mater.scichina.com link.springer.com Published online 30 November 2021 | https://doi.org/10.1007/s40843-021-1837-9 Grain boundary diffusion and viscous flow governed mechanical relaxation in polycrystalline materials Chuangchuang Duan 1,2 and Yujie Wei 1,2* ABSTRACT Grain boundary (GB) diffusion and viscous flow play dominant roles in mechanical relaxation of polycrystal- line materials. The pioneering work of Zener and Kê, by ac- counting for relaxation in GBs by viscous shearing, predicts a single peak in the internal friction spectrum. Later investiga- tions show the existence of two to three peaks in the internal friction spectrum when taking into account both GB diffusion and viscous flow for dissipation. In this paper, we further identify the characteristic relaxation modes in polycrystalline materials. We illustrate that competitive viscous flow and diffusion for normal stress relaxation give rise to distinct de- pendence of relaxation time on grain size. We construct an internal friction spectrum mapping based on the competitive deformation mechanisms including viscous flow in both normal and tangential directions and GB diffusion. The es- sential features of internal friction spectrum of polycrystalline materials from our analysis are consistent with available ex- perimental observations. These findings may also be applic- able to study relaxation dynamics of other material systems such as metallic glasses and porous materials. Keywords: grain boundary diffusion, viscous flow, internal frictionspectrum,polycrystallinematerials,Zener-Kêdissipation INTRODUCTION Mechanical loss spectra such as the internal friction spectrum and loss modulus spectrum hold important clues to the relaxation dynamics of materials [1–3].Typically,apeakappears in the mechanical loss spectrum when a particular dissipative deformation mode outweighs other competitive ones, which may tell us about the activation of the particular deformation mechanism at certain given conditions. Furthermore, as mechanical energy dissipation or mechanical loss from micro- structural relaxation often depends on both frequencies and temperatures, one may decipher the active deformation mechanisms in the frequency and temperature space. For instance, viscous flow and self-diffusion are two fundamental transport phenomena that occur in a wide range of materials. The coupling between these two processes is a central topic of condensed matter physics and plays a crucial role in the relaxation dynamics of materials [4–6]. For polycrystalline materials at elevated temperatures, self- diffusion and viscous flow in grain boundaries (GBs) constitute a significant portion of plastic deformation of polycrystalline materials [7,8] and hence lower the effective modulus [9,10]. The reduction in modulus is accompanied by mechanical energy dissipation and is a typical relaxation phenomenon [11] which has been investigated intensively. At elevated temperatures, due to relatively high mobility of atoms in GBs, the shearing resis- tance to GB sliding is dramatically less than plastic mechanisms in grain interiors [12,13]. Upon dynamic loading, Zener [9] predicted that GB sliding gives rise to a peak in the internal friction spectrum of polycrystalline materials as a result of free GB sliding. This dissipation peak P s was first observed by Kê [14] in experiments and subsequently confirmed by others [15– 18]. The relaxation via GB sliding is an idealized scenario: GB sliding cannot operate alone without other deformation mechanisms to accommodate the incompatibilities that would otherwiseappearatGBs.Whentheloadingtimescaleisshortor the temperature is relatively low, elastic deformation in grains will be the mode of accommodation [9,17,18]. The grains are distorted and the stored elastic strain will provide the driving force for reversible sliding of GBs upon unloading. Such beha- vior is an anelastic process originally proposed by Zener [19],in which the strain in the previous loading process is time- dependent but recoverable. In these elastically accommodated GB sliding models [9,17,18], viscous GB sliding is the sole mechanism for energy dissipation: the shear stress acting across GBs can be relaxed to zero whereas the normal stress is sus- tained. At high temperatures or low strain rates, deformation in the GB normal direction is also possible and therefore normal stress may be relaxed as well [10,20–24]. Raj and Ashby [10] con- sidered the case of GB sliding accommodated by GB diffusion and estimated the sliding displacement and velocity based on a wave-shaped bicrystal model. Morris and Jackson [22] and Lee et al. [23] calculatedtheinternalfrictionspectrumusingtheRaj- Ashby bicrystal model [10] and found a steady-state regime controlled by Coble creep [25], within which the internal fric- tion varies inversely with the loading frequency. In addition to diffusion, viscous flow may also give rise to separation or con- traction of GBs of a finite width [20,21,24]. Drucker [20] and Dryden et al. [21] analyzed the creep behavior of polycrystalline materials in which fluid-like matter in GBs is squeezed out to accommodateviscousslip.BesidesthepeakP s thatresultedfrom GB sliding, another peak P sq was found in the loss modulus spectrum due to this squeeze-out process, a direct resultant of normal stress relaxation [24,26]. 1 State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China 2 School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China * Corresponding author (email: yujie_wei@lnm.imech.ac.cn) SCIENCE CHINA Materials ARTICLES 1 © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021