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.

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.

Elasto-Plastic Finite Element Analysis of Three-Dimensional Pure Rolling Contact Above the Shakedown Limit

1991 ◽  
Vol 58 (2) ◽  
pp. 347-353 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Bearing Steel ◽  
Complex Stress State ◽  
Rolling Contact ◽  
Stress Strain ◽  
Element Analysis ◽  
Shakedown Limit

This paper describes calculations for repeated, frictionless, three-dimensional rolling contact, for a relative peak pressure (po/k) of 6.0 (above the shakedown limit) for a circular contact patch. This analysis was carried out for two material responses, elastic-perfectly plastic (EPP) and elastic-linear-kinematic-hardening plastic (ELKP), using the elasto-plastic finite element model developed earlier. The ELKP material parameters are those appropriate for hardened bearing steel. Frictionless three-dimensional rolling contact is simulated by repeatedly translating a Hertzian pressure distribution across the surface of an elasto-plastic half space. The half space is represented by a finite mesh with elastic boundaries. The paper describes the complex stress state existing in the half space and the attending plasticity, as the load translates. The calculations present the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain increments in the vicinity of the contact. Compared with the analyses at the shakedown limit, higher residual stresses and strains are observed.

Elastoplastic Finite Element Analysis of Three-Dimensional, Pure Rolling Contact at the Shakedown Limit

1990 ◽  
Vol 57 (1) ◽  
pp. 57-65 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Element Model ◽  
Rolling Contact ◽  
Stress Strain ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Shakedown Limit

This paper describes a three-dimensional elastoplastic finite element model of repeated, frictionless rolling contact. The model treats a sphere rolling on an elastic-perfectly plastic and an elastic-linear-kinematic-hardening plastic, semi-infinite half space. The calculations are for a relative peak pressure (po/k) = 4.68 (the theoretical shakedown limit for perfect plasticity). Three-dimensional rolling contact is simulated by repeatedly translating a hemispherical (Hertzian) pressure distribution across an elastoplastic semi-infinite half space. The semi-infinite half space is represented by a finite mesh with elastic boundaries. The calculations describe the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain ranges in the vicinity of the contact.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Shakedown analysis for the evaluation of strength and bearing capacity of multilayered railway structures

2018 ◽  
Vol 232 (9) ◽  
pp. 2324-2335 ◽  
Author(s):  
Kangyu Wang ◽  
Yan Zhuang ◽  
Hanlong Liu
Keyword(s):  
Bearing Capacity ◽  
Engineering Design ◽  
Permanent Deformation ◽  
Three Dimensional ◽  
Frictional Coefficient ◽  
Repeated Loading ◽  
Residual Stress Field ◽  
Shakedown Analysis ◽  
Traffic Loads ◽  
Shakedown Limit

Shakedown analysis is a robust approach for solving the strength problem of a structure under cyclic or repeated loading, e.g. railway structures subject to rolling and sliding traffic loads. Owing to the traffic loads, which are higher than the “shakedown limit”, railway structures may fail due to the excessive permanent deformation. This paper develops the analytical shakedown solutions based on Melan’s shakedown theorem, which is then applied for the evaluation of the strength and bearing capacity of multilayered railway structures. The shakedown solutions utilize the elastic stress fields obtained from the fully three-dimensional finite/infinite model, and calculate the shakedown multiplier for each layer of railway structures by means of a self-equilibrated critical residual stress field. The shakedown limits are then determined as the minimum shakedown multiplier among all layers. Parametric studies are also conducted, which indicate how the frictional coefficient, strength and stiffness of the materials, and the thickness ratio of ballast to subballast influence the shakedown limit and the stability condition of railway structures. The critical points of shakedown occur at the rail for low values of rail’s yield stress and large frictional coefficient, while they occur at the ballast layer when the frictional coefficient is relatively small. The shakedown limits are found to decrease with the increase in the strength and thickness of the ballast for a relatively small frictional coefficient. For the engineering design, there is an optimum combination of material properties and layer thickness, which provides the maximum bearing capacity of the railway structure based on this research. The results obtained from this study can provide a useful reference for the engineering design of railway structures.

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.

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

1991 ◽  
Vol 113 (3) ◽  
pp. 434-441 ◽  
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.

Hertz Contact Problem between Wheel and Rail

2013 ◽  
Vol 837 ◽  
pp. 733-738 ◽  
Author(s):  
Tiberiu Axinte
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Contact Problem ◽  
Contact Pressure ◽  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Contact ◽  
Hertz Contact ◽  
Shakedown Limit ◽  
Plastic Shakedown

Rail-wheel contact problems have been analyzed by the use of the three-dimensional finite element models. Based on these models, the paper presents a study regarding the applicability of the Hertz contact to rail-wheel contact problems. Beside a standard rail, the study also considers a crane rail and a switching component. The bodies of the contact problem are the standard rail UIC60 and the standard wheel UICORE. The maximum contact pressure which the material can support in the elastic range in steady state conditions is known as the shakedown limit. With an operating contact pressure below the shakedown limit the rail would be expected to remain elastic a long period of its lifecycle. However, examination of rail cross-sections shows severe plastic deformation in a sub-surface layer of a few tens of microns thickness; the contact patch size is in tens of millimeters. Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted in order to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. The Hertz theory is restricted to frictionless surfaces and perfectly elastic solids, but it is the best method for determining deformations and stress from pitch of contact. Form change due to wear and plastic deformation of a rail can reduce the service life of a track. The purpose of this investigation was to study the development of these damage mechanisms on new and three years old rails in a commuter track over a period of two years.

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