Lightweighting of vehicles while preserving crash-worthiness, in order to satisfy stringent restrictions imposed by the government on the automotive industry, has become a sought after solution which can be realized via hot-forming die quenching (HFDQ). HFDQ is a process where boron-manganese steel blanks, a grade of ultra-high strength steels with a thin eutectic Al-Si coating, are heated beyond TAc3 to achieve a fully austenitic microstructure, a precursor for martensite. Heat treatment is performed using 30 to 40 meter long roller hearth furnaces, comprised of multiple heating zones, with two key objectives: (1) ensure complete austenitization of blanks and (2) transformation of the Al-Si coating into a protective Al-Si-Fe intermetallic coating. Blank heating rates are controlled by the roller speed and zone set-point temperatures, which are currently set by trial-and-error procedures. Therefore, a thorough understanding of the furnace parameters and the industrial objectives are essential. Patched blanks, with spatially varying thickness, leads to inhomogenous heating, making this relationship elusive.
Previous furnace-based energy models only focused on simulating the sensible energy of the load with no explicit information about the latent energy associated with austenitization. Consequentially, the latent term had been incorporated into the sensible energy term thereby defining an effective specific heat. In order to realize how blank heating rate influences microstructural and Al-Si layer evolution, a model coupling heating and austenite kinetics is necessary. This integrated model serves as means for optimizing the heating process.
In this work a thermometallurgical model is developed, combining a heat transfer submodel with two austenite kinetic submodels, an empirical first-order kinetics model and a constitutive kinetics model, via the latent heat of austenitization. The models simultaneously predict the heating and austenitization curves, for unpatched/patched blanks heated within a roller hearth furnace. Validation studies showed that the first-order kinetics model reliably estimated heating and transformation kinetics compared to the constitutive model.
The validated models are then used to optimize the zone set-point temperatures, roller speed, and cycle length for a 12-zone roller hearth furnace whilst minimizing the cycle time in a deterministic setting. A gradient-based interior point method and hybrid scheme were used to assess the constrained multivariate minimization problem with two alternative austenitization constraints imposed: a soak-time based and explicitly modeled requirement. In both cases, the most savings in cycle time were achieved using the explicitly modeled phase fraction austenite constraint, with reductions of approximately 2 to 3 times from the nominal settings
