Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T19:31:56.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Brittle and Ductile Character of Amorphous Solids

Part of: Generalities, axiomatics, foundations of continuum mechanics of solids

Published online by Cambridge University Press:  27 January 2016

Miguel Lagos  and
Raj Das
Miguel Lagos
Affiliation:
Facultad de Ingeniería, Universidad de Talca, Campus Los Niches, Camino a los Niches , Km 1, Curicó, Chile
Raj Das*
Affiliation:
Department of Mechanical Engineering, University of Auckland, Auckland, New Zealand
*
*Corresponding author. Email: mlagos@utalca.cl (M. Lagos), r.das@auckland.ac.nz(R. Das)
Get access

Abstract.

Common silicate glasses are among the most brittle of the materials. However, on warming beyond the glass transition temperature Tg glass transforms into one of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology, indicating that it rests on the disordered structure instead on the nature of the chemical bonds. The micromechanics of a solid with bulk amorphous structure is examined in order to determine the most basic conditions the system must satisfy to be able of plastic flow. The equations for the macroscopic flow, consistent with the constrictions imposed at the atomic scale, prove that a randomly structured bulk material must be either a brittle solid or a liquid, but not a ductile solid. The theory permits to identify a single parameter determining the difference between the brittle solid and the liquid. However, the system is able of perfect ductility if the plastic flow proceeds in two dimensional plane layers that concentrate the strain. Insight is gained on the nature of the glass transition, and the phase occurring between glass transition and melting.

Keywords

Glassesbulk metallic glassshear bandsductilitymicromechanical modelling

MSC classification

Secondary: 74A45: Theories of fracture and damage 74A60: Micromechanical theories 74A20: Theory of constitutive functions
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 485 - 498
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Schroers, J. and Johnson, W. L., Ductile bulk metallic glass, Phys. Rev. Lett., 93 (2004), 255506.Google Scholar
[2]Eckert, J., Das, J., Kim, K. B., Baier, F., Tang, M. B., Wang, W. H. and Zhang, Z. F., High strength ductile Cu-base metallic glass, Intermetallics, 14 (2006), pp. 876–881.CrossRefGoogle Scholar
[3]Li, M., Eckert, J., Kecskes, L. and Lewandowski, J., Mechanical properties of metallic glasses and applications, J. Mater. Res., 22 (2007), pp. 255–257.Google Scholar
[4]Lu, J., Ravichandran, G. and Johnson, W. L., Deformation behavior of the Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass over a wide range of strain–rates and temperatures, Acta Mater., 51 (2003), pp. 3429–3443.Google Scholar
[5]Keryvin, V., Rouxel, T., Huger, M. and Charleux, L., Elastic moduli of a ZuCuAlNi bulk metallic glass from room temperature to complete crystallisation by in–situ pulse–echo ultrasonic echography, J. Ceramic Soc. Japan, 116 (2008), pp. 851–854.Google Scholar
[6]Schuh, C. A., Hufnagel, T. C. and Ramamurty, U., Mechanical behavior of amorphous alloys, Acta Mater., 55 (2007), pp. 4067–4109.Google Scholar
[7]Lagos, M., Theory of ductility: from brittle to superplastic behavior of polycrystals, Phys. Rev. B, 73 (2006), 224107.CrossRefGoogle Scholar
[8]Griffith, A. A., The phenomena of rupture and flow in solids, Phil. Trans. Roy. Soc. London A, 221 (1920), pp. 163–197.Google Scholar
[9]Irwin, G. R., Fracture Dynamics, in: Fracturing of Metals, Irwin, G. R. and Kies, J. A., (Eds.), American Society of Metals, Cleveland, Ohio (1948), pp. 147–166.Google Scholar
[10]Orowan, E., Fracture and strength of solids, Reports Prog. Phys., 12 (1948), pp. 185–232.Google Scholar
[11]Bilby, B. A., Cottrell, A. H. and Swinden, K. H., The spread of plastic yield from a notch, Proc. Roy. Soc. London Ser. A, 272 (1963), pp. 304–314.Google Scholar
[12]Rice, J. R. and Thompson, R., Ductile versus brittle behaviour of crystals, Phil. Mag. A, 29 (1974), pp. 73–97.Google Scholar
[13]Thompson, R., Physics of fracture, Sol. State Phys. 39 (1986), pp. 1–129.Google Scholar
[14]Hirsch, P. B., Roberts, S. G. and Samuels, J., The brittle-ductile transition in silicon, Proc. Roy. Soc. London Ser. A, 421 (1989), pp. 25–53.Google Scholar
[15]Khantha, M., Pope, D. and Vitek, V., Dislocation screening and the brittle-to-ductile transition: a kosterlitz-thouless type instability, Phys. Rev. Lett., 73 (1994), pp. 684–687.Google Scholar
[16]Hartmaier, A. and Gumbsch, P., On the activation energy for the brittle/ductile transition, Phys. Stat. Sol. B, 202 (1997), pp. R1–R2.3.0.CO;2-J>CrossRefGoogle Scholar
[17]Gumbsch, P., Riedle, J., Hartmaier, A. and Fischmeister, H. F., Controlling factors for the brittle-to-ductile transition in tungsten single crystals, Science, 282 (1998), pp. 1293–1295.Google Scholar
[18]Green, D. J., Tandon, R. and Sglavo, V. M., Crack arrest and multiple cracking in glass through the use of designed residual stress, Science, 283 (1999), pp. 1295–1297.Google Scholar
[19]Marder, M. and Liu, X., Instability in lattice fracture, Phys. Rev. Lett., 71 (1993), pp. 2417–2420.Google Scholar
[20]Batrouni, G. G. and Hansen, A., Fracture in three-dimensional fuse networks, Phys. Rev. Lett., 80 (1998), pp. 325–328.Google Scholar
[21]Henry, H. and Levine, H., Dynamic instabilities of fracture under biaxial strain using a phase field model, Phys. Rev. Lett., 93 (2004), 105504.Google Scholar
[22]Fineberg, J., Gross, S., Marder, M. and Swinney, H., Instability in the propagation of fast cracks, Phys. Rev. B, 45 (1992), pp. 5146–5154.Google Scholar
[23]Sharon, E., Gross, S. and Fineberg, J., Local crack branching as a mechanism for instability in dynamic fracture, Phys. Rev. Lett., 74 (1995), pp. 5096–5099.Google Scholar
[24]Sharon, E. and Fineberg, J., Energy dissipation in dynamic fracture, Phys. Rev. Lett., 76 (1996), pp. 2117–2120.Google Scholar
[25]Ching, E. S. C., Nakanishi, H. and Langer, J. S., Dynamic instabilities in fracture, Phys. Rev. Lett., 76 (1996), pp. 1087–1090.Google Scholar
[26]Slepyan, L. I., Dynamics of a crack in a lattice, Sov. Phys. Dok., 26 (1981), pp. 538–540.Google Scholar
[27]Mozzi, R. L. and Warren, B. E., The structure of vitreous silica, J. Appl. Cryst., 2 (1969), pp. 164–172.Google Scholar
[28]Berthier, L., Biroli, G., Bouchaud, J. P., Cipelletti, L., El Masri, D., L’hôte, D., Ladieu, F. and Pierno, M., Direct experimental evidence of a growing length scale accompanying the glass transition, Science, 310 (2005), pp. 1797–1800.Google Scholar
[29]Lagos, M., Elastic instability of grain boundaries and the physical origin of superplasticity, Phys. Rev. Lett., 85 (2000), pp. 2332–2335.Google Scholar
[30]Lagos, M. and Retamal, C., A theoretical approach to finite strain superplasticity and some of its applications, Phys. Scr., 81 (2010), 055601.Google Scholar
[31]Lagos, M. and Retamal, C., Grain dynamics and plastic properties of highly refined materials, Phys. Scr., 82 (2010), 065603.Google Scholar
[32]Lagos, M. and Retamal, C., An alternate theoretical approach to solid-state bonding, Scripta Mater., 64 (2011), pp. 402–405.Google Scholar
[33]Lagos, M. and Conte, V., Mathematical model for the plastic flow of a polycrystalline material medium, Scripta Mater., 65 (2011), pp. 1053–1056.Google Scholar