Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data.