Effects of Near-surface Composites on Frictional Rolling Contact Solved by a Semi-analytical Model

2021 ◽  
pp. 1-23
Author(s):  
Mengqi Zhang ◽  
Zhiqiang Yan
Keyword(s):  
Analytical Model ◽  
Surface Displacement ◽  
Normal Pressure ◽  
Element Model ◽  
Rolling Contact ◽  
Near Surface ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Tangential Traction

Abstract A semi-analytical model (SAM) to tackle the steady-state elastic frictional rolling contact problem involving composites is presented. Specifically, the frictional rolling contact is categorized into two subtypes, namely normal and tangential problems, and the conjugate gradient method (CGM) is used to figure out the normal pressure and tangential traction. In SAM, the equivalent inclusion method (EIM) is applied to analyze the influence of composites on the matrix, and the displacement disturbance resulting from such composites is added to the total surface displacement, which implements the coupling between surface contact and composites. The accuracy of the proposed model is verified by the finite element model. The effects of composites on the frictional rolling contact behavior are investigated. The results indicate that Young's modulus, as well as the size and location of the composites, are correlated with the distributions of tangential traction, subsurface stresses and the sizes of stick and sliding zones.

scholarly journals Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Keying Chen ◽  
Liangcai Zeng ◽  
Juan Chen ◽  
Xianzhong Ding
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Thickness Distribution ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Equation System ◽  
Line Contact ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

Elevated Temperature Neutron Measurements of Thermal Residual Stresses in a Sic Fibre Reinforced Al Alloy

1994 ◽  
Vol 376 ◽  
Author(s):  
Monica Ceretti ◽  
M. Kocsis ◽  
A. Lodini
Keyword(s):  
Residual Stresses ◽  
Al Alloy ◽  
Thermal Residual Stresses ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Al 7075 ◽  
Sic Whiskers ◽  
Stress Free State ◽  
Increasing Temperature

ABSTRACTThe main objective of the present investigation is to determine the evolution of residual stresses by neutron powder diffraction in an Al/SiC composite (Al 7075 reinforced by 27 vol.% SiC whiskers), originating from thermal treatment and mechanical loading. The results show that residual stresses in the matrix and in the reinforcement decrease in magnitude with increasing temperature and they reach the stress free state at the 'equivalent temperature'. As the temperature further increases, these stresses increase numerically in a reverse sense for both phases. The data obtained are analysed in terms of a simple model based on Eshelby's equivalent inclusion method.

The Stress Field and Intensity Factor due to Crazes Formed at the Poles of a Spherical Inhomogeneity

1994 ◽  
Vol 61 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Z. M. Xiao ◽  
K. D. Pae
Keyword(s):  
Stress Intensity Factor ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Moduli ◽  
Superposition Principle ◽  
Numerical Examples ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Good Agreement

The problem of two penny-shaped crazes formed at the top and the bottom poles of a spherical inhomogeneity has been investigated. The inhomogeneity is embedded in an infinitely extended elastic body which is under uniaxial tension. Both the inhomogeneity and the matrix are isotropic but have different elastic moduli. The analysis is based on the superposition principle of the elasticity theory and Eshelby’s equivalent inclusion method. The stress field inside the inhomogeneity and the stress intensity factor on the boundary of the craze are evaluated in the form of a series which involves the ratio of the radius of the penny-shaped craze to the radius of the spherical inhomogeneity. Numerical examples show the interaction between the craze and the inhomogeneity is strongly affected by the elastic properties of the inhomogeneity and the matrix. The conclusion deduced from the numerical results is in good agreement with experimental results given in the literature.

Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method

1975 ◽  
Vol 42 (4) ◽  
pp. 847-852 ◽  
Author(s):  
Z. A. Moschovidis ◽  
T. Mura
Keyword(s):  
Computer Program ◽  
Strain Field ◽  
Applied Strain ◽  
Stress And Strain ◽  
Isotropic Matrix ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Final Stress

The problem of two ellipsoidal inhomogeneities in an infinitely extended isotropic matrix is treated by the equivalent inclusion method. The matrix is subjected to an applied strain field in the form of a polynomial of degree M in the position coordinates xi. The final stress and strain states are calculated for two isotropic ellipsoidal inhomogeneities both in the interior and the exterior (in the matrix) by using a computer program developed. The method can be extended to more than two inhomogeneities.

Influence of Partial Slip Conditions on Rolling Contact Fatigue of 1070 Steel

2008 ◽  
Vol 44-46 ◽  
pp. 911-916
Author(s):  
Li Juan Lu ◽  
Xiao Gui Wang ◽  
Li Jian Zhuang ◽  
Zeng Liang Gao ◽  
Y.Y. Jiang
Keyword(s):  
Rolling Contact Fatigue ◽  
Contact Process ◽  
Contact Fatigue ◽  
Normal Pressure ◽  
Multiaxial Fatigue ◽  
Rolling Contact ◽  
Cyclic Plasticity ◽  
Partial Slip ◽  
Slip Conditions ◽  
Tangential Traction

Partial slip rolling contact was analyzed in this paper by the finite element method with the application of a robust cyclic plasticity model. The repeated rolling contact process was carried out by translating the normal pressure and the tangential traction across the contact surface step by step. The normal pressure and the tangential traction were applied to the nodes through the time-dependant amplitude functions as the concentrated nodal forces. With the detailed stress-strain responses output from the FE analysis, a general multiaxial fatigue criterion was used to predict fatigue initiation life and initiation position. The influences of partial slip conditions on the residual stresses, residual shear strain and the initiation lives are obtained.

Elastohydrodynamic Lubrication of Inhomogeneous Materials Using the Equivalent Inclusion Method

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Zhanjiang Wang ◽  
Dong Zhu ◽  
Qian Wang
Keyword(s):  
Film Thickness ◽  
Surface Deformation ◽  
Fluid Pressure ◽  
Surface Displacement ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Inhomogeneous Materials ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion

Solid materials forming the boundaries of a lubrication interface may be elastoplastic, heat treated, coated with multilayers, or functionally graded. They may also be composites reinforced by particles or have impurities and defects. Presented in this paper is a model for elastohydrodynamic lubrication interfaces formed with these realistic materials. This model considers the surface deformation and subsurface stresses influenced by material inhomogeneities, where the inhomogeneities are replaced by inclusions with properly determined eigenstrains by means of the equivalent inclusion method. The surface displacement or deformation caused by inhomogeneities is introduced to the film thickness equation. The stresses are the sum of those caused by the fluid pressure and the eigenstrains. The lubrication of a material with a single inhomogeneity, multiple inhomogeneities, and functionally graded coatings are analyzed to reveal the influence of inhomogeneities on film thickness, pressure distribution, and subsurface stresses.

Numerical methods for solving the equivalent inclusion equation in semi-analytical models

2021 ◽  
pp. 135065012110001
Author(s):  
Zhiqiang Yan ◽  
Mengqi Zhang ◽  
Shulan Jiang
Keyword(s):  
Matrix Material ◽  
Current Method ◽  
Equation System ◽  
Analytical Models ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Convergence Mechanism ◽  
Computing Accuracy

Equivalent inclusion method is the basis for semi-analytical models in tackling inhomogeneity problems. Equivalent eigenstrains are obtained by solving the consistency equation system of the equivalent inclusion method and then stress disturbances caused by inhomogeneities are determined. The equivalent inclusion method equation system can only be solved numerically, but the current fixed-point iteration method may not be able to achieve deep convergence when the Young's modulus of inhomogeneity is lower than that of the matrix material. The most significant innovation of this paper is to reveal the non-convergence mechanism of the current method. Considering the limitation, the Jacobian-free Newton Krylov algorithm is selected to solve the equivalent inclusion method equation. Results indicate that the new algorithm has significant advantages of computing accuracy and efficiency compared with the classic method.

Modeling of the Tensile Deformation Behavior of SiCp/Fe Composites

2012 ◽  
Vol 217-219 ◽  
pp. 79-85
Author(s):  
Yao Mian Wang ◽  
Huan Ping Yang ◽  
Cong Hui Zhang
Keyword(s):  
Particle Size ◽  
Deformation Behavior ◽  
Volume Fraction ◽  
Tensile Deformation ◽  
Equivalent Inclusion Method ◽  
Particle Cracking ◽  
Equivalent Inclusion ◽  
Tensile Deformation Behavior ◽  
The Matrix ◽  
Dislocation Strengthening

A combined model taking account of the dislocation strengthening effects and particle cracking during tensile straining based on Eshelby equivalent inclusion method is presented to model the deformation behavior of SiCp/Fe composites. Stress-strain curves of the composites were simulated and it is found that the curves vary obviously with the volume fraction and particle size. The yield stress is increased significantly by increasing the volume fraction and decreasing the particle size. Stress in particles is very high during straining and the fraction of cracked particles increased obviously with increasing the particle size. These results indicate that higher volume fraction and finer particles can give better mechanical properties of the composites attributed to the increased load sharing effect and dislocation strengthening effects of the matrix.

Equivalent Inclusion Method for the Stokes Flow of Drops Moving in a Viscous Fluid

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
H. M. Yin ◽  
P.-H. Lee ◽  
Y. J. Liu
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
The Body ◽  
Function Technique ◽  
Elongation Ratio ◽  
Spherical Drop ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

The equivalent inclusion method is presented to derive the Stokes flow of multiple drops moving in a viscous fluid at a small Reynolds number. The drops are replaced by inclusions with the same viscosity as the fluid, but an eigenstrain rate field that is a fictitious nonmechanical strain rate field is introduced to represent the viscosity mismatch between each drop and the matrix fluid. The velocity and pressure fields can be solved by considering the body force and eigenstrain rate on the inclusions with the Green's function technique. When one spherical drop is considered, the solution recovers the closed-form classic solution. This method is versatile and can be used in the simulation of a many-body system with different drop size, elongation ratio, and viscosity. Numerical examples demonstrate the capability and accuracy of the proposed formulation and illustrate particles' rotation and motion caused by particle interactions.

scholarly journals Analytical Model for Studying the Influence of Thickness on the Protective Effect

2021 ◽  
Vol 15 (4) ◽  
pp. 431-447
Author(s):  
Xiaoqi Song ◽  
Yukio Takahashi ◽  
Weiming He ◽  
Tohru Ihara ◽  
◽  
...  
Keyword(s):  
Protective Effect ◽  
Analytical Model ◽  
Cutting Tool ◽  
Tangential Force ◽  
Clear Understanding ◽  
Stress Distributions ◽  
Dry Cutting ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Proposed Model

This paper presents an analytical model to study the influence of the thickness of the built-up layer (BUL) / built-up edge (BUE) on its protective effect during cutting. A new elastic-plastic contact model at the tool-chip interface is proposed to analyze the sliding contact problem with a layer of adhesion (including the BUL and BUE). The equivalent inclusion method (EIM) is utilized to analyze the stress disturbance caused by the adhesion and to evaluate the protective effect of the adhesion. In this method, the adhesion is considered as an equivalent elliptical inclusion at the tool-chip interface. The protective effect of the adhesion and the influence of the adhesion thickness on its protective effect can be evaluated. The proposed analytical model was verified based on experimental data obtained from dry cutting of SUS304 stainless steel. From the results, it can be confirmed that BUL/BUE can protect the cutting tool by affecting the stress distributions in the tool, the positions of yield initiation, and the tangential force acting on the tool. It can also be concluded that a greater thickness improves the protective effect of the BUL/BUE. Furthermore, the proposed model can also provide a clear understanding of the BUL/BUE formation phenomenon.

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