| Summary: | 博士 === 國立成功大學 === 機械工程學系碩博士班 === 94 === Abstract
The present study is presented to study the behavior of two contact surfaces at yielding and to try to establish the relationships of the maximum contact pressure with the ellipticity of a contact area and the Poisson’s ratio of a material. The von Mises criterion was applied to determine the depth position of having the maximum second invariant of the stress deviator tensor. Then, the border of two subregions can be applied as the criterion to predict the depth position of having the maximum contact pressure at yielding to be on the contact surface or beneath the contact surface. Yielding is found more apt to start at the center of the contact surface if both and are sufficiently small. Conversely, yielding begins beneath the contact surface and on the -axis if both and are sufficiently large. The border of these two subregions shows that an increase in the ellipticity can lower the critical Poisson’s ratio at yielding. For the factor of the maximum contact pressure at yielding, there exists a discontinuity in the slope of the curve when has a sufficiently small value.
In the present study, the formulae for the asperity contact loads (Fec and Fpc) corresponding to the critical interferences at the inception of elastoplastic and fully plastic deformations are employed to establish their relationship with the ratio of these two critical interferences ( and ). The critical interference ratio ( ) can be expressed as a function of the critical contact load ratio, ( ), whose value was obtained from the experimental results of metallic materials. The interference ( ) corresponding to the inception of fully plastic deformation can thus be determined. The dimensionless analyses of an asperity contact area, average contact pressure, and contact load in the elastic and fully plastic regime reveals that these parameters in the elastoplastic regime can be expressed in a power form as a function of dimensionless interference ( ). The coefficients and exponents of the power form expressions can be determined by the boundary conditions set at the two ends of this regime. Four models are proposed in this study to compare the contact behavior in the elastoplastic regime. The applications of the contact of rough surfaces are also presented and discussed.
A new method was developed in the present study to determine the elastoplastic regime of a spherical asperity in terms of the interference of two contact surfaces. This method provides an efficient way to solve the problem of discontinuities often present in the reported solutions for the contact load and area or the gradients of these parameters obtained at either the inception or the end of the elastoplastic regime. Well-established solutions for the elastic regime and experimental data of metal materials using indentation tests are provided as the references to determine the errors of these contact parameters due to the use of the finite element method. These numerical errors provide the basis to adjust the contact area and contact load of a rigid sphere in contact with a flat such that the dimensionless mean contact pressure (Y: the yielding strength) and the dimensionless contact load ( , : the contact loads corresponding to the inceptions of the elastoplastic and fully plastic regimes, respectively) reach the criteria arising at the inception of the fully plastic regime, which are available from the reports of the indentation tests for metal materials. These two criteria are, however, not suitable for the present case of a rigid flat in contact with a deformable sphere. In the case of a rigid flat in contact with a deformable sphere, the proportions in the adjustments of these contact parameters are given individually are the same as those arising in the indentation case. The elastoplastic regime for each of these two contact mechanisms can thus be determined independently. By assuming that the proportion of adjustment in the elastoplastic regime is a linear function, the discontinuities appearing in these contact parameters are absent from the two ends of the elastoplastic regime in the present study. These results are presented and compared with the published results.
The determination of the elastoplastic deformation regime arising at the microcontact of a deformable elliptical asperity and a rigid smooth flat was the main purpose of this study. One-eighth of an ellipsoid and a flat plate were taken as the bodies in the finite element analysis. A mesh scheme of multi-size elements to refine the elements located near the contact area and the z-axis normal to this area was adopted in order to improve the precision of these contact parameter solutions, which is necessary to determine the inception of the fully plastic regime. Good precision in the numerical solutions of several contact parameters is identified first as compared with the theoretical solutions developed for the elastic deformation regime. The inception point of the fully plastic region occurs when the ( : average contact pressure over the contact area; Y: yielding strength) parameter reaches its maximum value at an interference. If the ellipticity (k) of an elliptical contact area is defined to be the ratio of the minor-axis to the major-axis, it is variable as a function of the interference and the ratio of the relative curvatures ( and are the relative radii of curvature of an ellipsoid formed at the contact point before occurring contact deformation). The factor of the maximum contact pressure arising at yielding is also expressed as a function of the Poisson ratio and the ellipticity of the contact area. These results indicate that the ellipticity (k) of a contact area is lowered by decreasing the value, and the slenderness of an elliptical contact area is enhanced by decreasing the value. The elastoplastic deformation regime is prolonged to a larger interference as the value is lowered. For a fixed interference, the dimensionless contact area is always lowered by decreasing the value. Conversely, the dimensionless contact load is increased by decreasing the value, thus resulting in a decrease in the average contact pressure. Comparisons of the results of the contact parameters obtained with a constant k and a variable k show substantial differences at various interferences.
|
|---|
