A new method is 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. The 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 Pave∕Y (Y: the yielding strength) and the dimensionless contact load Fpc∕Fec (Fec, Fpc: the contact loads corresponding to the inceptions of the elastoplastic and fully plastic regimes, respectively) reaches 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 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 ellipsoid 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 contact bodies in the finite element analysis, and a mesh scheme of multisize elements was applied. Two observed phenomena regarding the contact pressures and the equivalent von Mises stresses formed at the contact area are given in order to identify the inception of the fully plastic deformation regime of an ellipsoid with an ellipticity ke. If the ellipticity (k) of an elliptical contact area is defined as the length ratio of the minor axis to the major axis, it is asymptotic to the ke value when the interference is sufficiently increased, irrespective of the ke value. The dimensionless interference regime associated with the elastoplastic deformation regime is narrowed by increasing the ellipticity of the ellipsoid (ke). Significant differences in the microcontact parameters such as the contact pressure, the contact area, and the contact load were found to be a function of the interference and the ke parameter of an ellipsoid. The interferences corresponding to the inceptions of the elastoplastic and fully plastic deformation regimes are both increased if the ke value is lowered. The interference, the contact area, and the contact load predicted by the present model for the behavior demonstrated at the inception of the elastoplastic deformation regime are lower than those obtained from the Horng model (Horng, J. H., 1998, “An Elliptical Elastic-Plastic Asperity Microcontact Model for Rough Surfaces,” ASME J. Tribol., 120, pp. 82–88) and the Jeng-Wang model (Jeng, Y. R., and Wang, P. Y., 2003, “An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation,” ASME J. Tribol., 125, pp. 232–240). Big differences in the results of the average contact pressure, the contact area, and the contact load among the above microcontact models are discussed. The discrepancies are also explained from the developments of these models and boundary conditions set for the elastoplastic deformation regime.
In the present study, the formulas 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 relation with the ratio of these two critical interferences (δec and δpc). The critical interference ratio δpc/δec can thus be expressed as a function of the critical contact load ratio, Fpc/Fec, whose value was obtained from the experimental results of metallic materials. The interference δpc corresponding to the inception of fully plastic deformation can thus be determined. The dimensionless analyses of 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 power form and to be as a function of dimensionless interference δ/δec. 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 behaviors in the elastoplastic regime. The applications in contact of rough surfaces are also presented and discussed.
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