板条马氏体的无参数双剪理论
A Parameter Free Double Shear Theory for Lath Martensite
摘要：
介绍了双剪切理论，预测低碳钢中常见的{5 5 7}习惯面。该理论的新颖之处在于不需要参数拟合。相反，剪切系统的选择类似于原始的（单剪切）马氏体晶体学的唯象理论，宏观上等同于孪生。在所有由此产生的双剪切理论中，导致某些{h h k}习惯面的理论自然地出现为具有小形状应变幅度并且满足最大相容性条件的那些理论，从而使得任何参数拟合都是不必要的。一个有趣的发现是，预测的{hhk}习惯面的精确坐标敏感地依赖于面心立方（fcc）和体心立方（bcc）相的晶格参数。尽管如此，对于低碳钢中的各种实际晶格参数，预测的习惯面接近{5 5 7}。Fe-0.252C和Fe-0.6C的例子进行了详细的分析，以及由此产生的取向关系，始终接近Kurdjumov-Sachs模型。此外，还提供了一个MATLAB应用程序（可在github.com/AntonMu/LathApp上获得），该应用程序允许将该模型应用于经历fcc到bcc转变的任何其他材料。
英文摘要：
A double shear theory is introduced that predicts the commonly observed {5 5 7} habit planes in low-carbon steels. The novelty of this theory is that no parameter fitting is necessary. Instead, the shearing systems are chosen in analogy to the original (single shear) phenomenological theory of martensite crystallography as those that are macroscopically equivalent to twinning. Out of all the resulting double shear theories, the ones leading to certain {h h k} habit planes naturally arise as those having small shape strain magnitude and satisfying a condition of maximal compatibility, thus making any parameter fitting unnecessary. An interesting finding is that the precise coordinates of the predicted {h h k} habit planes depend sensitively on the lattice parameters of the fcc (face-centered cubic) and bcc (body-centered cubic) phases. Nonetheless, for various realistic lattice parameters in low carbon steels, the predicted habit planes are near {5 5 7}. The examples of Fe-0.252C and Fe-0.6C are analyzed in detail along with the resulting orientation relationships which are consistently close to the Kurdjumov-Sachs model. Furthermore, a MATLAB app (available at github.com/AntonMu/LathApp) is provided which allows the application of this model to any other material undergoing an fcc to bcc transformation.
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