Prediction of steel flow stresses at high temperatures and strain rates
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I.
INTRODUCTION
DURING the
past two decades, considerable research has been carried out on the computer modeling of hotrolling, including both the thermomechanical and metallurgical aspects. The need for greater accuracy of prediction has prompted a major upsurge in the development of accurate mathematical models for estimating the roll force. In this context, several models have been proposed, ranging from simple table "look-up" methods to formulae based on physical principles. ~ However, little published data are available regarding the numerical accuracy of these models. The absence of a good universal roll force model for hot-rolling is largely due to the lack of detailed information concerning the deformation resistance. Simple equations describing the stress/strain behavior in the roll gap can be used to compute the deformation resistance. However, most of these relations are empirical in nature and not based on any particular theoretical approach. The Hollomon equation I14] is widely used to approximate the plastic behavior of steel. This relation is easy to use and is sufficiently accurate to represent the stress/strain curve at low strains. A disadvantage of the Hollomon formulation is that the flow stress is zero at zero plastic strain, which is unrealistic. Other empirical equations for representing the flow curve, such as those of Ludwik, tlS] Swift, v61 and W o c e , [17] have also been employed in various models. The flow behavior of steels during hot-rolling is difficult to model, because the internal structure evolves with time through the interaction of mechanisms, such as work hardening, dynamic recovery, and dynamic recrystallization, t~8-25] Such behavior, in principle, can be
A. LAASRAOUI, Process Engineer, is with Hatch and Associates, 630 ouest boul. RenE-LevEsque, Montreal, Canada, H3B 1S6. J.J. JONAS, CSIRA/NSERC Professor, is with the Department of Metallurgical Engineering, McGill University, Montreal, Canada, H3A 2A7. Manuscript submitted March 15, 1990. METALLURGICAL TRANSACTIONS A
described by constitutive relations consisting of rate and evolution equations which have the following forms: = f(o-, T, S,)
d S J d t = g(or, T, S,)
[ 1a] [lb]
where ~ is the strain rate, o" the stress, T the temperature, and St a structure parameter. These relations recognize that the deformation resistance is affected by the temperature, accumulated strain or structure, and strain rate. Moreover, at high temperatures, microstructural changes have important effects on the resistance to hot deformation. Thus, in order to predict the roll force with accuracy, the effect of the microstructural changes on the deformation resistance must be accounted for. However, these factors are not completely understood in the case of plate- and, particularly, strip-rolling, and considerable further investigation into appropriate mathematical models is therefore required. The objective of this investigation was to describe the plastic behavior of steels at high temperatures and strain rates in terms of constitutive
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