Abstract The columnar-to-equiaxed transition is a technologically important phenomenon that controls the grain structure in the casting of alloys. Analytical and coarse-grained models, used to investigate this transition, rely on several assumptions concerning dendrite growth kinetics and grain structures. In the first part of this two part paper, we test these assumptions using a two-dimensional (2D) dendritic needle network model that describes both the transient growth dynamics of primary, secondary and higher order branches of the dendritic network within each grain and the solutal interactions between grains that can grow with arbitrary shapes. Our results provide novel insights into the columnar-to-equiaxed transition, distinguishing between abrupt and progressive transitions with different grain structures. Furthermore, they highlight the limitations of commonly used assumptions in analytical and coarse-grained numerical models of this transition. These results are extended to 3D in part II of the paper.

中文翻译：

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柱状到等轴过渡的树突针网络建模。第一部分：二维公式与理论比较

摘要 柱状向等轴相转变是控制合金铸造晶粒结构的重要技术现象。用于研究这种转变的分析和粗粒模型依赖于有关枝晶生长动力学和晶粒结构的几个假设。在这两部分论文的第一部分中，我们使用二维 (2D) 树突针网络模型来测试这些假设，该模型描述了每个晶粒内树突网络的初级、次级和更高阶分支的瞬态生长动态以及可以以任意形状生长的晶粒之间的溶质相互作用。我们的结果提供了对柱状到等轴转变的新见解，区分了具有不同晶粒结构的突然转变和渐进转变。此外，它们强调了这种转变的分析和粗粒度数值模型中常用假设的局限性。这些结果在论文的第二部分扩展到 3D。