Empirical or semi-empirical stress-strain relationships are of limited applicability because (i) they require a large number of constants to represent the effect of process variables, (ii) they are not able to adequately describe the typical hot deformation characteristics i.e., strain hardening at lower strains and steady state flow stress at higher strains, and (iii) they are not able to provide reliable extrapolation. In the present study, flow curves for hot deformation of a medium carbon steel in compression were obtained using a computer controlled thermo-mechanical simulator. The flow stress data were analyzed using three Arrhenius-type equations, each representing the flow stress in terms of strain rate and temperature at different strain levels. It was found that the hyperbolic-sine equation represented the data very well; each of the different activation parameters of this equation varied systematically with strain, and could be satisfactorily described using a power relationship. Using these proposed relationships the flow stress can be described in terms of the process variables—strain, strain rate and temperature—in an explicit fashion of use in finite-element analysis of hot deformation processes.

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