Os aços ferrítico-martensíticos de atividade radioativa reduzida (RAFM, do inglês \"Reduced Activation Ferritic Martensitic\"), são um dos principais candidatos a materiais estruturais para os futuros reatores de fusão nuclear ITER (acrônimo de \"International Thermonuclear Experimental Reactor\") e DEMO (futuro reator de fusão nuclear de demonstração nas quais os materiais utilizados para sua construção dependem dos resultados obtidos no reator experimental ITER, cujo início das operações é previsto para 2020). A designação Eurofer-97 corresponde a um aço RAFM desenvolvido pela União Européia com composição nominal 9Cr -1,1W - 0,125Ta - 0,25V - 0,105C - 0,6Mn - 0,036 N (% em peso) visando aplicações no reator ITER. O material para esse estudo foi cedido pelo KIT (Karlsruhe Institut für Technologie - Alemanha), após laminação a quente e revenimento em 760ºC. Em seguida, o material foi laminado a frio (redução de 80%) e tratado em duas diferentes temperaturas no campo austenítico (1050º e 1150ºC) por 30 min, seguido de resfriamento ao ar. Após o tratamento térmico de têmpera, o material foi submetido a diversos revenimentos por 2 h cada em diversas temperaturas até 800ºC. As amostras obtidas foram caracterizadas por meio de microscopia eletrônica de varredura, medidas de microdureza, magnetização e resistividade elétrica. Simulações termodinâmicas foram também realizadas para a previsão das fases presentes no material em função da temperatura. Para revenimentos em ? 500oC ocorreu um ligeiro aumento na microdureza do aço Eurofer-97, seguido por um amolecimento significativo do material para revenimentos realizados em mais altas temperaturas. A mesma tendência foi observada para a resistividade elétrica. O campo coercivo também apresentou uma forte queda para revenimentos realizados em temperaturas maiores que ?550oC. Esses resultados indicaram que o início da precipitação de nitretos e carbonetos no aço Eurofer-97 ocorre por volta de 500oC. Para revenimentos em temperaturas mais amenas o campo coercivo e a resistividade elétrica se mostraram mais sensíveis às mudanças microestruturais do material do que as medidas de microdureza. / Reduced-activation ferritic-martensitic (RAFM) steels are promising candidates as structural materials in future fusion power plants as ITER (International Thermonuclear Experimental Reactor) and DEMO (nuclear fusion power plant that is intended to build upon the expected success of the ITER, which is expected becomes operational in 2020). The Eurofer-97 is a RAFM steel developed by the European Union with nominal composition 9Cr -1,1W - 0,125Ta - 0,25V - 0,105C - 0,6Mn - 0,036 N (wt.%). The material for this study was supplied by KIT (Karlsruhe Institut für Technologie - Germany), after hot rolling followed by tempering at 760oC. Next the Eurofer-97 steel was cold rolled (80% reduction) and treated in two different temperatures in the austenitic field (1050º and 1150ºC) by 30 min, followed by air cooling. After quenching the material was tempered for 2 h at several temperatures up to 800ºC. The samples were characterized using scanning electron microscopy, microhardness tests, magnetization and electrical resistivity measurements. Thermodynamical simulations were also performed in order to predict the temperature dependence of the equilibrium phases in the material. For tempering at ?500oC it was observed a slightly increase in the microhardness of the Eurofer-97 steel, followed by pronounced softening for tempering performed at higher temperatures. The same trend was observed for the electrical resistivity. The coercive field also shown a strong decrease for tempering performed at higher temperatures than ?550oC. These results suggested that the beginning of nitrates and carbonates precipitation occurs around 500oC. For tempering performed in mild temperatures the coercive field and electrical resistivity are more sensitive than microhardness measurements to detect the microstructural changes in the investigated material.

Heat treatment can be defined as a combination of heating and cooling operations applied to a metal or alloy in solid state. It is an important manufacturing process, which controls the mechanical properties of metals, therefore contributes to the product quality. Computerized Heat Treatment Planning System for Quenching and Tempering (CHT-q/t), a windows based stand alone software, is developed to assist the heat treatment process design. The goal of CHT-q/t is to predict the temperature profile of load in batch as well as continuous furnace during heating, quenching and tempering of steel, then to predict the mechanical properties as Quenched & Tempered, and finally to optimize the heat treatment process design. The thesis reviews existing heat treating simulation software and identifies the industrial need of a software tool which integrates part load and furnace model with heat treating process. The thesis discusses cooling curve of specimen and Time Temperature Transformation (TTT) diagram to determine the microstructure evolution and subsequently the mechanical properties of steel after quenching. An extensive database has been developed to support the various function modules. The thesis focuses mainly in the TTT and quenchant database development, property prediction after quenching and tempering and the implementation of software. The properties determined in the thesis are hardness, ultimate tensile strength, yield strength, toughness and percentage elongation. Hardness has been predicted by the use of some well known analytical equations and the TTT database, finally regression analysis has been used to give the value as a function of carbon percentage and volume fraction of martensite. The other mechanical properties are calculated based on a relation of hardness and volume fraction of martensite. Various case studies were performed to show the application of CHT-bf and CHT-cf at Bodycote Thermal Processing, Worcester & Waterbury. The objective behind the case studies was to study the effect of change in load arrangement, production rate and cycle time on the heat treated parts and finally to give recommendations in order to save energy and improve productivity and quality.

Os resultados dos processos de alívio de tensões e demais alteraçõees em propriedades mecânicas no revenimento são dependentes do tempo e da temperatura do processo o qual pode ser correlacionado usando algum parâmetro como o de Holloman-Jaffe ou o de Larsen-Miller. Estes parâmetros medem o efeito térmico do processo na transformação metalúrgica do aço durante o revenimento. Processos apresentando o mesmo parâmetro devem apresentar o mesmo efeito nas propriedades mecânicas, como a dureza, por exemplo. No entanto, expressões numéricas mais tradicionais assumem que o processo de revenimento é isotérmico, o que raramente acontece nos fornos de produçãoo, devido ao período de aquecimento anterior ao encharcamento na temperatura de revenimento desejada. Embora a equação de Larsen-Miller e o parâmetro de Holloman-Jaffe sejam bem conhecidos, suas origens e limitações, e em alguns casos seus usos, geralmente não são discutidos em detalhes na maioria dos textos de tratamento térmico. Assim o que se deseja é estabelecer uma relação numérica mais precisa, utilizando redes neurais para simular os efeitos do processo de revenimento dos aços para beneficiamento, através da previsão de suas propriedades mecânicas. / The process results of stress relief and other alterations on mechanical properties on tempering are function of time and temperature process, which can be correlated using some parameter as Hollomon-Jaffe or Larsen-Miller. These parameters measure the process thermal effect of metallurgical transformation of steel during tempering. Processes showing the same parameter should have the same effect on mechanical properties, as hardness, for example. However, traditional numerical equations assume that the tempering process is isothermal, what rarely happens in production furnaces, due of the heating time prior to soaking on the desired tempering temperature. Although the equation of Larsen-Miller and the Hollomon- Jaffe parameter are well known, their origins and limitation, and in some case their uses, generally are not discussed in details in the majority of heat treatments texts. So if what it tor establish a more accurate numerical relation, using neural networks for simulating the effects of the tempering process, through its mechanical properties.

The free energy landscape of a protein-like chain is constructed from exhaustive simulation studies using a combination of discontinuous molecular dynamics and parallel tempering methods. The protein model is a repeating sequence of four kinds of monomers, in which hydrogen bond attraction, electrostatic repulsion, and covalent bond vibrations are modeled by step, shoulder and square-well potentials, respectively. These protein-like chains exhibit a helical structure in their folded states. The model allows a natural definition of a configuration by considering which beads are bonded. In the absence of a solvent, the relative free energy of dominant structures is determined from the relative populations, and the probabilities predicted from the calculated free energies are found to be in excellent agreement with the observed probabilities at different temperatures. The free energy landscape of the protein-like chain is analyzed and confirmed to have funnel-like characteristics, confirmed by the fact that the probability of observing the most common configuration approaches unity at low enough temperatures for chains with fewer than 30 beads. The effect on the free energy landscape of an explicit square-well solvent, where the beads that can form intra-chain bonds can also form (weaker) bonds with solvent molecules while other beads are insoluble, is also examined. Simulations for chains of 15, 20 and 25 beads show that at low temperatures, the most likely structures are collapsed helical structures. The temperature at which collapsed helical structures become dominant is higher than in the absence of a solvent. Finally, the dynamics of the protein-like chain immersed in an implicit hard sphere solvent is studied using a simple model in which the implicit solvent interacts on a fast time scale with the chain beads and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. Using a Markovian model of the kinetics of transitions between conformations, the equilibration process from an ensemble of initially extended configurations to mainly folded configurations is investigated at low effective temperatures for a number of different chain lengths. It was observed that folding profiles appear to be single exponentials and independent of temperature at low temperatures.

Experiments were conducted to investigate the potential of using a quench and self-tempering heat treatment process with AISI 1117 steel to satisfy the mechanical properties of ASTM A 706 rebar. A series of quenching tests were performed and the resulting microstructure and mechanical properties studied using optical microscopy, microhardness measurement, and tensile tests. The presence of martensite throughout the samples contributed to the enhanced strength and strain-hardening ratio (tensile to yield strength) of the material. The experimental results showed that AISI 1117 is capable of meeting the ASTM standard. In addition to the experiments, a computer model using the finite difference method and incorporating heat transfer and microstructure evolution was developed to assist in future optimization of the heat treatment process.

Experiments were conducted to investigate the potential of using a quench and self-tempering heat treatment process with AISI 1117 steel to satisfy the mechanical properties of ASTM A 706 rebar. A series of quenching tests were performed and the resulting microstructure and mechanical properties studied using optical microscopy, microhardness measurement, and tensile tests. The presence of martensite throughout the samples contributed to the enhanced strength and strain-hardening ratio (tensile to yield strength) of the material. The experimental results showed that AISI 1117 is capable of meeting the ASTM standard. In addition to the experiments, a computer model using the finite difference method and incorporating heat transfer and microstructure evolution was developed to assist in future optimization of the heat treatment process.

The free energy landscape of a protein-like chain is constructed from exhaustive simulation studies using a combination of discontinuous molecular dynamics and parallel tempering methods. The protein model is a repeating sequence of four kinds of monomers, in which hydrogen bond attraction, electrostatic repulsion, and covalent bond vibrations are modeled by step, shoulder and square-well potentials, respectively. These protein-like chains exhibit a helical structure in their folded states. The model allows a natural definition of a configuration by considering which beads are bonded. In the absence of a solvent, the relative free energy of dominant structures is determined from the relative populations, and the probabilities predicted from the calculated free energies are found to be in excellent agreement with the observed probabilities at different temperatures. The free energy landscape of the protein-like chain is analyzed and confirmed to have funnel-like characteristics, confirmed by the fact that the probability of observing the most common configuration approaches unity at low enough temperatures for chains with fewer than 30 beads. The effect on the free energy landscape of an explicit square-well solvent, where the beads that can form intra-chain bonds can also form (weaker) bonds with solvent molecules while other beads are insoluble, is also examined. Simulations for chains of 15, 20 and 25 beads show that at low temperatures, the most likely structures are collapsed helical structures. The temperature at which collapsed helical structures become dominant is higher than in the absence of a solvent. Finally, the dynamics of the protein-like chain immersed in an implicit hard sphere solvent is studied using a simple model in which the implicit solvent interacts on a fast time scale with the chain beads and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. Using a Markovian model of the kinetics of transitions between conformations, the equilibration process from an ensemble of initially extended configurations to mainly folded configurations is investigated at low effective temperatures for a number of different chain lengths. It was observed that folding profiles appear to be single exponentials and independent of temperature at low temperatures.

The main purpose of this thesis is to improve the fundamental knowledge of non-isothermal tempering of martensite phase and its effects on the reduction in hardness (softening) with respect the base metal occurring at the heat affected zone (HAZ) of resistance spot welded dual-phase (DP) steels. This thesis also aims at understanding the influence of HAZ-softening on the joint performance of various DP steel grades. The tempering of martensite occurring at the sub-critical HAZ (SC-HAZ) of resistance spot welded DP600, DP780 and DP980 steels has been systematically evaluated by microhardness testing through Vickers indentation and the degree of tempering has been correlated to the HAZ-softening. From the joint performance analysis of similar and dissimilar steel grade combinations assessed through standardized testing methods, three important issues have been targeted: a) the joint strength (maximum load to failure), b) the location of failure (failure mode), and c) the physical characteristic of the weld that determines certain type of failure (weld nugget size). In addition, a partial tensile test has been conducted in order to evaluate the initiation of failure in dissimilar steel grade combinations. It has been shown that HAZ-softening lowered the weld size at which transition from interfacial to pullout failure mode takes place along with increased load-bearing capacity and higher energy absorption. Thus, it is concluded from mechanical testing that HAZ-softening benefits the lap-shear tensile joint performance of resistance spot welded DP steels by facilitating pullout failures through failure initiation at the SC-HAZ (tempered region). Instrumented nanoindentation testing was employed to further investigate HAZ-softening along the SC-HAZ by evaluating individual phases of ferrite matrix and tempered martensite islands. Although the ferrite matrix presented a slight reduction in hardness at nanoscale, higher reduction in hardness (softening) resulted for tempered martensite; thus confirming that tempered martensite is the major contributor to softening at micro-scale. A comparison between nanohardness and microhardness testing made at different distances from the line of lower critical temperature of transformation (Ac1) allowed revealing the actual extension of the SC-HAZ. In this regard, good correlation was obtained between nanohardness results along the SC-HAZ and the microstructural changes analyzed by electron microscopy (i.e., the tempering of martensite occurring at various distances far from Ac1 was correlated to low temperature tempering of dual phase steels). An in-depth analysis of the tempering of martensite phase at high temperature in DP steel subjected non-isothermal conditions i.e., rapid heating, extremely short time at peak temperature and rapid cooling (resistance spot welding), has been carried out mainly through analytical transmission electron microscopy (TEM). In addition, an isothermal tempering condition (i.e., slow heating and long time at peak temperature) in DP steel has been evaluated for complementing the analysis. Both non-isothermal and isothermal conditions have been correlated to the softening behaviour. TEM analysis of the base metal in the DP steel indicated that the morphology of the martensite phase is dependent on its carbon content, and its tempering characteristics are similar to that of equal carbon containing martensitic steel. The isothermally tempered structure is characterized by coarsening and spheroidization of cementite (θ) and complete recovery of the martensite laths; whereas precipitation of fine quasi-spherical intralath θ-carbides, coarser plate-like interlath θ-carbides, decomposition of retained austenite into elongated θ-carbides, and partial recovery of the lath structure were observed after non-isothermal tempering of DP steel. This difference in tempering behaviour is attributed to synergistic effect of delay in cementite precipitation due to higher heating rate, and insufficient time for diffusion of carbon that delays the third stage of tempering process (cementite coarsening and recrystalization) during non-isothermal. The finer size and the plate-like morphology of the precipitated carbides along with the partial recovery of the lath structure observed after non-isothermal tempering strongly influenced the softening behaviour of DP steel. The chemical analysis of θ-carbides through extraction replicas for three different DP steels revealed that the chemistry of the carbides is inherited from the parent DP steel during non-isothermal tempering at high temperature confirming that non-isothermal tempering DP steel is predominantly controlled by carbon diffusion.

Stochastic sampling methods are ubiquitous in statistical mechanics, Bayesian statistics, and theoretical computer science. However, when the distribution that is being sampled is multimodal, many of these techniques converge slowly, so that a great deal of computing time is necessary to obtain reliable answers. Parallel and simulated tempering are sampling methods that are designed to converge quickly even for multimodal distributions. In this thesis, we assess the extent to which this goal is acheived.We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, meaning that it converges quickly. These conditions are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models in R^M as M increases, and for the mean-field Ising model.We also obtain upper bounds on the convergence rates of parallel and simulated tempering, yielding a single set of sufficient conditions for torpid mixing of both techniques. These conditions imply torpid mixing of parallel and simulated tempering on a normal mixture model with unequal covariances in $\R^M$ as $M$ increases and on the mean-field Potts model with $q \geq 3$, regardless of the number and choice of temperatures, as well as on the mean-field Ising model if an insufficient (fixed) set of temperatures is used. The latter result is in contrast to the rapid mixing of parallel and simulated tempering on the mean-field Ising model with a linearly increasing set of temperatures. / Dissertation

The Markov Chain Monte Carlo (MCMC) method has been widely used in practice since the 1950's in areas such as biology, statistics, and physics. However, it is only in the last few decades that powerful techniques for obtaining rigorous performance guarantees with respect to the running time have been developed. Today, with only a few notable exceptions, most known algorithms for approximately uniform sampling and approximate counting rely on the MCMC method. This thesis focuses on algorithms that use MCMC combined with an algorithm from optimization called simulated annealing, for sampling and counting problems. Annealing is a heuristic for finding the global optimum of a function over a large search space. It has recently emerged as a powerful technique used in conjunction with the MCMC method for sampling problems, for example in the estimation of the permanent and in algorithms for computing the volume of a convex body. We examine other applications of annealing to sampling problems as well as scenarios when it fails to converge in polynomial time. We consider the problem of randomly generating 0-1 contingency tables. This is a well-studied problem in statistics, as well as the theory of random graphs, since it is also equivalent to generating a random bipartite graph with a prescribed degree sequence. Previously, the only algorithm known for all degree sequences was by reduction to approximating the permanent of a 0-1 matrix. We give a direct and more efficient combinatorial algorithm which relies on simulated annealing. Simulated tempering is a variant of annealing used for sampling in which a temperature parameter is randomly raised or lowered during the simulation. The idea is that by extending the state space of the Markov chain to a polynomial number of progressively smoother distributions, parameterized by temperature, the chain could cross bottlenecks in the original space which cause slow mixing. We show that simulated tempering mixes torpidly for the 3-state ferromagnetic Potts model on the complete graph. Moreover, we disprove the conventional belief that tempering can slow fixed temperature algorithms by at most a polynomial in the number of temperatures and show that it can converge at a rate that is slower by at least an exponential factor.