Modeling and Prediction of Hot Deformation Flow Curves
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HOT deformation processing plays an important role in the industry for the production of materials with required mechanical properties while maintaining the production costs as low as possible. To achieve this goal, the parameters of the forming process must be controlled carefully. The understanding of the microstructural behavior of the material under consideration is therefore required, together with the constitutive relation describing material flow. The modeling of hot flow stress and the prediction of flow curves are important in metal-forming processes such as rolling and forging from the mechanical and metallurgical standpoints because any feasible mathematical simulation needs accurate flow description. As a result, considerable research has been carried out to model the flow stress of metals and alloys.[1] Many of these equations are considered as phenomenological models, which mathematically represent the dependence of flow stress on deformation conditions based on empirical data. Some other models are considered to be physically based. They account for the physical aspects of the material behaviors. Most of them are involved in the theory of thermodynamics, thermally activated dislocation movement, and kinetics of slips. Compared with the phenomenological descriptions, they allow for an accurate definition of material HAMED MIRZADEH, PhD Student, is with the Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran. Contact e-mail: [email protected] JOSE MARIA CABRERA, Professor, is with the Departamento de Ciencia de los Materiales e Ingenierı´ a Metalu´rgica, ETSEIB, Universitat Polite´cnica de Catalunya, 08028 Barcelona, Spain, and also with the Fundacio´ CTM Centre Tecnologic, Av. Bases de Manresa 1, 08242 Manresa, Spain. ABBAS NAJAFIZADEH, Professor, is with the Department of Materials Engineering, Isfahan University of Technology. Manuscript submitted January 11, 2011. Article published online July 27, 2011 108—VOLUME 43A, JANUARY 2012
behavior under wide ranges of loading conditions by some physical assumptions and a larger number of material constants. In the following sections, the most widely used methods that are related to the current study are reviewed. The simplest and most widely applied method in the literature is the modeling of flow stress using an expression which relates the Zener-Hollomon parameter (Z) to the flow stress (r)[2]: Q Z ¼ e_ expð Þ ¼ fðrÞ RT
½1
In this equation, the Zener-Hollomon parameter is the temperature-compensated strain rate and Q is the activation energy of deformation. It was shown by Sellars and Tegart[3,4] and others,[5–9] using the hyperbolic sine function suggested by Garofalo,[10] that hot working can be considered as a thermally activated process, and it can be described by strain rate equations similar to those employed in creep studies. Based on these early works, the Z parameter can be related to the flow stress in different ways[11]: The power law (Eq. [2]) at relatively low stresses, exponential law (Eq. [3]) at high stresses
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