ALSPEN-A mathematical model for thermal stresses in direct chill casting of aluminum billets
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I.
INTRODUCTION
D I R E C T chill (DC) semicontinuous casting of axisymmetric billets is one of the most important processes in the production of aluminum. A major problem, however, is the formation of residual stresses which can cause cold cracking. Furthermore, thermally induced stresses and strains can lead to defects during casting, and especially close to the liquid zone, this may result in hot tearing. The purpose of this paper is to present the mathematical and numerical model ALSPEN. In this model, the stresses and strains which develop during casting are calculated in order to predict the optimal process parameters and thereby avoid defects in the ingot. In parallel with the development of ALSPEN, the viscoplastic material properties of the A1MgSi alloy AA6063 have been studied in Reference 1,* and these *This Ph.D. thesis, which was written in English at the University of Oslo, wilt be made available to the public during L990/91.
properties are incorporated in the present version of ALSPEN. A successful Solution of the residual stress problem depends upon a correct solution of the thermal problem. For the present study, the thermal problem has been solved by the temperature model ALSIM-2 in which the heat transfer during casting is simulated. This model is described in References 2 and 3 and verified in References 4 through 7. Several models for simulating thermal stresses in continuous casting have been reported, and two-dimensional (2-D) models where either plane stress or plane strain is assumed are presented in References 8 through 10. The case of axisymmetric stress modeling of DC cast aluminum is studied in References 11 through 13. The
HALLVARD G. FJLER is with the Institutt for energiteknikk, 2007 Kjeller, Norway. ASBJORN MO is with the Senter for Industriforskning, 0314 Oslo 3, Norway. Manuscript submitted September 25, 1989. METALLURGICAL TRANSACTIONS B
important rate dependence of the constitutive equations, however, is not taken into account in Reference 11. In References 12 and 13, on the other hand, constitutive equations for both time-independent plastic strain and creep are implemented, but the papers do not give a detailed study of the material behavior. Other relevant papers to the present problems are References 14 and 15. The solidification of a cylindrical casting is studied in Reference 14. Here, the thermal and stress problems are solved, and the viscoplastic material model with one internal variable, given in Reference 16, is used in the stress problem. Reference 15 describes a mathematical model which calculates the thermal stresses generated in an ingot during solidification, and a rather general form of the constitutive equations, including a "structure parameter," is discussed. In the calculations, however, the viscoplasfic part of the strain is described only by a creep formula. In the present study, we have treated the problem in a transient manner, leading to a continually increasing solution domain consisting of the solid part of the billet. In the finite-element solut
