Influence of Different Interpolation Techniques on the Determination of the Critical Conditions for the Onset of Dynamic Recrystallisation

Abstract

Accurate modeling of dynamic recrystallization (DRX) is highly important for forming processes like hot rolling and forging. To correctly predict the overall level of dynamic recrystallization reached, it is vital to determine and model the critical conditions that mark the start of DRX. For the determination of the critical conditions, a criterion has been proposed by Poliak and Jonas. It states that the onset of DRX can be detected from an inflection point in the work hardening rate as a function of flow stress. The work hardening rate is the derivative of the flow stress with respect to strain. Flow curves are in general measured at a certain sampling rate, yielding tabular stress-strain data, which are per se not continuously differentiable. In addition, inevitable jitter occurs in measured flow curves. Hence, flow curves need to be interpolated and smoothed before the work hardening rate and further derivatives necessary for evaluating the criterion by Poliak and Jonas can be computed. In this paper, the polynomial interpolation originally proposed by Poliak and Jonas is compared to a new approach based on radial basis functions using a thin plate spline kernel, which combines surface interpolation of various flow curves and smoothing in a single step. It is shown for different steel grades that the interpolation method used has a crucial influence on the resulting critical conditions for DRX, and that a simultaneous evaluation by surface interpolation might yield consistent critical conditions over a range of testing temperatures.