Simulation of Thermal Distortion of a Steel Droplet Solidifying on a Copper Chill

A finite-element model has been developed to predict the evolution of temperature, stress, and shape of 10-mm diameter molten steel droplets solidifying against a water-cooled copper chill plate. The elastic-viscoplastic stress model accounts for thermal linear expansion / contraction behavior, creep, and phase transformations that vary with carbon content. Thermal contraction causes the quenched surface of the impinged droplet to bend away from the chill plate. This creates interfacial resistance that greatly lowers heat transfer. The droplet shape is predicted to evolve almost entirely during the first 0.1 second, when a thin solid skin first forms and becomes strong enough to contract. The final shape of the droplet interface predicted by the model agrees both qualitatively and quantitatively with previous measurements reported by Dong and coworkers. The most deformation, as indicated by the final curvature of solidified droplets, is found in high purity iron (0.003%C) and in peritectic steels (0.12%C). This deformation can be reduced by lowering heat transfer coefficient and avoiding sudden large drops in h. Large drops in heat transfer coefficient also cause reheating of the droplet surface, despite the neglect of nonequilibrium undercooling effects in the model. It is important to minimize surface roughness during initial solidification in order to avoid non-uniform solidification, which is responsible for many casting defects. 2 Introduction When molten metal impacts a chilled surface, it suddenly experiences many complex phenomena including rapid cooling, solidification, and thermal distortion. These phenomena control the heat transfer, microstructure, segregation, stresses, and deformation which determine the quality of the cast product. This behavior is critical to many different metals solidification processes besides those involving metal droplets. For example, most of the surface defects in continuous cast steel initiate during the early stages of solidification at the meniscus in the mold. These include surface depressions, longitudinal and transverse surface cracks. It is well-known that heat transfer during initial solidification is controlled by the contact resistance at the interface between the solidifying metal and the chill. This is affected greatly by the size of the gap, which is controlled by the shape of the solidifying metal surface. Although many previous experimental and heat transfer modeling studies have been done, very little previous attention has been given to predicting thermal distortion during initial solidification. As the solidifying droplet cools and distorts, it may lift away slightly from the substrate, creating gap(s) which greatly lower the heat transfer. This may be sensitive to small changes in composition. The present work is a preliminary attempt to model the evolution of the bottom surface shape of a solidifying steel droplet, in order to better understand these phenomena. Previous Work A few recent experimental studies have investigated phenomena during initial solidification, including measurement of the final surface shape. Dong and coworkers [1] melted and levitated 4-8 g droplets of steel and then dropped them 35 mm onto a #1500 Emery-paper-polished and watercooled copper chill plate, as pictured in Fig. 1. The final shape of the bottom surface of the droplets was measured for different grades and droplet sizes. For small (4-g 10 mm diameter) droplets, the bottom shape could be fit with a parabola, so the curvature was characterized with a single fitting parameter, Nd: gap = Nd y2 (1) It was further proposed that Nd could be estimated by one half of the maximum temperature gradient multiplied by the average thermal expansion coefficient. [1] This curvature varied with carbon content, as sketched in Fig. 2. For most droplets, the bottom surface bent away from the chill with a positive Nd curvature and gaps of 100-250 μm. Negative curvatures were observed for carbon contents between 0.6 and 2.5%. Larger droplets had a more complex bottom shape with a depression in the center.