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arXiv 1007.2708cond-mat.mtrl-sci
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位错对马氏体微观结构空间变化的影响

Influence of dislocations on the spatial variation of microstructure in martensites

R. Gröger, T. Lookman

摘要:

位错的连续统理论,主要由Kröner和Kosevich发展,将每个位错视为应变不相容的来源。我们表明,这一概念可以有效地采用朗道自由能泛函开发一个平均场的位错材料的介观模型。表示母相(通常为立方对称)畸变的序参量用弹性应变表示,这些应变本身通过不相容约束耦合。由于不相容性的“强度”取决于位错的局部密度,位错的存在影响微观结构的演化,反之亦然。该公式的优点在于位错之间的长程各向异性相互作用自然地出现在自由能的公式中。由于位错周围的晶体结构的畸变,它们在多相材料中的存在导致产物相的异质成核,从而也导致转变温度的变化。这种新颖的场论方法是非常方便的,因为它可以弥合差距,在研究材料的行为在长度和时间尺度上,是无法达到的原子或宏观模型。

英文摘要:

The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the "strength" of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.

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