Modernization of the Grossmann-Asimow Quench Severity Framework: Error Correction, Parametric Sensitivity, and PDE-Constrained Optimization

Abstract

This study presents a digital modernization and critical re-evaluation of the classical Grossmann–Asimow steel hard-enability model using an open-source 1D transient heat equation solver implemented in MATLAB. Beyond reproducing the historical 1940 master charts, the open code simulates complex profiles with temperature-dependent thermophysical properties ( ρ ( T ), C _p ( T ), k ( T )) and non-linear experimental heat transfer coefficients (HTC _exp ). Direct algorithmic superposition reveals that Grossmann’s historical H = 0,01 in ^(–1) curve corresponds precisely to a modern numerically solved H = 0,02 in ^(–1) trajectory, exposing a legacy mislabeling that has persisted in standards for decades. Parametric sensitivity analyses show that a constant thermal diffusivity ( α = 0,009 in ² /s) introduces minimal error across 875 °C to 400 °C, validating Grossmann’s steady-state assumption. Furthermore, cumulative metrics ( t _0,5 ,