A Mathematical Model to Predict Microstructure of Heat-Treated Steel

Abstract

The dual effects of chemical composition and cooling rate on microstructural evolution were theoretically simulated extending the Johnson-Mehl equation for non-isothermal pro-eutectoid ferrite transformation kinetics incorporating the effect of supercooling (ΔT) as well as for isothermal pearlite transformation kinetics assuming the exponent on time ‘n’ to vary inversely with time as, n = p/tm, for case carburized steel quenched in oil. Carbon concentration profile of steel carburized at 930 °C for 10 h was theoretically computed by solving the Fick’s diffusion equation. The cooling curves from surface to core were generated for typical 20.32 and 15.6 mm diameter steels using FEM package (ANSYS) for oil quenching, water quenching, and air cooling. The effect of varying carbon concentration from surface to core was incorporated in the heat transfer equations while generating cooling curves, at different case depths (surface, 0.31, 0.558, 1.239, and 3.469 mm). The cooling curves for oil quenching were superimposed on the published TTT diagrams of the steels of corresponding carbon content and using the empirical equations the evolution of different microconstituents, e.g., ferrite, pearlite, and martensite from the parent austenite phase were computed for the carburized 20.32 and 15.6 mm diameter steel samples. These steel samples were also case carburized experimentally at 930 °C for 10 h followed by oil quenching. The theoretically predicted case depth of 3.469 mm matched closely with the experimentally observed value. Microstructural studies were done on inverted microscope and quantitative image analyzer at different case depths/nodal points. Microhardnesses were also measured at case depths from 0.1 mm to center of the samples at selected areas to identify the different phases. The experimentally observed microstructures matched well with the theoretically predicted evolution of microconstituents.