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

2005 ◽  
Vol 128 (2) ◽  
pp. 236-244 ◽  
Author(s):  
D. Nélias ◽  
V. Boucly ◽  
M. Brunet
Keyword(s):  
Rough Surfaces ◽  
Companion Paper ◽  
Contact Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Mapping Algorithm ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Hardening Law ◽  
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, J. Appl. Mech., 69, pp. 657–662) 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, first, for initially smooth surfaces and, second, for rough surfaces. The effects of surface shear stress and hardening law are underlined.

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.

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.

A statistical model of elastic-plastic contact between rough surfaces

2019 ◽  
Vol 43 (1) ◽  
pp. 38-46 ◽  
Author(s):  
Guang Zhao ◽  
Sheng-xiang Li ◽  
Zhi-liang Xiong ◽  
Wen-dong Gao ◽  
Qing-kai Han
Keyword(s):  
Plastic Deformation ◽  
Interface Design ◽  
Present Model ◽  
Rough Surfaces ◽  
Contact Stiffness ◽  
Contact Point ◽  
Contact Model ◽  
Elastic Plastic ◽  
Classical Models ◽  
Asperity Deformation

In a mechanical interface, the contact surface topography has an important influence on the contact stiffness. In the contact processes of asperities, elastic-plastic change can lead to discontinuity and lack of smoothness at a critical contact point. The result is a large difference between the elastic-plastic deformation and the actual asperity deformation. Based on Hertz contact theory, the heights of asperities on a rough surface obey a Gaussian distribution. To take into consideration the continuity of elastic-plastic asperity deformation, we divide the elastic-plastic deformation into three stages: pre-elastic-plastic, mid-elastic-plastic, and post-elastic-plastic deformation. This establishes an elastic-plastic contact model of asperity at a continuous critical point. The contact model of a single asperity fits well with the Kogut–Etsion model and the Zhao–Maietta–Chang model, and the variation trend is consistent. At a lower plastic index, the present model coincides with classical models of contact area and contact load. At a higher plastic index, the simulation results of the present model differ from the Greenwood–Williamson model and the Chang–Etsion–Bogy model but are similar to results from the Kogut–Etsion and Zhao–Maietta–Chang models. This study provides a more accurate microscopic contact model for rough surfaces and a theoretical framework for interface design and analysis.

Dislocation-based approximate solution of the plastic zone of the mode II crack in an elastic perfectly plastic solid

1991 ◽  
Vol 435 (1893) ◽  
pp. 43-68 ◽  
Keyword(s):  
Approximate Solution ◽  
Dislocation Density ◽  
Companion Paper ◽  
Mode Ii ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Mode Ii Crack ◽  
Density Vector ◽  
Elastic Perfectly Plastic ◽  
Dislocation Crack

A dislocation-based (approximate) solution is found for the stress-strain field of the plastic zone (in small-scale yielding) of the stationary mode II crack in an elastic perfectly plastic and incompressible solid. General dislocation equations applicable for plane strain elastic-plastic conditions are presented and used to solve the problem. These equations have broader application than to the particular problem of the paper. The solution is obtained with use of dislocation crack tip shielding and the dislocation crack extension force. Derived dislocation boundary conditions which play an important role in the analysis are B t = 0 at an elastic–plastic boundary and, at elastic–plastic, plastic–plastic and crack plane boundaries, the jump condition [(1 – v )/2 G ) {∂σ tt /∂ x n } jump = { t· B } jump + ∂ B n /∂ x t , where G is the shear modulus, σ tt is the non-traction stress, v is Poisson’s ratio. B is the (area) dislocation density vector. B is the surface dislocation density vector and t and n are the tangential and normal directions to a boundary. The strain compatibility equation is [ G /(1 – v )] (∇ x B ) z = ∇ 2 ½(σ nn + σ tt ). The near tip strain and stress contours of fan sectors are given by the equation r = r c h(θ) , where r c is a constant and the azimuthal function h(θ) is given by the equation h'" + 9 h' = ( p 0 – 2 θ ) ( h" + h ), where p 0 is a constant and a prime denotes ∂/∂ θ . The (approximate) elastic region stress field solution is presented in the companion paper to this one. A mode I crack solution, similar in its structure to the mode II crack solution, also is presented in the paper. This latter solution is shown in the companion paper to be flawed.

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.

Fractal modeling of elastic-plastic contact between three-dimensional rough surfaces

2018 ◽  
Vol 70 (2) ◽  
pp. 290-300 ◽  
Author(s):  
Rufei Yu ◽  
Wei Chen
Keyword(s):  
Rough Surfaces ◽  
Fractal Theory ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Contact Model ◽  
Radial Clearance ◽  
Content Type ◽  
Elastic Plastic ◽  
Fractal Roughness ◽  
Conformal Contact

Purpose This paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters. Design/methodology/approach A modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature. Findings In most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness). Originality/value The contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

scholarly journals GBT-Based Elastic-Plastic Analysis of Cold-Formed Steel Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Plastic Material ◽  
Beam Theory ◽  
Mapping Algorithm ◽  
First Order ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Steel Members ◽  
Shell Finite Element ◽  
Elastic Perfectly Plastic

This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform thorough first-order elastic-plastic analyses of thin-walled members subjected to arbitrary deformations and made of an isotropic non-linear material. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of a simply supported Z-section beam made of an elastic-perfectly plastic material (e.g., carbon steel) and acted by a load uniformly distributed along the flanges. The set of GBT-based results comprises the load-deflection curves (equilibrium paths), displacement profiles, stress distributions (diagrams and 3D contours), and deformed shapes (modal amplitude functions and 3D configurations). These results are compared with the ones obtained from shell finite element analyses (SFEA) using ABAQUS. It is seen that the GBT results display a very good agreement with the SFEA values.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

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