## 1 Introduction  
Thermomechanical processing, used interchangeably in this paper as hot working, hot forming, or hot deformation, has remained one of the oldest and most prominent processing techniques for shaping semi-finished or finished metallic components for a wide range of applications [1]. Rolling, forging, extrusion, wire drawing, and sheet metal forming are prominent examples of thermomechanical processing techniques [2]. Apart from component forming, the most important advantage of thermomechanical processing is its opportunity for microstructural control [1; 2]. Hence, metallurgists can manipulate processing variables to achieve targeted microstructural features required to improve bulk and surface properties for optimal in-service performance [2]. Depending on the thermomechanical processing technique used, a wide range of process parameters are involved, but the key parameters that determine the response of materials to thermomechanical processing are strain rate, strain, deformation temperatures, and initial microstructure [1; 2]. Flow stress, the primary response of metallic alloys to imposed hot working parameters, is presented as true stress-true strain data [3]. Consequently, analysis of the trends of the true stress-true strain curves was the foremost method used to understand the hot working behavior of metallic alloys. However, this approach is only suggestive and cannot provide a convincing explanation of the physical mechanisms controlling hot working processes [4]. The secondary method that follows includes constitutive analysis or processing maps [2]. The constitutive analysis of flow stress follows either a phenomenological or physical approach depending on the prior information and the objective of the analysis [5]. For example, phenomenological constitutive analysis requires fewer constants and can be used to predict flow stress. However, it is not very effective in describing the mechanisms controlling the hot working process [6]. Although some authors attempted to apply some physical meaning to the phenomenological equation, which was successfully implemented on steel [6; 7], the modified model could not effectively describe the flow behavior of titanium alloys, especially those with a complex initial microstructure. [PERSON] et al. [5] comprehensively reviewed the different constitutive flow stress models. Physical constitutive models are quite reliable in predicting flow stress and explaining the physical mechanisms driving deformation processes, but they require prior knowledge of the material and lots of physical constants must be derived for them to be effective [5; 6; 7]. Therefore, using physical constitutive models to describe the flow stress for newly developed metallic alloys might be challenging. Additionally, the complexity of physical models has made them unattractive to researchers and experts in the metalworking sector. The processing map, which started in its simplistic form as the Raj map, is now based on dynamic materials models and extremum principles of irreversible thermodynamics [2; 8]. Researchers use this map extensively to identify dominant mechanisms driving deformation processes and optimize the hot working process. Although it cannot be used to predict flow stress, its versatility in establishing the optimum combination of hot working parameters for microstructural control has been well exploited in the metalworking industry. One key limitation of processing maps is the need for microstructural validation of its prediction because the instability criterion, based mainly on the extremum principle of irreversible thermodynamics, is not always accurate. Despite [PERSON] et al. 's [9] recent modification of the instability criterion, microstructural validations of the optimum and unsafe deformation regions are still required. It is worth mentioning that the validity of the secondary method heavily depends on the accuracy of the flow stress obtained from experimental testing.