An Elasto-plastic Contact Solving Method for Two Spheres

Abstract

The traditional Hertz contact theory has been widely used in solving contact problems. However, it is only applicable to the elastic contact, and cannot truly reflect the contact stress distribution and contact radius in the elasto-plastic contact. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elasto-plastic contact between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, and the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elasto-plastic contact can be solved. Finally, an elasto-plastic contact example of two spheres is given based on the power-law hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between the numerical results by finite element method and the predicted ones by the proposed method. It is shown that the proposed method can accurately calculate the maximum contact stress and contact radius in the elasto-plastic contact, and the relative errors of both maximum contact stress and contact radius are within $$\pm \,5{\%}$$. To sum up, the proposed fast solving method can be applied to perform the elasto-plastic contact analysis in engineering practice.