Analysis of the Potential Productivity of Continuous Cast Molds

Heat transfer in the mold is the heart of the continuous casting process and its quantitative analysis was pioneered by Keith Brimacombe. With many different processes currently competing, it is appropriate to apply modeling to investigate the theoretical limits of continuous casting speed and productivity. The heat transfer rate during solidification processes drops with time so the shell thickness at mold exit drops with increasing casting speed. A computational heat flow model similar to those of Brimacombe is applied to investigate the consequences of very high casting speed on shell thickness at mold exit. Next, a finite-element stress model is applied to predict the minimum shell thickness at mold exit that should have sufficient strength to avoid rupture due to longitudinal tearing of the weak shell under the forces of ferrostatic pressure. The critical shell thickness is predicted to be on the order of 3 mm for most grades and casting conditions. The models are then applied to predict maximum casting speeds for different steel grades, section sizes, and mold lengths. The theoretical limits to casting speed are predicted to be extremely high, exceeding 21 m/min for a conventional 800-mm long, 200-mm square bloom mold, which corresponds to 3.5 million tonnes per year. The infeasibility of these high limits in practice is due to other problems, such as achieving shell thickness uniformity and liquid flux lubrication. This work suggests that if shortening mold length can solve lubrication, taper, and other problems, then it should be explored as a potential means to increase productivity. Brimacombe Memorial Symposium, Vancouver, Canada, October 1-4, 2000, Met Soc., CIM, pp. 595-611. 596 INTRODUCTION As the steel industry continues to improve quality and reduce cost, there is growing interest in maximizing the productivity from a single continuous casting machine. Many different processes are currently competing, from conventional thick slab and blooms to thin slabs and strip casting, whose economic feasibility depends on their eventual productivities. Considering the high cost of plant experiments, it is appropriate to apply computational modeling to explore the theoretical limits of continuous casting speed and productivity. Many researchers have investigated heat transfer and shell solidification in the mold during the continuous casting of steel [1-6]. However, Keith Brimacombe and coworkers were the first to apply advanced computational models of both heat flow [1, 7] and stress [8, 9] to gain quantitative insight into these phenomena, which comprise the heart of the process [6]. Thus, it is fitting to apply such models to explore the limits of the process at this symposium to honor his memory. Productivity increases with increasing casting speed and increasing cross-section area. The casting speed is limited by several different phenomena, listed below. 1) Excessive level fluctuations and waves at the meniscus become worse with greater casting speed. This can cause surface quality problems and even sticker breakouts. This problem can be addressed by changing nozzle design (directing the flow more downward, possibly by adding a bottom vertical port), applying electromagnetic forces, changing mold fluxes, and using other methods to control the flow pattern in the mold. 2) Excessive axial strains caused by the oscillation and withdrawal forces needed to overcome friction between the solidifying shell and the interfacial layers in the mold can lead to transverse cracks and breakouts at mold exit. Schwerdtfeger [3] has calculated that these stresses are negligible if the liquid layer of the mold flux can be kept continuous over the entire mold surface. 3) Excessive transverse strains may be generated in the thin shell by the ferrostatic pressure of the liquid pool below the mold. This can lead to longitudinal cracks and breakouts if the shell is not thick enough at mold exit. 4) Any local nonuniformity in the shell growth can lead to locally hot and thin regions in the shell, which can initiate longitudinal cracks and breakouts even if the shell is above the critical thickness on average. This problem, which has been investigated by Brimacombe and others, [10] can be addressed by optimizing mold flux behavior during initial solidification, oscillation practice, and taper design, such that flux lubrication is continuous, the initial heat flux is low and uniform, and the mold wall taper matches the shell shrinkage profile [11]. Peritectic steel grades and austenitic stainless steel are most susceptible to this problem. Superheat delivered from the flowing steel jets can also contribute to Brimacombe Memorial Symposium, Vancouver, Canada, October 1-4, 2000, Met Soc., CIM, pp. 595-611. 597 this problem, especially near the narrow faces in slab casting with bifurcated nozzles. 5) Excessive bulging of the strand below the mold can lead to a variety of internal cracks and even breakouts if the bulging is extreme. Bulging can be controlled by choosing short enough support roll spacing, maintaining roll alignment, controlling spray cooling below the mold, and by avoiding sudden changes in roll pitch, sprays, or casting speed. 6) The distance below the meniscus of the point of final solidification of the center of the strand increases in direct proportion with casting speed for a given section thickness, which usually limits the maximum casting speed in a given steel plant. The torch cut-off, spray cooling system, and roll support system all must extend to accommodate this increase in metallurgical length. Contrary to intuition, this metallurgical length cannot be significantly shortened by increasing the spray cooling intensity [12]. This understanding is incorporated in the pioneering work of Brimacombe and coworkers to provide design criteria for spray zones [12, 13]. 7) Finally, there are many other special quality concerns which sometimes impose limits on casting speed. For example, in ultra-low carbon steels, a relatively slow upper limit in casting speed is required in order to reduce pencil pipe and other blister defects due to argon bubble entrapment on the inner radius of curved mold casters [14, 15]. Casting speed can only be increased in these situations by careful changes in operating conditions that avoid the specific defects of concern. Clearly, to increase the casting speed of a continuous casting process requires careful consideration of many different phenomena. The above list shows that at least seven separate criteria must be satisfied, any of which could limit the casting speed for a given operation. In practice, the complex problems associated with transient nonuniformities in the shell growth (criterion 4) are often responsible for limiting casting speed and corresponding production rates. This issue is being addressed elsewhere. Considering all of the above criteria, the most fundamental limit is criterion 3, which has also received very little attention in previous work. The shell at mold exit must have at least the critical thickness necessary to contain the liquid pool and avoid longitudinal rupture due to excessive creep strain of the thin shell. Thus, this work investigates the theoretical upper limits on casting speed and productivity imposed by this need. MODEL DESCRIPTION To explore the critical shell thickness and maximum potential casting speeds, this work applies two-dimensional transient finite element models of heat transfer and stress generation in a thin section through the solidifying shell. The model tracks the evolution of temperature, solidification, stress, and strain in a slice through the solidifying shell as it moves down through the caster [16]. The model domain, illustrated in Figure 1, is a Brimacombe Memorial Symposium, Vancouver, Canada, October 1-4, 2000, Met Soc., CIM, pp. 595-611. 598 slice through the solidifying shell at the center of one side of the continuous cast strand. This slice domain is 0.2 mm thick and has a maximum length of half of the strand section size. A fine mesh of 10 nodes per mm was required to achieve acceptable accuracy. This mesh was connected into 3-node and 6-node triangle elements for heat transfer and stress analysis, respectively. Ferrostatic Pressure P to Shell Force Applied F