A method for the evaluation of contact compliance of bodies with surface grooves
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A METHOD FOR THE EVALUATION OF CONTACT COMPLIANCE OF BODIES WITH SURFACE GROOVES B. E. Monastyrs’kyi
UDC 539.3
An axisymmetric model of imperfect elastic contact of an isotropic half space with a rigid base containing a system of circular grooves uniformly distributed over the surface is constructed. The model takes into account the influence of the collection of surface defects on the stress– strain state in the vicinity of a separate inhomogeneity. We propose a method for the evaluation of the integral elastic stiffness of the contact surface and perform the comparative analysis of the results obtained by using the proposed approach with the well-known solutions of three-dimensional problems.
Numerous well-known procedures used for the evaluation of the reduced characteristics (macroparameters) of the contact surface are based on the hypothesis that the actual contact of bodies is realized solely along microasperities whose area constitutes a small fraction of the total area of the nominal contact surface [1]. At the same time, there exist contact joints [2] for which, within certain ranges of external loads, the sizes of the region of direct contact become comparable with the sizes of the nominal contact surface and the regions of gaps between the surfaces, where the surfaces of the bodies are not in direct contact, turn into local. This is why it is necessary to study the behavior of contact couples of the indicated kind and develop efficient procedures for the evaluation of reduced parameters of the contact surface. Thus, for the elastic interaction of the bodies, it is customary to determine the so-called contact stiffness or contact compliance (the characteristic inverse to the contact stiffness). This parameter integrally takes into account the deformation of microirregularities of the surfaces and describes the decrease in the distance between the surfaces of the bodies as a result of additional deformation of the contact surfaces. In the present work, we propose an approach to the investigation of the elastic contact of bodies in the presence of a system of local circular grooves along which the surfaces of the bodies are not in contact. We develop an axisymmetric mathematical model of contact of this sort and use this model to pose and solve the corresponding axisymmetric problem of elasticity. The solution of this problem enables one to determine the contact compliance of the contact surface. Description of the Problem and Construction of the Axisymmetric Model Consider the case of unilateral frictionless contact of two semiinfinite bodies pressed to each other by uniform forces p applied at infinity. Without loss of generality, it is possible to assume that one of the bodies is elastic and isotropic and the other body is perfectly rigid (this body is called the base). The base contains a system of sufficiently deep local cylindrical circular (in plan) grooves of radius a uniformly distributed over the surface. The schematic diagram of contact of this sort is presented in Fig. 1a. Pidstryhach Institu
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