Principal stresses in a half-space caused by the action of a moving friction load on its surface
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PRINCIPAL STRESSES IN A HALF-SPACE CAUSED BY THE ACTION OF A MOVING FRICTION LOAD ON ITS SURFACE . . Evtushenko1, 2 and S. Yu. Pyr’ev1
UDC 539.3
We obtain a solution of a space quasistatic problem of thermoelasticity for a half-space whose surface, in a bounded domain, is subjected to the action of moving mechanical and thermal loads. We perform a numerical analysis of principal stresses in the case where pressure and the intensity of heat flow proportional to it have a Hertzian distribution and are given in an elliptic domain. Keywords: thermoelasticity, half-space, principal stresses, moving load, friction.
Sliding friction is often accompanied by scaling and crumbling of the material of working surfaces of tribojoints, which results in the loss of their workability [1]. One of the factors that cause this kind of damage to a subsurface layer is the excess of the maximum principal tensile stress over its critical value (ultimate strength). The problems of the theory of elasticity and thermoelasticity for a half-space with locally distributed moving mechanical and thermal loads given on its surface are model problems in the mechanics of contact interaction and tribology [2–4]. Solutions were constructed for two-dimensional problems [5–9], space problems with circular line of division of boundary conditions [10, 11], and quasistatic problems of thermoelasticity. A solution of the space problem of thermoelasticity for a half-space with the domain of a moving load of an arbitrary shape was obtained earlier [12]. In what follows, we investigate the distribution of principal stresses caused by the action of such loading on the surface of a half-space. Statement and Solution of the Problem Consider an elastic, homogeneous, isotropic half-space referred to a global Cartesian coordinate system Ox yz and a domain on the surface z = 0 that moves at a constant velocity V in the negative direction of the axis O x (Fig. 1). In the domain , a mechanical load (a normal pressure p(x, y) = p0 p (x, y) , where p0 is the characteristic value of pressure and p (x, y) is a dimensionless function of coordinates) and a thermal load (a heat flow whose intensity is equal to the specific power of friction q(x, y) = f Vp(x, y) , (x, y) , where f is the friction coefficient [13]) are given. Outside the domain , the surface of the half-space is free and heat-insulated. We also introduce a moving system of rectangular coordinates Oxyz , x = x + Vt , t 0 , y = y , z = z , with origin at the geometric center of the domain . In the Eulerian coordinate system Oxyz , the temperature field and the stress-strain state of the half-space are stationary, and the components of the stress tensor have the form [12] th mn (X, Y , Z ) = p0 [ e mn (X, Y , Z ) + wth mn (X, Y , Z )] , 1 2
m, n x, y, z ,
(1)
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine. Bialystok University of Technology, Bialystok, Poland; e-mail: [email protected]
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