A Mathematical Model of Interdendritic Thermometallurgical Strain for Dendritic Solidification Processes

A mathematical model of interdendritic thermometallurgical strain (ITM) generated during dendritic solidification of steel alloys has been developed. The model consists of two main parts in which the first part represents the derivation of ITM strain based on the concept of thermal storage energy. Consequently, the second one represents the volume changes associated with dendritic solidification phenomena during the interdendritic coherent region in the mushy zone. Calculations for Fe-C binary alloys show that the straining criteria such as strain rate and accumulated strain are sensitive to the solidification behavior of different steel alloys. The results also point out that good predications of different phases, accurate alloy properties (especially thermal expansion coefficient), and precise enthalpy functions during dendritic solidification are extremely necessary. Also, the predications show that the dendrite coherency criterion is considered an essential parameter to define ITM strain of particularly long solidification interval alloys. Model predications of ITM strain are compared and discussed with other established theoretical approaches and previous modeling work.