Hot stamping and die quenching (HS/DQ) process of AA7075 aluminum alloy is one of attractive forming techniques for producing high strength automotive structural components to encounter their poor formability at room temperature. In this technique, quenching rate of this alloy is very crucial as it affects precipitation kinetics after artificial ageing of part formed, which in turn determines the final in-service mechanical properties and corrosion performance of part. Thermal contact resistance (TCR) between two solid surfaces is the main parameter that controls heat transfer between hot AA7075 sheet and cold steel dies, and thus affects quenching rate of part formed. Therefore, the final properties of automotive parts produced by hot stamping is indirectly influenced by TCR. The common methods of determining TCR in HS/DQ are often impracticable as they require thermocouples to be inserted into complex-shaped stamping dies, punches and thin aluminum sheet (blank) to be formed. A potential mechanistic approach for determining TCR could be an attractive alternative due to its avoidance of embedded thermocouples into the tooling and blank. The mechanistic method emphasizes on physical mechanisms (roughness etc.) governing interfacial heat transfer between cold forming tools and hot blank. The proposed work focuses on utilizing the mechanistic method to predict TCR between multiple cylindrical asperities on a nominally flat (and heated) AA7075 blank surface and a rigid, flat, asperity-free (and cold) steel die surface. The asperities were considered to deform elastoplastically, increasing contact area. Subsequently, TCR correlation as a function of temperature, contact load, and contact area was formulated. To validate the mechanistic model, a series of surface asperity flattening experiments using thermocouple-embedded AA7075 blank and polished stainless steel planar dies were carried out. Good agreement between mechanistic model predictions and experimental results in term of contact area and TCR as a function of contact load were observed. / Thesis / Doctor of Philosophy (PhD)

Este trabalho trata da aplicação do método Design Construtal para investigar a transferência de calor através de caminhos de alta condutividade térmica com geometrias definidas. O objetivo é obter a configuração que reduz a temperatura máxima em excesso do sistema considerando que as áreas ocupadas pelos materiais de alta e baixa condutividade são tratadas como constantes. Assim, o objeto de estudo é um volume de área finita onde ocorre a geração de calor. O escoamento da energia térmica para fora do volume é feito através de um caminho condutor de alta condutividade térmica. O trabalho considerou a resistência térmica de contato entre o elemento condutivo e o corpo gerador de calor, onde um terceiro material com resistência térmica equivalente à resistência de contato é interposto entre os dois primeiros. Na solução da equação da difusão do calor, foi realizado um tratamento numérico através de um código baseado em elementos finitos e utilizando o toolbox PDETool, Partial Differential Equations Tool, que pertence ao aplicativo comercial MatLab®. O tratamento numérico foi realizado considerando-se caminhos condutivos com geometrias em forma de "I" e em forma de "T", mantendo-se as frações de área constantes e variando-se os comprimentos dos materiais de alta condutividade e os da resistência térmica de contato. A otimização geométrica foi feita considerando-se os graus de liberdade existentes para cada geometria, onde os valores otimizados para a situação ideal, ou de acoplamento térmico perfeito, foram comparados para os resultados envolvendo a resistência térmica de contato (RTC). Os resultados indicam que a RTC pode aumentar a temperatura máxima em excesso, assim como tem efeito significativo sobre as ótimas configurações calculadas quando a resistência de contato é levada em consideração para ambas as configurações "I" e "T" estudadas. / This work applies Constructal Design to investigate the heat transfer through high conductive pathways with defined geometries. The objective is to find the configuration which reduces the maximal excess of temperature considering the areas with high and low thermal conductivity are constants. Thus, the object studied here is a volume with a finite area and heat generation. The outside heat flux is conducted through a high thermal conductive pathway. Here, special attention is given to the thermal contact resistance between the high conductive pathway and the solid body, where a third material with a thermal resistance equivalent to the thermal contact resistance is inserted between them. A numerical treatment was given in order to solve the heat diffusive equation. It was used a numerical code based on finite elements and the toolbox – PDETool, Partial Differential Equations Tool, which is part of the MatLab® applicative. The numerical treatment was achieved considering "I" and "T" geometries for the high conductive pathways keeping the areas fraction constants and varying the lengths of both high conductive and the equivalent thermal contact layer materials. The optimization was performed considering the degrees of freedom of each geometry, where the optimized values for the ideal situation, i.e., perfect thermal contact were compared with the results considering the thermal contact resistance. The results indicate that the thermal contact resistance can increase the excess of temperature, as well as it has a significant effect on the optimal configurations when using perfect thermal contact or taking into account the thermal contact resistance for "I" and "T" shaped geometries.

Este trabalho trata da aplicação do método Design Construtal para investigar a transferência de calor através de caminhos de alta condutividade térmica com geometrias definidas. O objetivo é obter a configuração que reduz a temperatura máxima em excesso do sistema considerando que as áreas ocupadas pelos materiais de alta e baixa condutividade são tratadas como constantes. Assim, o objeto de estudo é um volume de área finita onde ocorre a geração de calor. O escoamento da energia térmica para fora do volume é feito através de um caminho condutor de alta condutividade térmica. O trabalho considerou a resistência térmica de contato entre o elemento condutivo e o corpo gerador de calor, onde um terceiro material com resistência térmica equivalente à resistência de contato é interposto entre os dois primeiros. Na solução da equação da difusão do calor, foi realizado um tratamento numérico através de um código baseado em elementos finitos e utilizando o toolbox PDETool, Partial Differential Equations Tool, que pertence ao aplicativo comercial MatLab®. O tratamento numérico foi realizado considerando-se caminhos condutivos com geometrias em forma de "I" e em forma de "T", mantendo-se as frações de área constantes e variando-se os comprimentos dos materiais de alta condutividade e os da resistência térmica de contato. A otimização geométrica foi feita considerando-se os graus de liberdade existentes para cada geometria, onde os valores otimizados para a situação ideal, ou de acoplamento térmico perfeito, foram comparados para os resultados envolvendo a resistência térmica de contato (RTC). Os resultados indicam que a RTC pode aumentar a temperatura máxima em excesso, assim como tem efeito significativo sobre as ótimas configurações calculadas quando a resistência de contato é levada em consideração para ambas as configurações "I" e "T" estudadas. / This work applies Constructal Design to investigate the heat transfer through high conductive pathways with defined geometries. The objective is to find the configuration which reduces the maximal excess of temperature considering the areas with high and low thermal conductivity are constants. Thus, the object studied here is a volume with a finite area and heat generation. The outside heat flux is conducted through a high thermal conductive pathway. Here, special attention is given to the thermal contact resistance between the high conductive pathway and the solid body, where a third material with a thermal resistance equivalent to the thermal contact resistance is inserted between them. A numerical treatment was given in order to solve the heat diffusive equation. It was used a numerical code based on finite elements and the toolbox – PDETool, Partial Differential Equations Tool, which is part of the MatLab® applicative. The numerical treatment was achieved considering "I" and "T" geometries for the high conductive pathways keeping the areas fraction constants and varying the lengths of both high conductive and the equivalent thermal contact layer materials. The optimization was performed considering the degrees of freedom of each geometry, where the optimized values for the ideal situation, i.e., perfect thermal contact were compared with the results considering the thermal contact resistance. The results indicate that the thermal contact resistance can increase the excess of temperature, as well as it has a significant effect on the optimal configurations when using perfect thermal contact or taking into account the thermal contact resistance for "I" and "T" shaped geometries.

Este trabalho trata da aplicação do método Design Construtal para investigar a transferência de calor através de caminhos de alta condutividade térmica com geometrias definidas. O objetivo é obter a configuração que reduz a temperatura máxima em excesso do sistema considerando que as áreas ocupadas pelos materiais de alta e baixa condutividade são tratadas como constantes. Assim, o objeto de estudo é um volume de área finita onde ocorre a geração de calor. O escoamento da energia térmica para fora do volume é feito através de um caminho condutor de alta condutividade térmica. O trabalho considerou a resistência térmica de contato entre o elemento condutivo e o corpo gerador de calor, onde um terceiro material com resistência térmica equivalente à resistência de contato é interposto entre os dois primeiros. Na solução da equação da difusão do calor, foi realizado um tratamento numérico através de um código baseado em elementos finitos e utilizando o toolbox PDETool, Partial Differential Equations Tool, que pertence ao aplicativo comercial MatLab®. O tratamento numérico foi realizado considerando-se caminhos condutivos com geometrias em forma de "I" e em forma de "T", mantendo-se as frações de área constantes e variando-se os comprimentos dos materiais de alta condutividade e os da resistência térmica de contato. A otimização geométrica foi feita considerando-se os graus de liberdade existentes para cada geometria, onde os valores otimizados para a situação ideal, ou de acoplamento térmico perfeito, foram comparados para os resultados envolvendo a resistência térmica de contato (RTC). Os resultados indicam que a RTC pode aumentar a temperatura máxima em excesso, assim como tem efeito significativo sobre as ótimas configurações calculadas quando a resistência de contato é levada em consideração para ambas as configurações "I" e "T" estudadas. / This work applies Constructal Design to investigate the heat transfer through high conductive pathways with defined geometries. The objective is to find the configuration which reduces the maximal excess of temperature considering the areas with high and low thermal conductivity are constants. Thus, the object studied here is a volume with a finite area and heat generation. The outside heat flux is conducted through a high thermal conductive pathway. Here, special attention is given to the thermal contact resistance between the high conductive pathway and the solid body, where a third material with a thermal resistance equivalent to the thermal contact resistance is inserted between them. A numerical treatment was given in order to solve the heat diffusive equation. It was used a numerical code based on finite elements and the toolbox – PDETool, Partial Differential Equations Tool, which is part of the MatLab® applicative. The numerical treatment was achieved considering "I" and "T" geometries for the high conductive pathways keeping the areas fraction constants and varying the lengths of both high conductive and the equivalent thermal contact layer materials. The optimization was performed considering the degrees of freedom of each geometry, where the optimized values for the ideal situation, i.e., perfect thermal contact were compared with the results considering the thermal contact resistance. The results indicate that the thermal contact resistance can increase the excess of temperature, as well as it has a significant effect on the optimal configurations when using perfect thermal contact or taking into account the thermal contact resistance for "I" and "T" shaped geometries.

As a result of manufacturing processes, real surfaces have roughness and surface curvature. The real contact occurs only over microscopic contacts, which are typically only a few percent of the apparent contact area. Because of the surface curvature of contacting bodies, the macrocontact area is formed, the area where microcontacts are distributed randomly. The heat flow must pass through the macrocontact and then microcontacts to transfer from one body to another. This phenomenon leads to a relatively high temperature drop across the interface. Thermal contact resistance (TCR) is a complex interdisciplinary problem, which includes geometrical, mechanical, and thermal analyses. Each part includes a micro and a macro scale sub-problem. Analytical, experimental, and numerical models have been developed to predict TCR since the 1930's. Through comparison with more than 400 experimental data points, it is shown that the existing models are applicable only to the limiting cases and none of them covers the general non-conforming rough contact. The objective of this study is to develop a compact analytical model for predicting TCR for the entire range of non-conforming contacts, i. e. , from conforming rough to smooth sphere-flat in a vacuum. The contact mechanics of the joint must be known prior to solving the thermal problem. A new mechanical model is developed for spherical rough contacts. The deformation modes of the surface asperities and the bulk material of contacting bodies are assumed to be plastic and elastic, respectively. A closed set of governing relationships is derived. An algorithm and a computer code are developed to solve the relationships numerically. Applying Buckingham Pi theorem, the independent non-dimensional parameters that describe the contact problem are specified. A general pressure distribution is proposed that covers the entire spherical rough contacts, including the Hertzian smooth contact. Simple correlations are proposed for the general pressure distribution and the radius of the macrocontact area, as functions of the non-dimensional parameters. These correlations are compared with experimental data collected by others and good agreement is observed. Also a criterion is proposed to identify the flat surface, where the influence of surface curvature on the contact pressure is negligible. Thermal contact resistance is considered as the superposition of macro and micro thermal components. The flux tube geometry is chosen as the basic element in the thermal analysis of microcontacts. Simple expressions for determining TCR of non-conforming rough joints are derived which cover the entire range of TCR by using the general pressure distribution and the flux tube solution. A complete parametric study is performed; it is seen that there is a value of surface roughness that minimizes TCR. The thermal model is verified with more than 600 data points, collected by many researchers during the last 40 years, and good agreement is observed. A new approach is taken to study the thermal joint resistance. A novel model is developed for predicting the TCR of conforming rough contacts employing scale analysis methods. It is shown that the microcontacts can be modeled as heat sources on a half-space for engineering applications. The scale analysis model is extended to predict TCR over the entire range of non-conforming rough contacts by using the general pressure distribution developed in the mechanical model. It is shown that the surface curvature and contact pressure distribution have no effect on the effective micro thermal resistance. A new non-dimensional parameter is introduced as a criterion to identify the three regions of TCR, i. e. , the conforming rough, the smooth spherical, and the transition regions. An experimental program is designed and data points are collected for spherical rough contacts in a vacuum. The radius of curvature of the tested specimens are relatively large (in the order of m) and can not be seen by the naked eye. However, even at relatively large applied loads the measured joint resistance (the macro thermal component) is still large which shows the importance of surface out-of-flatness/curvature. Collected data are compared with the scale analysis model and excellent agreement is observed. The maximum relative difference between the model and the collected data is 6. 8 percent and the relative RMS difference is approximately 4 percent. Additionally, the proposed scale analysis model is compared/verified with more than 880 TCR data points collected by many researchers. These data cover a wide range of materials, surface characteristics, thermal and mechanical properties, mean joint temperature, directional heat transfer effect, and contact between dissimilar metals. The RMS difference between the model and all data is less than 13. 8 percent.

A Resistência Térmica de Contato entre a ferramenta de forjamento e a peça é um parâmetro importante para a otimização, por simulação computacional, do comportamento do material forjado. Os procedimentos atuais destinados à determinação da Resistência Térmica de Contato apresentam discrepância significativa nos resultados. A falta de valores confiáveis deste parâmetro afeta a precisão da simulação. Visando a importância das ferramentas computacionais para a otimização do processo de forjamento, no presente trabalho foi desenvolvida uma nova técnica para determinar a Resistência Térmica de Contato. A técnica inovadora inclui o método de medição de temperaturas interfaciais desconhecido anteriormente, a montagem para realizá-lo e o sistema de medição de temperaturas volumétricas. Esta técnica é destinada ao uso sob condições de altas e moderadas temperatura e pressão muito grande, o que é característico da zona de contato material forjado–ferramenta. A inovação foi testada com sucesso para alguns materiais típicos (aço, liga de alumínio e liga de titânio) utilizados no forjamento a quente ou a morno. Os valores da Resistência Térmica de Contato, obtidos nos testes, são recomendados para uso em programas de simulação computacional. / The Thermal Contact Resistance between a die and a blank is an important parameter in the computer simulation used for the optimization of the blank plastic deformation. The known procedures intended for the determination of the Thermal Contact Resistance show significant discrepancy in results. The lack of reliable values of this parameter affects the precision of the simulation. Taking in account the importance of computer tools for the optimization of the forging process, a new technique for the determination of the Thermal Contact Resistance has been developed in the present study. The developed technique includes a method for the measurement of the interface temperatures, which was unknown before, and the equipment for the realization of this method as well as the system for the measurement of the volumetric temperatures. This technique is intended for use under moderate and high temperature / high pressure conditions at the die–workpiece interface. The innovation has been tested successfully on some typical materials (steel, aluminium alloy e titanium alloy) used in warm and hot forging. Values of the Thermal Contact Resistance obtained by these tests are recommended for use in computer simulations.

Measurements of in situ planetary thermal conductivity are typically made using long needle-like probes inserted in a planet's surface, which measure effective thermal conductivity (ETC) in radial direction (parallel to surface). The desired vertical (perpendicular to surface) ETC is assumed to be the same as the horizontal. However, ETC of particle beds in vertical and horizontal directions is known to be an anisotropic property under low compressive pressures. This study further examines the anisotropy of bed ETC under low and high compressive pressures in both vacuum and air environments. The ratio of vertical to horizontal stress, K0, is measured for the particles used in these experiments. A resistance network heat transfer model has been developed in predicting the vertical and the horizontal ETC as a function of applied compressive pressure. The model predicts vertical ETC by using only macro-contact thermal resistances for both high and low applied compressive pressure regimes. It is proposed that the vertical and horizontal ETC of particle beds under uniaxial compression is related by compressive pressures in each direction. The horizontal compressive pressure, which is perpendicular to the applied compressive pressure, can be calculated with the use of at-rest pressure coefficient and subsequently used in macro-contact thermal resistance to predict the horizontal ETC. The vertical ETC is obtained using the same model by substituting vertical compressive pressure into macro-contact thermal resistance. A two-dimensional axisymmetric finite element model in the COMSOL Multiphysics software package has been developed to simulate heat transfer coupled with structural deformation of spheres under compressive pressures in a simple cubic (SC) packing arrangement. The numerical model is used as a tool to predict the lower limit of bed ETC as well as validating thermal contact resistance used in the theoretical model. The predictions from the numerical model can be extended to particle beds with different packing arrangements.

As a result of manufacturing processes, real surfaces have roughness and surface curvature. The real contact occurs only over microscopic contacts, which are typically only a few percent of the apparent contact area. Because of the surface curvature of contacting bodies, the macrocontact area is formed, the area where microcontacts are distributed randomly. The heat flow must pass through the macrocontact and then microcontacts to transfer from one body to another. This phenomenon leads to a relatively high temperature drop across the interface. Thermal contact resistance (TCR) is a complex interdisciplinary problem, which includes geometrical, mechanical, and thermal analyses. Each part includes a micro and a macro scale sub-problem. Analytical, experimental, and numerical models have been developed to predict TCR since the 1930's. Through comparison with more than 400 experimental data points, it is shown that the existing models are applicable only to the limiting cases and none of them covers the general non-conforming rough contact. The objective of this study is to develop a compact analytical model for predicting TCR for the entire range of non-conforming contacts, i. e. , from conforming rough to smooth sphere-flat in a vacuum. The contact mechanics of the joint must be known prior to solving the thermal problem. A new mechanical model is developed for spherical rough contacts. The deformation modes of the surface asperities and the bulk material of contacting bodies are assumed to be plastic and elastic, respectively. A closed set of governing relationships is derived. An algorithm and a computer code are developed to solve the relationships numerically. Applying Buckingham Pi theorem, the independent non-dimensional parameters that describe the contact problem are specified. A general pressure distribution is proposed that covers the entire spherical rough contacts, including the Hertzian smooth contact. Simple correlations are proposed for the general pressure distribution and the radius of the macrocontact area, as functions of the non-dimensional parameters. These correlations are compared with experimental data collected by others and good agreement is observed. Also a criterion is proposed to identify the flat surface, where the influence of surface curvature on the contact pressure is negligible. Thermal contact resistance is considered as the superposition of macro and micro thermal components. The flux tube geometry is chosen as the basic element in the thermal analysis of microcontacts. Simple expressions for determining TCR of non-conforming rough joints are derived which cover the entire range of TCR by using the general pressure distribution and the flux tube solution. A complete parametric study is performed; it is seen that there is a value of surface roughness that minimizes TCR. The thermal model is verified with more than 600 data points, collected by many researchers during the last 40 years, and good agreement is observed. A new approach is taken to study the thermal joint resistance. A novel model is developed for predicting the TCR of conforming rough contacts employing scale analysis methods. It is shown that the microcontacts can be modeled as heat sources on a half-space for engineering applications. The scale analysis model is extended to predict TCR over the entire range of non-conforming rough contacts by using the general pressure distribution developed in the mechanical model. It is shown that the surface curvature and contact pressure distribution have no effect on the effective micro thermal resistance. A new non-dimensional parameter is introduced as a criterion to identify the three regions of TCR, i. e. , the conforming rough, the smooth spherical, and the transition regions. An experimental program is designed and data points are collected for spherical rough contacts in a vacuum. The radius of curvature of the tested specimens are relatively large (in the order of m) and can not be seen by the naked eye. However, even at relatively large applied loads the measured joint resistance (the macro thermal component) is still large which shows the importance of surface out-of-flatness/curvature. Collected data are compared with the scale analysis model and excellent agreement is observed. The maximum relative difference between the model and the collected data is 6. 8 percent and the relative RMS difference is approximately 4 percent. Additionally, the proposed scale analysis model is compared/verified with more than 880 TCR data points collected by many researchers. These data cover a wide range of materials, surface characteristics, thermal and mechanical properties, mean joint temperature, directional heat transfer effect, and contact between dissimilar metals. The RMS difference between the model and all data is less than 13. 8 percent.

As silicon-based transistor technology continues to scale ever downward, anticipation of the fundamental limitations of ultimately-scaled devices has driven research into alternative device technologies as well as new materials for interconnects and packaging. Additionally, as power dissipation becomes an increasingly important challenge in highly miniaturized devices, both the implementation and verification of high mobility, high thermal conductivity materials, such as low dimensional carbon nanomaterials, and the experimental investigation of heat transfer in the nanoscale regime are requisite to continued progress. This work furthers the current understanding of structure-property relationships in low dimensional carbon nanomaterials, specifically carbon nanotubes (CNTs) and graphene, through use of combined thermal conductance and transmission electron microscopy (TEM) measurements on the same individual nanomaterials suspended between two micro-resistance thermometers. Through the development of a method to measure thermal contact resistance, the intrinsic thermal conductivity, [kappa], of multi-walled (MW) CNTs is found to correlate with TEM observed defect density, linking phonon-defect scattering to the low [kappa] in these chemical vapor deposition (CVD) synthesized nanomaterials. For single- (S) and double- (D) walled (W) CNTs, the [kappa] is found to be limited by thermal contact resistance for the as-grown samples but still four times higher than that for bulk Si. Additionally, through the use of a combined thermal transport-TEM study, the [kappa] of bi-layer graphene is correlated with both crystal structure and surface conditions. Theoretical modeling of the [kappa] temperature dependence allows for the determination that phonon scattering mechanisms in suspended bi-layer graphene with a thin polymeric coating are similar to those for the case of graphene supported on SiO₂. Furthermore, a method is developed to investigate heat transfer through a nanoscale point contact formed between a sharp silicon tip and a silicon substrate in an ultra high vacuum (UHV) atomic force microscope (AFM). A contact mechanics model of the interface, combined with a heat transport model considering solid-solid conduction and near-field thermal radiation leads to the conclusion that the thermal resistance of the nanoscale point contact is dominated by solid-solid conduction. / text

This thesis is devoted to the calculation of thermal contact resistance in various molecular systems based on carbon nanotubes (CNTs) and few layer graphene (FLG). This work has been performed through equilibrium molecular dynamics (EMD) simulations. We adopted the temperature difference fluctuations method in our EMD calculations. This method only needs the input of the temperatures of the subsystems whereas the heat flux, which is involved in all the other approaches, remains more difficult to compute in terms of simulation time and algorithm. Firstly, three cases were studied to validate this method, namely: (i) Si/Ge superlattices; (ii) diameter modulated SiC nanowires; and (iii) few-layer graphenes. The validity of the temperature difference fluctuations method is proved by equilibrium and non-equilibrium MD simulations. Then, by using this method, we show that an azide-functionalized polymer (HLK5) has a lower contact resistance with CNT than the one between CNT and PEMA, because HLK5 could form covalent bonds (C-N bonds) with CNT through its tail group azide, while only weak Van der Waals interactions exist in the case of CNT-PEMA contact. The data from our EMD simulations match with the results from experiments in a reasonable range. We then report the thermal contact resistance between FLG and a SiO2 substrate, which could be tuned with the layer number. Taking advantage of the resistive interface, we show that a SiO2 /FLG superlattices have a thermal conductivity as low as 0.30 W/mK, exhibiting a promising prospect in nano-scale thermal insulation. In the last part, we investigated the layer number dependence of the cross-plane thermal resistances of suspended and supported FLGs. We show that the existence of a silicon dioxide substrate can significantly decrease the cross-plane resistances of FLGs with low layer numbers, and the effective thermal conductivities were increased accordingly. The Frenkel-Kontorova model was introduced to explain the substrate-induced band gaps in FLG dispersion relations and the corresponding thermal energy transfer. The enhanced thermal conduction in the cross-plane direction is ascribed to the phonon radiation that occurs at the FLG-substrate interface, which re-distributes the FLG in-plane propagating energy to the cross-plane direction and to the substrate.