Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys

Recent experiments have shown that inhomogeneous deformation in amorphous alloys critically depends on the environmental temperature and the applied strain rate, and that the temperature field inside the shear-band can rise up to the glass transition temperature. A free-volume-based, thermo-viscoplastic constitutive law is developed in which the thermal transport equation includes contributions from the heating from plastic work and the heat conduction. For homogeneous deformation, the instantaneous temperature rise during the strain softening stage can lead to thermal softening and promote the initiation of shear bands. A linear stability analysis is carried out to examine the conditions for the unstable growth of temperature fluctuations. It is found out that the short-wavelength fluctuations, the amplitudes of which would decay at low strain rate and moderately high environmental temperature (but still much lower than the glass transition temperature), become unstable at high strain rate and low temperature, so that the resulting shear-band spacing will be shorter. A deformation mechanism map is constructed to delineate this transition of inhomogeneous deformation from coarse to fine shear-band arrangements. The theoretical results agree well with a nanoindentation experiment where there is varying applied strain rate and environmental temperature and with a microindentation experiment in which the evolution of the effective strain rate during loading influences the spatial distribution of the shear-band spacing observed using the bonded interface technique.