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枝晶凝固過程中的微觀偏析半解析數學模型

Semi-analytical model of microsegregation during dendritic solidification

  • 摘要: 基于典型微觀凝固單元體內的溶質質量守恒,結合前人的研究工作,建立了一個適合于枝晶凝固方式的二元合金微觀偏析半解析模型.本模型同時考慮了反向擴散和粗化對微觀偏析的影響,并對枝晶臂間距的粗化直接進行計算,因此更為精確.若只考慮反向擴散的影響,本模型可以簡化為BF模型形式;而如果只考慮粗化的影響,本模型可簡化為Mortensen模型.本模型完整地統一了以BF模型為代表的反向擴散類模型和以Mortensen模型為代表的粗化模型.利用本模型同樣可以對多元合金的微觀偏析進行很好預測.以Fe-C-X(Si,Mn,P,S)合金體系為例對本模型的求解過程進行了詳細的闡述.本模型可以很好地預測Al-4.9%Cu二元合金的共晶分數以及Fe-C-X(Si,Mn,P,S)多元合金體系的零強度溫度和零塑性溫度,并與實測值吻合良好.

     

    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 calculated 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.

     

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