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Register a new userMicroscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses
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The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the many-body Smoluchowski equation. The resulting nonlinear stress-strain (constitutive) relation is very simple, with few fitting parameters, yet contains all the microscopic physics. The theory is successfully tested against experimental data on metallic glasses, and it is able to reproduce the ubiquitous feature of stress-strain overshoot upon varying temperature and shear rate. A clear atomic-level interpretation is provided for the stress overshoot, in terms of the competition between the elastic instability caused by nonaffine deformation of the glassy cage and the stress buildup due to viscous dissipation.
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We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local defects to such materials. We propose a scalar noise field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.
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We numerically study the evolution of the vibrational density of states $D(omega)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(omega) sim omega^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(omega) sim omega^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.
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