Abstract Internal friction is essential for nearly all solids to dissipate kinetic energy through internal mechanisms. The pioneering analyses by Zener (Phys. Rev. 60 (1941) 906-908) and Ke (Phys. Rev. 71 (1947) 533-546) demonstrated the existence of a single friction peak in the loss modulus spectrum of polycrystalline solids, which is attributed to viscous sliding in grain boundaries. In this study, we establish a continuum model coupled elastic deformation, viscous creep and diffusion in grain boundaries and reveal the existence of a second loss modulus peak resulted from viscous deformation within grain boundaries. The corresponding two frequencies when internal dissipation reaches its local maximum depend on grain size d, one is inversely proportional to d, and the other is proportional to d − 3 . The effects of local elasticity and diffusion in grain boundaries on the loss modulus spectrum are examined and the condition when the two peaks emerge is identified. The findings can be applied to granular and porous materials, and complex rheology in geosciences, where internal dissipation is momentous for waves and seismic activities.

中文翻译：

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多晶固体内部耗散对晶粒尺寸和频率的缩放

摘要 内摩擦对于几乎所有固体通过内部机制耗散动能至关重要。Zener (Phys. Rev. 60 (1941) 906-908) 和 Ke (Phys. Rev. 71 (1947) 533-546) 的开创性分析证明了多晶固体的损耗模量谱中存在单个摩擦峰，这归因于晶界中的粘性滑动。在这项研究中，我们建立了一个耦合弹性变形、粘性蠕变和晶界扩散的连续模型，并揭示了晶界内粘性变形导致的第二个损耗模量峰的存在。内部耗散达到其局部最大值时对应的两个频率取决于晶粒尺寸 d，一个与 d 成反比，另一个与 d − 3 成正比。检查了局部弹性和晶界扩散对损耗模量谱的影响，并确定了两个峰出现时的条件。这些发现可应用于粒状和多孔材料，以及地球科学中的复杂流变学，其中内部耗散对波浪和地震活动至关重要。