Zbigniew S. Olesiak

Debonding of thin surface layers generated by thermal and diffusive fluxes

The hardening of surface layers is frequently necessary for technological reasons. Coated solids get the required properties and become resistant to friction. The coatings, however change the material properties, in the result the solid is no longer homogeneous. In the case of sharp changes in the values of material constants the redistribution of stresses, arising from a heat flux or (and) diffusive mass flux can be significant. The effect of thin coating of a material with high Young’s modulus is particularly pronouncing. In the limit cases one can assume that the layer is inextensible. This assumption let us make the use of the methods and notions of the fracture mechanics.

ON A METHOD OF SOLUTION OF MIXED BOUNDARY-VALUE PROBLEMS OF THERMOELASTICITY

A method is presented that enables thermal crack and contact problems to be reduced in a simple way to those of the isothermal case and pertinent solutions to be obtained. The method is valid for elastic space or semispace and for a layer that is isotropic or transversally isotropic. Illustrative examples are given for axially symmetric cases.

Influence of surface heating on coated elastic solids

The purpose of the paper is twofold. First, we derive certain relationships between the stress tensor components and the field of temperature for a coated solid body. Second, we solve a particular problem with axial symmetry, and draw pertinent conclusions.

NOTE ON A SOLUTION OF HEAT FLUX PROBLEMS DISTURBED BY AN INSULATED CRACK

Abstract A method is presented that makes it possible to reduce the title problem to a problem of thermal stresses and the isothermal problem of the theory of elasticity. The auxiliary problem is that of a semispace with an inextensible membrane, bonded at the bounding plane and heated on part of it. There exist direct relationships between the distributions of temperature and stresses.

Stress Distribution in Rotating Solids with Frictional Heat Excited Over Contact Region

The present contribution is devoted to discussion of axially symmetric contact problems for two smooth solids, pressed against each other in relative rotation, generating heat due to the friction between them. We discuss and compared solutions for two extreme cases, namely when the unloaded surfaces of solids are thermally insulated, and when the heat exchange is so large that it is justified to assume that the temperature of the outside region of contact can be assumed zero. We prove that the distribution of contact pressure and the radius of contact region are the same in both the cases of thermal conditions. The thermal stresses, however, differ considerably. We analyze the distribution of the second invariant of the stress deviator, and we discuss the possibility of appearance of tensile stresses.

A NONIDEAL CONTACT PROBLEM OF THERMOELASTICITY FOR TWO SOLIDS WITH A HEAT SOURCE

A generalized Hertz problem of thermoelastic solids in pressure, contacting over convex surfaces, has been discussed. At a certain moment of time a concentrated source of heat starts acting. Therefore the heat flux flowing through the region of contact is nonstationary. The problem considered is axially symmetric. The purpose is twofold: first the problem of thermoelasticity with time variation of temperature is taken into account; second the “paradox of a cooled sphere” has been investigated under time-dependent conditions. There is a possibility that the character of the boundary conditions can change in time. To obtain the solution we have applied the Laplace and Hankel integral transforms. The main point is to discuss the cases when the boundary conditions are such that the problem can be considered in terms of classical thermoelasticity and when the Barber-type boundary conditions have to be used. The solution has been obtained by means of a devised numerical algorithm such that the procedure is simplified. The results have been presented in diagram form suitable for discussion.

EFFECT OF A HEATED BOUNDARY ON THE DISTRIBUTION OF NORMAL STRESS IN A MICROPOLAR SEMISPACE

The behavior and distribution of the normal component of the force stress tensor exerted by a change of temperature on a part of the bounding plane is examined. The temperature change, on a circle or an annulus, is prescribed so that the amount of heat applied is constant. The effect of the material constants a0 and l2 on the distribution of stresses is also investigated. Results are shown in diagram form. We also point out that some approximate methods of computing the Hankel transforms encountered in problems of micropolar thermoelasticity may lead to erroneous results.

MIXED BOUNDARY VALUE PROBLEM FOR POISSON'S EQUATION IN AN UNBOUNDED MULTI-LAYERED REGION

The problem of existence of the solution is investigated for Poissons equation inunbounded multi-layered domains. A method has been presented, leading to effective numericalcalculations for composites, problems of rock mechanics, and for arbitrary number of layers.We have discussed the mixed boundary value problems, taking into account nonideal contactconditions, corresponding to those appearing in the theory of the mechanics of solids and layeredcomposites.

TRIBUTE TO WITOLD NOWACKI (1911–1986)

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ON THERMAL STRESSES IN A MICROPOLAR LAYER

The purpose of this paper is twofold. First, the pertinent formulas are derived for the components of the displacement vector and rotation vector and those of the force and moment stress tensors in the case of an arbitrary, integrable distribution of tractions and temperature on the layer bounding planes. Second, the distribution of the force stress component normal to the boundary, exerted by heating of a circular area of the bounding planes, is discussed. Numerical results, given in diagram form, take into account the variation of the material constants l2 and a0, as well as the ratio of the heated-area diameter to the width of the layer.