Partial Slip Contact Research Articles

Investigation on the influence of the slip at the wheel-rail contact patch on the shakedown limit of rail material

Research on factors affecting rolling contact fatigue (RCF) damage of rail materials has become increasingly important since developing effective measures to mitigate RCF damage is crucial. This study focuses on exploring the influence of full slip and partial slip contact modes at the wheel-rail contact patch on the RCF damage behavior and the shakedown limit of the pearlite rail material through wheel-rail RCF rolling-sliding tests. Firstly, based on the wheel-rail adhesion-creep curves in dry, water and oil environments, the creepage required to achieve full slip during the rolling-sliding tests was determined. Then, rolling-sliding tests under full slip contact with different adhesion coefficients were carried out in a dry atmosphere and with the assistance of a third body medium (i.e., oil and water), respectively. Meanwhile, rolling-sliding tests under partial slip contact with the similar contact parameters were performed in a dry atmosphere. The results indicated that RCF damage and wear rates of the rail material under a full slip contact with an adhesion coefficient below the saturation peak on the adhesion-creep curve were significantly less than those under partial slip contact with similar contact parameters. Moreover, under full slip contact with an adhesion coefficient below the saturation peak on the adhesion-creep curve, the pearlite rail materials could exhibit a higher shakedown limit. Furthermore, the influence of full slip and partial slip contact on wheel-rail contact behavior was further analyzed using finite element simulations. Finally, a novel friction modification strategy to mitigate RCF damage and wear of rails was proposed. By applying a specific low-coefficient friction modifier to the wheel-rail interface, the operation of powered wheelsets under controlled creepage conditions that reach the threshold of full slip contact at the wheel-rail contact interface could be employed to achieve the desired adhesion coefficient. Thus, this approach could ensure that the achieved adhesion coefficient met the on-site target adhesion force while reducing RCF damage and wear of rail materials.

Surface effect on the partial-slip contact of a nano-sized flat indenter

The partial-slip contact at nano-scale is always influenced by a surface effect. A new model based on the Gurtin-Murdoch (G-M) surface elasticity theory is proposed in this paper to study the partial-slip contact behavior of a rigid flat nano-indenter on an elastic half-space. The surface effect in the partial-slip contact is characterized via a non-classical boundary condition involving a surface-induced normal traction related to the residual surface stress and a surface-induced tangential traction related to the surface elasticity, the influences of which on stress and displacement fields and the stick-slip state at the contact surface are investigated. It is found that, with the increase of residual surface stress, both the normal pressure and vertical and horizontal displacements in the contact zone decrease, the relative slip between indenter and substrate reduces and the stick region is enlarged. Such effects are basically attributed to the action of the surface-induced normal traction opposite to the externally applied compression. However, the increase of surface elastic constants is conductive to the relative slip and results in a shrinkage of the stick region, which is attributed to the action of the surface-induced tangential traction opposite to the frictional stress. An interesting phenomenon is further unveiled that, when the frictional coefficient increases, the dominant role in affecting the stick-slip state changes from the surface-induced tangential traction to the normal one, thus inspiring a feasible route to manipulate the surface effect by tuning the frictional coefficient of substrate. The present research enables one to better understand the partial-slip contact behavior of nano-indenters, which is of guiding value for anti-wear designs in nano-mechanical devices.

Elasto-plastic partial slip contact modeling of graded layers

A calculation model is developed to solve elasto-plastic partial slip contact problems of graded layer-substrate systems. With the high dependence of contact stress on the local region near the contact spot, the graded layer-substrate system of interest is modeled as a homogeneous half-plane with an embedded, finitely long inclusion. Unlike the conventional finite element method, the elasto-plastic responses are solved within a considerably small region rather than an oversized truncated domain. The computational domain allows arbitrary distributions of elasto-plastic properties and is directly discretized without tedious separation and assembling skills. The resulting disturbance fields are calculated by the numerical equivalent inclusion method. Additionally, the plastic strain is determined via the return-mapping algorithm, and the generated residual responses are directly obtained based on the explicit theoretical solutions. The conjugate gradient method is utilized to solve surface tractions, and the induced elasto-plastic fields are calculated by the technique of fast Fourier transform. Some parametric studies are subsequently conducted based on the developed model to explore the effects of property inhomogeneity and friction coefficient on the elasto-plastic response.

A dislocation-based model for shear cracks in arbitrary orientations under contact loading

Mechanical transmission components are generally under the risk of contact fatigue, resulting in cracks initiated from the subsurface. When subject to compressive stress, these cracks might be forced to be closed, thus their faces are in partial slip contact. Under such conditions, the interactions of stick and slip zones cannot be directly determined, which is one of the greatest challenges of contact fatigue problems. In this study, the distributed dislocation technique is adopted to investigate the stick–slip friction along the alignment of shear cracks in arbitrary orientations in a half-plane under contact loading. The unknown dislocation density describing the crack face displacement is iteratively calculated based on the stress conditions and then introduced to update the surface gap between contacting bodies. The complex expressions of the influence coefficients used to determine the stress and displacement induced by the dislocations are derived and the FORTRAN codes are provided in the Supplementary Materials. A step-by-step loading method is proposed to progressively capture the slip history of crack faces. The model is also capable of simulating rolling contact problems. The results are comparable to those predicted using the finite element method with more robust convergence properties. The effects of friction coefficient, crack alignment, and locations of crack faces are discussed in detail. The model paves the foundation for further studies on competing mechanisms of crack propagation and crack face wear, and provides insights into the frictional fracture of materials under contact loading.

Research on Partial Slip Contact Behaviors Under Temperature Effects

Research on Partial Slip Contact Behaviors Under Temperature Effects

Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading

Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case.

Partial slip contact problem between a transversely isotropic half-space of multi-ferroic composite medium and a spherical indenter

This article concerns partial slip contact problem of a composite medium half-space punched by a spherical indenter. The indenter is subjected to the normal indentation force, electric and magnetic loads, and then exerted by a progressively increasing tangential load. The tangential load, which is not sufficient to cause complete sliding, results in the contact region split into the slip region and the stick region. Coulomb friction law is adopted in the slip region and four possible physical cases are considered in view of the magneto-electric properties of indenter. Three-dimensional (3D) magneto-electro-elastic coupling fields associated with four cases are obtained in terms of the elementary functions by use of the potential theory and ignoring effect of the tangential load on the generalized normal stresses in the contact region. The contact radius and the stick radius are determined by the equilibrium equations. The stress intensity factors are introduced to characterize the stress singularity. The obtained solutions are verified by comparing with results related to the frictionless contact problem and the fundamental solutions. Influence of the frictional coefficient and the magneto-electric properties of indenter on the physical quantities are analyzed. It is worth noting that the frictional coefficients have obvious effect on the von Mises stress and the maximum shear stress. The suitable electric and magnetic loads may eliminate the stress concentration. These results not only are the theoretical fundamental to the forthcoming indentation experiments and the fretting contact, but also serve as guiding design of the smart devices.

Partial slip contact of materials with vertically aligned cracks near surface

This study develops a numerical model for the partial slip contact of fractured substrates with embedded cracks aligned vertically. Each crack is assumed to be a mixed mode one (modes I and II) with separated faces and closed tips. The discrete dislocation technique is adopted to simulate the crack by a distribution of climb and glide dislocations with unknown densities, which are iteratively determined in a subroutine based on the conjugate gradient method. Tangential displacements induced by the dislocations are integrated into the model to investigate the effects of cracks on the tractions in slip and stick regions. The stress intensity factors are determined based on the solutions of dislocation densities. The model is capable of solving multiple-crack problems with the consideration of interactions among cracks and contact bodies, and the effects of cracks on the loading distribution and stress fields are discussed in detail. The contact loading produces a tendency to close crack faces and a vertical crack prevents surfaces from deforming. The interactions of the normal and tangential forces lead to the shift of the stresses along the direction of friction. The conclusions provide insights into the behaviors of fractures near a material surface under fretting contact conditions.

Viscoelastic Effects during Tangential Contact Analyzed by a Novel Finite Element Approach with Embedded Interface Profiles

A computational approach that is based on interface finite elements with eMbedded Profiles for Joint Roughness (MPJR) is exploited in order to study the viscoelastic contact problems with any complex shape of the indenting profiles. The MPJR finite elements, previously developed for partial slip contact problems, are herein further generalized in order to deal with finite sliding displacements. The approach is applied to a case study concerning a periodic contact problem between a sinusoidal profile and a viscoelastic layer of finite thickness. In particular, the effect of using three different rheological models that are based on Prony series (with one, two, or three arms) to approximate the viscoelastic behaviour of a real polymer is investigated. The method allows for predicting the whole transient regime during the normal contact problem and the subsequent sliding scenario from full stick to full slip, and then up to gross sliding. The effects of the viscoelastic model approximation and of the sliding velocities are carefully investigated. The proposed approach aims at tackling a class of problems that are difficult to address with other methods, which include the possibility of analysing indenters of generic profile, the capability of simulating partial slip and gross slip due to finite slidings, and, finally, the possibility of simultaneously investigating dissipative phenomena, like viscoelastic dissipation and energy losses due to interface friction.

Partial slip contact analysis for a monoclinic half plane

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

Stress Distributions in the Cattaneo–Mindlin Problem on a Contact With Slip and Adhesion of Two Cylindrical Bodies

Two-dimensional Cattaneo – Mindlin problem on a partial slip contact between two elastic bodies of the same material is considered in classical statement for circular cylinders as well as in more general statements: for non-circular cylinders with higher order of touch and cylindrical bodies with a wavy periodic surface. Stress distributions are found both in the contact area and inside the bodies. The question of how the friction affects a formation of stick zone in the contact area and distribution of maximum tangential stress within the bodies is investigated.

Three-dimensional study of rolling contact fatigue using crystal plasticity and cohesive zone method

A three-dimensional (3D) finite element model that includes the microstructure of grains and grain boundaries is developed for studying the rolling contact fatigue (RCF) damage caused by a rolling steel wheel on a steel railway. The 3D model uses a crystal plasticity-based micromechanical framework for simulation of stress-strain behavior inside the grains, and cohesive elements with traction-separation law for modeling the intergranular fatigue damages. A combination of moving normal Hertzian load and tangential loads are employed to mimic the rolling contact conditions. The effect of various parameters such as friction coefficient, traction, partial slip contact and wheel load on RCF is studied. The results reveal that RCF cracks initiate slightly below the surface for large wheel loads and low tractions. The cracks migrate toward the surface as the wheel-rail traction increases. For high tractions, the cracks initiate at the rolling surface. Under partial slip contact condition, there is a large change in rail life for small normalized tractions. With a slight increase in the latter, the rail life significantly decreases. For moderate to large tractions, rail life remains relatively unchanged or slightly increases. The results of the study appear to agree with anecdotal observations by the U.S. railroads from revenue service operation.

Methods to solve half-plane partial slip contact problems

There exists a family of methods for finding the extent of partial slip in contact problems between elastically similar bodies, capable of idealisation by half-planes. Closed form solutions are given to problems subject to a constant normal load and subsequent application of either an increasing shear force or differential bulk tension parallel with the surface. The starting point may be either a sliding contact (as is customary), or a fully adhered contact. The corrections required to impose a point-wise interpretation of Coulomb’s law of friction may be either in the form of a shear traction distribution or as dislocation arrays. The latter, when applied to the fully adhered contact, has the merit of automatically preserving the locked-in relative surface strains.

Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension

This article provides a new form of solution to half-plane contact problems in partial slip where a normal load has been applied, held constant and is subsequently loaded with both a shear force and differential bulk tension. It uses a formulation where a displacement correction is made to the fully stuck solution. An approximate solution is used to study an isolated contact edge, which employs an asymptotic solution to each edge of the contact. A comparison of the approximation with the exact solution is given to show the range of loading where the asymptotic solution gives good results.

Semi-analytical study of microscopic two-dimensional partial slip contact problem within the framework of couple stress elasticity: Cylindrical indenter

In the present work, a size-dependent partial slip contact model of an elastic half-plane indented by a rigid cylindrical punch is established within the framework of couple stress elasticity. The proposed model introduces an internal material length to characterize the size effect of materials and assumes that the friction between two bodies is one of the Coulomb friction type. The Fourier transform in conjunction with the generalized stress function formulation is adopted to obtain the relationship between the coupled normal pressure and tangential traction in the form of a set of singular integral equations. Employing an iterative approach, the coupled system of integral equations is numerically solved and the effects of the couple stress and the friction coefficient upon the contact response are highlighted. The results show significant departure from the predictions of previous contact models based on the classical elasticity or the couple stress elasticity under frictionless condition. Moreover, it is demonstrated that the predicted contact responses of microindentation problems are underestimated if the material is assumed to have a smooth surface or treated as a classical elastic material.

Partial slip problem in frictional contact of orthotropic elastic half-plane and rigid punch

Planar partial-slip contact problem of a rigid indenter with flat end and an orthotropic elastic material is analytically and numerically investigated. In the analytical way, the coupled singular equations of this problem are reduced to a Fredholm integral equation with a regular kernel. The analytical solutions are derived in the forms of the Goodman’s and Spence’s approximations. In the numerical way, a linear complementarity formulation is developed by reformulating the governing equations are as coupled Volterra integral equations. And, a Newton-based optimization algorithm based on smoothing approximation is used to solve the problem. The validness of both the Goodman and Spence approximate solutions is verified by comparing with the numerical results for different orthotropic elastic materials.

Stress intensity factor solutions for fretting fatigue using stress gradient factor

This paper presents stress intensity factor (SIF) solutions for fretting fatigue conditions by including a stress gradient factor (SGF) to correct the classic geometry factor for tension semi-infinite strip (TSIS) specimen. This gradient factor considers the stress gradient due to the pressure of the pad on the surface of the specimen, which creates a high concentration of stresses around the contact of the bodies. To obtain these solutions, 2D finite element model simulations were performed varying important fretting parameters, namely: coefficient of friction, bulk stress intensity, pad radius and material. All configurations respected a partial slip contact condition and the results obtained show agreement with the ones obtained analytically. Weight functions were used to obtain stress intensity factors under mode I, then to compute the SGF, which were fit into equations with a unique structure, varying only coefficients. To consider real problems, a 3D correction factor was introduced. The final SGF presented a general form to compute SIF under fretting conditions when applied in suggested methods, such as: Strain-based Fracture Mechanics, Theory of Critical Distances (TCD) and Stress Gradient.

On contact problem with finite friction for a graded piezoelectric coating under an insulating spherical indenter

In this paper, the partial slip behavior of a spherical indenter on a functionally graded piezoelectric coating attached to a piezoelectric substrate is considered. The electromechanical constants of the functionally graded piezoelectric coating vary as the exponential gradation form within the thickness-coordinate. The partial slip contact problem is reduced to a system of singular integral equations with Cauchy kernels by making use of the Hankel transform technology. To solve the coupled singular integral equations, an approximate solution method is employed. The impact of the gradient index, friction coefficient and different piezoelectric substrates on the normal and radial tangential tractions are analyzed and discussed.

On the fully coupled partial slip contact problems of orthotropic materials loaded by flat and cylindrical indenters

Fully coupled partial slip contact problems for orthotropic materials are considered in this paper. The problem is formulated by virtue of the Fourier transform method. The governing singular integral equations are solved numerically for both flat and cylindrical stamps under the plane strain conditions. An extensive parametric study is carried out to investigate the effect of material orthotropy parameter as well as the coefficient of friction on the contact stresses and the stress intensity factors. It is found that the coefficient of friction and the orthotropic material parameters have a great effect on the stress intensity and the in-plane contact stresses as well as stick and slip zones. Especially, the shearing ratio parameter has a pronounced effect on the stress distribution of cylindrical punches which is important from the crack initiation and fretting wear point of view. The results obtained from this study can be used as benchmark results in the design of contacting parts with orthotropic material properties.

Axisymmetric partial slip contact of a functionally graded piezoelectric coating under a conducting punch

This article considered the axisymmetric partial slip contact problem of a functionally graded piezoelectric coated half-space indented by a rigid spherical punch subjected to a normal load. It is assumed that the punch within the contact region is a perfect conductor with a constant electric potential. The electro-mechanical properties of the functionally graded piezoelectric materials vary exponentially along the thickness direction. The whole contact region consists of an inner circular stick region surrounded by an outer annular slip region obeying Coulomb’s law of friction. The problem is reduced to a set of coupled Cauchy singular integral equations by employing the Hankel integral transform. An iterative method is used to determine the unknown stick/slip region, normal contact pressure, electric charge, and radial tangential traction. The effects of the resultant electric charge, friction coefficient, and gradient index on the surface electro-mechanical fields are presented in detail.