Phase-field modeling of shock initiation in <i>β</i> -HMX: From hotspot growth to steady detonation

Understanding how hotspots affect detonation in energetic materials has important scientific and engineering value. The unique material properties of energetic materials impose limitations on research methods, particularly concerning the dynamic characteristics of mesoscale microstructures. In the present work, a coupled crystal plasticity and phase-field model is proposed to address shock initiation in β-HMX explosives. This model employs the phase-field approach to describe hotspot growth processes, enabling entire process simulation from individual hotspot evolution to steady detonation. It quantitatively links collective evolution of multiple hotspots with experimentally measured macroscopic initiation characteristics across stages from slow reaction, through rapid growth, to steady detonation. Phase-field simulations provide a clear physical picture of shock-to-detonation transition (SDT): the growth of individual hotspot leads to the generation of a compression wave that interacts with and catches up to the shock front; numerous compression waves converge at the shock front to form steady detonation waves. Given the strong dependence of explosive SDT on hotspot density and distribution, this method quantifies how individual hotspot growth affects initiation properties. Consequently, it enables evaluation of internal hotspot density and distribution by inversely analyzing macroscopic shock-initiated particle velocity profiles. Furthermore, crystal plasticity simulations allow assessment of how shear strain energy and single-crystal anisotropy influence detonation performance. This work provides a novel means for simulating SDT in energetic explosives, demonstrating substantial engineering application prospects.