Formulação tridimensional completa para o aquecimento a laser de sólidos em regime não-linear : modelo e aplicações
Omar de Oliveira Diniz Neto
TESE
Português
T/UNICAMP D615f
Campinas, SP : [s.n.], 1995.
117 f. : il.
Orientador: Carlos Alberto da Silva Lima
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
Resumo: O advento dos lasers causou uma grande revolução na área de processamento de materiais, que atingiu um rápido desenvolvimento, nos últimos anos. O amplo espectro de materiais processáveis atualmente com lasers o comprova. Ainda assim, um grande número de pesquisadores continua buscando...
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Resumo: O advento dos lasers causou uma grande revolução na área de processamento de materiais, que atingiu um rápido desenvolvimento, nos últimos anos. O amplo espectro de materiais processáveis atualmente com lasers o comprova. Ainda assim, um grande número de pesquisadores continua buscando respostas para aspectos ainda não elucidados dos desafios lançados pela interação de laser com a matéria, em condições de alta intensidade de irradiação. Dentro desse contexto, nossa Tese dedicou-se a investigar em extensão e profundidade o controle paramétrico do aquecimento a laser, tendo em vista explorar numa etapa posterior sua influência na viabilização do controle conformacional do processo de microperfuração de materiais com lasers. Estudando, entre outras coisas, as condições e as características peculiares do avanço da frente de calor num sólido irradiado por um laser potente, em diversas configurações operacionais, investigamos, em particular, os efeitos da forma espacial e duração do pulso do laser, condutividade térmica e da difusividade térmica da amostra, assim como os efeitos de variações nas grandezas físicas que interferem no processo de acoplamento laser-sólido, tais como a refletividade e o coeficiente de absorção, sobre a forma e evolução temporal das isotermas nas amostras. Isto se dá porque a variação da temperatura afeta todos os parâmetros físicos que regem o processo de aquecimento a laser. Em nosso estudo consideramos, além de amostras homogêneas, amostras estratificadas de duas e três camadas, e amostras intrinsicamente heterogêneas, i.e., amostras onde a condutividade e difusividade térmicas variam continuamente com a profundidade da amostra. Para obter a distribuição temporal e espacial da temperatura num sólido aquecido localmente por um laser, e proceder os estudos acima delineados, nossa abordagem partiu especificamente de uma versão não-linear da equação parabólica para difusão de calor , porém com estrita observação dos limites de validade da teoria de Fourier. Além da não-linearidade que advém da dependência explícita dos parâmetros térmicos do material com a temperatura, interessou-nos também, investigar, em detalhe, os efeitos da variação correspondente da refletividade e coeficiente de absorção. A metodologia de tratamento que demos ao problema envolve a solução numérica das equações linear e não-linear de difusão de calor. Desenvolvemos e exploramos um novo algoritmo, específico para tratar a formulação dada a questão no presente trabalho. Nele, a discretização das funções e derivadas que aparecem na equação de difusão é feita através do método das diferenças finitas. Usamos uma versão modificada, que desenvolvemos, da formulação de Crank - Nicholson para obtermos um sistema de equações algébricas acopladas, que foi resolvido pelo método iterativo das sobre relaxações sucessivas (SOR). A implementação deste método foi feita em linguagem FORTRAN, executada no computador IBM 3090 da UNICAMP, e posteriormente, em estação de trabalho SUN-SPARC II. Em resumo, os cálculos com base em nosso modelo levaram-nos a concluir que é possível, em princípio, controlar a forma e a velocidade de avanço da frente de calor (isoterma de fusão) num sólido, a temperatura máxima no centro focal, o tempo necessário para alcançá-la e as taxas de aquecimento e resfriamento, dentre outros, atuando-se judiciosamente tanto sobre os parâmetros térmicos como sobre os parâmetros ópticos da amostra. Por exemplo, ao tratar com as amostras estratificadas (camadas sucessivas com propriedades adequadamente diferenciadas) ficou evidente uma clara tendência da isoterma de fusão a assumir uma conformação cada vez mais cilíndrica, em oposição ao perfil tipicamente cônico da correspondente isoterma em materiais homogêneos. Este efeito se torna ainda mais crítico quando o material tem essas propriedades variando continuamente com a profundidade. Esta Tese, enfim, elucida em detalhe os fundamentos teóricos e práticos que devem ser observados no controle paramétrico do processamento de materiais com laser com vista à obtenção de uma moldagem conformacional, como por exemplo, na micro-perfuração de materiais com lasers
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Abstract: Laser processing of materials has undergone substantial development in recent years and there is an ever growing family of
materials that are now amenable to such treatment. Yet, some problems in this area are far from settled, and the pertinent
scientific research is still responsible... Ver mais Abstract: Laser processing of materials has undergone substantial development in recent years and there is an ever growing family of
materials that are now amenable to such treatment. Yet, some problems in this area are far from settled, and the pertinent
scientific research is still responsible for a wealthy of papers.
This Thesis is a contribution towards some of these problems. Specifically, we have considered in depth and in breadth the
problem related to the possibility of parametric control of the laser heating. We meant to studying its influence upon the
controlled shaping of holes in laser microdril1ing processes. A full model and its numerical implementation have been developed
accordingly and applications under different conditions have been considered.
In particular, in a careful study of the heat front surface advance in a laser heated solid under different operational
configurations, we have dealt with the effects upon the form and evolution of the fusion isotherm in the sample, coming from the
shape and length of the laser pulse, the changes in the thermal conductivity and in the thermal diffusivity, as well as those in other
physical variables interfering in the laser vs. Solid interaction, such as the optical reflectivity and absorption coefficient. Such
effects are due to the fact the temperature affects all the physical parameters involving the laser heating process.
Our studies were applied to homogeneous samples and to both stratified samples(with two and three layers) and intrinsically
heterogeneous samples, e.g., those where such properties as thermal conductivity and thermal diffusivity vary continuously with
depth.
To calculate spatial and temporal temperature distributions in the laser heated sample and carry on the forementioned
studies, we resorted to a formulation based on the mathematically non-linear heat parabolic equation, under strict observation
of the bounds imposed by Fourier law. Thus, besides investigating the effects of the non-linearity that arise from both thermal
parameters of the material being temperature dependent, we have also considered , in detail, the effects of the corresponding
variations in the reflectivity and absorption coefficient. The calculations were based on a procedure that resorted to the use of
Kirchoff transform followed by numerically solving the resulting equation under the given boundary conditions using finite
differences through our modified version of the Crank-Nicholson scheme and a numerical iteration that explored the successive
over relaxation (SOR) method. This was implemented by coding a corresponding program in FORTRAN to run in the IBM
3090 vector processing computer which, later on, was also adapted to run in SUN-SPARC II workstations.
To sum up, our model calculations took us to conclude that, in principle, it is possible to control both shape and speed of the
laser heating front (fusion isotherm), the maximum focal temperature, the time it takes to reach it and the heating and cooling
rates, among others, by judiciously acting upon both the thermal and the optical sample parameters. For example, in the case of
stratified samples (several layers in succession having adequately differentiated properties) it became clear that there appears a
clear trend on the fusion isotherm towards becoming gradually more cylindrical in shape, as opposed to the typical conical
shape exhibited by the corresponding isotherm in laser heated homogeneous materials. This behavior can be seen to be even
more critical when we one takes on a sample where these properties vary continuously with depth.
Overall, this Thesis discloses in detail the theoretical and practical foundations that have to be considered when the
parametric control of the laser processing of a material, to achieve conformational molding, e.g. in laser microdrilling of
materials, is at issue Ver menos
materials that are now amenable to such treatment. Yet, some problems in this area are far from settled, and the pertinent
scientific research is still responsible... Ver mais Abstract: Laser processing of materials has undergone substantial development in recent years and there is an ever growing family of
materials that are now amenable to such treatment. Yet, some problems in this area are far from settled, and the pertinent
scientific research is still responsible for a wealthy of papers.
This Thesis is a contribution towards some of these problems. Specifically, we have considered in depth and in breadth the
problem related to the possibility of parametric control of the laser heating. We meant to studying its influence upon the
controlled shaping of holes in laser microdril1ing processes. A full model and its numerical implementation have been developed
accordingly and applications under different conditions have been considered.
In particular, in a careful study of the heat front surface advance in a laser heated solid under different operational
configurations, we have dealt with the effects upon the form and evolution of the fusion isotherm in the sample, coming from the
shape and length of the laser pulse, the changes in the thermal conductivity and in the thermal diffusivity, as well as those in other
physical variables interfering in the laser vs. Solid interaction, such as the optical reflectivity and absorption coefficient. Such
effects are due to the fact the temperature affects all the physical parameters involving the laser heating process.
Our studies were applied to homogeneous samples and to both stratified samples(with two and three layers) and intrinsically
heterogeneous samples, e.g., those where such properties as thermal conductivity and thermal diffusivity vary continuously with
depth.
To calculate spatial and temporal temperature distributions in the laser heated sample and carry on the forementioned
studies, we resorted to a formulation based on the mathematically non-linear heat parabolic equation, under strict observation
of the bounds imposed by Fourier law. Thus, besides investigating the effects of the non-linearity that arise from both thermal
parameters of the material being temperature dependent, we have also considered , in detail, the effects of the corresponding
variations in the reflectivity and absorption coefficient. The calculations were based on a procedure that resorted to the use of
Kirchoff transform followed by numerically solving the resulting equation under the given boundary conditions using finite
differences through our modified version of the Crank-Nicholson scheme and a numerical iteration that explored the successive
over relaxation (SOR) method. This was implemented by coding a corresponding program in FORTRAN to run in the IBM
3090 vector processing computer which, later on, was also adapted to run in SUN-SPARC II workstations.
To sum up, our model calculations took us to conclude that, in principle, it is possible to control both shape and speed of the
laser heating front (fusion isotherm), the maximum focal temperature, the time it takes to reach it and the heating and cooling
rates, among others, by judiciously acting upon both the thermal and the optical sample parameters. For example, in the case of
stratified samples (several layers in succession having adequately differentiated properties) it became clear that there appears a
clear trend on the fusion isotherm towards becoming gradually more cylindrical in shape, as opposed to the typical conical
shape exhibited by the corresponding isotherm in laser heated homogeneous materials. This behavior can be seen to be even
more critical when we one takes on a sample where these properties vary continuously with depth.
Overall, this Thesis discloses in detail the theoretical and practical foundations that have to be considered when the
parametric control of the laser processing of a material, to achieve conformational molding, e.g. in laser microdrilling of
materials, is at issue Ver menos
Formulação tridimensional completa para o aquecimento a laser de sólidos em regime não-linear : modelo e aplicações
Omar de Oliveira Diniz Neto
Formulação tridimensional completa para o aquecimento a laser de sólidos em regime não-linear : modelo e aplicações
Omar de Oliveira Diniz Neto
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