Mathematical model of the thermal processing of steel ingots: Part II. Stress model
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I.
INTRODUCTION
STEEL ingots are subject to many defects that arise during processing as a consequence of metallurgical weaknesses in combination with stress generation. One such defect is panel crack formation which affects aluminum-treated, plain carbon steel ingots over a range of compositions and ingot sizes. The loss of ductility in steel at intermediate temperatures, which is partly responsible for the problem, has received a great deal of study which was reviewed in a previous paper. ~ However, the generation of stresses in ingots, which is also a great contributor to the problem, 2 has received relatively little attention. The stress generated in a static-cast ingot during processing prior to rolling is caused almost entirely by the volumetric expansions and contractions accompanying changing thermal gradients within the ingot. As the first step in calculating these stresses, it is therefore important to determine accurately the internal thermal state of the ingot as a function of time. Thus, the objective of the first part of this work was to develop a mathematical model to calculate the temperature distribution in a steel ingot as a continuous process from the end of teeming to the start of rolling, including solidification, cooling in the mold and in air, reheating in the soaking pit, and subsequent air cooling. Many mathematical heat-transfer models of static-cast ingot processing have been documented and used in recent years. 3-15 However, relatively few of the models were designed with subsequent thermal stress modeling in mind, and no model reported in the literature has yet been utilized to study panel cracking. Most previous models have been formulated using a finite-difference method and have modeled the ingot as a square or rectangle. 3-5'7-11'15 While this B.G. THOMAS, formerly a Graduate Student at the University of British Columbia, is Assistant Professor in the Department of Mechanical and Industrial Engineering, University of Illinois, 1206 West Green Street, Urbana, IL 61801. I. V. SAMARASEKERA, Associate Professor, and J.K. BRIMACOMBE, Stelco/NSERC Professor and Director, are with The Centre for Metallurgical Process Engineering at the University of British Columbia, Vancouver, BC, Canada, V6T 1W5. Manuscript submitted February 3, 1986.
METALLURGICAL TRANSACTIONS B
approximation can be used effectively to predict total solidification time, 3'7-9'15 the actual temperature fluctuations, important to stress generation, are more sensitive. Since the importance of mold corrugations on stress development was not known, the present model was formulated using a version of the finite-element method in order to simulate the exact geometry including the effects of rounded comers and mold corrugations. In a later paper, both the heat-flow and stress models will be applied to elucidate the mechanisms behind panel crack formation. Thus, a number of assumptions made in the formulation of both models reflect this end use. In particular, the steel compositions, physical and mechanical property data, in
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