Flow Curve Determination for Metal under Dynamic Recrystallization Using Inverse Analysis

Abstract

A new method for determining flow curves of hot metal under dynamic recrystallization is proposed in this paper. Thermomechanical finite element analysis of a tool and a workpiece under hot compression is used to evaluate the upsetting force obtained by an experiment, as a function of the distributed flow stress of the workpiece. In order to compensate the effect of inhomogeneous distributions of deformation and temperature on the flow curve, inverse analysis for calculating coefficients in a flow stress curve under dynamic recrystallization is coupled with the thermomechanical finite element analysis. The discrepancy in upsetting force between the experiment and thermomechanical finite element analysis is used as an error estimator in the inverse analysis. A new regression formula of the flow curve, which includes four independent parameters, is introduced. It can express the flow curve of hot metal under dynamic recrystallization as well as dynamic recovery and work hardening. Also, four independent parameters included in the proposed formula have clear physical meanings. The proposed method is applied to the hot compression test of plain carbon steel at elevated temperatures. Flow curves are successfully determined for diversified conditions of strain rate and forming temperature. From the determined parameters of the flow curve by the proposed inverse analysis method, it can be concluded that 1) the critical strain for the onset of dynamic recrystallization is dependent on strain rate as well as temperature, 2) the stain rate sensitivity of m ¼ 0:13 is acceptable for plain carbon steel under testing conditions, and 3) the temperature sensitivity A is approximately 3000-3600 [K À1 ]. Through investigation, it has become clearer that an accurate flow curve can be determined by the proposed method. In addition to a quantitative description of the flow curve as a function of strain, strain rate and temperature, metallurgical parameters such as the critical strain for the onset of dynamic recrystallization and steady-state stress could also be estimated directly by the proposed method.

Regression Method of Determining Generalized Description of Flow Curve of Steel under Dynamic Recrystallization

“…The Arbitrary Lagrangean Eularian (ALE) scheme is used in the thermal analysis of the tool, 14) because the coordinate of nodal points embedded in the tool moves towards the radial direction due to the plastic flow of the test piece during a hot compression test. Then, the following equation is applied to thermal analysis.…”

“…14) In the present research, the electromagnetic analysis of induction heating during heating and a hot compression test is newly introduced in thermomechanical FEM in the inverse analysis, with the aim of realizing a more accurate estimation of the inhomogeneous temperature field of a test piece. From the accurately determined coefficients of the flow curve corresponding to the wide ranges of temperature and strain rate, a method of developing a generalized description of a flow curve is presented.…”

“…Strain rate and temperature distribute across the cross section of the test piece, because of the inhomogeneous distributions in plastic deformation and temperature. Variations, or errors, in flow stress resulting from these distributions are compensated in the inverse analysis of the flow curve, 14) which enables us to obtain a flow curve with ideal uniaxial deformation at a constant temperature. …”

“…Table 5 summarizes the coefficients in the flow curve obtained by the inverse analysis, using the initial guess of rate sensitivity m 0 ϭ0.13 and temperature sensitivity A 0 ϭ 3400. 7,14) 4.2. Regression of Rate Sensitivity and Temperature Sensitivity Equation (11) As can be seen in Table 5, work hardening coefficients n are scattered, and the clear tendency of n to vary with temperature and strain rate is not observed.…”

Rolling Technology and Theory for the Last 100 Years: The Contribution of Theory to Innovation in Strip Rolling Technology

“…As for a numerical analysis technique to control the internal structure by the processing process, [139][140][141][142][143] Yanagimoto and others showed an acquisition method of material genome based on the results of compression tests. It is the method to identify the material genome which is necessary to analyze the internal structure by obtaining the followings from ① to ⑤: ① a load-displacement curve by one step compression tests, ② one axis compression flow stress curve (at constant strain velocity and temperature) by the reverse analysis of the load-displacement curve, ③ a loaddisplacement curve by two steps compression tests, ④ one axis compression flow stress curve (at constant strain velocity and temperature) by the reverse analysis and the softening rate, ⑤ the grain size by the quenching structure freeze tests.…”