Simulation of Austenite Formation During Continuous Heating from Low Carbon Martensite with Poly-dispersed Cementite
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INTRODUCTION
UNDERSTANDING the mechanisms and kinetics of austenitization is vitally important for the development of dual phase steel, TRIP steel, and 3rd generation AHSS etc. Austenite can be nucleated on grain boundaries of the ferrite matrix, prior austenite grain boundaries, martensite packet, block and lath boundaries, and carbides which formed on these boundaries.[1–6] In plain carbon steel, the subsequent growth of austenite is rate-controlled by carbon transport from cementite particles on which it was nucleated as well as those dissolving in the matrix. After cementite vanished, the growth is controlled by carbon diffusion in austenite induced to equilibrate the carbon distribution within the austenite. In a previous report,[7] austenitization during continuous heating was simulated in low carbon martensite in which cementite particles of a single size were dispersed. The simulation revealed that the transformation curves
M. ENOMOTO is the Emeritus Professor of Ibaraki University, Bunkyo, Mito, 310-8512, Japan. Contact e-mail: masato.enomoto. [email protected] K. HAYASHI is with the Nippon Steel Corporation, Futtsu, Chiba 293-8511, Japan. Manuscript submitted July 10, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
of austenite were dependent upon the fraction and size of cementite particles. It is well known that ferrite nucleation at intragranular inclusions depends significantly on the size of an inert inclusion.[8] Austenitization is expected to be more complex because carbides dissolve exchanging carbon with the growing austenite. In this report, austenite nucleation and growth is simulated in plain carbon martensite with multi-dispersion of cementite assuming that austenite nucleation occurs solely on cementite particles. The particle size distribution (PSD) of cementite is measured metallographically at a temperature close to Ae1 by distinguishing the boundaries on which cementite particles are formed. Then, the nucleation rate on the particles whose size changes momentarily is calculated using the critical nucleus model at spherical interphase boundaries by Lee et al.[9,10] This model is modified to incorporate the influence of the boundary energy on which the particles reside. The growth of austenite is simulated using the quasi-steady state (invariant field[11]) approximation by Judd and Paxton,[2] which was extended to include the influence of carbon diffusion in the matrix.[7] Then, the evolution of the phase fraction, number, mean size and PSD of austenite grains is simulated until austenitization is completed. Austenite grain growth after completion is also simulated using the equation of grain growth of polycrystalline single phase materials.[12]
II.
SIMULATION METHOD
A. Nucleation of Austenite According to classical nucleation theory (CNT),[9] the nucleation rate of austenite J* is calculated from the equation, s DG J ¼ NV b Z exp ½1 exp t kT where NV is the number of nucleation sites per unit volume, b* is the frequency factor, Z is the Zeldovich non-equilibrium facto
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