Duplex Stainless Steels (DSS) and Superduplex Stainless Steels (SDSS) are an important class of stainless steels because they combine the benefits of austenite and ferrite phases, resulting in steels with better mechanical properties and higher corrosion resistance. Due to these characteristics are widely employed in various industries. However, the appearance of deleterious phases in their microstructure impairs the properties of DSS and SDSS. Among the deleterious phases, the main one is the sigma phase (σ), which can be nucleated when the steel is exposed to the temperature range between 650 °C and 900 °C, reducing its toughness and resistance to corrosion. In a previous work, Fonseca and collaborators used two descriptors of the microstructural path to analyze the formation of sigma phase (σ), SV, interfacial area per unit volume between sigma phase and austenite, and <λ>, mean chord length of sigma, both in function of the VV, volume fraction of sigma, known in the literature as microstructural partial path (MP). In this work, the contiguity ratio is applied for the first time to describe the microstructural path in the study of sigma phase precipitation in SDSS. The contiguity ratio showed that the distribution of the ferrite/sigma boundaries is homogeneous. Thus, it is reasonable to infer that one has a uniform distribution of sigma phase nuclei within the ferrite. About the kinetics of sigma phase formation, the DSS can be described by the classical JMAK equation, whereas for the SDSS, the kinetics tends to follow the Cahn model for grain edge nucleation. Finally, we present the 3D reconstruction of the sigma phase in SDSS. The results demonstrate that the sigma phase nucleates at the edges of the ferrite/austenite interfaces. Moreover, the sigma phase grows consuming the ferrite, but it is not fully interconnected.

In this paper, an icosahedral non – body centered model to simulate the periodic structure of homogeneous particulate composites, by predicting the particle arrangement, is presented. This model has yielded three different variations which correspond at three different deterministic particle configurations. In addition, the concept of boundary interphase between matrix and inclusions was taken into account. Thus, the influence of particle vicinity was examined in parallel with the interphase concept on the thermomechanical properties of the overall material. Next, by the use of this model the authors derived a closed – form expression to estimate the thermal conductivity of this type of composites. To test the validity of the model, the theoretical values arising from the proposed formula were compared with other theoretical predictions obtained from several accurate formulae found in the literature and an adequate accordance was observed.

In this paper, a geometric body-centered model to simulate the periodic structure of unidirectional fibrous composites is presented. To this end, three prescribed configurations are introduced to predict in a deterministic manner the arrangement of internal and neighboring fibers inside the matrix. Thus, three different representative volume elements (RVEs) are established. Furthermore, the concept of the interphase has been taken into account, stating that each individual fiber is encircled by a thin layer of variable thermomechanical properties. Next, these three unit cells are transformed in a unified manner to a coaxial multilayer cylinder model. This advanced model includes the influence of fiber contiguity in parallel with the interphase concept on the thermomechanical properties of the overall material. Then, by the use of this model, the authors propose explicit expressions to evaluate the longitudinal and transverse thermal conductivity of this type of composite. The theoretical predictions were compared with experimental results, as well as with theoretical values yielded by some reliable formulae derived from other workers, and a reasonable agreement was found.

Spatial auto-regressive (SAR) models are widely used in geosciences for spatial analyses; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of parameter and forecast estimates strongly depend on the structure of such matrices. The least squares (LS) method is the most flexible and can estimate systems of large dimensions; however, it is not consistent in the presence of multilateral (sparse) matrices. Instead, the unilateral specification of SAR models provides triangular weight matrices which allow good statistical properties to LS and enable the implementation of sequential prediction functions. In this paper we show the better performance in out-of-sample forecasting of unilateral SAR and LS with respect to multilateral and maximum likelihood (ML) methods. This conclusion is supported by extensive numerical simulations and applications to real geological data, both on regular lattice and irregular polygonal form.