Abstract
Two-dimensional Cattaneo – Mindlin problem on a partial slip contact between two elastic bodies of the same material is considered in classical statement for circular cylinders as well as in more general statements: for non-circular cylinders with higher order of touch and cylindrical bodies with a wavy periodic surface. Stress distributions are found both in the contact area and inside the bodies. The question of how the friction affects a formation of stick zone in the contact area and distribution of maximum tangential stress within the bodies is investigated.
Highlights
If elastic bodies are made of the same material and their sizes as well as the radii of curvature of their surfaces are much larger than the size of contact area, a mutual slip of contacting surfaces will not occur in the case of normal contact
A study of distribution of maximum tangential stress in elastic bodies, which are under conditions of smooth and sliding contact, was performed by Belyaev (1924), Sneddon (1946, 1948), Kuznetsov (1978), Kuznetsov and Gorokhovsky (1978), Johnson (1985), Ostryk (2015a,b), Klimchuk and Ostrik (2017), and Klimchuk and Ostryk (2018)
Distribution of stress τmax for a contact with slip and adhesion is transitional between the same distribution for the smooth and sliding contacts
Summary
If elastic bodies are made of the same material and their sizes as well as the radii of curvature of their surfaces are much larger than the size of contact area, a mutual slip of contacting surfaces will not occur in the case of normal contact. A study of distribution of maximum tangential stress in elastic bodies, which are under conditions of smooth and sliding contact, was performed by Belyaev (1924), Sneddon (1946, 1948), Kuznetsov (1978), Kuznetsov and Gorokhovsky (1978), Johnson (1985), Ostryk (2015a,b), Klimchuk and Ostrik (2017), and Klimchuk and Ostryk (2018) Results of such studies enable to reveal zones with high values of tangential stresses, where a plastic flow of material appears according to the Tresca yield criterion
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