A Simple Model for Conventional Hot Rolling of Sheet Materials
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I.
INTRODUCTION
HOT rolling of sheet materials is a widespread deformation processing operation. The apparent simplicity of the process, however, belies the complexity of transients whose nature may be thermal, microstructural, or both. In many cases, the temperature transients are strongly coupled to the microstructures that are developed because of the sharp dependence of phenomena such as dynamic recrystallization and decomposition of metastable phases on temperature and temperature losses. Depending on specific rolling parameters and dynamic phase-transformation behavior, substantial undesirable gradients in microstructure ( e . g . , grain size, transformation products) may be developed through the thickness or along the length of the sheet. Such gradients may be difficult to eliminate during subsequent deformation or heat-treatment processes and may present problems with regard to service property variations. The process modeling methodology offers a useful and powerful tool for the investigation of temperature transients during conventional hot-working processes. As suggested first by Bishop t~t in the 1950s, most models for such processes involve decoupled numerical solutions in which deformation and heat transfer are assumed to occur during sequential small time increments. Lahoti and Altan t2,3j popularized such an approach in the 1970s for the analysis of various extrusion and drawing processes, primarily for the prediction of working loads. Subsequently, Sellars and co-workers t4-81 used a similar approach for the analysis of extrusion of steel billets and S.L. SEMIATIN, Senior Scientist, is with the Metals and Ceramics Division, Materials Directorate, Wright Laboratory, WL/MLLN, Wright-Patterson Air Force Base, OH 45433-7817. J.C. SOPER, Undergraduate Student, is with Wright State University, Dayton, OH 45435. R. SHIVPURI, Associate Professor, is with the Industrial and Systems Engineering Department, Ohio State University, Columbus, OH 43210-1271. Manuscript submitted August 27, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
the rolling of thick slabs of steel and aluminum. Besides the prediction of temperatures, Sellars and co-workers incorporated material models for dynamic and static recovery and recrystallization into their analyses to predict grain size, etc., during processing in single-phase fields for these types of materials. Similar work has been conducted by Yada, t9l Devadas et al. t~~ and Chen et al. t~31 on hot rolling of steel slabs, by Seetharaman et al. 1141 and Goetz et al. tlS~ on canned extrusion of gamma titanium aluminide alloys, and Serniatin et al. t~6~on hot pack rolling of high-temperature sheet alloys. In the present article, a simple finite-difference model is developed and applied to quantify the magnitude of the temperature transients during multipass rolling of sheet. The modeling approach was validated via rolling trials on an alloy, Ti-6A1-4V, whose flow stress and microstructure development are particularly sensitive to temperature and temperature history. II.
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