Several recent studies have reported that the elastic strain in metallic glasses, as measured from peak shifts in the pair correlation functions of samples under load, increases with distance from an average atom, approaching the macroscopic strain at large distances. We have verified this behavior using high-energy x-ray scattering on metallic glasses loaded under uniaxial compression, uniaxial tension, and pure shear, and show that the apparent length-scale dependence of elastic strain is not an artifact of the assumption of structural isotropy in the data analysis. Molecular dynamics simulations of a binary Lennard-Jones glass loaded in uniaxial tension reproduce, qualitatively, the behavior observed in the experiments when the elastic strain is calculated from the shifts in the peaks of the pair correlation function. Under hydrostatic loading, however, the length-scale dependence of elastic strain observed in the simulations is greatly reduced. This suggests that non-affine atomic displacements, which are smaller under hydrostatic loading than under uniaxial loading, may play a key role in the length-scale dependence of elastic strain. Furthermore, no length-scale dependence is observed in simulations, for either uniaxial or hydrostatic loading, when the elastic strain is calculated from the average local deformation gradient tensor. We explain this apparent contradiction and show that the atomic displacements resulting from elastic loading are largest in the low density regions between atomic shells around an average atom. Finally, we present an analysis of length-scale dependence of elastic strain calculated from the pair correlation function for the case of homogeneous deformation, which is in good agreement with the simulations conducted under hydrostatic loading. For uniaxial loading, however, the analysis diverges from both the experimental and simulated results in the first two near-neighbor atomic shells. This suggests, in agreement with our observations from the molecular dynamics simulations, that the observed length-scale dependence of elastic strain from scattering measurements reflects the nature of the non-affine atomic displacements in the glass.
We have used high-energy x-ray scattering to map the strain fields around crack tips in fracture specimens of a bulk metallic glass under load at room temperature and below. From the measured strain fields we can calculate the components of the stress tensor as a function of position and determine the size and shape of the plastic process zone around the crack tip. Specimens tested at room temperature develop substantial plastic zones and achieve high stress intensities () prior to fracture. Specimens tested at cryogenic temperatures fail at reduced but still substantial stress intensities () and show only limited evidence of crack-tip plasticity. We propose that the difference in behavior is associated with changes in the flow stress and elastic constants, which influence the number density of shear bands in the plastic zone and thus the strain required to initiate fracture on an individual band. A secondary effect is a change in the triaxial state of stress around the crack tip due to the temperature dependence of Poisson's ratio. It is likely that this ability to map elastic strains on the microscale will be useful in other contexts, although interpreting shifts in the position of the scattering peaks in amorphous materials in terms of elastic strains must be done with caution.
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