On rolling and sliding of a cylinder along a perfectly plastic half-space with allowance for contact friction

Plastic deformation of rough surface by a sliding tool

“…for ξ and for η, (4) where ϕ is the angle of slope of the tangent to the slip line ξ with the x axis by the Hencky relations for the average stress σ and the angle ϕ σϕ = const along ξ and σ + ϕ = const along η, (5) and by the Geiringer relations for the projections of the velocities V ξ and V η on the slip lines (6) Equations (4) and (5) make up the system for cal culating coordinates of node points of the slip lines, as well as values of σ and ϕ in these points, using numer ical procedures presented in work [10]. Equations (6) determine the orthogonal reflections of the curved slip lines ξ' and η' on the plane of the hodograph of the velocities V x and V y (7) which are used to calculate the velocity field on the hodograph plane.…”

“…The stresses in the plastic zone ABCDE, which obey Eqs. (4) and (5) with the boundary condition σ = -0.5 at the free boundary AB and the condition of contact friction τ c = μ at the boundary AE, are determined by the uniform stress state in the zones ABC and ADE, as well as the centered spiral fan with the angle of the fan ψ at point A. The normal pressure applied to the tool is found using the following formula:…”

“…In the majority of SPD processes, plastic defor mation propagates to a depth that substantially exceeds the height of microasperities. The modeling of stationary SPD processes during the sliding and roll ing of tools with various shapes is considered in works [4,5]. These results are of interest from the viewpoint of estimating process parameters of SPD and studying problems of rolling and sliding friction under heavy loads [6].…”

“…The Prandtl contact friction stress is taken into account. The ultimate deformation of asperities of the original roughness of the surface under machining is limited by a high Prandtl contact pressure; when the contact pressure begins to exceed ing this pressure, plastic deformation propagates deep into the surface layer following the mechanisms con sidered in works [4,5]. Figure 1 shows the plastic deformation of the rough surface by the rigid tool with the circular contact sur face.…”