Effect of friction and adhesion on the load–displacement of a spherical probe in contact with a compliant incompressible elastic coating

The mechanical properties of thin films are extracted from the measured load displacement relation in a contact test conducted using micro or nano instruments. At this micro or nano force scale, the adhesion and friction operating between the test tip and thin film surface will contribute to the deformation. The well established Johnson–Kendall–Roberts (JKR) theory provided a relationship between the normal load and elastic central displacement for the adhesion contact. But because of its semi-infinite half-space hypothesis, the standard JKR theory is not applicable to thin film contact problem. Experimental verification demonstrates the numerical version of JKR theory is suitable for compliant thin film adhesion analysis, but it does not include the friction effect. In this paper, the load–displacement relation of totally bonded friction contact with adhesion is studied and compared with that of frictionless case. The practical thin film contact will lie in these two limits. The effect of friction to load and displacement seems very small except for the transition range from film to substrate response. Empirical expressions for the contact compliance are obtained from the detailed finite element study.     

A new algorithm for computing the indentation of a rigid body of arbitrary shape on a viscoelastic half-space

In this paper the contact problem between a rigid indenter of arbitrary shape and a viscoelastic half-space is considered. Under the action of a normal force the penetration of the indenter and the distribution of contact pressure change. We wish to find the relations which link the pressure distribution, the resultant force on the indenter and the penetration on the assumption that the surfaces are frictionless. For indenters of arbitrary shape the problem may be solved numerically by using the Matrix Inversion Method (MIM), extended to viscoelastic case. In this method the boundary conditions are satisfied exactly at specified “matching points” (the mid-points of the boundary elements). It can be validated by comparing the numerical results to the analytic solutions in cases of a spherical asperity (loading and unloading) and a conical asperity (loading only). Finally, the method was implemented for a finite cylindrical shape with its curved face indenting the surface of the half-space. This last example shows the efficiency of the method in case of a prescribed penetration as well as a given normal load history.     

Surface undulation instability of the viscoelastic half-space covered with the stack of layers in bi-axial compression

The near-surface undulation stability loss problems of the viscoelastic half-space covered with the stack of layers in bi-axial compression in the layers’ plane are investigated within the framework of the piecewise homogeneous body model by employing the three-dimensional linearized theory of stability of deformable bodies (TLTSDB). The equations of the TLTSDB are obtained from the three-dimensional geometrically nonlinear exact equations of the theory of viscoelasticity by the use of the boundary-form perturbation technique. By employing Laplace transform, the method for the solution to these problems is developed. It is supposed that the layers in the stack have an insignificant initial imperfection and as a stability loss criterion the case is considered where this imperfection starts to increase and grows indefinitely.The developed method is employed for the investigation of concrete problems. As a result of these investigations the influence of the rheological parameters of the layers and half-space materials on the values of the critical time is studied. The viscoelasticity of the materials is described by the fractional–exponential operator of Rabotnov.     

The buckling of an orthotropic layer on a half-space

The buckling of an orthotropic layer bonded to an isotropic or orthotropic half-space subjected to compression loading under plane strain is presented. Mechanics of incremental deformation, which considers the effect of the initial stress field on the incremental stress field, is applied to describe the buckling behavior of both the layer and the half-space. The problem is converted to an eigenvalue–eigenvector case, from which the critical buckling strains or stresses are obtained and the effect of orthotropy on buckling is assessed. The results show that the effect of orthotropy becomes more obvious when the modulus ratio, the ratio of longitudinal moduli of the layer to the half-space, is less and that approximating the problem by using isotropic properties for both the layer and the half-space will be unconservative and may cause unexpected failure.     

An approximate solution for the contact area and elastic compliance of a smooth punch of arbitrary shape

An approximate solution is developed for the contact area and the load-penetiation relation for frictionless indentation of the elastic half-space by a punch of arbitrary profile. The method makes use of a previous result to the effect that the contact area in this problem is that which maximizes the total indenting force. An estimate of this force is obtained by applying the reciprocal theorem to the solution for indentation by a flat punch of the same plan-form, for which an approximate solution has recently been developed by Fabrikant. The method is illustrated using an example, the results of which are compared with a direct numerical solution using Hartnett's algorithm.     

Finite element modeling of adhesive contact using molecular potential

A finite element technique for analysis of adhesive contact is developed in which the adhesive force is modeled as a body force derived from Lennard–Jones 12–6 potential. Adhesive contact of an elastic hemispherical asperity with the plane surface of a semi-infinite rigid body is analyzed. Variations of the interaction force and contact radius during approach and withdrawal, and the dependence of pull-off force on the asperity radius are shown to be in good agreement with those of Maugis–Dugdale model. Analysis results reveal that smaller asperity is superior for preventing stiction and for reducing adhesive friction, but is subject to more severe adhesive wear. It is anticipated that this technique can be utilized in designing a low-adhesion surface profile for MEMS applications since the effect of various surface geometries can be examined.     

Solution of a plane contact problem of the theory of elasticity on the basis of an elastic half-space model

A theoretical solution of a plane contact problem of the theory of elasticity based on a method of determination of the convergence of elastic bodies using an elastic half-space model is presented, and the contact deformation (diameter change) of circular cylinders with parallel axes is deter-mined on its basis. The possibility of obtaining a precise solution for the problem, using an elastic half-space model based on the Hertz theory, is demonstrated for the first time. It is shown that the known Kovalskii solution for contact deformation of circular cylinders with parallel axes is a rough approximation of a more precise solution of the problem. It is found that the obtained result agrees well with the Dinnik’s experimental data.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Collision between a ring and a beam

With car–parapet collision accidents in mind, a normal collision between a free-flying half ring and a simply supported beam with/without axial constraints is studied, in which an elastic–plastic half ring with an attached mass and the elastic–plastic beam are taken as the simplest models of a car and a parapet, respectively. Particular attention is paid to the energy partitioning between the two structures and the evolution of the contact regions during collision. A mass–spring finite difference (MS–FD) model is employed whilst the large deflection and axial stretching/compression are incorporated. The numerical results show that the less stiff (i.e. softer) structure will dissipate more energy and the contact regions will move away from the initial contact points. With the increase of the relative thickness of the beam to the ring, the final deformation of the half ring will transform from a “U” shape to a “W” shape.     

Hybrid analytical–numerical solution for the shear angle in orthogonal metal cutting — Part II: experimental verification

The hybrid analytical–finite element model described in Part I is applied to predict the shear angle for a range of cutting velocity, uncut chip thickness, and two tool orthogonal rake angles. Experimental results and an empirical equation are also presented for the influence of the cutting conditions and cutting tool geometry on the chip–tool contact length. It is shown that there is a linear dependence between the chip–tool contact length/uncut chip thickness ratio and chip thickness/uncut chip thickness ratio over the range of cutting conditions assumed. The increase of the shear angle with the tool orthogonal rake is mostly due to the reduction of the specific shear energy in the primary shear zone and the specific friction energy in the secondary shear zone accompanied by a reduction of the chip–tool contact zone. The uncut chip thickness and cutting velocity influence the shear angle through their effect on the interface temperature and hence on the material flow stress in the secondary shear zone. The change in both parameters does not change significantly the specific shear energy in the primary shear zone. The model results are compared with the experimental results for a work material 0.18% C steel. The agreement between the predicted and experimental results is seen to be exceptionally good.     

Simulation of thermal stresses due to grinding

An efficient finite element procedure has been developed to calculate the temperatures and stresses arising due to a moving source of heat. The procedure is applied to calculate the thermal stresses produced in hardened steels during grinding. The thermal load during grinding is modeled as a uniformly or triangularly distributed, 2D heat source moving across the surface of a half-space, which is insulated or subjected to convective cooling. The grinding of elastic and elastic–plastic workpiece materials has been simulated. The calculated transient stresses and temperatures in an elastic solid are found to be in good agreement with prior analytical and numerical results. In an elastic–plastic workpiece material, for which no analytical solution is available for the residual stress distributions, the finite element calculations show that the near surface residual stress is predominantly tensile and that the magnitude of this stress increases with increasing heat flux values. Based on an analysis of the effects of workpiece velocity, heat flux magnitude and convective cooling, on the residual stress distributions in an elastic–plastic solid, it is seen that the calculated thermal stress distributions are consistent with experimentally measured residual stresses on ground surfaces. Furthermore, the results explain often cited observations pertaining to thermally induced grinding stresses in metals.     

Stresses in hard coating due to a rigid spherical indenter on a layered elastic half-space

The axisymmetrical contact problem of elasticity connected with an indentation of a rigid spherical indenter in an elastic semi-space covered by an elastic layer is considered. Stress tensor components in interior points of the non-homogeneous half-space by numerical calculation of some integrals was obtained. Detailed analysis of the maximal tensile stress distributions and Huber-von Mises reduced stress distributions produced by contact pressure is presented. The dependence between these stresses and the ratio between the layer thickness and contact area width is explored. The obtained results for stresses are compared with results obtained for half-space loaded by the Hertz pressure.     

Finite element analysis of a subsurface penny-shaped crack with crack-face contact and friction under a moving compressive load

A three-dimensional subsurface penny-shaped crack in an elastic half-space subjected to a compressive moving load is analyzed using the finite element method. The compressive load is applied through a spherical asperity, which moves from left to right on the top surface of the half-space. Normal contact between the crack faces of the penny-shaped crack is modeled using the classical Lagrange multiplier method for constraint enforcement; the tangential contact between the crack faces is assumed to exhibit frictional behavior. Therefore, although the present analysis is limited to a purely linear elastic quasistatic approach, the analysis results show the loading path dependence caused by the frictional contact. Based on linear elastic fracture mechanics, stress intensity factors along the crack front of the penny-shaped crack are evaluated as functions of the crack-front angle, frictional coefficient, normalized load position, and the ratio of the crack depth to the crack length. Finite element analysis shows that shearing-mode failure rather than tearing-mode failure is the dominant cracking mechanism of the penny-shaped crack. This shearing-mode failure tends to occur in the direction of the loading path.     

Simulation of Operation of Dry Point Contact Probes in the Emission Regime

Displacements of longitudinal and transverse waves driven by sources like point vertical and horizontal forces acting on the surface of elastic half-space are obtained in the form of Fourier–Bessel integral representations using the Smirnov–Sobolev method which makes it possible to transform two-dimensional solutions of wave equations into three-dimensional solutions. Asymptotic expressions of the displacements are obtained for the far zone. Results of numerical estimates are given.     

The tribological behavior of Ni–Cu–Ag-based PVD coatings for hybrid bearings under different lubrication conditions

In a cryogenic environment, components like bearings with interacting surfaces in relative motion (tribosystems) often generate undesired heat and experience high wear. Because the properties of conventional bearing materials like stainless steel cannot be applied to this temperature range, the PVD coating based on metal–metal pairs with better frictional properties must be employed. To test the suitability of the Ni–Cu–Ag-based PVD coatings of hybrid bearings for liquid rocket engine turbopumps and to obtain reliable coating material data in the extreme environment, the tribological behaviors of coatings under the cryogenic fluid (liquid oxygen and liquid nitrogen) and water lubricated conditions are studied, respectively. In the paper, the specimens are in a vibrocryotribometer with the ball-on-plane contact type, and various running conditions in terms of lubricants, contacting loading, and contacting velocity are examined. The simulated experiment for testing the actual tribological performance of Ni–Cu–Ag-based PVD coatings for hybrid bearings is tested. The results of the tests indicate that the coatings can be suitable for cryogenic tribosystems of turbopumps. In the cryogenic environment, the volume wear rate of coatings increases rapidly with the contacting loading, but 15 min later, the volume wear volume of coatings turns into 2.5–15×10⁻⁴ mm³. Besides, under the liquid oxygen condition in simulating the liquid rocket engine turbopumps environment, the friction coefficients are 0.03–0.1.     

Seizure mechanisms of wheel–rail contacts under lubricated conditions using a transient ball-on-disc test method

This study focuses on the transition from mild to severe wear in the wheel and rail contact. Such a transition has been observed at increased loading (normal load, sliding velocity, or bulk temperature) which can be compared to a change from a wheel thread–rail head contact to a wheel flange–rail gauge contact. This transition was experimentally studied using a transient test method of ball-on-disc type at different sliding velocities, contact pressures, and lubricants. It can be seen in the results that different seizure mechanisms are active for different sliding velocities. Also the amount of applied lubricant clearly affects the transition to seizure.     

Contact between an axisymmetric indenter and a viscoelastic half-space

Lee & Radok introduced a simple method of solving viscoelastic contact problems by replacing the elastic modulus by the viscoelastic creep function, (Lee EH, Radok JRM. Journal of Applied Mechanics 1960;27:438-44) but explained why it fails when the contact area decreases. Ting's discovery (Ting TCT. Journal of Applied Mechanics 1966;35:845-54) of the essential mechanism governing unloading of a contact between a sphere and a viscoelastic half-space is used here to develop a relatively simple method of analysis by superposition of an assembly of viscoelastic “Boussinesq” punch indentations. The new method leads to a more convenient form for the variation of the approach during unloading, and this is evaluated for a three-element solid. The same method, with only minor modifications, is then used to evaluate indentation by a conical indenter.     

Evaluation of a semi-empirical model in predicting erosion–corrosion

The phenomenon of erosion–corrosion has been studied extensively by various investigators but no accurate model has been developed to predict the interactions between erosion and corrosion. This is mainly attributed to the complexity of the interactions that generate either a synergistic or antagonistic wear effect for a particular material in a certain environment. A semi-empirical model has recently been developed at the University of Southampton which incorporates dynamic Hertzian contact mechanics to model the damage during particle impact and accommodates the effect of erodent deforming the surface leading to an increased corrosion activity. The model was found to have good agreement with erosion–corrosion rates of carbon steel. The aim of this paper is to evaluate the robustness of this semi-empirical model by testing it on a passive metal. UNS S31603 was chosen due to its inherent passivity to corrosion. A slurry pot erosion tester was used as the test rig to perform the experiments. It was found that this passive metal produces high synergistic levels when exposed to erosion–corrosion in 0.3 M HCl with variation in erodent concentrations and flow velocities. SEM and surface profilometry show typical ductile material behaviour with cutting mechanism and deformation mechanism occurring simultaneously. A wear map is presented and it is observed that the increase in velocity and sand concentration causes the material to shift from a corrosion–erosion dominated region to an erosion–corrosion dominated region. This paper will also evaluate the semi-empirical model and discuss its applicability in predicting erosion–corrosion.     

A new method for determining the preload in a wire race ball bearing

This paper explores a numerical method to calculate the frictionless three-dimensional non-conforming contact problem associated with a wire race ball bearing used in a certain aircraft simulating rotary table, for challenging the conventional method on the determination of the preload magnitude. A computer program based on the Hertz elastic contact theory and a mathematical model of two critical loading conditions was performed in MATLAB^® by using an example of a wire race ball bearing having an approximately 900 mm diameter. The normal contact forces, the contact deformation, the maximum contact pressure, the semi-major axes and the semi-minor axes of contact ellipses of the ball-wire race were computed. The analytic results show that the overturning moment, the pitting corrosion and the shear failure due to combined stresses can be avoided by controlling preload values in the range 11.3–169.9 μm. The experimental results are closely in agreement with the theoretical results, and verify the availability of the numerical method. The research provides theoretical support for the development and further application of wire race ball bearings with large diameters.     

Machining with tool–chip contact on the tool secondary rake face—Part II: analysis and discussion

The forces, chip thickness, and natural tool–chip contact length in machining with a double-rake-angled tool are predicted in Part II of the present study. It is revealed that in comparison with a single-rake-angled tool, a double-rake-angled tool increases the forces, especially the thrust force. However, the increase in chip thickness and tool–chip contact length is not significant under the input conditions specified in the present study. The effect of seven input variables of the proposed model is quantitatively investigated. The predicted variations of forces, chip thickness, and natural tool–chip contact length are in good agreement with theoretical and experimental results obtained by other researchers. The interrelationships among the resultant force, the chip thickness, and the natural tool–chip contact length are established, which provides a new and promising method to estimate the tool–chip contact length by employing the resultant force. It is demonstrated that the model can also be extended to study the problem of machining with a groove-type chip breaker tool.