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According to the microstructure of amorphous crystal, the percolation theory, which is a theoretical approach to dealing with the inhomogeneous physical systems or random fractals, is used to describe the plastic flows of amorphous alloys under shear yielding. In order to understand in depth the critical problems about the shear band initiations in amorphous alloys, a percolation model for shear transformations of these alloys is established by combining with the existing free volume model and shear transformation zone model. Taking the binary amorphous alloy Cu25Zr75 for example, the percolation threshold for the shearing instability of the atomic clusters prone to producing plastic flows in the shear transformation zone is calculated when a shear band comes into being. In addition, the size of the above-mentioned cluster is also roughly estimated. The calculated results show that the percolation threshold of the shearing instability is similar to the critical reduced free volume value (xC) of~2.4% for the onset of yielding in amorphous alloy although this threshold is closely related to the dispersity of free volume. The present study may provide a new idea and method of studying the ductile-brittle transition in amorphous alloy.
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Keywords:
- amorphous alloy /
- percolation theory /
- shear instability /
- percolation threshold
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[2] Ding D, Zhang Y Q, Xia L 2015 Chin. Phys. Lett. 32 106101
[3] Schroers J 2013 Phys. Today 66 32
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[5] Gao W, Feng S D, Qi L, Zhang S L, Liu R P 2015 Chin. Phys. Lett. 32 116101
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[7] Wang W H, Yang Y, Nieh T G, Liu C T 2015 Intermetallics 67 81
[8] Wang Q, Zhang S T, Yang Y, Dong Y D, Liu C T, Lu J 2015 Nat. Commun. 6 7876
[9] Spaepen F 1977 Acta Metall. 25 407
[10] Argon A S 1979 Acta Mater. 27 47
[11] Wang J G, Zhao D Q, Pan M X, Wang W H, Song S X, Nieh T G 2010 Scripta Mater. 62 477
[12] Liu A J, Nagel S R 1998 Nature 396 21
[13] Chen D Z, Shi C Y, An Q, Zeng Q, Mao W L, Greer J R 2015 Science 349 1306
[14] Broadbent S R, Hammersley J M 1957 Math. Proc. Cambridge 53 629
[15] Wu S H 1985 Polymer 26 1855
[16] Li Q, Zheng W G, Qi Z N, Zhu X G, Cai Z L 1992 Sci. China:Chem. 22 236(in Chinese)[李强, 郑文革, 漆宗能, 朱晓光, 蔡忠龙1992中国科学:化学 22 236]
[17] Pan D, Inoue A, Sakurai T, Chen M W 2008 Proc. Nat. Acad. Sci. USA 105 14769
[18] Senkov O N, Miracle D B 2001 Mater. Res. Bull. 36 2183
[19] Huang R, Suo Z, Prevost J H, Nix W D 2002 J. Mech. Phys. Solids 50 1011
[20] Liu L F, Hu J, Cai Z P, Li H Q, Guo S B, Zhang G Y 2012 Acta Mech. Solida Sin. 33 69(in Chinese)[刘龙飞, 胡静, 蔡志鹏, 李会强, 郭世伯, 张光业2012固体力学学报 33 69]
[21] Hu J 2011 M. S. Thesis (Xiangtan:Hunan University of Science and Technology) (in Chinese)[胡静2011硕士学位论文(湘潭:湖南科技大学)]
[22] Arogn A S, Demkowice M J 2008 Metall. Mater. Trans. A 39 1762
[23] Wu X Z, Zhu X G, Qi Z N 1991 Proceedings of the 8th International Conference on Deformation, Yield and Fracture of Polymers London 1991 p78
[24] Irani R R, Callis C F 1963 Particle Siz:Measurement, Interpretation and Application (New York:Wiley) p40
[25] Liu Z H, Zhu X G, Zhang X D, Qi Z N, Cai Z L, Wang F S 1998 Acta Polym. Sin. 1 32(in Chinese)[刘浙辉, 朱晓光, 张学东, 漆宗能, 蔡忠龙, 王佛松1998高分子学报 1 32]
[26] Liu L F, Dai L H, Bai Y L, Ke F J 2008 Sci. China:Phys. Mech. Astron. 51 1367
[27] Wang B P, Wang L, Xue Y F, Wang Y W, Zhang H F, HuaMeng F U 2016 Trans. Nonferrous Met. Soc. China 26 3154
[28] Jeon C, Kang M, Kim C P, Kim H S, Lee S 2016 Mater. Sci. Eng. A 650 102
[29] Yang B, Li X, Luo W, Li Y 2015 Acta Metall. Sin. 51 465
[30] Wu Y C, Wang B, Hu Y C, Lu Z, Li Y Z, Shang B S, Wang W H, Bai H Y, Guan P F 2017 Scripta Mater. 134 75
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[1] Wang W H 2013 Prog. Phys. 33 177(in Chinese)[汪卫华2013物理学进展 33 177]
[2] Ding D, Zhang Y Q, Xia L 2015 Chin. Phys. Lett. 32 106101
[3] Schroers J 2013 Phys. Today 66 32
[4] Jiang M Q 2014 Mater. China 33 257(in Chinese)[蒋敏强2014中国材料进展 33 257]
[5] Gao W, Feng S D, Qi L, Zhang S L, Liu R P 2015 Chin. Phys. Lett. 32 116101
[6] Jiang M Q 2012 Acta Mech. Solida Sin. 33 227(in Chinese)[蒋敏强2012固体力学学报 33 227]
[7] Wang W H, Yang Y, Nieh T G, Liu C T 2015 Intermetallics 67 81
[8] Wang Q, Zhang S T, Yang Y, Dong Y D, Liu C T, Lu J 2015 Nat. Commun. 6 7876
[9] Spaepen F 1977 Acta Metall. 25 407
[10] Argon A S 1979 Acta Mater. 27 47
[11] Wang J G, Zhao D Q, Pan M X, Wang W H, Song S X, Nieh T G 2010 Scripta Mater. 62 477
[12] Liu A J, Nagel S R 1998 Nature 396 21
[13] Chen D Z, Shi C Y, An Q, Zeng Q, Mao W L, Greer J R 2015 Science 349 1306
[14] Broadbent S R, Hammersley J M 1957 Math. Proc. Cambridge 53 629
[15] Wu S H 1985 Polymer 26 1855
[16] Li Q, Zheng W G, Qi Z N, Zhu X G, Cai Z L 1992 Sci. China:Chem. 22 236(in Chinese)[李强, 郑文革, 漆宗能, 朱晓光, 蔡忠龙1992中国科学:化学 22 236]
[17] Pan D, Inoue A, Sakurai T, Chen M W 2008 Proc. Nat. Acad. Sci. USA 105 14769
[18] Senkov O N, Miracle D B 2001 Mater. Res. Bull. 36 2183
[19] Huang R, Suo Z, Prevost J H, Nix W D 2002 J. Mech. Phys. Solids 50 1011
[20] Liu L F, Hu J, Cai Z P, Li H Q, Guo S B, Zhang G Y 2012 Acta Mech. Solida Sin. 33 69(in Chinese)[刘龙飞, 胡静, 蔡志鹏, 李会强, 郭世伯, 张光业2012固体力学学报 33 69]
[21] Hu J 2011 M. S. Thesis (Xiangtan:Hunan University of Science and Technology) (in Chinese)[胡静2011硕士学位论文(湘潭:湖南科技大学)]
[22] Arogn A S, Demkowice M J 2008 Metall. Mater. Trans. A 39 1762
[23] Wu X Z, Zhu X G, Qi Z N 1991 Proceedings of the 8th International Conference on Deformation, Yield and Fracture of Polymers London 1991 p78
[24] Irani R R, Callis C F 1963 Particle Siz:Measurement, Interpretation and Application (New York:Wiley) p40
[25] Liu Z H, Zhu X G, Zhang X D, Qi Z N, Cai Z L, Wang F S 1998 Acta Polym. Sin. 1 32(in Chinese)[刘浙辉, 朱晓光, 张学东, 漆宗能, 蔡忠龙, 王佛松1998高分子学报 1 32]
[26] Liu L F, Dai L H, Bai Y L, Ke F J 2008 Sci. China:Phys. Mech. Astron. 51 1367
[27] Wang B P, Wang L, Xue Y F, Wang Y W, Zhang H F, HuaMeng F U 2016 Trans. Nonferrous Met. Soc. China 26 3154
[28] Jeon C, Kang M, Kim C P, Kim H S, Lee S 2016 Mater. Sci. Eng. A 650 102
[29] Yang B, Li X, Luo W, Li Y 2015 Acta Metall. Sin. 51 465
[30] Wu Y C, Wang B, Hu Y C, Lu Z, Li Y Z, Shang B S, Wang W H, Bai H Y, Guan P F 2017 Scripta Mater. 134 75
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