A Three-Dimensional Friction Model for Elastic-Plastic Contact With Tangential Loading: Application to Dented Surfaces

2004 ◽  
Author(s):  
Eduard Antaluca ◽  
Daniel Ne´lias ◽  
Spiridon Cretu
Keyword(s):  
Stress State ◽  
Pressure Distribution ◽  
Contact Pressure ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Friction Model ◽  
Reciprocal Theorem ◽  
Elastic Plastic ◽  
Fine Mesh ◽  
Von Mises

A three-dimensional numerical model based on a semi-analytical method in the framework of small strains and small displacements with respect of Hertz’s hypotheses is presented for solving an elastic-plastic dented contact with friction. The calculation of surface deformations and pressure distribution, which is the most time consuming step during the elastic-plastic algorithm, is obtained using a method based on a variational principle with a Fast Fourier Transform (FFT) and a Conjugate Gradient Method (CGM). The method is fast enough to allow investigating the effect of a small size surface defect, here a debris denting, on the subsurface elastic-plastic stress state, requiring a fine mesh with around 106 surface grid points. Further, the FFT approach is also involved in the calculation of internal stress state. The plasticity model is based on an incremental load and Von Mises yield criterion. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces yield from the Betti’s reciprocal theorem with initial strain. The code is used to compute a few smooth and dented contacts, with several types of contact interfaces conditions, including frictionless and Coulomb friction. The effects of surface dents and friction on the contact pressure and subsurface stress field are presented and discussed.

scholarly journals A Three-Dimensional Semianalytical Model for Elastic-Plastic Sliding Contacts

2007 ◽  
Vol 129 (4) ◽  
pp. 761-771 ◽  
Author(s):  
Daniel Nélias ◽  
Eduard Antaluca ◽  
Vincent Boucly ◽  
Spiridon Cretu
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Computing Time ◽  
Three Dimensional ◽  
Gradient Methods ◽  
Reciprocal Theorem ◽  
Contact Pressure Distribution ◽  
Sliding Contacts ◽  
Elastic Plastic ◽  
Residual Strains

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb’s law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti’s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor∕plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.

Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code

2002 ◽  
Vol 124 (4) ◽  
pp. 653-667 ◽  
Author(s):  
C. Jacq ◽  
D. Ne´lias ◽  
G. Lormand ◽  
D. Girodin
Keyword(s):  
Three Dimensional ◽  
Indentation Test ◽  
Closed Form Expression ◽  
Reciprocal Theorem ◽  
Plastic Strains ◽  
Surface Geometry ◽  
Fe Method ◽  
Elastic Plastic ◽  
Fine Mesh ◽  
The Reciprocal Theorem

A three-dimensional elastic-plastic contact code based on semi-analytical method is presented and validated. The contact is solved within a Hertz framework. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact pressure and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The resolution of the elastic-plastic contact using the finite element (FE) method is discussed, and the semi-analytical code presented in this paper is validated by comparing results with experimental data from the nano-indentation test. Finally, the resolution of the rolling elastic-plastic contact is presented for smooth and dented surfaces and for a vertical or rolling loading. The main advantage of this code over classical FE codes is that the calculation time makes the transient analysis of three-dimensional contact problems affordable, including when a fine mesh is required.

Contact Analysis of Multilayered Elastic/Plastic Solids With Rough Surfaces for Decreasing Friction and Wear

2005 ◽  
Author(s):  
Shaobiao Cai ◽  
Bharat Bhushan
Keyword(s):  
Surface Roughness ◽  
Contact Area ◽  
Yield Criterion ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Maximum Displacement ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Von Mises

A numerical three-dimensional contact model is presented to investigate the contact behavior of multilayered elastic-perfectly plastic solids with rough surfaces. The surface displacement and contact pressure distributions are obtained based on the variational principle with fast Fourier transform (FFT)-based scheme. Von Mises yield criterion is used to determine the onset of yield. The effective hardness is modeled and plays role when the local displacement meet the maximum displacement criterion. Simulations are performed to obtain the contact pressures, fractional total contact area, fractional plastic contact area, and surface/subsurface stresses. These contact statistics are analyzed to study the effects of the layer-to-substrate ratios of stiffness and hardness, surface roughness, and layers thickness of rough, two-layered elastic/plastic solids. The results yield insight into the effects of stiffness and hardness of layers and substrates, surface roughness, and applied load on the contact performance. The layer parameters leading to low friction, stiction, and wear are investigated and identified.

scholarly journals Elasto-plastic analysis of the contact region between a rigid ellipsoid and a semi-flat surface

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879739 ◽  
Author(s):  
Pengyang Li ◽  
Lingxia Zhou ◽  
Fangyuan Cui ◽  
Quandai Wang ◽  
Meiling Guo ◽  
...  
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Plastic Strain ◽  
Contact Pressure ◽  
Contact Region ◽  
Three Dimensional ◽  
Von Mises Stress ◽  
Effective Plastic Strain ◽  
Normal Forces ◽  
Von Mises

When the load acting on a mechanical structure is greater than the yield strength of the material, the contact surface will undergo plastic deformation. Cumulative plastic deformation has an important influence on the lifespan of mechanical parts. This article presents a three-dimensional semi-analytical model based on the conjugate gradient method and fast Fourier transform algorithm, with the aim of studying the characteristic parameters of the contact region between a rigid ellipsoid and elasto-plastic half-space. Moreover, normal forces and tangential traction were considered, as well as the contact pressure resulting from various sliding speeds and friction coefficients. The contact pressure, effective plastic strain, von Mises stress, and residual stress were measured and shown to increase with increasing sliding velocity. Finally, when the friction coefficient, contact pressure, and effective plastic strain are increased, the von Mises stress is also shown to increase, whereas the residual stress decreases.

Overstraining of flush plain cross-bored cylinders

2004 ◽  
Vol 218 (2) ◽  
pp. 143-153 ◽  
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Finite Element Method ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Solution Technique ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Incremental Theory Of Plasticity

A three-dimensional finite element method computer program was developed to establish the elastic-plastic, residual and service stress distributions in thick-walled cylinders with flush and non-protruding plain cross bores under internal pressure. The displacement formulation and eight-noded brick isoparametric elements were used. The incremental theory of plasticity with a 5 per cent yield condition (an element is assumed to have yielded when the effective stress is within 5 per cent of the material yield stress) and von Mises yield criterion were assumed. The frontal solution technique was used. The incipient yield pressure and the pressure resulting in a 0.3 per cent overstrain ratio were established for various cylinder thickness ratios and cross bore-main bore radius ratios. For a thickness ratio of 2.25 and a cross bore-main bore radius ratio of 0.1, the stresses were determined for varying overstrain and an optimum overstrain ratio of 37 per cent was established. To find the accuracy of the results, the more stringent yield condition of 0.5 per cent was also considered. The benefits of autofrettage were presented and alternative autofrettage and yield condition procedures proposed.

Three Dimensional Simulations on Stress Distribution and Fatigue Damage Life of Wheel/Rail Contact Region

2011 ◽  
Vol 284-286 ◽  
pp. 1262-1265
Author(s):  
Norie Akeel ◽  
Zainuddin Sajuri ◽  
Ahmad Kamal Ariffin ◽  
Mohamed M. Abdulrazzaq
Keyword(s):  
Stress Distribution ◽  
Crack Initiation ◽  
Fatigue Damage ◽  
Contact Region ◽  
Three Dimensional ◽  
Fine Mesh ◽  
Crack Initiation Life ◽  
Von Mises ◽  
Mesh Technique ◽  
Initiation Stress

This paper discusses the effect of different loading analysis on crack initiation life of wheel/rail in the contact region. A simulated three dimensional (3D) elastoplastic model of a wheel/rail contact is modelled using the fine mesh technique in the contact region by using Finite Element Method FEM code ANSYS 11.0 software. Different loads of approximately 70, 80, 90, 100, 110, 120, 130 and 140 KN were applied to the wheel tread during the running surface of the railhead to simulate stress distribution (Von Mises) and a life prediction of the crack initiation. Stress analysis is performed and the fatigue damage to the railhead surface is calculated numerically by using a multi-axial fatigue life of crack initiation model. Results obtained from previous researches are compared with this research.

scholarly journals Finite Difference Solution of Elastic-Plastic Thin Rotating Annular Disk with Exponentially Variable Thickness and Exponentially Variable Density

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Sanjeev Sharma ◽  
Yadav Sanehlata
Keyword(s):  
Finite Difference ◽  
Variable Thickness ◽  
Yield Criterion ◽  
Variable Density ◽  
Hardening Material ◽  
Annular Disk ◽  
Elastic Plastic ◽  
Flat Disk ◽  
Finite Difference Solution ◽  
Von Mises

Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.

An Analytical Solution for Three-Dimensional Elliptical Elastic-Plastic Rolling Contact

2014 ◽  
Vol 658 ◽  
pp. 207-212
Author(s):  
Gabriel Popescu
Keyword(s):  
Residual Stresses ◽  
Yield Criterion ◽  
Tangential Force ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Plastic Behavior ◽  
Elastic Plastic

An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

Elastic-Plastic Partial Slip Rolling Wheel-Rail Contact With an Oblique Rail Crack

2004 ◽  
Author(s):  
Yung-Chuan Chen ◽  
Jao-Hwa Kuang
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Friction Force ◽  
Element Model ◽  
Partial Slip ◽  
Contact Pressure Distribution ◽  
Tractive Force ◽  
Plastic Energy ◽  
Elastic Plastic ◽  
Pressure Distributions

The effect of rail surface crack on the wheel-rail contact pressure distribution under partial slip rolling was studied in this work. The elastic-plastic finite element model was employed for stress analyses. The numerical simulations were used to explore the effects of the contact distances and tractive force on the normal and tangential contact pressure distributions, tip plastic energy and critical wheel applied load. Contact elements were used to simulate the interaction between wheel and rail and crack surfaces. Numerical results indicate that the contact pressure distributions are significantly affected by the rail crack. Traditional contact theories are not available to describe the contact pressure distribution on the contact crack surfaces. Results also indicate that a higher friction force on the contact crack surfaces is observed for wheel subjected a larger tractive force. A larger crack surfaces friction force can reduce the sliding between crack surfaces and leads to a smaller tip plastic energy.

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