Modelling the anomalous shock response of titanium diboride

Abstract

In planar shock compression experiments, polycrystalline titanium diboride ( TiB 2 ) often exhibits double-yield phenomena, atypical among non-transforming ceramics, in particle velocity histories. A finite-strain phase-field theory, with order parameters accounting for fracture and dilatation, followed by limited plastic slip and compaction, is specialized to study the uniaxial shock response of TiB 2 . The model accurately depicts longitudinal stress up to 120 GPa on the Hugoniot from multiple published sources, as well as shear stress inferred elsewhere from experimental shock data. A novel phase-field analysis enables one-, two- or three-wave structures depending on impact stress. These results are observed in experimental data and have not been successfully captured by prior numerical models. Results support the conjecture that (i) fracture and dilatation, followed by (ii) plastic deformation and compaction, and then (iii) fragmentation to a comminuted, viscous granular medium is a plausible sequence of physical mechanisms as shock stress increases. The first break in the velocity profile always corresponds to micro-cracking in the model, which correlates with the first yield point on the Hugoniot. In the three-wave regime, two plastic waves correlate with two yield points, where the first plastic wave after the precursor is due to fracture and the second dominated by plasticity. When impact is severe enough such that the second plastic wave overtakes the first, a single plastic waveform with multiple kinks emerges in particle velocity histories, consistent with some experimental data. These kinks are well explained by pressure-dependent viscosity in crack kinetics and by small-magnitude plastic deformation, and corresponding stress perturbations need not precisely correspond to particular cusps on the stress–volume Hugoniot.