A combined solubility product/new PHACOMP approach for estimating temperatures of secondary solidification reactions in
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I.
INTRODUCTION
A. Importance of Solidification Sequence
THE sequence and associated temperatures of secondary solidification reactions in engineering alloys have a large influence on weld metal solidification cracking propensity.[1] For example, alloys that terminate solidification by a eutectic-type reaction at a relatively high temperature are generally more resistant than alloys that end solidification by a reaction occurring at a lower temperature.[2] In view of this, methods for predicting the effect of alloy composition on the sequence of solidification reactions and their associated transformation temperatures are valuable for assessing possible links between alloy composition and fusion zone cracking tendency. The most common approach to modeling such relations is to combine solute redistribution equations with the binary phase diagram (for a two-component system) or liquidus surface (for a ternary system).[3] With this method, the solute redistribution calculations can be used to track the variation in liquid composition and remaining fraction liquid during solidification, while the phase diagram provides the liquid composition(s) and temperature(s) at which secondary solidification reactions occur. The coupling of this information can provide the complete liquid composition-fraction liquid-temperature history of the solidification reactions and serves as useful input for interpreting weldability results. Unfortunately, most alloys of practical interest, such as superalloys, are multicomponent systems for which experimentally verified phase diagrams are not available. As a result, it is often difficult to predict the value of liquid comJ.N. DuPONT, Associate Director, Energy Liaison Program, is with the Energy Research Center, Lehigh University, Bethlehem, PA 18015. Manuscript submitted October 1, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
position (e.g., eutectic composition), which corresponds to the initiation of secondary solidification transformations. An alternative approach is to monitor the evolution of composition in the solid via solute redistribution calculations and combine these results with solubility data to estimate the temperature at which the maximum solid solubility of alloying elements in the primary dendrites has been exceeded with respect to various secondary solid phases (e.g., carbides and intermetallics). The solubility product approach is often more convenient, as such relations have been experimentally determined for multicomponent alloys,[4,5] whereas experimentally verified liquidus surfaces are often difficult to locate and cannot always be applied to quaternary and higher order systems. A pseudoternary approach has recently been developed and applied to the alloys of interest in this present study and is discussed elsewhere.[6,7] The analogy between the two approaches lies within the relation between the eutectic composition in the liquid and the maximum solubility in the solid. This is most easily understood with the aid of the simple binary phase diagram in Figur
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