arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1002.1580cond-mat.mtrl-scicond-mat.mes-hall
收藏

成分与应力相互作用下多晶材料的振幅方程

Amplitude equations for polycrystalline materials with interaction between composition and stress

Robert Spatschek, Alain Karma

摘要:

我们研究了标架不变振幅方程[G. H.古纳拉特纳角Ouyang和H. Swinney,Phys. Rev. E { \bf 50},2802(1994)]定量描述了多晶微结构的演变,我们将这种方法扩展到包括组成和应力之间的相互作用。元素材料的验证,包括研究的Asaro-Tiller-Grinfeld形态不稳定的应力晶体表面,从熔体中的多晶生长,晶界能量在很宽的范围内的取向差,和晶界运动耦合到剪切变形。振幅方程与加速应变松弛的固体中示出准确地模拟Asaro-Tiller-Grinfeld不稳定性。多晶生长也被很好地描述。然而,晶界能的调查表明,该方法仅适用于有限范围内的取向差作为一个直接后果的振幅扩张。这个范围大约覆盖了晶体对称性所允许的整个范围的一半,对于膨胀中使用的一些固定的参考密度波。在此范围内,耦合运动剪切是很好地描述了已知的几何规则和过渡,从耦合到滑动运动也重现。在金兹伯格-朗道的精神,合金的振幅方程推导唯象。Vegard的法律被证明是自然的描述,寻求一个规范不变的形式下的变换,对应于一个晶格膨胀和Vegard的法律偏差可以很容易地纳入这些方程。这些方程现实地描述了稀合金的限制,并具有相同的灵活性,作为传统的相场模型,将任意的自由能/组成曲线。

英文摘要:

We investigate the ability of frame-invariant amplitude equations [G. H. Gunaratne, Q. Ouyang, and H. Swinney, Phys. Rev. E {\bf 50}, 2802 (1994)] to describe quantitatively the evolution of polycrystalline microstructures and we extend this approach to include the interaction between composition and stress. Validations for elemental materials include studies of the Asaro-Tiller-Grinfeld morphological instability of a stressed crystal surface, polycrystalline growth from the melt, grain boundary energies over a wide range of misorientation, and grain boundary motion coupled to shear deformation. Amplitude equations with accelerated strain relaxation in the solid are shown to model accurately the Asaro-Tiller-Grinfeld instability. Polycrystalline growth is also well described. However, the survey of grain boundary energies shows that the approach is only valid for a restricted range of misorientations as a direct consequence of an amplitude expansion. This range covers approximately half the complete range allowed by crystal symmetry for some fixed reference set of density waves used in the expansion. Over this range, coupled motion to shear is well described by known geometrical rules and a transition from coupling to sliding motion is also reproduced. Amplitude equations for alloys are derived phenomenologically in a Ginzburg-Landau spirit. Vegard's law is shown to be naturally described by seeking a gauge invariant form of those equations under a transformation that corresponds to a lattice expansion and deviations from Vegard's law can be easily incorporated. Those equations realistically describe the dilute alloy limit and have the same flexibility as conventional phase-field models for incorporating arbitrary free-energy/composition curves...

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑