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(Received 3 October 2011; accepted 1 May 2012)

**Published Online:** 20 September 2012

**CODEN:** MPCACD

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Mathematical modeling is a powerful tool to design, control and optimize heat-treating processes. However, the complex interactions occurring between the thermal, microstructural, and stress fields inside the part during those processes (which must be taken into account in detailed modeling work) precludes its use in many instances—especially in a production environment. Thus, it is desirable to find methodologies that can speed up the simulations while maintaining the mathematical model close to reality. In this work, the evolution of the microstructural field was estimated from fraction-transformed-temperature correlations derived directly from a published continuous-cooling-transformation (CCT) diagram, which uses the cooling rate at 750°C as the *x*-axis. This approach “softens” the coupling between the thermal and fraction-transformed fields resulting in an efficient algorithm. The thermal field evolution was computed using standard procedures embedded in the commercially available code Abaqus, whereas empirical equations describing the fraction transformed-temperature relationships were programmed through user subroutines. The mathematical model was validated by comparing measured and model-predicted thermal response and final microstructure. In the experiments, austenitized AISI 4140 steel cylindrical probes (0.5-in. diameter × 2-in. length) were cooled in: (1) still air, and (2) a fluidized bed reactor, both at room temperature. The thermal response was measured during the cooling process by inserting two thermocouples: one at the geometrical center of the probe and the other near the probe surface, at mid-length. The latter was input to a code developed in-house to estimate the surface heat flux history, which constitutes the active boundary condition for the direct heat conduction problem and was, in turn, fed to the computational model. Once heat treated, the probes were prepared for metallographic observation using standard techniques. The results indicate that the proposed methodology can be used for predicting the thermo-microstructural evolution during a heat-treating process.

**Author Information:**

Hernández-Morales, B. *Depto. de Ingeniería Metalúrgica, Facultad de Química, Universidad Nacional Autónoma de México, Circuito Institutos s/n, Cd. Universitaria, México,*

Téllez-Martínez, J. S.*Depto. de Ingeniería Metalúrgica, Facultad de Química, Universidad Nacional Autónoma de México, Circuito Institutos s/n, Cd. Universitaria, México,*

Dueñas-Pérez, A. M.*Depto. de Ingeniería Metalúrgica, ESIQIE-IPN, UPALM, México,*

Díaz-Cruz, M. *Depto. de Ingeniería Metalúrgica, ESIQIE-IPN, UPALM, México,*

**Stock #:** MPC104392

**ISSN:**2165-3992

**DOI:** 10.1520/MPC104392

Title Mathematical Modeling of Steel Heat Treating Using CCT Diagrams

Symposium ,

Committee A01