Мodel of the Relationship between the Coulomb and Siebel Friction Coefficients for Plastic Materials

The work is devoted to a comparative analysis of the stress state parameters for micro protrusions of the contacting materials surfaces in the region of low contact pressures characteristic for the Amontons-Coulomb friction law and in the region of high pressures characteristic of the Siebel plastic friction model used in the theory of material processing by pressure.

The aim of the work is to substantiate theoretically and calculate the relationship between the Coulomb and Siebel friction coefficients for plastic materials based on micromechanical modeling of the elastic-plastic contact interaction parameters for the surface roughness protrusions using the adhesive friction theory. The roughness of the deformable surface layer was modeled by spherical micro protrusions. The analysis was based on the fact that the deformation of micro roughnesses occurs in three successive stages. Initially, the material is deformed elastically, then a plastic state region, surrounded by elastically deformable material, arises in the near-surface layer, and free plastic flow occurs at the final stage. It is accepted in the first approximation that Hooke's law is applicable for small constrained elastic-plastic deformations. In the main part of the work, on the basis of the proposed micro contact interaction model, the force parameters of the transition from constrained elastic-plastic deformation of micro protrusions to free plastic flow are determined, taking into account the action of contact friction, according to Siebel, on model contact spots. Subsequently, a transition from averaged contact pressures and specific friction forces on single contact spots to nominal pressures and specific friction forces is performed. An analytical dependence is obtained linking the Coulomb and Siebel friction coefficients, as well as the Poisson ratio of the material subjected to plastic deformation. Using carbon and alloy steels, as well as non-ferrous metals and alloys as examples, a calculated assessment of the relationship between the Coulomb and Siebel friction coefficients is made for a wide range of variations of the Poisson ratio. The calculated values are consistent with the available experimental data. The research results can be used in the educational process, as well as in engineering and scientific research practice.

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