IMECH-IR  > 非线性力学国家重点实验室
多晶体晶界弛豫与内耗的尺寸效应
Alternative TitleThe size dependence of grain boundary relaxation and mechanical dissipation in polycrystalline solids
段闯闯
Thesis Advisor魏宇杰 ; 郑仰泽
2021-05-18
Degree Grantor中国科学院大学
Place of Conferral北京
Subtype博士
Degree Discipline固体力学
KeywordZener模型,“葛峰”,晶界弛豫,尺寸效应,内耗谱,损耗模量峰
Abstract

  内耗指材料振动过程中的能量耗散,它度量材料的阻尼性能,是一个重要的工程参数,同时也反映了材料内部独特的微观结构信息。Zener和葛庭燧关于晶界弛豫的奠基性工作发现了由晶界粘滞滑动引起的内耗峰(“葛峰”),是晶界具有粘滞性质的有力证据。此后,晶界弛豫与晶界内耗的研究得到了广泛的关注。

  随着纳米多晶材料的涌现,积累了很多关于多晶体材料弛豫与晶粒尺寸关系的实验结果,而现有模型都无法给出全面合理的解释。基于这一背景,本文深入研究晶界几何与变形特征的影响,揭示这些特征与晶界弛豫及其引起的损耗之间的关系。论文工作所取得的主要创新性成果如下:

       (1) 从晶界的微观变形机理出发,建立了基于连续介质描述的晶界相模型,给出了晶界的粘弹性变形与扩散耦合的理论,发展了相应的数值方法来计算多晶体力学损耗的频率响应。

       (2) 基于晶界相模型,研究了晶界粘滞变形引起的能量耗散与弛豫。发现多晶体损耗模量谱中新的损耗模量峰,与周知的粘滞滑动峰不同,它由晶界粘滞挤压变形引起。该特征峰的弛豫时间正比于晶粒尺寸的三次方;与之对照,粘滞滑动峰的弛豫时间正比于晶粒尺寸。

       (3) 引入晶界扩散机制,获得了晶界扩散引起的损耗模量峰。晶界扩散的弛豫机理有别于粘滞弛豫。根据获得的多晶体损耗模量谱上可能出现的峰值的所有情况,提出了一个包含晶界粘滞变形,晶界扩散,以及晶界弹性效应的唯象力学模型,揭示了各弛豫机制的晶粒尺寸效应。

       (4) 研究了葛峰”(晶界内耗峰)弛豫强度的晶粒尺寸效应,发现晶界内耗峰高度随晶界体积分数线性增加。同时,发现双晶试样的晶界内耗峰峰值正比于试样的宽厚比。在保持双晶试样宽厚比不变的情况下,峰值与晶界体积分数成线性关系。

       (5) 通过对比晶界相模型所得到的损耗模量峰的展宽发现晶粒尺寸越小,粘滞滑动峰的展宽越宽。进一步分析发现,多晶体晶粒尺寸分布以及晶界角度分布不影响粘滞滑动峰的展宽,晶界粘滞系数的分布是粘滞滑动峰变宽的原因。总体上,计算获得的损耗模量峰展宽比Debye峰更宽。

       (6) Honeycomb多晶模型的粘滞内耗谱上发现在某一频率区间内,内耗随频率的-1/3 次方变化,这与地质材料的内耗实验结果一致。晶粒尺寸与晶界扩散的快慢不影响这一区间的幂指数关系,但该区间的频率范围随晶界扩散加快而变窄,而晶粒变大使其变宽。

  本文在Zener和葛庭燧工作的基础上,考虑晶界粘滞变形引起的耗散,基于连续介质描述的晶界相模型,发现多晶体损耗模量谱上由晶界粘滞挤压变形引起的新的峰值。同时,根据本文的晶界相模型,研究了葛峰”(粘滞滑动峰)的晶粒尺寸效应,取得了与实验观察一致的结果。进一步,引入扩散机制,揭示了晶界扩散对晶界粘滞变形的调控作用,并得到了由晶界扩散导致的损耗模量峰。当晶界具有适当的扩散速率与长时模量时,多晶体的内耗谱上可能同时存在三个峰值。这三个峰值是否出现与晶界的性质有关,这也解释了实验中不同多晶材料内耗谱结果的差异。本文的工作对晶界内耗峰的物理机制的研究具有重要意义,同时也有利于地震波在地球介质传播过程中的衰减与地震行为的研究。

Other Abstract

        Internal friction is responsible for all solids to transform kinetic energy into heat. It measures the damping properties of materials and provides unique information about the inner structure of solids. The pioneering analyses by Zener and Kê demonstrated the existence of an internal friction peak (the Kê peak) in polycrystalline solids resulted from viscous sliding of grain boundaries. Since then, grain boundary relaxation and the associated mechanical dissipation behavior have been widely investigated.

       While the existing models based on the interface assumption are incapable of explaining serval experimental observations as grain size decreases. From the knowledge of the geometric characteristics and deformation mechanisms of grain boundaries, we established a continuum model to investigate grain boundary relaxation and the associated mechanical dissipation in polycrystalline solids. The following results are obtained:

      (1) A continuum model coupled elastic deformation, viscous creep and diffusion in grain boundaries is established. Micromechanical based finite element modelling has been employed to study the inherent frequency response of internal dissipation in both three-dimensional and two-dimensional polycrystalline aggregates.

      (2) The viscous dissipation behavior of polycrystalline solids with finite grain boundary thickness is investigated based on the continuum model. Excepted for the loss peaks resulted from viscous sliding, a second loss peak resulted from viscous squeezing of grain boundaries is found in the loss modulus spectra. The relaxation time of the viscous squeezing peak is proportional to the cubic of grain size d , while the relation time of the viscous sliding peak is proportional to grain size. The newly revealed peak is attributed to the relaxation of the normal forces across grain boundaries.

      (3) When grain boundary diffusion involves, the relaxation mechanism of grain boundary diffusion and its relationship with viscous squeezing are clarified. Another loss modulus peak resulted from grain boundary diffusion is found. Based on the calculated loss modulus spectra, a phenomenological model that includes the two viscous deformation modes, grain boundary diffusion, and local elasticity of grain boundaries is developed. The phenomenological model can capture the grain-size effect of all the three relaxation mechanisms.

       (4) The amplitude (relaxation strength) of the viscous sliding peak is found to increase linear with grain boundary fraction, for both polycrystalline and bi-crystal samples. The key parameter controlling the amplitude of the viscous sliding peak in bi-crystal samples is identified. It is shown that the amplitude of the viscous sliding peak in bi-crystal is proportional to the ratio of the width to the thickness of the bi-crystal sample.

      (5) The loss modulus peaks resulted from viscous deformation according to the continuum model are essentially broader than a single Debye peak. As grain size goes down, the viscous sliding peak broadens progressively. Moreover, it is shown that the viscous sliding peak broadens when introducing different viscosities for different grain boundaries. However, the variation in grain sizes and grain corners don’t change the width of the viscous sliding peak.

      (6) Mild–frequency dependent behavior of internal friction observed consistently in geological materials is also found in our calculation. For honeycomb samples, the exponent is -1/3 . The role of grain boundary diffusion on the mild–frequency dependent behavior is analyzed. It is shown that with growing diffusion rate, the frequency range of the mild–frequency dependent region is reduced, while the exponent keeps invariant. Another factor that influences the frequency range of the region is grain size. The larger the grain size, the wider the region.

      We follow the treatment employed by Zener and Kê, and consider relaxation aroused from viscous grain boundaries based on our continuum grain boundary model. We reveal the existence of a second loss peak resulted from viscous squeezing in grain boundaries. The grain size effect of the peak is investigated based on our continuum model and predict results that are consistent with experimental observations. We further include grain boundary diffusion as relaxation mechanism and obtain a third loss modulus peak. The role of grain boundary diffusion on viscous relaxation within grain boundaries is clarified. Three loss peaks may exist in the same internal friction spectrum under certain conditions. The findings in this thesis provide physical mechanisms for multi-peaks found in the internal friction spectrum of polycrystalline solids and can be applied to granular and porous materials, and complex rheology in geosciences, where internal dissipation is momentous for waves and seismic activities.

Language中文
Document Type学位论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/86541
Collection非线性力学国家重点实验室
Recommended Citation
GB/T 7714
段闯闯. 多晶体晶界弛豫与内耗的尺寸效应[D]. 北京. 中国科学院大学,2021.
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