Proposal for a computational method to solve the Zener- Hollomon equation (Garofalo)

Abstract

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.