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Wang XJ, Lu YZ, Lu X, Huo JT, Wang YJ, Wang WH, Dai LH, Jiang MQ. Elastic criterion for shear-banding instability in amorphous solids. Phys Rev E 2022; 105:045003. [PMID: 35590559 DOI: 10.1103/physreve.105.045003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 04/05/2022] [Indexed: 06/15/2023]
Abstract
In amorphous solids, plastic flow is prone to localization into shear bands via an avalanche of shear-transformation (ST) rearrangements of constituent atoms or particles. However, such banding instability still remains a lack of direct experimental evidence. Using a real 3D colloidal glass under shear as proof of principle, we study STs' avalanches into shear banding that is controlled by strain rates. We demonstrate that, accompanying the emergent shear banding, the elastic response fields of the system, typical of a quadrupole for shear and a centrosymmetry for dilatation, lose the Eshelby-type spatial symmetry; instead, a strong correlation appears preferentially along the banding direction. By quantifying the fields' spatial decay, we identify an elastic criterion for the shear-banding instability, that is, the strongly correlated length of dilatation is smaller than the full length of shear correlation. Specifically, ST-induced free volume has to be confined within the elastic shear domain of ST so that those STs can self-organize to trigger shear banding. This physical picture is directly visualized by tracing the real-space evolution of local dilatation and ST particles. The present work unites the two classical mechanisms: free volume and STs, for the fundamental understanding of shear banding in amorphous solids.
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Affiliation(s)
- X J Wang
- State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Y Z Lu
- School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, People's Republic of China
| | - X Lu
- School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, People's Republic of China
| | - J T Huo
- Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, People's Republic of China
| | - Y J Wang
- State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - W H Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - L H Dai
- State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - M Q Jiang
- State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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Abstract
Contrary to crystalline solids, amorphous solids always become softer when vitrifying the melts under higher cooling rates. Understanding this phenomenon is of utmost importance in providing a basis for the mechanical-performance control of amorphous solids. However, the underlying mechanisms leading to this cooling-rate-induced softening of amorphous solids have remained elusive, especially the dynamic reasons are neglected. Here, we use a colloidal glass as the model system to directly study this issue. Shear modulus is used as the representative parameter to monitor the stress-bearing properties of colloidal glass. The space-spanning immobile particles, whose population is sensitive to the cooling rate, are found to make the dominant contribution to the shear modulus. The rapid solidification induced softening of colloidal glass is observed to originate from fewer immobile particles formed at higher cooling rates.
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