Thermal explosion theory for shear localizing energetic solids

The behaviour of energetic solids subjected to simple shear loading is modelled to predict ignition. The model is transient, one dimensional and includes effects of thermal diffusion, plastic work and exothermic reaction with one-step irreversible Arrhenius kinetics. A common power-law constitutive model for shear stress which accounts for strain hardening, strain-rate hardening and thermal softening is used. For the energetic solid composite LX-14 subjected to an average strain rate of γ̇ = 2800 s−1, the model predicts reactive shear localization after an induction time of approximately t = 5 ms, in which regions of high strain rate (γ̇ > 20 000 s−1) are confined to thin spatial zones. An approximate thermal explosion theory which enforces spatially homogeneous stress, temperature and reaction progress as well as accounting for the early-time dominance of plastic work over exothermic reaction allows the development of simple analytic expressions for the temporal evolution of all variables. The simple expressions give predictions which agree well with both: (a) numerical predictions of a spatially homogeneous theory which allows simultaneous influences of reaction and plastic work and (b) numerical predictions of a spatially inhomogeneous theory which accounts for spatial stress distributions, thermal diffusion and spatially localized reaction. In particular, the induction time to ignition is captured accurately by the approximate theory; hence, while reactive shear localization may accompany an ignition event, ignition causality is most dependent on plastic work done during the time of spatially homogeneous shear.