Contact strength of two elastic half spaces with circular groove
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CONTACT STRENGTH OF TWO ELASTIC HALF SPACES WITH CIRCULAR GROOVE B. Monastyrs’kyi1 and A. Kaczyski2
UDC 539.3
We present the analysis of the stress-and-strain state of a contact couple formed by two isotropic semiinfinite solids one of which has a small surface groove. Based on the classical fracture criteria, namely, on the criterion of maximal principal stresses and the criterion of maximal shear stresses, we determine the regions of the most possible formation of the zones of crack initiation and plastic zones. Brittle cracking can be induced both by tensile and compressive stresses arising on the interface. For some shapes of the groove considered as an example, our analysis reveals that the fracture process starts from the boundary of contacting solids. Keywords: contact problem, conforming boundaries, local contact fault, contact strength, criterion of maximal principal stresses, and criterion of maximal shear stresses.
The present work is a continuation of our previous study [1] of the problem of frictionless contact of two compressed elastic half spaces one of which possesses a small circular surface groove. The aim of the present work is to examine the behavior of contacting solids from the viewpoint of contact fracture mechanics. The strength analysis is carried out by using the closed-form solution obtained in [1] for a special form of the groove by using some classical fracture criteria. The knowledge of solutions (especially analytic) to contact problems serves as a ground for the investigation of strength, durability, and fatigue of contacting couples. The major part of works on the strength of contact joints is based on the solutions obtained within the framework of the theory of Hertzian contact. But these solutions are useful only for the contact of solids with mismatching surfaces (see the classification by Johnson [2]). The extensive literature on the subject is discussed in the book by Kolesnikov and Morozov [3]. On the contrary, the contact interaction of bodies with conformable surfaces is much less investigated. The contact strength of solids with grooves was studied in [4]. The approaches using this kind of interaction take into account the existence of imperfections (grooves, pits, protrusions, concavities, etc.) of the surfaces related to their small deviations from the flat surfaces on local parts. These perturbations lead to the local absence of contact and, hence, the intercontact gaps are created. The problem under study belongs to the class of nonclassic contact problems involving contact interactions of solids with conformed surfaces. Description of the Problem This present work deals with an axisymmetric problem of elastic contact of two different isotropic elastic semiinfinite solids one of which (denoted by 1 in Fig. 1) possesses a local surface groove occupying a circular region of radius b. 1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Science, Lviv, Ukraine; e-mail: [email protected] (corresponding author). 2 Faculty of
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