Roughness of the free surface of thin-walled tubes under compression

The problem of the stress-strain state with axisymmetric steady-state deformation of thin-walled tubes is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some compression parameters of the tubes on the surface roughness parameters of the workpiece. The empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.