For effective machining modelling, a comprehensive constitutive model is needed to capture complex strain hardening and dynamic strain aging in carbon steels during deformation under high plastic strains, strain rates, temperatures, and heating rates. A novel material model was developed for hypo-eutectic carbon steels that considers the effect of carbon content on strength, strain hardening and dynamic strain aging. This model was calibrated using data obtained with a rapidly-heated compression Kolsky bar experiment and then used to simulate orthogonal cutting tests on AISI 1018 and 1045 steels. A Johnson-Cook material model, calibrated using the same Kolsky bar data, was also used to simulate the cutting tests. The new model is briefly described, and the simulation results obtained for each model are compared against the test data. During this exercise, it became clear that additional data were needed at large plastic strains (> 1) to properly calibrate these material models and to investigate their relative utility for machining simulations, particularly in terms of their strain hardening behavior at large strains. A shear compression specimen (SCS) geometry was investigated to obtain dynamic data at large strains, and preliminary results are presented.