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

Abstract

A regression method of obtaining a generalized description of a flow curve is proposed in this paper. The flow curve of a metal at a constant temperature and a constant strain rate is precisely obtained by an inverse analysis of hot compression. To eliminate the error in the flow curve induced by the inhomogeneous distribution of temperature in the test piece, an electromagnetic analysis of induction heating is performed with thermal analysis throughout the heating and hot compression of a test piece. The coefficients embedded in the flow curve are determined by the inverse analysis associated with thermomechanical FE (Finite Element) analysis. The obtained coefficients, which cover wide ranges of hot-forming temperature and high strain rate, are regressed using the proposed regression method, and a generalized flow curve for a C-Si-Mn steel is obtained. Although the proposed regression method is demonstrated for only one type of C-Si-Mn steel, it could also be used to obtain a generalized description of a flow curve for other types of steel under dynamic recrystallization, which could be used to estimate the force characteristics of hot metals in bulk forming processes, such as forging and rolling.KEY WORDS: generalized flow curve; hot compression test; regression; inverse analysis; dynamic recrystallization.analysis of hot compression is implemented in the inverse analysis of the flow curve using the measured change in the compression force versus stroke curve. Previously, 14) the empirical relationship was applied to estimate the internal heat generation induced by induction heating, which may have resulted in the error in the flow curve obtained by the inverse analysis. Also, this empirical relationship could not be applied to induction heating during upsetting in a hot compression test.As the present investigation is aimed at presenting a generalized description of a flow curve, which could be used in the development of forming technologies, we should reduce the error in the flow curve as much as possible. Then, a new electromagnetic analysis of induction heating for estimating the nonuniform generation of internal heat is developed, which is coupled with the thermomechanical analysis of hot compression. Electromagnetic Analysis of Induction HeatingThe magnetic field induced by electric current is governed by Eqs. (1) and (2) for generalized three-dimensional problems. Here, J 0 and J e are the magnetizing current density and eddy current density, respectively. n n, Q, L L and f are the reluctivity, electric conductivity, magnetic vector potential and electric scalar potential, respectively.The cylindrical specimen is used as the test piece in this research (Fig. 1). The spiral geometry of the coil that surrounds the test piece may require a three-dimensional solution of the electromagnetic field, but we could assume that the internal heat generation induced by the electromagnetic field will exhibit rather uniform distributions in the circumferential direction, because a cylindrical specimen is used in the ...

Modeling Static and Dynamic Kinetics of Microstructure Evolution in Type 316 Stainless Steel

“…In this equation m is the strain rate sensitivity, A is the temperature sensitivity, and T 0 is the reference temperature. m and A are obtained through regression analysis of the flow curves in various temperatures and strain rates …”

“…m and A are obtained through regression analysis of the flow curves in various temperatures and strain rates. [21] The flow curve temperature sensitivity obtained is A ¼ 6175, and Equation 5 shows the regressed form of the strain rate sensitivity.…”

“…The kinetics of DRX is based on the change in dislocation density which is reflected on the coefficients of the flow curve. And, together with regression analysis, it gives a generalized description of the flow curves . The softening fraction and kinetics of SRX are obtained by double‐compression tests, inverse analysis, and the strain recovery method .…”

“…And, together with regression analysis, it gives a generalized description of the flow curves. [20,21] The softening fraction and kinetics of SRX are obtained by double-compression tests, inverse analysis, and the strain recovery method. [22] These set of equations describe the kinetics of microstructural evolution and can be called the "material genome".…”

Multistage and High-speed Compression Testing Machine for Obtaining Flow Stress and Microstructure Evolution in Hot Forming of Steels

“…(b) Calculated results of temperature history The temperature history was calculated using electromagnetic-thermomechanical FEM 16) to estimate the inhomogeneous temperature distribution, the heat generation by the plastic deformation and heat removal by the mist cooling in Table 3. Chemical compositions of test pieces (mass %).…”