A model for coupling prediction of inverse segregation and porosity for up-vertical unidirectional solidification of Al–Cu alloys

A mathematical model for coupling prediction of inverse segregation and porosity for up-vertical unidirectional solidification of Al–Cu alloys is established, based on the analysis of the redistribution behaviors of both gas element and the alloying elements in the mushy zone. The model first investigates the mass variation during solidification, including the specific mass variation and the volume shrinkage during the solidification of both primary phase and eutectic, which give rise to the back flow towards the dendrite roots. Then, the porosity fraction is obtained by combing hydrogen segregation and pressure depression associated with the feeding flow through a porous media being solved with Darcy's equation. Consequently, both the feeding flow and the 'local solute redistribution equation' are modified with the presence of porosity. Finally, the solute distribution is obtained by coupling a finite difference solidification model with the modified segregation model. Numerical results show that the overall back-flow, which is needed to compensate the volume shrinkage, decreases with the increase of initially dissolved hydrogen concentration. As a result, the inverse segregation induced mainly by the back-flow of liquid enriched with solute, decreases with the increase in porosity fraction. The numerical predictions show rather good agreement compared with the experimental results reported in literature with the same condition. This model is capable of predicting inverse segregation with the presence of porosity in vertical unidirectional solidification of Al–Cu alloys.