论文部分内容阅读
基于典型微观控制单元体(通常指二次枝晶臂间距半长)内的溶质质量守恒关系,建立了适用于枝晶凝固方式的二元共晶/包晶合金微观偏析半解析数学模型,模型中充分考虑了固相反向扩散和枝晶结构粗化对液相溶质浓度的稀释效果。在引入适当的假设条件下,通过严格的数学推导,获得了模型的完整核心控制方程。在推导过程中应用了标准的粗化模型、二次方形式的固相溶质浓度分布以及抛物线固相生长方式等重要假设。其中,采用精度较高的四阶经典龙格—库塔数值微分方法,并结合具体的冷却条件,对模型的常微分核心控制方程来进行数值计算。为验证所建微观偏析模型的合理性和适用性,本文针对Al-4.9wt%Cu二元共晶合金进行了模型研究,通过将本模型的计算结果与已有的实验测试数据以及其它特点各异的微观偏析半解析数学模型的预测结果进行对比分析,表明本文所建立的微观偏析半解析数学模型具有相对较高的预测精度和能力,其预测结果最为接近于实测值。
Based on the conservation of solute mass in a typical microscopic control unit (usually referred to as the half-length of the secondary dendrite arm), a semi-analytical semi-analytical mathematical model of the binary eutectic / peritectic alloy suitable for dendrite solidification was established. The model In full account of the solid phase reverse diffusion and dendritic structure coarsening dilute the liquid solute concentration effect. With proper assumptions introduced, the complete kernel control equations of the model are obtained through rigorous mathematical derivation. In the derivation process, standard rough models, quadratic form solid-phase solute concentration distribution, and parabolic solid-phase growth are used. Among them, the fourth-order classical Runge-Kutta numerical differential method with high accuracy is adopted, and the numerical calculation of the ordinary differential core control equation of the model is carried out with specific cooling conditions. In order to verify the rationality and applicability of the microsegregation model, a model study of Al-4.9wt% Cu binary eutectic alloy was carried out. By comparing the calculated results of the model with the existing experimental test data and other characteristics The results of the semi-analytical mathematical model of different microsegregation are comparatively analyzed. The results show that the semi-analytical mathematical model of microsegregation established in this paper has a relatively high prediction accuracy and ability, and the prediction results are the closest to the measured values.