Carlos A. Hernández

General expression of the Zener-Hollomon parameter as a function of the chemical composition of low alloy and microalloyed steels

Using torsion tests the Zener-Hollomon parameter has been determined in a selection of 18 steels with compositions appropriate for the study of the influence of each alloying element (C, Mn, Si, Mo, Ti, V, Nb) on the Zener-Hollomon parameter (ϵexp(QRT) = A(sinh ασp)n). It is demonstrated that all the alloying elements influence, to a greater or lesser extent, the activation energy (Q). A rise in the content of any alloy was found to increase the activation energy, except in the case of carbon which has the opposite effect. An expression is given for Q as a function of the content of each alloying element and the second side of the equation is completed by determining the optimum values of α and n for all the steels, giving 0.01187 MPa−1 and 4.458, respectively. It is demonstrated that A is not a constant but is a function of the activation energy. In this way it is possible to calculate the peak stress (σp) at any temperature and strain rate for any low alloy or microalloyed steel in the austenite phase. This study brings a new dimension to the Zener-Hollomon parameter and potentially improves its applications, for example in the calculation of stress-strain curves.

Modelling of the dynamic recrystallization of austenite in low alloy and microalloyed steels

Using torsional tests in the austenite phase, the dynamic recrystallization of a selection of low alloy and microalloyed steels was studied and Avrami`s equation was modelled. The model is based on the experimental determination of flow curves and their subsequent modelling, making it possible to calculate the recrystallized fraction (X{sub d}) as a function of all the variables which intervene in hot deformation: temperature, strain rate, austenite grain size and the chemical composition of the steel. The influence of the first three variables is quantified using the Zener-Hollomon parameter where the activation energy is expressed as a function of the content of each alloy. The start of dynamic recrystallization was determined by regression, finding a value of 0.95{epsilon}{sub p}. In testing conditions all the elements were found in solution in the austenite, except Ti which was found partially precipitated. The results of these tests indicate that C, Si (low content), Mn and V have hardly any influence on the start of recrystallization while Mo, Ti and especially Nb delay it. Finally, the dynamic recrystallization kinetics are illustrated through the study of the microstructure during deformation.

Modelling austenite flow curves in low alloy and microalloyed steels

Abstract A model has been developed to predict the austenite flow curves of low alloy and microalloyed steels. The model consists basically of two expressions for stress, as a function of strain, temperature, strain rate and the chemical composition of the steel. The first predicts the hardening and dynamic recovery region and the second predicts the softening caused by dynamic recrystallization, the algebraic sum of both expressions predicting the complete flow curve. The models different parameters are a function of the dimensionless parameter Z A of Sellars and Tegarts equation, which in turn has been modelled not only as a function of temperature and strain rate but also as a function of the chemical composition. In this way one single model may be applied to any hot deformed steel whose composition is the same as or similar to those studied.

The influence of chemical composition on peak strain of deformed austenite in low alloy and microalloyed steels

Abstract Using hot torsional tests, the influence of the most common elements in low alloy steels (C, Mn, Si, Mo) and in microalloyed steels (Ti, V, Nb) on peak strain has been studied. At the temperatures (900, 1000 and 1100°C) and strain rates (0.544, 1.451, 3.628 and 5.224 s −1 ) at which the tests were carried out all the elements remained in solution during deformation with the exception of titanium which was in part previously precipitated. In these conditions, the results indicate that C, Si and Mn have hardly any influence on the value of peak strain ( ϵ p ) while Mo, V, Ti and particularly Nb considerably increase its value. The study has been completed with the modelling of ϵ p as a function of the Zener-Hollomon parameter and the austenite grain size for all the steels studied, showing the quantitative influence of the different alloying elements.

ON THE TAYLOR SPECTRUM OF LEFT-RIGHT MULTIPLIERS

The Taylor spectrum of a mixed pair of multiplication operators is determined on an ultraprime Banach algebra. Suppose A is a complex Banach algebra, with identity 1 and invertible group A−1 (more generally, much of what we have to say may make sense in an additive category A); then we can define various kinds of “joint spectrum” for systems of elements in A: Definition 1. Write σ A (A ) = {a ∈ A : 1 / ∈ n ∑ j=1 Aaj} and σ A (A) = {a ∈ A : 1 / ∈ n ∑

Influence of vanadium on the static recrystallization of austenite in microalloyed steels

Torsion tests were conducted to study the static recrystallization of three microalloyed steels manufactured by electroslag remelting (ESR) with different percentages of vanadium, 0.043%. 0.060% and 0.095%, respectively, and approximately equal percentages of the other alloyforming elements. It was seen that, in contrast to niobium, dissolved vanadium has no influence on the activation energy. The influence only becomes notable when the precipitates start to form and the activation energy increases rapidly, thus inhibiting recrystallization. The critical temperature at which inhibition commences was measured as a function of the vanadium content and the deformation performed, and in all cases it was lower than the dissolution temperature deduced from the solubility products for nitrides, mainly because the testing conditions lacked thermodynamic equilibrium. Finally, a comparison was made of the microstructures obtained in two commercial steels, namely a C-Mn type steel and a vanadium microalloyed steel. Both were subjected to the same cycle of successive deformations, whose temperatures were lower than the critical temperature. After the last deformation, a much harder austenite was obtained in the microalloyed steel than in the C-Mn steel.

Synthesis of Ranolazine Derivatives Containing the (1S,4S)-2,5-Diazabicyclo[2.2.1]Heptane Moiety and Their Evaluation as Vasodilating Agents

Two diazabicyclic analogues of ranolazine, (S,S,S)‐5 and (S,S,R)‐5, and their epimeric mixture were synthesized. Furthermore, their vasomotor effects on rat aorta rings precontracted with phenylephrine were analyzed. These compounds showed vasodilating effects significantly greater than ranolazine. The vasodilating activities of these analogues have two components, one that depends on the endothelium, due to the release of NO, and another one due to a direct effect on the vascular smooth muscle. The compounds [(S,S,S)(S,S,R)]‐5 and (S,S,R)‐5 induce, in a manner similar to ranolazine, the release of a prostanoid from the cyclooxygenase pathway, whose vasoconstrictor effect is masked by the predominant vasodilation induced by these compounds.

Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

Comparison between WLS and Kalman Filter method for power system static state estimation

Traditional state estimators, which are based on steady state system model, cannot capture the time-history data. The problem of state estimation combined with multiple sets of measurements is posed in a Kalman Filtering scheme, using a discrete-time model. In this paper, the power system state estimation process, based on Kalman Filtering techniques is discussed; an IEEE 6-bus test system is used to compare the performance with the Weighted Least Square (WLS) method.