This paper reviews the flow behavior and mathematical modeling of various metals and alloys at a wide range of temperatures and strain rates. Furthermore, it discusses the effects of strain rate and temperature on flow behavior. Johnson-Cook is a strong phenomenological model that has been used extensively for predictions of the flow behaviors of metals and alloys. It has been implemented in finite element software packages to optimize strain, strain rate, and temperature as well as to simulate real behaviors in severe conditions. Thus, this work will discuss and critically review the well-proven Johnson-Cook and modified Johnson-Cook-based models. The latest model modifications, along with their strengths and limitations, are introduced and compared. The coupling effect between flow parameters is also presented and discussed. The various methods and techniques used for the determination of model constants are highlighted and discussed. Finally, future research directions for the mathematical modeling of flow behavior are provided.
Keywords: Johnson–Cook; constitutive modeling; elevated temperature; high strain rate; hot deformation; modified Johnson–Cook.