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  • Rapid Communication

Derivation of the Johnson-Samwer T2/3 temperature dependence of the yield strain in metallic glasses

Ratul Dasgupta, Ashwin Joy, H. G. E. Hentschel, and Itamar Procaccia
Phys. Rev. B 87, 020101(R) – Published 28 January 2013
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Abstract

Metallic glasses are prone to fail mechanically via a shear-banding instability. In a remarkable paper Johnson and Samwer demonstrated that this failure enjoys a high degree of universality in the sense that a large group of metallic glasses appears to possess a yield strain that decreases with temperature following a −T2/3 law up to logarithmic corrections. In this Rapid Communication we offer a theoretical derivation of this law. We show that our formula fits very well simulation data on typical amorphous solids.

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  • Received 17 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.020101

©2013 American Physical Society

Authors & Affiliations

Ratul Dasgupta1, Ashwin Joy1, H. G. E. Hentschel1,2, and Itamar Procaccia1

  • 1Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
  • 2Department of Physics, Emory University, Atlanta, Georgia, USA

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Vol. 87, Iss. 2 — 1 January 2013

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  • Figure 1
    Figure 1
    The total plastic energy Eq. (3) for the creation of an array of quadrupoles with density ρ for three values of γ: γ=γY−0.1 (upper curve), γ=γY−0.05 (middle curve), and γ=γY (lower curve). In the present case γY=0.07. To generate this picture we use the measured constants E≈ 37.2, ν≈0.31, ε*≈0.082, and a=1.83. Finally Up≈0.22. Note that the interaction between quadrupoles had been computed in the far-field approximation; thus these graphs can be trusted only for ρ≪1.Reuse & Permissions
  • Figure 2
    Figure 2
    Visualization of the process of shear localization in the AQS simulations whose full details can be found in Ref. 7. The arrows indicate the incremental nonaffine displacement. Even with the quasistatic protocol with arbitrary long waiting times if necessary one cannot resolve the formation of the full structure of shear localized band of quadrupoles (lower panel) from the creation of a single quadrupole (upper panel). The lower panel appears instantly after the upper panel.Reuse & Permissions
  • Figure 3
    Figure 3
    Typical stress vs strain curve obtained at finite temperature and finite strain rate. The yield stress was estimated by fitting a cubic to the curve (see inset) and finding the maximum of the curve.Reuse & Permissions
  • Figure 4
    Figure 4
    Comparison of the simulation data of γ(T,γ̇) to the prediction Eq. (13). The dotted line was obtained by finding the best fit for N*. The error bars indicate averaging over three independent realizations.Reuse & Permissions
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