Hollomonligningen

Hollomonligningen, also known as the Hollomon equation, is a mathematical relationship used to describe the effect of temperature on the hot workability of metals. It was developed by John H. Hollomon in the mid-20th century. The equation empirically relates the true stress required to achieve a certain strain rate at a given temperature to the processing temperature.

The Hollomon equation is typically expressed in the form: $\sigma = K \epsilon^n$, where $\sigma$ is the true stress, $\epsilon$ is the true strain, and $n$ is the strain hardening exponent. While this is the original form, in the context of hot workability, it's often modified to include temperature effects. A common form that incorporates temperature is $\dot{\epsilon} = A (\sinh(\alpha \sigma))^n \exp(-Q/RT)$, where $\dot{\epsilon}$ is the strain rate, $\sigma$ is the true stress, $A$, $\alpha$, and $n$ are material constants, $Q$ is the activation energy for hot deformation, $R$ is the universal gas constant, and $T$ is the absolute temperature. This latter form, often referred to as a hyperbolic sine law, is more representative of the temperature-dependent behavior observed in hot working.

The Hollomon equation and its temperature-dependent modifications are valuable tools for engineers in the field of materials processing. They help predict the forces required for deformation processes like forging, rolling, and extrusion at elevated temperatures. Understanding these relationships allows for the optimization of processing parameters to achieve desired material properties and minimize defects. The equation provides a simplified model that captures the essential aspects of how temperature influences the plastic behavior of metals under deformation.