Hollomon Equation for Strain Hardening

The Hollomon equation provides a simple yet effective mathematical model for the phenomenon of strain hardening (or work hardening), where a ductile material becomes stronger and harder as it is plastically deformed. The strain-hardening exponent, ‘n’, is a key material property derived from this equation. It typically ranges from 0 (for a perfectly plastic solid) to 1. A higher ‘n’ value indicates a greater capacity for strain hardening. For many metals, ‘n’ is numerically equal to the true strain at the point of ultimate tensile strength. The strength coefficient, ‘K’, represents the true stress at a true strain of 1.0. This equation is valid only in the plastic region, after yielding and before necking begins. It is determined by plotting true stress versus true strain on a log-log scale; the data in the plastic region should form a straight line. The slope of this line is ‘n’, and the intercept at \(\epsilon_t = 1\) is ‘K’. While it is an empirical model and doesn’t capture all complexities of plastic deformation (like the Bauschinger effect), its simplicity and utility have made it a standard tool in materials science and mechanical engineering for analyzing and predicting the response of metals to plastic deformation.