Onset and Direction of Shear Banding Instability in Metallic Glasses

doi:10.1016/j.jmst.2014.05.005

Abstract

Abstract: The shear banding instability occurs as the homogenous deformation in metallic glasses (MGs) develops to a critical point, at which the discontinuity in deformation rate is incipient across nano-scale shear bands. When and where the shear instability takes place is an important issue for understanding the shear band origin. However, such condition and direction of shear localization concerning the unique properties of MGs is still lacking for general stress state. In this paper, a new constitutive is introduced for MGs accounting for the pressure sensitivity, dilatancy and structural evolution; the shear banding is regarded as the appearance of instability in the constitutive description of inelastic deformation. Tying the bifurcation theory to the new constitutive, the general condition of deformation localization is derived. The shear band orientation corresponding to the easiest direction of shear instability is then obtained in dependence on pressure sensitivity, dilatancy and Poisson's ratio for MGs. The range of the predicted shear band angles is consistent with the experimental observations.

Key words: Metallic glasses, Shear banding instability, Bifurcation

Chen Yan, Dai Lanhong. Onset and Direction of Shear Banding Instability in Metallic Glasses[J]. J. Mater. Sci. Technol., 2014, 30(6): 616-621.

References

[1] A.L. Greer, Y.Q. Cheng, E. Ma,Mater. Sci. Eng. R, 74 (2013), pp. 71–132
[2] L.H. Dai,B. Dodd,Y.L. Bai (Eds.),Adiabatic Shear Localization: Frontiers and Advances,Elsevier,London (2012), pp. 311–361
[3] L.H. Dai, M. Yang, L.F. Liu, Y.L. Bai,Appl. Phys. Lett., 87 (2005),p. 141916
[4] L.H. Dai, Y.L. Bai,Int. J. Impact Eng., 35 (2008), pp. 704–716
[5] M.Q. Jiang, L.H. Dai,J. Mech. Phys. Solids, 57 (2009), pp. 1267–1292
[6] S.X. Song, T.G. Nieh,Intermetallics, 19 (2011), pp. 1968–1977
[7] L. Wang, Z.P. Lu, T.G. Nieh,Scripta Mater., 65 (2011), pp. 759–762
[8] M.Q. Jiang, W.H. Wang, L.H. Dai,Scripta Mater., 60 (2009), pp. 1004–1007
[9] M.Q. Jiang, L.H. Dai,Acta Mater., 59 (2011), pp. 4525–4537
[10] R. Maa?, D. Klaumünzer, J.F. L?ffler,Acta Mater., 59 (2011), pp. 3205–3213
[11] Y. Shao, K. Yao, M. Li, X. Liu,Appl. Phys. Lett., 103 (2013),p. 171901
[12] Y. Chen, M.Q. Jiang, L.H. Dai,Int. J. Plasticity, 50 (2013), pp. 18–36
[13] W.H. Wang,J. Appl. Phys., 110 (2011),p. 053521
[14] C. Schuh, T. Hufnagel, U. Ramamurty,Acta Mater., 55 (2007), pp. 4067–4109
[15] M.W. Chen,Annu. Rev. Mater. Res., 38 (2008), pp. 445–469
[16] A.S. Argon,Acta Metall., 27 (1979), pp. 47–58
[17] F. Spaepen,R. Balian (Ed.) et al., Les Houches Lectures XXXV on Physics of Defects, North-Holland, Amsterdam (1981), pp. 133–174
[18] W. Johnson, K. Samwer,Phys. Rev. Lett., 95 (2005),p. 195501
[19] M.L. Falk, J.S. Langer,Phys. Rev. E, 57 (1998), pp. 7192–7205
[20] P. Thamburaja, R. Ekambaram,J. Mech. Phys. Solids, 55 (2007), pp. 1236–1273
[21] R. Huang, Z. Suo, J.H. Prevost, W.D. Nix,J. Mech. Phys. Solids, 50 (2002), pp. 1011–1027
[22] H. Zhang, S. Maiti, G. Subhash,J. Mech. Phys. Solids, 56 (2008), pp. 2171–2187
[23] Z.F. Zhang, J. Eckert,Phys. Rev. Lett., 94 (2005),p. 094301
[24] Y. Chen, M.Q. Jiang, Y.J. Wei, L.H. Dai,Philos. Mag., 91 (2011), pp. 4536–4554
[25] C.A. Schuh, A.C. Lund,Nat. Mater., 2 (2003), pp. 449–452
[26] C.H. Hsueh, H. Bei, C.T. Liu, P.F. Becher, E.P. George,Scripta Mater., 59 (2008), pp. 111–114
[27] J. Fornell, A. Concustell, S. Suri?ach, W.H. Li, N. Cuadrado, A. Gebert, M.D. Baró, J. Sort,Int. J. Plasticity, 25 (2009), pp. 1540–1559
[28] R. Hill, J. Mech,Phys. Solids, 10 (1962), pp. 1–16
[29] J.W. Rudnicki, J.R. Rice,J. Mech. Phys. Solids, 23 (1975), pp. 371–394
[30] R. Hill, J.W. Hutchinson,J. Mech. Phys. Solids, 23 (1975), pp. 239–264
[31] J.R. Rice,W.T. Koiter (Ed.),Theoretical and Applied Mechanics,North-Holland,Amsterdam (1976), pp. 207–220
[32] Y.F. Gao, L. Wang, H. Bei, T.G. Nieh,Acta Mater., 59 (2011), pp. 4159–4167
[33] H.H. Ruan, L.C. Zhang, J. Lu,Int. J. Solids Struct., 48 (2011), pp. 3112–3127
[34] V. Tvergaard,Int. J. Fract., 18 (1982), pp. 237–252
[35] V. Tvergaard,Int. J. Fract., 17 (1981), pp. 389–407
[36] Q. Yang, A. Mota, M. Ortiz,Comput. Mech., 37 (2006), pp. 194–204
[37] G.S. Grest, M.H. Cohen,Adv. Chem. Phys., 48 (1981), pp. 455–525
[38] W.L. Johnson, J. Lu, M.D. Demetriou,Intermetallics, 10 (2002), pp. 1039–1046
[39] M.Q. Jiang, Z. Ling, J.X. Meng, L.H. Dai,Philos. Mag., 88 (2008), pp. 407–426
[40] Y.F. Gao,Model. Simul. Mater. Sci. Eng., 14 (2006), pp. 1329–1345
[41] Z.F. Zhang, G. He, J. Eckert, L. Schultz,Phys. Rev. Lett., 91 (2003),p. 045505
[42] J.J. Lewandowski, W.H. Wang, A.L. Greer,Philos. Mag. Lett., 85 (2005), pp. 77–87
[43] S.J. Poon, A. Zhu, G.J. Shiflet,Appl. Phys. Lett., 92 (2008),p. 261902