Strain-dependent activation energy of shear transformation in metallic glasses

Abstract

Shear transformation (ST) plays a decisive role in determining the mechanical behavior of metallic glasses, which is believed to be a stress-assisted thermally activated process. Understanding the dependence in its activation energy on the stress imposed on the material is of central importance to model the deformation process of metallic glasses and other amorphous solids. Here a theoretical model is proposed to predict the variation of the minimum energy path (MEP) associated with a particular ST event upon further deformation. Verification based on atomistic simulations and calculations are also conducted. The proposed model reproduces the MEP and activation energy of an ST event under different imposed macroscopic strains based on a known MEP at a reference strain. Moreover, an analytical approach is proposed based on the atomistic calculations, which works well when the stress varies linearity along the MEP. These findings provide necessary background for understanding the activation processes and, in turn, the mechanical behavior of metallic glasses.

Predicting Shear Transformation Events in Metallic Glasses

“…Clearly, in the one-dimensional case, ξ * = V ∂τ ∂x . As has been demonstrated in our previous work [19], Eq. 3 can be solved by numerical integration if the whole one-dimensional energy landscape is known.…”

“…s , with an energy barrier of Q(γ 0 ) = Q 0 . If the corresponding minimum energy path (MEP) can be approximated by a cubic polynomial (which has often observed in MGs as a fold catastrophe [12,20]), and the stress gradient ∂τ ∂x remains constant for any x, then the solution of the above equation of motion can be expressed analytically, and information on the initial minimum and the transition state configuration at the referential strain level will be sufficient to define the unknown parameters [19]. Especially, the critical macroscopic shear strain at which the ST event will be triggered would be given by [19]:…”

“…In this letter, ARTn will be employed to harvest the ST events in a Cu 64 Zr 36 MG model, which contains 10000 atoms in total and was generated with a cooling rate of 10 9 K/s. This model was also used in our previous work [19]. The "activation" was initiated by imposing a random displacement to the local cluster centered on a chosen atom with a radius of 3.7Å, which corresponds to the first minimum of the pair correlation function of the Cu 64 Zr 36 MG.…”

“…The full MEP of these four events are then calculated by using the nudged elastic band (NEB) method. Based on the information from the NEB calculations the respective triggering strains of these events are re-predicted (refined) by using the full numerical integration [19] instead of the analytical approximation of Eq. 5.…”

“…Two more events are ruled out according to the re-prediction (The appendix in Ref. [19] illustrated a typical example that should be ruled out). Thus, only two events are predicted to be triggered with critical shear strains in the range of 0.00% < γ xy < 5.00%.…”