Zener-Hollomon Equation Research Articles

The high temperature flow behavior modeling of AZ81 magnesium alloy considering strain effects

In the field of deformation process modeling, constitutive equations are invariably used as a calculation basis to estimate the materials flow responses. Accordingly, in the present study, a constitutive analysis has been conducted on the AZ81 magnesium alloy employing experimental stress–strain data obtained from isothermal hot compression tests. These tests had been done in the temperature range of 250–450°C under strain rates of 0.003, 0.03 and 0.3s−1. The effects of the temperature and strain rate on hot deformation behavior have been expressed in terms of an exponent-type Zener–Hollomon equation. Furthermore, the influence of strain has been included in the constitutive equation by considering its effect on different material constants. Consequently, a model to predict the high-temperature flow behavior of AZ81 magnesium alloy has been established. The true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results, thereby confirming the validity of the developed constitutive relation.

Study on the behavior of medium carbon vanadium microalloyed steel by hot compression test

This article investigates the hot working behavior of medium carbon vanadium microalloyed steel by hot compression tests over the temperature range of 850–1100 °C and strain rate range of 0.001–0.5 s −1 to strain of 0.8. In this study, the general constitutive equations were used to determine the hot working constants. The peak stress ( σ P) and strain ( ɛ P) for initiation of dynamic recrystallization (DRX) at different temperatures and strain rates were calculated. The power law, exponential and hyperbolic sinusoidal types of Zener–Hollomon equations were used to determine the hot deformation activation energy ( Q). The results suggested that the highest correlation coefficient was achieved for the hyperbolic sine law for the studied material. The magnitude of hot deformation activation energy ( Q) was obtained as 319.910 kJ/mol. The classical single peak DRX was observed in most of temperatures and strain rates. However, for temperature of 1100 °C and strain rates of 0.001 s −1, 0.01 s −1, and also for temperature of 950 °C and strain rate of 0.001 s −1 the multiple peak dynamic recrystallization (MDRX) was observed, which showed that the ‘recrystallization’ was an observed strain rate behavior.

Propuesta de un método de ordenador para resolver el ajuste a la ecuación de Zener-Hollomon (Garofalo)

An integrated computational method to solve the Zener-Hollomon equation has been developed by the authors. This method solves the fitting problem of the equation of Zener-Hollomon for wide ranges of applied stress, strain rate and work temperature by means of the progressive application of three kinds of algorithms. In the first place a program, by means of a reiterated linear regression by planes, allows to get some values that will be later the initial values of a second block of algorithms. It permits also to purify the experimental data set. The second block of algorithms carries out a fitting by nonlinear least squares using a variation of the modified Gauss-Newton method. In the third place a group of programs is chained that permit iterate starting by the solution of the previous program approaching (if it is necessary) line by line in R2 until the optimum value is reached. All this with a support of statistical analysis for they determine the accuracy of each step, of the data, of the residuals and of the last fitting reached.

Influence of titanium on the static recrystallization of a medium carbon microalloyed steel

Static recrystallization kinetics of three medium carbon steels, microalloyed with vanadium and titanium (titanium varied from 0.003 to 0.039% in weight), were studied by hot torsion test simulation. A higher recrystallization time was observed in the steel with 0.019 wt% Ti. This difference in recrystallization time was checked by metallographic observations and mechanical softening. This time shift implies different activation energies, which were calculated by the time needed to obtain a 50% recrystallized structure and also by solving the Zener-Hollomon equation. Evolution of the kinetics of recrystallization as a function of temperature was also studied. In addition, the critical allowable temperature for a fully recrystallized structure was investigated.

Structure-thermomechanical parameters relationship and Zener-Hollomon equation for two vanadium microalloyed steels

Hot torsion tests were conducted to simulate forging processes in two vanadium microalloyed steels, types 40MVS6 and 30MSiV62, varying both the conditions of test temperature and time as well as the strain and strain-rate conditions, in order to obtain final results comparable to the classic Q+T steels, direct from the forge. The Zener-Hollomon equations were also calculated, indicating the conditions of application which theoretically permit the prediction of forging parameters, in accordance with the needs or possibilities of an industrial plant.