On Semi-analytical Method For Elastoplastic Contact Analysis Of Heterogeneous Materials And Its Application

Mechanical components,such as gears and bearings,are among the core elements of a transmission system;they play important roles in transmitting motion and power,supporting rotating bodies,and ensuring rotation accuracy.These parts are subjected to concentrated contact loads that often result in highly localized stresses compared with other structures of a transmission system,and they are more vulnerable to fatigue failure.Furthermore,inhomogeneities amplify the stress concentration effects and have a significant influence on the rolling contact fatigue of materials.Therefore,the investigation of the contact characteristics of heterogeneous materials containing inhomogeneities is especially significant to the improvement of the service life of gears and bearings.Semi-analytical modeling(SAM)is a promising method for solving contact problems of inhomogeneous materials.It considers the coupling between contact and inhomogeneity effect and provides subsurface stress fields.However,the current SAM is only useable for the elastic analysis of inhomogeneities.Although its solution approach is efficient,its computational speed still needs to be improved.This thesis deals with the research on modeling methods for the contact of inhomogeneous materials and their applications on contact characteristics of such materials on the basis of elastoplastic theories and numerical methods in the frame of SAMbased approaches.The modeling method development work includes:A semi-analytical model for analyzing the elastic contact of inhomogeneous materials.The calculations of contact pressure distribution,subsurface elastic stress and eigenstress are provided.The consistency equation of the equivalent inclusion method is derived,and the iterative formats of the equation are built for different material properties of inhomogeneities.A fixed-point iteration method is used for solving the consistency equation.A dual-grid method for accelerating the model calculation,with which the contact problem is solved on a coarse mesh to obtain equivalent eigenstrains,and a fine mesh for refined results.The eigenstrain data from the coarse mesh are as high-quality initial values to the fine mesh solutions,thus less iteration steps are required when solving the same contact problem on the time-consuming fine mesh.Parallel computing is involved in the model by dividing a largescale computation into small pieces to be performed on multiple processers.The high-efficiency elastic contact model lays the foundation for further in-depth work.The first elasto-plastic inhomogeneity contact model for inhomogeneous materials.The consistency equation of inhomogeneous inclusion is derived.The calculation methods for plastic strain increment,residual stresses,and surface residual displacements are introduced,and the corresponding algorithm is established.The advantages in precision and efficiency of the new semi-analytical model are verified by comparison with the finite element modeling.A novel multi-scale semi-analytical model for inhomogeneous materials containing distributed fine particles.Macroscopic and microscopic elements are used.The influence coefficients and equivalent eigenstrain coefficients for the macroscopic elements,which take material microstructures into account,are derived.A small number of macroscopic elements is utilized for obtaining contact pressure distribution as the boundary condition,while the stress and strain fields around inhomogeneities are calculated in the microscale.The proposed models are used to study the contact characteristics of heterogeneous materials,including:The effects of inhomogeneities on contact pressure distributions.The results suggest that the stiffer particles lead to higher contact pressure while the more compliant ones decrease the contact pressure.The influence of inhomogeneities on contact becomes stronger when the distance from an inhomogeneity to the surface decreases,or the difference of Young’s moduli of inhomogeneities and the matrix increases,or the inhomogeneity becomes larger.The effects of inhomogeneities on the critical load(the load of plastic yield inception)of inhomogeneous materials.The results suggest that,for the cases of a single spherical inhomogeneity,the critical load is decreased by stiff inhomogeneities.However,a compliant inhomogeneity may cause the critical load to increase or decrease,depending on the particle location.This because when the particle is close to the contact surface,the contact pressure is significantly reduced,resulting in a lower the subsurface elastic stress.The reduction of elastic stresses offsets the stress concentration caused by the compliant inhomogeneity,so that in some cases the critical load may be increased.The effect of inhomogeneities on the plastic deformation of the matrix material considering various factors such as the properties,size,position and yield strength of the inhomogeneities.The results show that inhomogeneities cause significant plastic strain concentration.The relationship between Young’s modulus of the inhomogeneity and that of the matrix material—that is,whether the impurity is stiff or compliant—determines the location and shape of the plastic strain concentration zone.For all stiff inhomogeneities,the plastic strain concentration zone appears in the upper and/or lower portions of the particle;for compliant inhomogeneities,the plastic strain concentration zone is located in the strip region surrounding the inhomogeneity and parallel to the contact surface.The other parameters,such as the size and location of the impurities,only affect the degree of plastic strain concentration.A method for estimating the yield strength of the matrix by simulation is proposed and verified by experimental data,which has been applied to the study of the properties of the matrix of a carburized bearing steel.The effect of particle clusters on the contact characteristics of heterogeneous materials.The results show that the maximum von Mises stress and the maximum principal stress in inhomogeneities of the composite with particle clusters are higher than that of the composite with particles in a uniform distribution,suggesting that the clustered material is more likely to yield and that the particles in a cluster have more vulnerable to fracture.For stiff particles,the stress volumetric integral increases with the particle distribution heterogeneity,but for compliant ones,the uniform distribution of particles leads to the highest stress volumetric integral value.