A Numerical Three-Dimensional Model for the Contact of Layered Elastic/Plastic Solids With Rough Surfaces by a Variational Principle

2000 ◽  
Vol 123 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Wei Peng ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Fast Fourier Transformation ◽  
Three Dimensional Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Influence Coefficients ◽  
Elastic Perfectly Plastic

A new numerical model for the three-dimensional contact analysis of a layered elastic–perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich–Neuber potentials with fast Fourier transformation. The model is extended to elastic–perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, layer thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.

A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

1996 ◽  
Vol 118 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Xuefeng Tian ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Contact Problem ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Computation Time ◽  
Inversion Method ◽  
Three Dimensional Model ◽  
Perfectly Plastic ◽  
Contact Points ◽  
Uniqueness Of The Solution

A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

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

2001 ◽  
Vol 124 (1) ◽  
pp. 46-61 ◽  
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.

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.

Methods for the simulation of the pressure, stress, and temperature distribution in the contact of fractal generated rough surfaces

2016 ◽  
Vol 231 (4) ◽  
pp. 489-502 ◽  
Author(s):  
Balázs Magyar ◽  
Bernd Sauer
Keyword(s):  
Surface Roughness ◽  
Temperature Distribution ◽  
Plastic Material ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Sliding Contact ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Pressure Stress

In this paper, the influence of surface roughness on the local tribological load with a dry sliding contact is studied. First, three artificial rough surfaces with similar structure but different asperity heights are generated and projected on a smooth ball. After that, a contact pattern is determined between a rough ball and a smooth surface taking into account the elastic only as well as the linear elastic-perfectly plastic material description. On the basis of the calculated contact pressure distribution, the subsurface stresses and a three-dimensional temperature distribution in the sliding contact are calculated. The solutions show that a low surface roughness not necessarily results in low local tribological load of the surface.

Elastic-Plastic Contact Between Rough Surfaces: Proposal for a Wear Model

2005 ◽  
Author(s):  
D. Ne´lias ◽  
V. Boucly ◽  
M. Brunet
Keyword(s):  
Rough Surfaces ◽  
Companion Paper ◽  
Contact Model ◽  
Mapping Algorithm ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Plastic Sphere ◽  
Elastic Perfectly Plastic ◽  
Von Mises

A semi-analytical thermo-elastic-plastic contact model has been recently developed, and presented in a companion paper. The main advantage of this approach over the classical Finite Element Method (FEM) is the treatment of transient problems with the use of fine meshing, and the possibility of studying the effect of a surface defect on the surface deflection as well as on subsurface stress state. A return-mapping algorithm with an elastic predictor / plastic corrector scheme and a Von Mises criterion is now used, which improves the plasticity loop. This improvement in the numerical algorithm increases the computing speed significantly, and shows a much better convergence and accuracy. The contact model is validated through a comparison with the FEM results of Kogut and Etsion (2002), which correspond to the axisymmetric contact between an elastic-perfectly plastic sphere and a rigid flat. A model for wear prediction based on the material removal during cyclic loading is then proposed. Results are presented for rough surfaces.

Numerical Study of Defect Free Elbows Subjected to In-Plane Bending Moment

2011 ◽  
Vol 189-193 ◽  
pp. 1494-1497
Author(s):  
Wang Chen ◽  
Yin Pei Wang ◽  
Pei Ning Li ◽  
Chen Jin ◽  
Xiao Ming Sun
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Three Dimensional ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Piping System ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Bending Radius ◽  
Elastic Perfectly Plastic

Elbow is a type of components widely used in a piping system, and so it is very important to know the plastic carrying capacity of elbow. In this study, the elastic-plastic behavior of elbows with various ratios of t/rm and relative bending radius R/rm were investigated in detail by using of three-dimensional (3D) non-linear finite element (FE) analyses, assuming elastic-perfectly-plastic material behaviour and taking geometric nonlinearity into account. The analyses indicated that elbow exhibited different behavior obviously at the elastic-plastic states subjected to In-Plane opening bending moment and closing bending moment. The closed form equations of elbow involving effect of tangent pipes were established.

Combined Viscous and Plastic Deformations in Two-Dimensional Large Strain Finite Element Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Input Parameter ◽  
Time Integration ◽  
Strain Increment ◽  
Total Strain ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Time Stepping ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Capabilities for the analysis of combined viscous and plastic behavior have been added to an existing finite element computer program for two-dimensional elastic-plastic calculations. This program (PAPSTB) has been formulated for elastic-plastic stress and deformation analyses of two-dimensional and axisymmetric structures. It has the ability to model large strains and large deformations of elastic-perfectly plastic, multi-linear hardening, or power-hardening materials. The program is based on incremental plasticity theory with a von Mises yield criterion. Time dependent behavior has been introduced into the PAPSTB program by adding a viscous strain increment to the elastic and plastic strain increment to form the total strain increment. The viscous calculations presently employ a power-law relationship between the viscous strain rate and the effective stress. The finite element code can be easily modified to handle more complex viscous models. The Newmark method for time integration is used, i.e., an input parameter is included which enables the user to vary the time domain approximation between forward (explicit) and backward (implicit) difference. Automatic time stepping is used to provide for stability in the viscous calculations. It is controlled by an input parameter related to the ratio of the current viscous strain increment to the total strain. The viscoplastic capabilities of the PAPSTB program are verified using the axisymmetric problem of an internally pressurized, thick-walled cylinder. The transient viscoplastic case is analyzed to demonstrate that the elastic-perfectly plastic solution is obtained as a steady-state condition is approached. The influence of varying the time integration parameter for transient viscoplastic calculations is demonstrated. In addition, the effects of time step on solution accuracy are investigated by means of the automatic time stepping algorithm in the program. The approach is then applied to a simple forging problem of cylinder upsetting.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

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