Analysis on elastic–plastic spherical contact and its deformation regimes, the one parameter regime and two parameter regime, by finite element simulation

In this paper the contact problem of a rigid sphere against an elastic–plastic sphere and a spherical elastic–plastic cavity is studied by means of finite element simulation for a wide range of radius ratios. Our results indicate that the deformation range naturally divides into two regimes, i.e. a one parameter regime (covering the elastic, small elastic–plastic and similarity deformation) and a two parameter regime (covering the finite deformation). In these two regimes average contact pressures (as well as contact area) versus indentation depth can be described respectively by the single parameter, i.e. indentation depth h/Re, and the two parameters, i.e. h/Re and radius ratio R1/R2. Moreover, the variation trends of average contact pressure with the increase of indentation depth differ markedly in different deformation regimes. The numerical evolution of pressure distribution indicates that with increase of indentation depth the pressure distribution becomes more peaked at the center of the contact area meanwhile the maximum contact pressure, limited by the flow stress, increases slightly. Therefore in the two parameter regime, the average pressure would stop growing and get lower rather than continuously higher as it does in the one parameter regime.

Research highlights
► The spherical contact is examined for a broader range of radius ratio.
► The contact can be divided into two regimes: one parameter and two parameter regime.
► Numerical results of evolutions of contact pressure and area are presented.
► The evolutions are explained by solid mechanics, contact geometry and material.