A boundary layer analysis for the initiation of reactive shear bands

A one-dimensional model for the initiation of shear bands in a reactive material is developed, which accounts for thermal softening, strain hardening and strain-rate effects, and models the chemical reaction using an Arrhenius source term. An inhomogeneity in the heat flux is used as the stimulus for localized plastic deformation, and a solution is sought as a perturbation to the elastic solution. In the analysis, the thin zone of localization is identified as a boundary layer. It is found that the behaviour of the perturbations to the temperature, stress and strain hardening variable in the localization zone are governed by four dimensionless parameters which are known in terms of various material properties including density, the heat of reaction, strain-rate sensitivity, thermal sensitivity and strain sensitivity. The resulting equations are solved numerically and a criterion for the onset of shear banding is discussed. The analysis highlights key physical properties which control the reactive shear banding process and gives a deeper insight into how such a process may be understood as a mechanism for the accidental ignition of reactive materials.