Papers by Author: Paulo Rangel Rios

Abstract: In recent papers Rios and Villa resorted to developments in stochastic geometry to revisit theclassical KJMA theory and generalize it for situations in which nuclei were located in space accordingto both homogeneous and inhomogeneous Poisson point processes as well as according to Materncluster process and surface and bulk nucleation in small specimens. Rigorous mathematical methodswere employed to ensure the reliability of the new expressions. These results are briefly described.Analytical expression for inhomogeneous Poisson point process nucleation gives very good agreementwith Cellular Automata simulations. Cellular Automata simulations complement the analyticalsolutions by showing the corresponding microstructural evolution. These new results considerablyexpand the range of situations for which analytical solutions are available.

Abstract: The theoretical description of grain growth was based for many years on the so-calledspherical model. The spherical model represents a polyhedral grain with N faces and a volume, V ,by a sphere with an equal volume having the equivalent grain radius, R. That model leads to severalinteresting results concerning normal and abnormal grain growth as well as grain size distribution.Nevertheless, representation of grains by spheres entails a fundamental limitation: namely, all topo-logical information of the polyhedral grain is forsaken. The rich variety of grain shapes occurringin three-dimensional polycrystalline networks, however, makes their energetic and kinetic analysesextremely difficult. To simplify analyses of isotropic polycrystals, average N-hedra and generalizedN-hedra ANHs or GNHs .N D 3; 4; 5;1/ were created as a set of regular polyhedra, consisting ofN identical faces that act as topological proxies for analyzing irregular grains containing N mixedfaces. The adoption of ANH/GNH as representations of polyhedral grains led to further progress inour understanding of grain growth, particularly those aspects related to topological behavior. This pa-per summarizes some recent advances of representing polyhedral grains by ANHs/GNHs rather thanby spheres.

Abstract: In a recent work, the present authors developed a new formal kinetics methodology suitablefor the situation in which transformations take place simultaneously or sequentially. In this work themain results of such a methodology are briefly presented in a simplified form. It is shown here howthis new methodology may be used for obtaining expressions for simultaneous or sequential reactionsfrom models of the kinetics of each reaction in isolation. It is also shown how one may extract theo-retical information from the experimentally measured quantities. Moreover, the methodology is usedto analyse published data on the recrystallization kinetics of IF steels.

Abstract: Grain boundary pinning by particles is widely used to prevent grain growth during heat treatment in a variety of commercial alloys. Its practical relevance is matched by a considerable amount of theoretical work that has been devoted this problem. A key issue of boundary pinning is the particle/interface interaction mechanism and its associated pinning force. According to Ashby et al. an interface may interact with a particle in two ways: either it goes through the particles or, more usually, bends round and envelopes the particle. Based on these mechanisms one may derive quantitative expressions relating the characteristics of the particle dispersion and a critical or limiting grain radius. Thus, Zener expression assumes that the interface goes through the particles whereas Rios expression assumes that the interface bends round and envelopes the particle. Both the mechanisms and the resulting expressions are discussed here in detail and compared with available experimental data.

Abstract: During the life cycle of an API steel there are occasions when it will be submitted to thermal cycle. For tubes produced by the UOE process, for the oil and gas industry, severe thermal cycles occur during the welding procedure and when the tube requires hot induction bending. It is therefore of interest to learn about the influence of different cooling rates on the microstructure of these steels, produced by TMCP (Thermomechanical Controlled Process), since these changes can be reflected in a variation in the mechanical properties and hence in the performance of the pipeline. In this work three steels of class API 5L X80, with additions of, Nb-Cr, Nb-Cr-Mo and Nb-Cr-Mo-V, and otherwise similar alloy content, produced by TMCP without accelerated cooling were investigated. These alloys were submitted to austenitization at 900oC for 1 hour followed by three different cooling rates of 1.5oC/s, 30oC/s, 115oC/s, in air, oil and water respectively. It is well known that the main strengthening mechanism in TMCP, which allows a simultaneous increase in strength and toughness, is the reduction of the grain size. Other mechanisms such as solid solution hardening, precipitation and increasing dislocation density also contribute. For the steels in this study, all having a similar base chemical composition and yield strength, all the different thermal cycles applied promoted a reduction in the grain size, and only for the higher cooling rate (115oC/s) were there significant observable phase transformations. The Nb-Cr-Mo-V system exhibited a higher percentage of martensite than the Nb-Cr and Nb-Cr-Mo systems.

Abstract: Theories of abnormal grain growth (AGG) in three dimensions usually approximate an abnormal grain by a sphere. The abnormal grain is then represented by its spherical equivalent grain radius. This study, by contrast, treats AGG in terms of concepts that include both the boundary curvature and the number of faces of the abnormal grain. We treat AGG for the case of pinned matrices, including the phenomena of initiation and growth kinetics. The influence of interfacial energy and mobility of the abnormal grain boundary are also discussed.

Abstract: The multiplicity and variety of grain shapes in three-dimensional polycrystalline metals makes their energetic and kinetic analyses difficult. To help simplify the analysis of isotropic polycrystals, average N-hedra (ANHs) (N=3,4,5,…∞) were created as a set of regular polyhedra, consisting of N identical faces, which act as topological “proxies” for analyzing the corresponding class of irregular grains containing mixed faces of the same number. This paper outlines a further generalization of the ANH concept that extends three-dimensional analysis to include the growth or shrinkage of a small population of grains embedded in a textured matrix.

Abstract: Alongside volume fraction, VV, and area per unit of volume, SV, the integral interface curvature per unit of volume, MV, or the average interface curvature, H, are important microstructural descriptors. For grain growth, the grain boundary curvature is of special importance because, in addition to its geometrical significance, it is also the driving force for boundary migration. Notwithstanding its importance, curvature has been seldom measured and utilized in the analysis of polycrystals. Geometrical models were derived for the average curvature of individual grains, of grain boundaries and of grain edges, as a function of the mean intercept length. These models show good agreement with curvature measurements in an Al-1mass%Mn alloy. Furthermore, this work shows how grain boundary curvature measurement can be applied to normal grain growth as well as to the effect of particles on grain boundary pinning.

Abstract: One common point amongst extant theories of abnormal grain growth (AGG) is that they treat this phenomenon in terms of the relative grain size, or grain radius, of the abnormal grains. Topological and metrical quantities of abnormal grains, such as the number of their faces, or their grain boundary curvature, are taken into account only indirectly through the grain size itself. This paper, by contrast, treats AGG in terms of concepts, that include both the boundary curvature and the number of faces of the abnormal grain. Two cases are examined: 1) AGG, in which the matrix grains are fully pinned, so normal grain growth cannot occur; 2) AGG in which the matrix grains are free to evolve, so that normal grain growth ensues simultaneously in the matrix.

Abstract: The processing of SmCo5 sintered magnets involves a post-sintering heat treatment, where the intrinsic coercivity of the magnets may increase more than one order of magnitude. Variables of the heat treatment like time, temperature and cooling rate have strong influence on coercivity. We describe a method for modeling the heat treatment, which includes microstructural features as precipitate size and 2nd phase volume fraction. The numerical solution was obtained using the Finite Volume Method to solve Fick´s second law. Experimental data like the diffusion coefficient of Sm into SmCo5 phase and the Sm-Co phase Diagram are used for the modeling.