Computational modelling of submicron-sized metallic glasses

Abstract

The present contribution is concerned with the modelling and computation of stable shear localization process in submicron-sized metallic glasses. To this end, a non-local thermodynamically consistent, continuum mechanical, constitutive model is developed. In our previous work, we formulated the model in the small strain framework. In current work, this model is extended to finite strains. The numerical implementation is carried out with the help of the finite element method. Numerical examples are presented – illustrating the general model behaviour which is correlated to experimental observations. It is shown that the proposed finite deformation model is well suitable to predict the stable shear localization process in submicron-sized metallic glasses and its size effect. The model confirms that with decreasing sample size the shear localization process starts at a later deformation state. Additionally, the finite deformation model is able to predict the failure process in submicron-sized metallic glasses as well as the delay of it with decreasing sample size qualitatively correct.

Keywords:

• metallic glass
• constitutive model
• viscoplasticity
• size effect
• finite element method
• shear localization
• failure

Acknowledgments

The authors are grateful for the many valuable comments supplied by the referees of this paper.

Notes

1. denotes the referential gradient operator.

2. represents a kind of material constant mimicing the energy at the tip of the shear band. The value can be determined via density functional theory, as done in [41]. It has been observed and explained experimentally [18] that shear band confinement changes the deformation mode as long as the spacing of the second phases matches the plastic zone size of the related metallic glass matrix. When the size of the fracture process zone, which is in turn correlated with the fracture (surface) energy through Griffith’s criterion, is greater than the sample size, the deformation can be localized and constrained through the formation of a shear band without forming a real free surface. A transition from shear localization (inhomogeneous) to homogeneous deformation was observed when the size of the sample decreases below approximately 100 mm at room temperature and quasi-static condition, where no shear banding is observed under these conditions. In general, the deformation via shear-banding does not necessarily correspond to any fracture process. Here, our notation is based on the notation in the literature (see e.g. [41, 42]), where sometimes the shear deformation zone is referred to as fracture zone.