Modelo termodinamico para o aquecimento não-linear, a laser, e suas aplicações ao processamento de materiais

AUTOR(ES)
DATA DE PUBLICAÇÃO

1994

RESUMO

The subject of the computer modeling of the laser processing of materials continues to be highly topical in Materials Science. Basic to such an achievement was to have an well posed proposition to determine the time evolution of the temperature anywhere in the laser heated sample. Though models of such a kind abound in the literature, they are either rather crude approaches to the problem or, in one stage or another of the model formulation and/or numerical computations, they call for approximations that normally render them applicable only under severely restricted conditions. To further complicate this picture, pulsed laser heated solids frequently undergo so large temperature excursions, at such incredibly large heating/ cooling rates, that make them cross the boundaries of one or more phase transitions and/or make them the seat of markedly endothermic or exothermic processes along with the heating itself. It is no longer feasible to ignore the temperature variation of the various parameters entering the heat diffusion equation, associated with optical and or thermal propertied of the solid. this not only makes the equation highly non-linear but asks that it be solved with moving boundary conditions. The numerical computations are the Bole hope to get any solution to this problem, but even them are now severely restricted by prohibitively large computer processing times, or by uncontrollable numerical instabilities. All this have justified, in a certain sense, the use of the forementioned approximations for the full problem of materials processing under highly non-linear heating laser irradiation conditions. We decided, in this Thesis, to face such a formidable problem in its fullest picture. Minimally, we expected to get out of such enterprise with a carefully evaluated picture of the pitfalls and shortcomes that result from unduly applications of certain approximated formulations to specific laser processing problems. However, we ended up with an approximations free formulation for the three-dimensional fully non-linear laser heating problem, which explored well justified aspects of local equilibrium thermodynamics. It proved to have sufficient generality and flexibility to be applicable to a large spectrum of laser heating and/or processing problems, even when they included intervention of local specific processes, in parallel to the heating itself, which develop / consume heat energy (such as phase transitions, chemical reactions, etc). We started out by laying the physical foundations of the model by introducing a local temperature T(x,y,z,t) for the system (laser heated solid) which, while being globally in a non-equilibrium condition, could be divided up into macroscopically small individual cells within which the postulate of local thermodynamic equilibrium could be applied. This allowed UB not only to define the local thermodynamic temperature, and other thermodynamic variables, but as well to define the local densities for the various thermodynamic potentials. This required reformulating the heat diffusion problem in terms of a pair of the thermodynamically related quantities: the enthalpy density (W(x,y,z,t)) and temperature (T(x,y,z,t)). They had to be numerically computed in a self-consistent fashion using the integro-differential system of equations formed by the fully non-linear 3-D heat equation, with an arbitrary laser source as the heating element, and the thermodynamic constitutive relation linking enthalpy density and temperature. As a result W(x,y,z,t) and T(x,y,z,t) were self-consistenly computed and from them, using the normal thermodynamic definitions, we got the local densities for the entropy, for Gibss free energy and for the standard free energy. In order to able to numerically implement the physical model described above we had to devise afresh a computational scheme and develop the corresponding numerical algorithm. Prepared to run in a vector processing IBM-3090 computer and / or in SUN - SPARC Work Stations, a FORTRAN code was written which explored an explicit finite differences numerical scheme. Applications of the model addressed two problems in laser processing: (a) ?micro fusion with IR lasers (b) -laser induced thermochemical deposition of oxide layers on metallic substrates. In both cases the predictions of the model were confronted with experiment, wherever possible, with very good agreement. The laser induced oxide layer deposition problem was dealt with at length, constituting one of the chapters in the Thesis. Overall, we have developed and applied an alternative scheme based on local equilibrium thermodynamics that is particularly suited to deal with laser processing problems when the irradiation conditions bring the associated thermal problem into a highly non-linear regime

ASSUNTO(S)

materiais - aquecimento lasers em fisica termodinamica - materiais

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