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Shear banding in metallic glasses under low strain rates is discussed by elaborating on the coupling of
the underlying thermal and free volume diffusion with plastic strain gradients. Linear stability analysis is
employed to examine the interplay between strain, temperature and free volume internal lengths on the onset
of instability, as this is determined within a multiphysics / multiscale system of partial differential
equations of the reaction - diffusion (R-D) type. Size-dependent stability criteria are derived and
size-dependent diagrams are constructed indicating that shear banding can be completely suppressed below
a critical (nanoscale) size in accordance with experimental trends found in the literature. These results are
qualitatively similar to those observed in nanocrystalline and ultrafine grain polycrystals.
The effect of the different length scales on the shear band thickness is also investigated by solving the system of governing equations numerically using the method of lines along with the spectral element method. It is found that free volume diffusion controls the development of nano-scale shear bands, while strain gradients govern the evolution and morphology of micron-scale shear bands that have been reported in the literature. In both cases the influence of thermal diffusion turns out to be negligible for the quasi-static loading conditions considered herein. This is in contrast to most of the previous adiabatic shear banding stability analyses of various authors which resorted to thermal diffusion and heat conductivity to deduce stability criteria for thermally softening materials. |
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