Numerical modeling of the thermal expansion of an energetic material

• We use 3D tessellation models to simulate a polycrystal microstructure.
• We introduce a modified Johnson–Mehl model that reproduce the observed granulometry.
• The material’s thermoelastic response is computed numerically by a Fourier method.
• Strong internal stresses are observed upon heating.
• The binder’s softening effect is simulated by an interphase around crystals.

The thermoelastic response of a TATB-based pressed explosive is studied using morphological modeling and a numerical Fourier scheme. First, we characterize the polycrystalline-like microstructure in terms of the (2D) granulometry and covariance functions, measured on SEM micrograph images. The granulometry is found to be close to a Rayleigh distribution. Second, we represent the polycrystal by a modified Johnson–Mehl tessellation with time-varying germination-rate, in order to approach the wide size distribution observed on the SEM images. We find excellent agreement between the numerically optimized model and the real material in terms of granulometry. Third, we compute the thermoelastic response of the microstructure model by means of full-field Fourier-based computations. Each crystal is assigned uncorrelated random orientations. The thermomechanical response of single crystals is provided by the molecular dynamic simulations of Bedrov et al. (2009) and the X-ray diffraction results of Kolb et al. (1979). Macroscopic (uniform) temperature or strain loadings are applied along various directions (tension, shear or hydrostatic). We observe strong internal stresses upon heating, owing to the highly anisotropic thermoelastic response of TATB and random crystallographic orientations in the polycrystal. The largest stress and strain gradients are observed at grain boundaries, enforcing the idea that grain boundary fracture is indeed the irreversible mechanism underlying ratchet growth. As a first attempt to account for the plastic binder, a 4-voxels soft interphase is inserted at grain boundaries. This results in a strong softening effect on elastic macroscopic properties.