Thermo-Viscoplastic Analysis

The main concern here is the analysis of plastic deformation processes in the warm and hot forming regimes. When deformation takes place at high temperatures, material properties can vary considerably with temperature. Heat is generated during a metal-forming process, and if dies are at a considerably lower temperature than the workpiece, the heat loss by conduction to the dies and by radiation and convection to the environment can result in severe temperature gradients within the workpiece. Thus, the consideration of temperature effects in the analysis of metal-forming problems is very important. Furthermore, at elevated temperatures, plastic deformation can induce phase transformations and alterations in grain structures that, in turn, can modify the flow stress of the workpiece material as well as other mechanical properties. Since materials at elevated temperatures are usually rate-sensitive, a complete analysis of hot forming requires two considerations—the effect of the rate-sensitivity of materials and the coupling of the metal flow and heat transfer analyses. A material behavior that exhibits rate sensitivity is called viscoplastic. A theory that deals with viscoplasticity was described in Chap. 4. It was shown that the governing equations for deformation of viscoplastic materials are formally identical to those of plastic materials, except that the effective stress is a function of strain, strain-rate, and temperature. The application of the finite-element method to the analysis of metal-forming processes using rigid-plastic materials leads to a simple extension of the method to rigid-viscoplastic materials. The importance of temperature calculations during a metal-forming process has been recognized for a long time. Until recently, the majority of the work had been based on procedures that uncouple the problem of heat transfer from the metal deformation problem. Several researchers have used the following approach. They determined the flow velocity fields in the problem either experimentally or by calculations, and they then used these fields to calculate heat generation. Examples of this approach are the works of Johnson and Kudo on extrusion, and of Tay et al. on machining. Another approach uses Bishop’s numerical method in which heat generation and transportation are considered to occur instantaneously for each time-step with conduction taking place during the time-step.