Breaking of Contact Between an Elastic Half Space and a Rigid Base in a Circular Region Under the Action of a Circular H
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BREAKING OF CONTACT BETWEEN AN ELASTIC HALF SPACE AND A RIGID BASE IN A CIRCULAR REGION UNDER THE ACTION OF A CIRCULAR HEAT SINK Kh. I. Serednyts’ka,1,2 M. M. Mykytyn,1 and R. M. Martynyak1
UDC 539.3
We study the process of local delamination between an elastic heat-conducting half space and a rigid thermally insulated base in a circular domain under the action of heat sinks distributed along the circle. The corresponding axisymmetric contact problem of thermoelasticity is reduced to an integral equation of the Abel type, and its closed solution is obtained. We analyze the dependences of the shape of the gap between the bodies and the normal contact stresses outside the gap on the intensity of heat sinks and the distance of these sinks from the interface between the half space and the base. Keywords: elastic half space, rigid base, circular heat sink, circular delamination.
Introduction In the course of interaction of the bodies with matching surfaces, the phenomenon of delamination may occur between these bodies and lead to the formation of gaps under the action of force and thermal loads concentrated in the near-surface regions. A survey of works dealing with the violation of contact between the bodies under mechanical loads can be found in [1]. The plane and axisymmetric problems of violation of contact between the bodies caused by the presence of concentrated heat sinks were solved in [2] and in [1, 3], respectively. The problem of delamination of elastic half planes one of which contains a circular inclusion caused by their heating to a constant temperature was studied under the conditions of smooth contact [4] and their seizure with sliding [5]. The thermomechanical violation of contact between the half spaces under the conditions of imperfect thermal contact with thermal resistance in local areas was studied in [6–9]. The problem of contact of the elastic half space with a rigid thermally insulated base under the action of a heat sink uniformly distributed over a circle of radius R located at a distance d from the boundary of the half space was studied in [10]. The analysis of normal contact stresses formed in this case shows that if the intensity of heat sink increases and d is smaller than a certain critical distance d cr ( d cr ≈ 1.1R ), then both annular and circular delaminations of the bodies may occur. However, if d > d cr , then we observe only circular delaminations. The possibility of annular delamination for d < d cr was studied in [11]. In the present work, we consider the case of circular delamination. Statement of the Problem Consider the case of one-sided contact of an elastic heat-conducting half space with a rigid thermally insulated base under the action of a pressure p applied to the half space at infinity and a heat sink with constant 1 2
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 55, No. 3
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