Energy-based model of the Garofalo equation

Abstract

The determination of deformation resistance was conducted using a DIL805A/D quenching dilatometer equipped with a hydraulic unit, enabling compression tests during high-temperature forming at specified strain rates. Deformation resistance was experimentally defined for a 5x5 testing matrix, covering deformation temperatures (800, 900, 1000, 1100, and 1200 °C) and strain rates (0.001, 0.01, 0.1, 1, and 10 s⁻¹). Boron-alloyed steel, also known as BCT steel, was used as the experimental material. The Garofalo equation was employed to evaluate the experimental measurements of deformation resistance. This equation describes the hot metal forming process, where deformation resistance is a function of strain rate and temperature. The material constants of the Garofalo equation were determined based on peak stress values obtained from individual deformation curves. The technological process of metal forming is defined by three parameters: strain rate, deformation temperature, and strain level. The Garofalo equation does not include the last parameter, strain level, as an independent variable. Therefore, the Garofalo equation was modified into a strain-dependent model by transforming the material constants into functions of strain. Each material constant was expressed as an n-th degree strain polynomial. In this manner, the third independent variable, strain level, was introduced into the Garofalo equation. To improve the correlation between measured and calculated data, the degree of the strain polynomials was increased. Some publications have utilised strain polynomials up to the 14th degree; however, such a model requires up to 60 material constants. This paper presents the transformation of the Garofalo equation into an energy-based model. The core of this transformation lies in expressing the activation energy constant as a function of strain rate, temperature, and strain level. The material constants Alpha, n, and C remain unchanged, retaining their original meaning as defined by Garofalo. The activation energy is defined by 14 material constants. Together with the remaining three constants, a total of 17 material constants sufficiently define the incorporation of the strain level into the Garofalo equation. A 3D visualisation of the energy model of the Garofalo equation showed that this equation has an extremum, a global maximum of deformation resistance.