枝晶凝固过程中的微观偏析半解析数学模型

Semi-analytical model of microsegregation during dendritic solidification

基于典型微观凝固单元体内的溶质质量守恒,结合前人的研究工作,建立了一个适合于枝晶凝固方式的二元合金微观偏析半解析模型.本模型同时考虑了反向扩散和粗化对微观偏析的影响,并对枝晶臂间距的粗化直接进行计算,因此更为精确.若只考虑反向扩散的影响,本模型可以简化为BF模型形式;而如果只考虑粗化的影响,本模型可简化为Mortensen模型.本模型完整地统一了以BF模型为代表的反向扩散类模型和以Mortensen模型为代表的粗化模型.利用本模型同样可以对多元合金的微观偏析进行很好预测.以Fe-C-X(Si,Mn,P,S)合金体系为例对本模型的求解过程进行了详细的阐述.本模型可以很好地预测Al-4.9%Cu二元合金的共晶分数以及Fe-C-X(Si,Mn,P,S)多元合金体系的零强度温度和零塑性温度,并与实测值吻合良好.

ABSTRACT Based on mass conservation in a typical micro-solidification volume element combining with previous work, a semi-analytical model of microsegregation was established for binary alloys with dendritic solidification. The effects of back-diffusion and coarsening on microsegregation are both considered in the semi-analytical model, and the coarsening of arm spacing is directly calculat-ed to make the semi-analytical model more precise. The semi-analytical model will be simplified to the BF model or the Mortensen model when back-diffusion or coarsening is considered only, respectively. The diffusion model and the coarsening model separately represented by the BF model and the Mortensen model are well unified by the semi-analytical model. Moreover, the semi-analytical model can be extended to multicomponent alloys. The Fe-C-X（ Si, Mn, P, S） alloy was taken as an example to elaborate the solving process. The eutectic fractions of the Al-4.9%Cu alloy and the zero strength temperature （ZST） and zero ductility temperature （ZDT） of carbon steel Fe-C-X（ Si, Mn, P, S） during solidification can be well predicted by the semi-analytical model.