|Alternative Title||The size dependence of grain boundary relaxation and mechanical dissipation in polycrystalline solids|
|Thesis Advisor||魏宇杰 ; 郑仰泽|
|Place of Conferral||北京|
(6) 在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。
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 Kê 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.
|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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