Mathematical model of the thermal processing of steel ingots: Part I. Heat flow model

Abstract

A two-dimensional mathematical model has been developed to predict stress generation in static-cast steel ingots during thermal processing with the objective of understanding the role of stress generation in the formation of defects such as panel cracks. In the first part of a two-part paper the formulation and application of a heat-flow model, necessary for the prediction of the temperature distribution which governs thermal stress generation in the ingot, are described. A transverse plane through the ingot and mold is considered and the model incorporates geometric features such as rounded corners and mold corrugations by the use of the finite-element method. The time of air gap formation between mold and solidifying ingot skin is input, based on reported measurements, as a function of position over the ingot/mold surface. The model has been verified with analytical solutions and by comparison of predictions to industrial measurements. Finally, the model has been applied to calculate temperature contours in a 760×1520 mm, corrugated, low-carbon steel ingot under processing conditions conducive to panel crack formation. The model predictions are input to an uncoupled stress model which is described in Part II.