Constitutive Equations For Hot Working Of Metals

Constitutive Equations for the Rate-Dependent Deformation of Metals at Elevated Temperatures

Introduction

The mechanical behavior of metals at elevated temperatures is a complex phenomenon that involves a number of competing physical mechanisms. These mechanisms include dislocation motion, grain boundary sliding, and diffusion. The relative importance of these mechanisms depends on the temperature, the strain rate, and the microstructure of the metal. Accurate constitutive equations that can model the behavior of metals under these conditions are essential for the design and analysis of high-temperature engineering components.

Background

The first constitutive equations for the rate-dependent deformation of metals were developed in the early 20th century. These equations were based on the assumption that the deformation was caused by the motion of dislocations. However, these equations were not able to capture the complex behavior of metals at elevated temperatures. In the 1960s, a new class of constitutive equations was developed that was based on the concept of internal variables. These equations were able to capture a wider range of behavior and have been widely used since then.

Recent Developments

In recent years, there has been a growing interest in the development of constitutive equations that can capture the behavior of metals under extreme conditions. These conditions include very high temperatures, very high strain rates, and very large strains. The development of these equations is a challenging task, but it is essential for the design and analysis of advanced engineering components.

Conclusion

Constitutive equations for the rate-dependent deformation of metals at elevated temperatures are essential for the design and analysis of high-temperature engineering components. The development of these equations is a challenging task, but it is essential for the design and analysis of advanced engineering components.