A double-shear theory is introduced that predicts the commonly observed {5 5 7}γ habit planes in low-carbon steels. The novelty of this theory is that 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}γ 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}γ habit planes depend sensitively on the lattice parameters of the face-centered cubic (f.c.c.) and body-centered cubic (b.c.c.) phases. Nonetheless, for various realistic lattice parameters in low-carbon steels, the predicted habit planes are near {5 5 7}γ. 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 `Lath Martensite' is provided which allows the application of this model to any other material undergoing an f.c.c. to b.c.c. transformation.

中文翻译：

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板条马氏体无参数双剪切理论

引入双剪切理论来预测常见的 {5 5 7}γ低碳钢的习惯平面。该理论的新颖之处在于，剪切系统的选择类似于马氏体晶体学的原始（单剪切）唯象理论，因为宏观上相当于孪生。在所有由此产生的双剪切理论中，导致某些{赫克}γ习惯平面自然地出现为那些具有较小形状应变大小并满足最大相容性条件的平面，因此不需要任何参数拟合。一个有趣的发现是预测的精确坐标{赫克}γ习性平面敏感地取决于面心立方（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，预测的习性平面接近 {5 5 7}γ。详细分析了 Fe–0.252C 和 Fe–0.6C 的示例以及所得的取向关系，这些关系始终接近 Kurdjumov-Sachs 模型。此外，一个MATLAB应用程序`板条马氏体' 的提供允许将此模型应用于任何其他经历 fcc 到 bcc 转换的材料。