Contact Slip Research Articles

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.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics.

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Multi-directional behavior of granular materials and its relation to incremental elasto-plasticity

The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which follow an initial monotonic axisymmetric triaxial loading. The model used non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo–Mindlin model for the contact interactions. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain or principal stress rotation), with small strains increments of 2×10−6. The reversible response was linear but exhibited a high degree of stiffness anisotropy. The irreversible behavior, however, departed in several respects from classical elasto-plasticity. A small amount of irreversible strain and contact slipping occurred for all directions of the stress increment (loading, unloading, transverse loading, etc.), demonstrating that an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations. Irreversible strain occurred in directions tangent to the primary yield surface, and the direction of the irreversible strain varied with the direction of the stress increment. For stress increments within the deviatoric pi-plane, the irreversible response had rounded-corners, evidence of multiple plastic mechanisms. The response at these rounded corners varied in a continuous manner as a function of stress direction. The results are placed in the context of advanced elasto-plasticity models: multi-mechanism plasticity and tangential plasticity. Although these models are an improvement on conventional elasto-plasticity, they do not fully fit the simulation results.

Multi-step wear evolution simulation method for the prediction of rail wheel wear and vehicle dynamic performance

This paper presents a complete model to estimate the effects of wheel wear on the dynamic behavior and ride comfort of a railway vehicle. A co-simulation of the vehicle dynamics modeled in ADAMS VI-Rail and wear evolution modeled in MATLAB is performed in a loop. The outputs from the vehicle dynamics simulation are used to compute the wear evolution, which in turn affects the vehicle dynamics. The local contact parameters, such as normal contact force, tangential stresses and slip, etc., and wear distribution for each cell of the contact surface are estimated with the help of Kalker’s simplified theory of rolling contact and Archard’s wear model, respectively. The wear distribution and smoothening of the wheel profile are obtained for a short travel distance and are then scaled up for larger travel distance. The worn wheel profile is updated in the vehicle dynamics model after every 10,000 km of travel for further dynamic analysis and this process is repeated until either the critical dynamic performance or wheel wear limits are reached. Several new results emerge by considering both acceleration and braking on a tangent track with sinusoidal irregularities. Critical speed appears to increase initially and then decrease quickly, whereas worn wheels give better ride comfort in both lateral and vertical directions as compared to new wheels. According to the results in this work, wheels may be recommended for re-profiling or replacement much before the critical wear depth recommended in maintenance guidelines is reached.

Study of adhesion and friction drag on a rough hydrophobic surface: Sandblasted aluminum

Roughness is a crucial prerequisite for fabricating superhydrophobic surfaces. However, the enormous economic cost of fabricating rough surfaces seriously limits the industrial application of superhydrophobic surfaces. To overcome this drawback, we present herein a simple, low cost, user-friendly, and rapid method to fabricate rough surfaces with micro- and nanostructured features. By modifying the sandblasting pressure, we fabricated aluminum surfaces of varying roughness, which we then decorated with polydimethylsiloxane to reduce the surface energy. The contact angle, slip velocity, slip length, and drag-reduction ratio all increase with increasing sandblasting pressure, and the maximum contact angle of a droplet, the slip velocity, the length, and the drag-reduction ratio are 151.74 ± 1°, 0.1617 m/s, 0.04276 mm, and 19.2%, respectively, for a sandblasting pressure of 0.8 MPa. The adhesive force of the samples decreases with increasing sandblasting pressure to a minimum of 0.096 mN. The process by which trapped air escapes from the sample surface is visualized by using fluent software, and the results show that the low adhesive and low friction properties of the superhydrophobic surface, which are due to air being trapped in the space between protrusions, may effectively prevent water from moving into these spaces.

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.

Deformation Features on the Free Surface and Rigid Interface during Elastic Wave Reflection

Analytical expressions defining the reflection coefficients have been derived in the framework of the known problem of elastic wave reflection from the free surface and rigid interface. The found reflection coefficients are used to analyze the dependences of different strain and rotation components during elastic wave reflection from the free surface and rigid interface in the case of ideal contact and possible slip on the wave incidence angle and elastic parameters of the medium. Deformation features of elastic media at the studied interfaces are considered for incident longitudinal and transverse waves.

Wet Single Clutch Engagement Behaviors in the Dual-Clutch Transmission System

A frictional torque was generated by a lubricated slip contact between a wet clutch pad and a steel separator during a wet clutch engagement. It is necessary to understand the generation of frictional torque to improve the performance of the frictional torque transfer and the durability of the wet clutch system. The analytical modeling of wet clutch torque transfer considers the effects of surface roughness, permeability, the elastic modulus of the frictional material, lubricant viscosity, temperature, etc. Experimental apparatus for wet clutch engagement was designed for the measurement of frictional torque transfer during wet clutch engagement. The experimental results were compared with the analytical results under various operational conditions for the verification of the theoretical analysis to evaluate the performance of the wet clutch system. Some correlations were investigated between the experimental and analytical results. We found that computation by analytical modeling can predict the effects of oil temperature, applied force, and slip speed, as well as engagement period and frictional torque transfer shapes.

Prediction of the coexistence of rail head check initiation and wear growth

A method for predicting the coexistence of the rail head check (HC) initiation and wear growth was presented to divide the continuous process of HC initiation and wear growth into many of the same discrete processes, each of which included wear and fatigue damage by wheel/rail stick–slip contact, wear-induced rail profile evolution, cumulative fatigue damage until a random material point in the rail reached the fatigue failure criterion. The method was applied to predict HC initiation for a U75V heat-treated rail, this being the sharp curve high rail used in China’s heavy-haul railway, and was compared with the method considering no wear and validated by field tests. The result shows that the HC initiation life was about 2.17 × 105 wheel cycles and the average vertical wear growth rate was about 4.2651 μm/104 wheel cycles, values which were close to the field observation. Because the wear growth and profile evolution, the HC initiation position was closer to the rail center than when using the method considering no wear and the development of the fatigue damage was nonlinear from slow to fast .

Quasi-static incremental behavior of granular materials: Elastic–plastic coupling and micro-scale dissipation

The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo–Mindlin model. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of 2×10−6. At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.

Spontaneous imbibition in fractal tortuous micro-nano pores considering dynamic contact angle and slip effect: phase portrait analysis and analytical solutions

Shales have abundant micro-nano pores. Meanwhile, a considerable amount of fracturing liquid is imbibed spontaneously in the hydraulic fracturing process. The spontaneous imbibition in tortuous micro-nano pores is special to shale, and dynamic contact angle and slippage are two important characteristics. In this work, we mainly investigate spontaneous imbibition considering dynamic contact angle and slip effect in fractal tortuous capillaries. We introduce phase portrait analysis to analyse the dynamic state and stability of imbibition. Moreover, analytical solutions to the imbibition equation are derived under special situations, and the solutions are verified by published data. Finally, we discuss the influences of slip length, dynamic contact angle and gravity on spontaneous imbibition. The analysis shows that phase portrait is an ideal tool for analysing spontaneous imbibition because it can evaluate the process without solving the complex governing ordinary differential equations. Moreover, dynamic contact angle and slip effect play an important role in fluid imbibition in fractal tortuous capillaries. Neglecting slip effect in micro-nano pores apparently underestimates imbibition capability, and ignoring variations in contact angle causes inaccuracy in predicting imbibition speed at the initial stage of the process. Finally, gravity is one of the factors that control the stabilisation of the imbibition process.

Development of Direct-printed Tactile Sensors for Gripper Control through Contact and Slip Detection

This work demonstrates the use of printed tactile sensors for detection of contact location and slip in a robot gripper. Research and development of robots for behaviors similar to those of humans are being conducted by many institutions. For these robot systems, flexible tactile sensors imitating human tactile senses have been developed and applied to robots. The sensors used in this work were fabricated through a direct-print process using a multi-walled carbon nanotube (MWCNT)/polymer composite. These sensors are a resistance type and were characterized by detecting changes in resistance of MWCNT networks within the composite in response to external forces. With tactile sensors attached to gripper fingers, signals generated when the gripper grasped objects were analyzed and the resulting information was used for robot gripper control.

Relationship between Slip Length and Contact Angle on Hydrophobic Surfaces

Relationship between Slip Length and Contact Angle on Hydrophobic Surfaces

Wear depth calculation and influence factor analysis for groove ball bearing

Based on Hertz contact theory and load distribution, the formulas for contact stress cycle times, slip distance and wear depth measurements are derived, and the influences of load, curvature coefficient, roll body diameter and friction coefficient on the contact region wear depth and distributions are thoroughly analyzed. The results show that the wear depth is zero at the pure rolling point and the long half-axle terminals of contact ellipse, and reaches maximum value near by the long half-axle terminals of the contact ellipse, and further shows that the wear depth increases with increase of the load and friction coefficient, however decreases with increase of the curvature coefficient and roll body diameter.

Surface roughness effects on contact line motion with small capillary number

In this work, we investigate how surface roughness influences contact line dynamics by simulating forced wetting in a capillary tube. The tube wall is decorated with microgrooves and is intrinsically hydrophilic. A phase-field method is used to capture the fluid interface and the moving contact line. According to the numerical results, a criterion is proposed to judge whether the grooves are entirely wetted or not at vanishing capillary numbers. When the contact line moves over a train of grooves, the apparent contact angle exhibits a periodic nature, no matter whether the Cassie-Baxter or the Wenzel state is achieved. The oscillation amplitude of apparent contact angle is analyzed and found to be inversely proportional to the interface area. The contact line motion can be characterized as stick-jump-slip in the Cassie-Baxter state and stick-slip in the Wenzel state. By comparing to the contact line dynamics on smooth surfaces, equivalent microscopic contact angles and slip lengths are obtained. The equivalent slip length in the Cassie-Baxter state agrees well with the theoretical model in the literature. The equivalent contact angles are, however, much greater than the predictions of the Cassie-Baxter model and the Wenzel model for equilibrium stable states. Our results reveal that the pinning of the contact line at surface defects effectively enhances the hydrophobicity of rough surfaces, even when the surface material is intrinsically hydrophilic and the flow is under the Wenzel state.

Adaptive Finite Element‐Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre‐Existing Fractures

Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre‐existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element‐discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre‐existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre‐existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B‐values, Hudson source type plots, and focal spheres.

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.

An advanced abrasion model for tire wear

The abrasion processes of rubber or tires are extremely complex phenomena and basically different from those of other materials. Much research in tire industry has been done to predict the wear of a tire tread. However, such studies have not considered the history dependency of abrasion as well as directional effects. This paper is to propose an advanced abrasion model for rubber that will takes these two effects into account. As a result the new model can be applied to predict tire tread wear. Within this model, directional damage will be introduced to characterize the history of frictional sliding contact including the change of slip directions. It also covers local contact conditions such as contact pressure, slip velocity or flash temperature. The model will be analyzed theoretically and numerically. A FEM simulation for the Grosch-wheel with different loading conditions using the new abrasion model is performed and validated by experimental data.

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.