Rolling contact of a rigid sphere/sliding of a spherical indenter upon a viscoelastic half-space containing an ellipsoidal inhomogeneity

2015 ◽  
Vol 80 ◽  
pp. 1-25 ◽  
Author(s):  
Koffi Espoir Koumi ◽  
Thibaut Chaise ◽  
Daniel Nelias
Keyword(s):  
Half Space ◽  
Spherical Indenter ◽  
Rolling Contact ◽  
Rigid Sphere ◽  
Ellipsoidal Inhomogeneity

Three-Dimensional Repeated Elasto-Plastic Point Contacts, Rolling, and Sliding

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
W. Wayne Chen ◽  
Q. Jane Wang ◽  
Fan Wang ◽  
Leon M. Keer ◽  
Jian Cao
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Indentation Test ◽  
Rolling Contact ◽  
Repeated Loading ◽  
Rigid Sphere ◽  
Point Contacts ◽  
Volume Integral ◽  
The Finite Element Method ◽  
Shakedown Limit

Accumulative plastic deformation due to repeated loading is crucial to the lives of many mechanical components, such as gears, stamping dies, and rails in rail-wheel contacts. This paper presents a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elasto-plastic half-space. This model is a semi-analytical model based on the discrete convolution and fast Fourier transform algorithm. The half-space behaves either elastic-perfectly plastically or kinematic plastically. The analyses using this model result in histories of stress, strain, residual displacement, and plastic strain volume integral (PV) in the half-space. The model is examined through comparisons of the current results with those from the finite element method for a simple indentation test. The results of rolling contact obtained from four different hardening laws are presented when the load exceeds the theoretical shakedown limit. Shakedown and ratchetting behaviors are discussed in terms of the PV variation. The effect of friction coefficient on material responses to repeated sliding contacts is also investigated.

The Contact Stresses Between a Rigid Indenter and a Viscoelastic Half-Space

1966 ◽  
Vol 33 (4) ◽  
pp. 845-854 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Contact Area ◽  
Contact Stresses ◽  
Spherical Indenter ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Hertz Problem ◽  
Monotonically Increasing Function ◽  
Increasing Function

The Hertz problem for a rigid spherical indenter on a viscoelastic half-space was studied by Lee and Radok [1] in which the radius a(t) of the contact area is a monotonically increasing function of time t. Later, Hunter [2] studied the rebound of a rigid sphere on a viscoelastic half-space so that the contact radius a(t) increases monotonically to a maximum and then decreases to zero monotonically. The contact problem in which a(t) increases for the second time and decreases again does not seem to have been studied; nor has the contact problem in which a(t) is nonzero initially and decreases monotonically been studied. In this paper, a method is introduced so that the contact problem can be solved for arbitrary a(t). The rigid indenter is assumed to be smooth and axisymmetric but otherwise arbitrary. The viscoelastic solutions are expressed in terms of the associated elastic solutions. A means for measuring the viscoelastic Poisson’s ratio is suggested.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

THREE-DIMENSIONAL SURFACE CRACK ANALYSIS OF ELASTIC HALF-SPACE UNDER ROLLING CONTACT LOAD

2009 ◽  
Vol 06 (02) ◽  
pp. 317-332 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
HUI-QIN YU
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Rolling Contact ◽  
Contact Load ◽  
Hypersingular Integral ◽  
Space Body ◽  
Planar Crack

In this work a three-dimensional planar crack on the surface of elastic half-space was analyzed under rolling contact load. The stresses interior to an elastic half-space body under rolling contact load and those produced by an infinitesimal displacement jump loop for the elastic half-space body were used to reduce the planar crack problem to the solution of a system of two-dimensional hypersingular integral equations with unknown displacement jump. The ideas of finite element discretization were employed to construct numerical solution schemes for solving the integral equations. An appropriate treatment of the associated hypersingular integral in the numerical solution to the integral equations was proposed in Hadamard's finite-part integral sense. The numerical results showed that the present procedure yields solutions with high accuracies. The stress intensity factors near the crack front edge under rolling contact load were indicated in graphical form with varying the crack shape, the radius of rolling contact zone and the friction coefficients, respectively. In addition, the influence of the lubricant infiltrating the crack surfaces on the crack propagation was also discussed in the paper.

Influence of Internal Stresses on the Stressing of Material in Components Subjected to Rolling-Contact Loads

1984 ◽  
Vol 106 (4) ◽  
pp. 499-504 ◽  
Author(s):  
E. Broszeit ◽  
J. Adelmann ◽  
O. Zwirlein
Keyword(s):  
Half Space ◽  
Stress Level ◽  
Maximum Stress ◽  
Equivalent Stress ◽  
Local Stress ◽  
Rolling Contact ◽  
Internal Stresses ◽  
Contact Loads ◽  
Distortion Energy ◽  
Von Mises

The stressing of a material in concentrated contacts can be calculated using f.e. the equivalent stress hypothesis by Huber, von Mises, Hencky (distortion energy hypothesis). The stress level can be directly related to the local yield properties of the material. For the calculation of the equivalent stress the influence of friction and internal stresses in the material have to be taken into account. The local stress level in the half space strongly depends on friction and internal stresses. It will be demonstrated, that it is necessary to have a look at a greater part of the full half space to find the maximum stress level.

A Finite Element Analysis of the Effect of Hardening Rules on the Indentation Test

1998 ◽  
Vol 120 (2) ◽  
pp. 143-148 ◽  
Author(s):  
N. Huber ◽  
Ch. Tsakmakis
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Indentation Test ◽  
Rigid Sphere ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Hardening Rules

Using the Finite Element Method, an analysis is given of the indentation of an elasticplastic half-space by a rigid sphere. In particular, attention is focused on the effect of hardening rules on the material response. The materials considered are supposed to exhibit isotropic and kinematic hardening. Moreover, it is shown that the possibility of similar behavior due to effects of friction can be ruled out.

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