Modelling hot flow stress during grain refinement operations of fcc metals has largely included the use of an Avrami type equation to describe the decrease in stress due to Dynamic Recrystallization (DRX). However when refining large-grained copper, the processing temperatures and strain rates often produce a multi peak behaviour, which is not predictable by an Avrami equation alone. If an initial grain size, D0, is greater than the stable dynamically recrystallized grain size, Drex, which is a function of the Zener-Hollomon Parameter, Z, then the material will tend to refine. However if the current the Zener-Hollomon value, given by current temperature and strain rate conditions, is lower than a critical value, Zc, which depends on D0, then a multi peak stress behaviour is expected while refining. The latter Relative-Grain-Size model (i.e. the D0-Zc and Drex-Z relationships plotted on the same log-log graph) is a practical model that allows determination of whether a material will grain coarsen or refine and whether the dynamic recrystallization behaviour will be monotonic or with multi peaks. The present authors devised a dynamic recrystallization algorithm to measure the stress due to the diminishing initial grain volume and to measure the correction stress due to recrystallizing grains. Analysis on the hot (600°C-950°C) compression data of a 99.9% pure copper inductively lead to the use of an Avrami type equation to describe the stress contribution produced by the deformation of the remaining initial grain volume and a damped cosine equation to describe the stress contribution of the synchronized volume of new grains. This work discusses the experimental evidence and analytical findings that inductively support the mathematical description of the stress-strain curve given by a Damped Cosine Avrami Model for discontinuous DRX.