm≡(E^*/H)σm (closely related to Mikic's index) can be used to predict the behaviour of surfaces in contact.     

Rolling fatigue tests of three polyglycol lubricants

In this work, the rolling fatigue lives of three polyglycols (PAG-9, PAG-12 and BREOX-B-135X) are determined using IP-300 standard. A four-ball test machine was used and 10% life (L₁₀) and 50% life (L₅₀) were obtained. In addition, the stress-time curves for L₁₀ and L₅₀ were also determined. This work showed that: firstly, all polyglycols were tested under boundary lubrication regime (λ < 1) where in rolling contacts the surface mode of failures prevails; secondly, in oils of the same family, the pressure-viscosity coefficient is relatively constant, therefore an increase in viscosity improve the minimum film thickness with the consequent increase of the λ ratio; and finally, differences in λ ratio for the three polyglycols resulted in different asperity interactions and rolling contact fatigue lives.     

Micro-contact analysis for the initial contact in nanoindentation tests

The force-depth behavior of initial contact between a Berkovich indenter and S45C steel specimens has been examined. The indenter is considered as a rigid sphere with a radius of 300 nm since the blunt tip is dominant under initial contact. The S45C steel specimens were prepared to have different surface characteristics. The specimen surface profile was decomposed by Fourier cosine series; then the statistical evaluation for force and area of micro-contact was proposed. The influence of surface roughness on the real contact area and thus the contact pressure arising in the indentation test can be investigated from the proposed analyses. The force-depth responses obtained by the proposed method revealed good agreement with the experimental results for the prepared specimens with their different surface characteristics. The evaluated results of the force fractions in the elastic, elastoplastic, and plastic deformation regions showed that the S45C steel specimens had fully plastic deformation under the initial contact load of 5 μN. The average values of real contact pressure evaluated by the current method rapidly reached the hardness value. Through the proposed method, the dominant radii of summits were evaluated and their relation to the indentation depth was demonstrated.     

FEA calculation of pressure distortion coefficients of gas-operated pressure balances – EURAMET project 1039

Finite element analysis methods were developed and applied to gas piston–cylinder units (PCUs) of piston- and cylinder-floating configuration (2, 5, 10 and 20) cm² nominal effective area, operated in gauge and absolute mode at pressures (0.06–7.5) MPa to determine their zero pressure and pressure-dependent effective areas, as well as pressure distortion coefficients (λ) with associated uncertainties. Real dimensional properties of the PCUs were used. λ were found to be independent of gas (ideal, N₂, He) within the viscous flow model, but strongly dependent on the gap shape, operation mode and elastic properties. Results demonstrate good agreement for λ, with its uncertainty for different PCUs varying between (0.03 and 0.21) × 10⁻⁶ MPa⁻¹ corresponding to maximum relative uncertainties in pressure of (0.07–0.34) × 10⁻⁶.     

A surface roughness parameter in Hertz contact

The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by $\text{α }\text{σR}\text{a}{}_0{}^2$ where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a₀ is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.     

The contact and friction between flat belts and pulleys

Rubber coated nylon flat belts running over pulleys in practice display friction coefficients between 0·3 and 0·8. This paper studies the causes of the friction variations. Adhesive friction theory considers the friction force to be the product of the real areas of contact between the sliding surfaces and the shear stress at the contacts: these two quantities have been separately measured by running belts over transparent perspex pulleys and directly observing the contacts. It has been found that variations in contact from one belt to another due to their method of manufacture are as significant in explaining differences in their friction behaviour as are variations in shear stress caused by their different rubber formulations. Real areas of contact were less than one third of the apparent area and varied with load, elastic modulus and roughness of the belt surface in a way broadly understandable in terms of elastic contact mechanics. Shear stress were about 0·5 Nmm⁻², perhaps determined by hydrocarbon films. Some belts showed real areas of contact not directly proportional to load. This led to their friction coefficients being load dependent.     

Quasi-fluid nano-layers at the interface between rubbing bodies: simulations by movable cellular automata

Most of technical surfaces show roughness on different space scales. When pressed against each other, they initially come into contact only in small number of micro-contacts. Our aim was to study the processes occurring in a single micro-contact between two rubbing bodies. The solids were simulated in the frame of the method of movable cellular automata (MCA). The main finding of our simulations is formation of a boundary layer where intensive plastic deformation and mixing processes occur. The boundary layer is well localized and does not spread to deeper layers.We investigated how the thickness of the boundary layer and the friction force stemming from the processes in this layer do depend on parameters of material and loading. To this end, all the parameters involved in the numerical model have been varied and the average friction coefficient as well as thickness of the layer determined for each set of parameter. We found that at velocities much smaller than velocity of sound and normal pressures much smaller than the yield stress, the thickness of the quasi-fluid layer is proportional to effective viscosity of the medium and the friction coefficient does depend only on two dimensionless parameters: κ₁=ρv²E/σ₀² and κ₂=PE/σ₀².     

Stress-In-Motion (SIM) system for capturing tri-axial tyre–road interaction in the contact patch

A unique measuring system for the quantification of tri-axial (3-D) tyre contact force (or stress) distributions was designed, developed and used in several studies since 1994. The uniqueness of the system is defined by a textured measuring surface in order to represent a typical “textured” road surface. The system is referred to as the Stress-In-Motion (SIM) system. A single SIM measuring pad testing area comprises a total of 1020 supporting pins and a transverse array of 21 sensing elements, covering the entire tyre contact patch with in a single run. The SIM pad measuring system is modular in concept, allowing multiple SIM measuring pads to be used for e.g. wide base truck tyres, or a dual tyre configuration, or full axle measurements – using a quad SIM pad measuring system configuration. Tyre contact force (or stress) distributions are simultaneously captured in the three orthogonal directions X, Y and Z for a single, dual or full axle truck tyre configuration. Each of the sensing elements has a 9.7 mm diameter circular contact surface area (∼73.9 mm²) and is dimensionally optimised, allowing measurements in various tyre rolling conditions on a textured measuring surface. The textured surface induces some pre-conditioning of tyre–road contact properties, as it has small gaps around all supporting and measuring pins. The system is installed flush with the road surface, preferably on a rigid support base, and can be used for real tyre (or truck) rolling conditions. A single SIM measuring pad contains 63 strain measuring channels (3 × 21) for the sensing elements. Aspects such as SIM system design, sensing element calibration, system usage and outputs of specially developed software are illustrated. Several results of tri-axial road contact stress distributions are also presented.     

A contribution to the theory of friction

The nature of the interaction between a rigid spherical asperity and an asperity governed by the stress/strain law $\text{}\text{?}\text{gs = B}\text{}\text{?}\text{ge}{}^{\mathrm{n}}$ is studied. The interfacial shear stress is defined by fτ_max where $\text{0 </ ? </ 1}$, τ_max being the maximum allowable shear stress at the contact. By integrating the total effect of a population of such surface asperities expressions for the total frictional forces and the total load are derived. The value of the coefficient of friction is thus obtained and the special conditions for perfectly plastic and elastic behaviour are considered. In both cases the friction coefficient is seen to contain a term defined by the deformation and dependent on surface roughness and a term totally defined by ?.     

An Analytical Solution for Elastic and Elastic-Plastic Contact Models

In tribology often a closed form solution for calculation of contact stress and real contact area is required for the purposes of, for example, developing wear maps and temperature profiles at asperities. In assuming a Gaussian distribution of asperity heights it is not possible to obtain an analytical solution for the contact load and real contact area for many analytical models such as those developed by Greenwood and Williamson (elastic model), Chang, et al. (elastic-plastic model) and Horng (elliptic elastic-plastic model). In this paper, two exponential functions have been derived from a fitting procedure applied to the numerical results of the Gaussian height distribution thus offering an analytical expression for the above three models. It has been demonstrated that the two exponential functions (φ₂* and φ₄*) can give a fair approximation to the contact load and the real contact area in the separation of 0 to 4σ. In addition, variations in plasticity index (ψ) and effective asperity radius (γ) do not significantly affect the approximated accuracy. The results obtained by the newly derived exponential functions have been compared with the exponential function φ₁*; suggested by Greenwood and Williamson, 1966 and it has been shown that use of φ₁* invariably gives a larger error than using two exponential functions over two ranges of separation distances.     

Thermal stresses due to time exponentially decaying laser pulse: elasto-plastic wave propagations

In the present study, thermal stress developed in the substrate material, which is subjected to a laser heating pulse is formulated. The closed form solutions for the temperature and stress fields due to time exponentially decaying laser pulse are presented. The Laplace transformation method is employed when deriving the governing equations. The elastic and plastic propagation of the stress waves are considered and the depth of the plastic zone is predicted. In order to account for the recoil pressure generated during the evaporation process, stress boundary at the free surface of the workpiece is considered. It is found that the magnitude of stress wave, due to stress boundary at the surface, well exceeds the elastic limit of the substrate material. Once the magnitude of the recoil pressure reduces considerably, elastic wave is generated. This occurs after t^*=0.032. Since the elastic wave propagates faster than the plastic wave, both waves meet at some depth below the surface. This, in turn, defines the depth of the plastic zone. In the present case, the depth of elastic zone extends to about x^*=9.2 below the surface. The magnitude of the stress wave generated due to temperature gradient is less than the yield strength of the substrate material; in which case, its magnitude decreases with increasing depth from the surface.     

Investigations on machined metal surfaces through the stylus type and optical 3D instruments and their mathematical modeling with the help of statistical techniques

The measurement of roughness on machined metal surfaces is of considerable importance to manufacturing industries as the roughness of a surface has a significant influence on its quality and function of products. In this paper, an experimental approach for surface roughness measurement has been based on the comparison of roughness values taken from the stylus and optical type instruments on the machined metal surfaces (turning, grinding and milling) is presented.Following this experimental study, all measured surface roughness parameters have been analyzed by using Statistical Package for Social Science (SPSS 15.0) statistically and mathematical models for the two most important and commonly used roughness parameters R_a and R_z have been developed so that R_a = R_a (F, P, C) and R_z = R_z (F, P, C, M), whereas F expresses feed, P periodicity, C contrast and M the type of material. The statistical results from numerous tests showed that there has been a correlation between the surface roughness and the properties of the surface topography and there have been slight differences among three measurement instruments on machined metal surfaces in this experimental study.     

Residual stresses in TiN, DLC and MoS2 coated surfaces with regard to their tribological fracture behaviour

Thin hard coatings on components and tools are used increasingly due to the rapid development in deposition techniques, tribological performance and application skills. The residual stresses in a coated surface are crucial for its tribological performance. Compressive residual stresses in PVD deposited TiN and DLC coatings were measured to be in the range of 0.03-4 GPa on steel substrate and 0.1-1.3 GPa on silicon. MoS₂ coatings had tensional stresses in the range of 0.8-1.3 on steel and 0.16 GPa compressive stresses on silicon. The fracture pattern of coatings deposited on steel substrate were analysed both in bend testing and scratch testing. A micro-scale finite element method (FEM) modelling and stress simulation of a 2 μm TiN-coated steel surface was carried out and showed a reduction of the generated tensile buckling stresses in front of the sliding tip when compressive residual stresses of 1 GPa were included in the model. However, this reduction is not similarly observed in the scratch groove behind the tip, possibly due to sliding contact-induced stress relaxation. Scratch and bending tests allowed calculation of the fracture toughness of the three coated surfaces, based on both empirical crack pattern observations and FEM stress calculation, which resulted in highest values for TiN coating followed by MoS₂ and DLC coatings, being K_C = 4-11, about 2, and 1-2 MPa m^1/2, respectively. Higher compressive residual stresses in the coating and higher elastic modulus of the coating correlated to increased fracture toughness of the coated surface.     

A modified fractal microcontact model developed for asperity heights with variable morphology parameters

The cross-sections formed by the contact asperities of two rough surfaces at an interference are actually island-shaped, rather than having the commonly assumed circular or elliptic contour. These island-shaped contact area contours show fractal behavior with fractal dimension D_s of the two-dimensional profile. The three-dimensional surface fractal dimension for the topography of asperity heights is defined as D and the topothesy is defined as G. In Mandelbrot's study, the relationship between D and D_s was given as D = D_s + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and D_s are considered to be varying with the mean separation between two contact surfaces. The D–D_s relationships for the contacts at the elastic, elastoplastic, and fully plastic deformation regimes are derived and the inceptions of the elastoplastic and fully plastic deformation regimes are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). A revised elastic–plastic contact model of a single fractal asperity is also proposed. The revised model shows that a fractal asperity behaves according to classical contact mechanics, but not those predicted by the MB model. The contact parameters, including the total force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and D_s parameters in these deformation regimes increased with increasing mean separation.     

Collective Effects at Frictional Interfaces

We discussed the role of the long-range elastic interaction between the contacts inside an inhomogeneous frictional interface. The interaction produces a characteristic elastic correlation length ??_c?=?a ² E/k _c (where a is the distance between the contacts, k _c is the elastic constant of a contact, and E is the Young modulus of the sliding body), below which the slider may be considered as a rigid body. The strong inter-contact interaction leads to a narrowing of the effective threshold distribution for contact breaking and enhances the chances for an elastic instability to appear. Above the correlation length, r?>???_c,?the interaction leads to screening of local perturbations in the interface, or to appearance of collective modes??frictional cracks propagating as solitary waves.     

A comparative study on performance of multilayer coated and uncoated carbide inserts when turning AISI D2 steel under dry environment

The present work deals with a comparative study on flank wear, surface roughness, tool life, volume of chip removal and economical feasibility in turning high carbon high chromium AISI D2 steel with multilayer MTCVD coated [TiN/TiCN/Al₂O₃/TiN] and uncoated carbide inserts under dry cutting environment. Higher micro hardness of TiN coated carbide samples (1880 HV) compared to uncoated carbide (1430 HV) is observed and depicts better resistance against abrasion. The low erosion rate was observed in TiN coated insert compared to uncoated carbide. The tool life of TiN coated insert is found to be approximately 30 times higher than the uncoated carbide insert under similar cutting conditions and produced lower surface roughness compared to uncoated carbide insert. The dominant wear mechanism was found to be abrasion and progression of wear was steady using multilayer TiN coated carbide insert. The developed regression model shows high determination coefficient i.e. R² = 0.977 for flank wear and 0.94 for surface roughness and accurately explains the relationship between the responses and the independent variable. The machining cost per part for uncoated carbide insert is found to be 10.5 times higher than the multilayer TiN coated carbide inserts. This indicates 90.5% cost savings using multilayer TiN coated inserts by the adoption of a cutting speed of 200 m/min coupled with a tool feed rate of 0.21 mm/rev and depth of cut of 0.4 mm. Thus, TiN coated carbide tools are capable of reducing machining costs and performs better than uncoated carbide inserts in machining D2 steel.     

An Engineering Model for Three-Dimensional Elastic-Plastic Rolling Contact Analyses

Fatigue life of heavily loaded rolling bearings is strongly dependent on elastic-plastic material properties. For bearing steels these elastic-plastic properties can be accurately obtained by performing monotonic or half-compressive tests. A three-dimensional strain deformation analysis based on the incremental theory of plasticity and the use of Prandtl-Reuss relations in conjunction with the von Mises yield criterion was developed in order to evaluate the permanent deformation in dry contacts loaded above the elastic limit in case of normal loading. The Ramberg-Osgood stress-strain relation for two martensitically hardened variants of SAE 52100 bearing steel considered the nonlinear kinematic and/or isotropic material behavior. Parameters describing the influence of retained austenite are modeled by using a nonlinear isotropic law. Pressure distribution and contact surface displacements during incremental loading are evaluated by using a conjugate gradient method and the internal stress field is derived by using the superposition principle. Further, a fast analysis of smooth surfaces in elastic-plastic static and rolling contact is developed based on analytical relations for the internal stress field. Cyclic evaluation of plastic strains and residual stresses is carried out until shakedown. In order to verify the theoretical model, rolling contact tests under high normal load were performed. Residual stresses and residual profiles measurements show excellent agreement between numerical and measured cyclic values.     

Using a monocular optical microscope to assemble a wetting contact angle analyser

The ability of a solid surface to be wetted by a liquid can be classified by its wetting contact angle, θ_C: hydrophilic (θ_C < 90°), hydrophobic (90° ? θ_C ? 150°), or super-hydrophobic (θ_C > 150°). To study the wetting behaviour of material surfaces, commercial contact angle analysers are generally employed. In this paper, we report on the construction and testing of a wetting contact angle analyser. To test the performance of the measurement system, we have measured the contact angles of films from commercial paraffin wax and polytetrafluoroethylene (PTFE). The contact angles are found to be in good agreement with the values described in the literature; thus, our analyser can be useful not only for research but also for educational purposes.