Novel extended C-m models of flow stress for accurate mechanical and metallurgical calculations and comparison with traditional flow models

Here, we developed novel extended piecewise bilinear power law (C-m) models to describe flow stresses under broad ranges of strain, strain rate, and temperature for mechanical and metallurgical calculations during metal forming at elevated temperatures. The traditional C-m model is improved upon by formulating the material parameters C and m, defined at sample strains and temperatures as functions of the strain rate. The coefficients are described as a linear combination of the basis functions defined in piecewise patches of the sample strain and temperature domain. A comparison with traditional closed-form function flow models revealed that our approach using the extended piecewise bilinear C-m model is superior in terms of accuracy, ease of use, and adaptability; additionally, the extended C-m model was applicable to numerical analysis of mechanical, metallurgical, and microstructural problems. Moreover, metallurgy-related values can be calculated directly from the flow stress information. Although the proposed model was developed for materials at elevated temperatures, it can be applied over a broad temperature range.