Shear band formation due to a thermal flux inhomogeneity

The one-dimensional model for the unidirectional shearing of a slab is investigated for the situation in which localized plastic deformation is induced by an inhomogeneity in the thermal flux. The problem is treated as a perturbation of the elastic solution, which persists until plastic deformation becomes significant. The analysis utilizes singular perturbation techniques, with the thin zone of shear localization identified as a boundary layer. It is found that the evolution of the temperature and stress perturbations are governed by only one parameter, which involves the various material constants. Numerical results indicate that the magnitude of this parameter plays an essential role in the growth of the perturbations and hence in the formation of a shear band.