On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space

The elastic solution of a tangentially loaded contact is known as the Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. It is found that the influence coefficients are of the same order of magnitude as the ones describing the normal displacement. This result is of great importance for stick-slip contact problem when coupling the normal and tangential behavior in the elastic-plastic regime, and also for metals and alloys with low or moderate yield stress.

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Guided Surface Waves on an Elastic Half Space

Journal of Applied Mechanics ◽

10.1115/1.3408973 ◽

1971 ◽

Vol 38 (4) ◽

pp. 899-905 ◽

Cited By ~ 5

Author(s):

L. B. Freund

Keyword(s):

Wave Propagation ◽

Surface Wave ◽

Surface Waves ◽

Half Space ◽

Body Wave ◽

Three Dimensional ◽

Elastic Half Space ◽

Normal Displacement ◽

Rigid Barrier ◽

Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

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Experimental Study of Static Friction in a Spherical Elastic-Plastic Contact

Volume 3: Design; Tribology; Education ◽

10.1115/esda2008-59008 ◽

2008 ◽

Author(s):

Andrey Ovcharenko ◽

Gregory Halperin ◽

Izhak Etsion

Keyword(s):

Friction Force ◽

Normal Load ◽

Static Friction ◽

Tangential Displacement ◽

Accurate Identification ◽

Elastic Plastic ◽

Static Friction Coefficient ◽

Wide Range ◽

Material Good ◽

Contact Diameter

The elastic-plastic contact between a deformable sphere and a rigid flat during pre-sliding is studied experimentally. Measurements of friction force and contact area are done in real time along with an accurate identification of the instant of sliding inception. The static friction force and relative tangential displacement are investigated over a wide range of normal preloads for several sphere materials and diameters. It is found that at low normal loads the static friction coefficient depends on the normal load in breach of the classical laws of friction. The pre-sliding displacement is found to be less than 5 percent of the contact diameter, and the interface mean shear stress at sliding inception is found to be slightly below the shear strength of the sphere material. Good correlation is found between the present experimental results and a recent theoretical model in the elastic-plastic regime of deformation.

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Experimental Study of Adhesive Static Friction in a Spherical Elastic-Plastic Contact

Journal of Tribology ◽

10.1115/1.2842247 ◽

2008 ◽

Vol 130 (2) ◽

Cited By ~ 34

Author(s):

A. Ovcharenko ◽

G. Halperin ◽

I. Etsion

Keyword(s):

Friction Force ◽

Normal Load ◽

Static Friction ◽

Tangential Displacement ◽

Accurate Identification ◽

Elastic Plastic ◽

Static Friction Coefficient ◽

Wide Range ◽

Material Good ◽

Contact Diameter

The elastic-plastic contact between a deformable sphere and a rigid flat during presliding is studied experimentally. Measurements of friction force and contact area are done in real time along with an accurate identification of the instant of sliding inception. The static friction force and relative tangential displacement are investigated over a wide range of normal preloads for several sphere materials and diameters. Different behavior of the static friction is observed in the elastic and in the elastic-plastic regimes of sphere deformation. It is found that at low normal loads, the static friction coefficient depends on the normal load in breach of the classical laws of friction. The presliding displacement is found to be less than 5% of the contact diameter, and the interface mean shear stress at sliding inception is found to be slightly below the shear strength of the sphere material. Good correlation is found between the present experimental results and a recent theoretical model in the elastic-plastic regime of deformation.

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Pre-Sliding of a Spherical Elastic-Plastic Contact

STLE/ASME 2008 International Joint Tribology Conference ◽

10.1115/ijtc2008-71085 ◽

2008 ◽

Author(s):

Andrey Ovcharenko ◽

Gregory Halperin ◽

Izhak Etsion

Keyword(s):

Friction Force ◽

Normal Load ◽

Static Friction ◽

Tangential Displacement ◽

Accurate Identification ◽

Elastic Plastic ◽

Static Friction Coefficient ◽

Wide Range ◽

Material Good ◽

Contact Diameter

The elastic-plastic contact between a deformable sphere and a rigid flat during pre-sliding is studied experimentally. Measurements of friction force and contact area are done in real time along with an accurate identification of the instant of sliding inception. The static friction force and relative tangential displacement are investigated over a wide range of normal preloads for several sphere materials and diameters. It is found that at low normal loads the static friction coefficient depends on the normal load in breach of the classical laws of friction. The pre-sliding displacement is found to be less than 5 percent of the contact diameter, and the interface mean shear stress at sliding inception is found to be slightly below the shear strength of the sphere material. Good correlation is found between the present experimental results and a recent theoretical model in the elastic-plastic regime of deformation.

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Prediction of Resonant Response of Shrouded Blades With 3D Shroud Constraint

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education ◽

10.1115/98-gt-485 ◽

1998 ◽

Cited By ~ 1

Author(s):

B. D. Yang ◽

J. J. Chen ◽

C. H. Menq

Keyword(s):

Relative Motion ◽

Normal Load ◽

Three Dimensional ◽

Force Model ◽

Resonant Response ◽

Equivalent Stiffness ◽

Stick Slip ◽

Contact Plane ◽

Blade System ◽

Stiffness And Damping

In this paper, the 3D shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely 2D constraint and 3D constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

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Elasto-Plastic Finite Element Analysis of Repeated Three-Dimensional, Elliptical Rolling Contact With Rail Wheel Properties

Journal of Tribology ◽

10.1115/1.2920643 ◽

1991 ◽

Vol 113 (3) ◽

pp. 434-441 ◽

Cited By ~ 17

Author(s):

S. M. Kulkarni ◽

G. T. Hahn ◽

C. A. Rubin ◽

V. Bhargava

Keyword(s):

Finite Element ◽

Plastic Strain ◽

Half Space ◽

Kinematic Hardening ◽

Rolling Direction ◽

Three Dimensional ◽

Rolling Contact ◽

Cyclic Plasticity ◽

Wheel Load ◽

Stress Strain

This paper presents an elasto-plastic analysis of the repeated, frictionless, three-dimensional rolling contact similar to the ones produced by the rail-wheel geometry. This paper treats an elliptical contact rolling across a semi-infinite half space. The contact shape and loading: semi-major axis (in the rolling direction), w1 = 8 mm, and semi-minor axis, w2 = 5.88 mm, reflect standard rail and wheel curvatures and a wheel load of 149 KN (33,000 lb). A three-dimensional, elasto-plastic finite element model, developed earlier, is employed together with the elastic-linear-kinematic-hardening-plastic (ELKP) idealization of the cyclic plastic behaviour of a material similar to rail and wheel steels. The calculations present the displacements, the stress-strain distributions, stress-plastic strain histories and the plastic strain ranges in the half-space. The cyclic plasticity approaches a steady state after one contact with further contacts producing open but fully reversed stress-strain hysteresis loops, i.e., plastic shakedown.

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Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces

Journal of Tribology ◽

10.1115/1.1401018 ◽

2001 ◽

Vol 124 (1) ◽

pp. 46-61 ◽

Cited By ~ 16

Author(s):

Wei Peng ◽

Bharat Bhushan

Keyword(s):

Surface Deformation ◽

Rough Surfaces ◽

Normal Load ◽

Three Dimensional ◽

Sliding Contact ◽

Fast Fourier Transformation ◽

Maximum Pressure ◽

Asperity Contact ◽

Elastic Plastic ◽

Von Mises

A three-dimensional numerical model is presented to investigate the quasi-static sliding contact behavior of layered elastic/plastic solids with rough surfaces. The model is applicable for both single-asperity contact and multiple-asperity contacts. The surface deformation is obtained based on a variational principle. The surface and subsurface stresses in the layer and the substrate are determined with a Fast Fourier transformation (FFT) based scheme and von Mises and principal tensile stresses are computed accordingly. Contact statistics, such as fractional contact area, maximum pressure/E2 and relative meniscus force are predicted. The results are used to investigate the effect of the contact statistics on friction, stiction, and wear problems such as debris generation, brittle failure, and delamination of layered media. Optimum layer parameters are identified. It allows the specification of layer properties, according to the contact statistics, to reduce friction, stiction, and wear of materials. A normalization procedure is presented to apply the results on various combinations of surface roughness, material properties, and normal load.

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Simulation of Plasto-Elastohydrodynamic Lubrication in a Rolling Contact

Journal of Tribology ◽

10.1115/1.4032137 ◽

2016 ◽

Vol 138 (3) ◽

Cited By ~ 3

Author(s):

Tao He ◽

Dong Zhu ◽

Jiaxu Wang

Keyword(s):

Plastic Deformation ◽

Plastic Strain ◽

Rolling Direction ◽

Three Dimensional ◽

Elastohydrodynamic Lubrication ◽

Surface Plastic Deformation ◽

Rolling Contact ◽

Surface Plastic ◽

Contact Center ◽

Elastic Plastic

Surface plastic deformation due to contact (lubricated or dry) widely exists in many mechanical components, as subsurface stress caused by high-pressure concentrated in the contact zone often exceeds the material yielding limit, and the plastic strain accumulates when the load is increased and/or repeatedly applied to the surface in a rolling contact. However, previous plasto-elastohydrodynamic lubrication (PEHL) studies were mainly for the preliminary case of having a rigid ball (or roller) rotating on a stationary elastic–plastic flat with a fixed contact center, for which the numerical simulation is relatively simple. This paper presents an efficient method for simulating PEHL in a rolling contact. The von Mises yield criteria are used for determining the plastic zone, and the total computation domain is discretized into a number of cuboidal elements underneath the contacting surface, each one is considered as a cuboid with uniform plastic strain inside. The residual stress and surface plastic deformation resulted from the plastic strain can be solved as a half-space eigenstrain–eigenstress problem. A combination of three-dimensional (3D) and two-dimensional (2D) discrete convolution and fast Fourier transform (DC-FFT) techniques is used for accelerating the computation. It is observed that if a rigid ball rolls on an elastic–plastic surface, the characteristics of PEHL lubricant film thickness and pressure distribution are different from those of PEHL in the preliminary cases previously investigated. It is also found that with the increase of rolling cycles, the increment of plastic strain accumulation gradually approaches a stable value or drops down to zero, determined by the applied load and the material hardening properties, eventually causing a groove along the rolling direction. Simulation results for different material hardening properties are also compared to reveal the effect of body materials on the PEHL behaviors.

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Three-Dimensional Finite Element Elastic–Plastic Model for Subsurface Initiated Spalling in Rolling Contacts

Journal of Tribology ◽

10.1115/1.4025841 ◽

2013 ◽

Vol 136 (1) ◽

Cited By ~ 18

Author(s):

John A. R. Bomidi ◽

Farshid Sadeghi

Keyword(s):

Finite Element ◽

Plastic Strain ◽

Fatigue Damage ◽

Three Dimensional ◽

Rolling Contact ◽

Material Behavior ◽

Lower Percentage ◽

Fe Model ◽

Plastic Model ◽

Elastic Plastic

In this investigation, a three-dimensional (3D) finite element (FE) model was developed to study subsurface initiated spalling observed in rolling line contact of tribo components such as bearings. An elastic–kinematic hardening–plastic material model is employed to capture the material behavior of bearing steel and is coupled with the continuum damage mechanics (CDM) approach to capture the material degradation due to fatigue. The fatigue damage model employs both stress and accumulated plastic strain based damage evolution laws for fatigue failure initiation and propagation. Failure is modeled by mesh partitioning along unstructured, nonplanar, intergranular paths of the microstructure topology represented by randomly generated Voronoi tessellations. The elastic–plastic model coupled with CDM was used to predict both ratcheting behavior and fatigue damage in heavily loaded contacts. Fatigue damage induced due to the accumulated plastic strains around broken intergranular joints drive the majority of the crack propagation stage, resulting in a lower percentage of life spent in propagation. The 3D FE model was used to determine fatigue life at different contact pressures ranging from 2 to 4.5 GPa for 33 different randomly generated microstructure topology models. The effect of change in contact pressure due to subsurface damage and plastic strain accumulation was also captured by explicitly modeling the rolling contact geometry and the results were compared to those generated assuming a Hertzian pressure profile. The spall shape, fatigue lives, and their dispersion characterized by Weibull slopes obtained from the model correlate well with the previously published experimental results.

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