Abstract

    The thermo-physical and physical properties of the liquid and solid phases are critical components in the modelling of casting simulations. Such properties include the fraction solid transformed, enthalpy release, thermal conductivity, volume and density all as a function of temperature. Due to the difficulty in experimentally determining such properties at solidification temperatures, little information exists for multicomponent alloys. As part of the development of a new computer programme for modelling of materials properties (JMatPro), extensive work has been carried out on the development of sound, physically based models for these properties. Wide ranging results will presented for Ni-based alloys, which will include more detailed information concerning the phases formed during solidification and their composition and the density change of the liquid that intrinsically occurs during solidification due to its change in composition.

1. INTRODUCTION

    Previous modelling work1,2,3,4,5,6,7,8 has shown that excellent results can be obtained can be obtained for the phases formed on solidification ,  and their composition, by using thermodynamic modelling based on the CALPHAD9 methodology. In particular, CALPHAD methods have been applied to Ni-based Superalloys and results checked in detail against experiment5,6,7,8. However, although useful in their own right, both for process modelling and modelling of microstructures, such calculations fall short of supplying physical property data for the phases, which is critical for successful simulation of solidification. At low temperatures, physical properties can be readily measured, although it may be a time-consuming and expensive procedure to obtain all relevant properties. Experimental measurement becomes far more problematical at high temperature and especially if the liquid phase is involved. To this end, it is highly desirable to calculate thermo-physical and physical properties over the complete relevant temperature range for as wide a range of alloys as possible. The present paper describes a methodology that extends the existing CALPHAD models to further calculate properties such as density, thermal conductivity, specific heat (Cp), solidification shrinkage etc., and applies it for Ni-based multicomponent alloys. A significant advantage of the current method is that properties for each phase are calculated so fine detail can be obtained; for example the density change of the liquid during the solidification, which is governed both by an intrinsic change with temperature and by the composition changes that accompany solidification.

   The current work forms part of the development of a more generalised software package (JMatPro) for the calculation of a wide range of materials properties.10 A feature of the new programme is that great store has been placed on using models that, as far as possible, are based on sound physical principles rather than purely statistical methods. Thus, many of the shortcomings of methods such as regression analysis can be overcome.

    For example, the same model and model parameters are used for density calculations for all alloy types, whether it be for a commercially pure Al-alloy or a complex Ni-based superalloy. The paper will discuss briefly the Scheil-Gulliver solidification model that is used to directly calculate phase amounts, Cp, enthalpy and latent heat of solidification. Details concerning the creation of a molar volume database that enables a variety of properties to be calculated, such as solidification shrinkage, density, thermal expansion coefficient, will then be presented. The calculation of thermal conductivity and modulus will also be discussed. Examples of the linking of the solidification models with the physical property calculations are made and properties calculated during solidification will be presented.

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