Anisotropy of the fracture toughness in β-HMX crystals: A computational study

The reliability, stability, and secure handling of $\beta$-cyclo-tetramethylene tetranitramine ($\beta$-HMX) crystals, a high explosive (HE) material commonly used in polymer-bonded explosives (PBX), depend heavily on their fracture properties. Cracks in HE crystals are known to localize temperature or form hotspots due to interfacial friction and can also facilitate the propagation of chemical reactions, leading to early ignition and initiation. Hence, to develop safe and reliable HEs, it is essential to characterize the fracture toughness of $\beta$-HMX, which is believed to be highly anisotropic. Furthermore, it is important to understand the origin of fracture anisotropy in HMX crystals, which is hypothesized to depend not only on the surface energy of the fracture plane, as it occurs in brittle fracture, but also on plastic deformation due to crystallographic slip. For this purpose, we performed finite element simulations of single $\beta$-HMX crystals under Mode I deformation with an atomistic-informed crystal plasticity model. Fracture toughness is estimated computationally for crystals with cracks oriented in different directions using the J-integral method. Our results confirm that the fracture toughness of HMX is highly dependent on the crystal orientation, owing to both elastic and plastic anisotropy. Furthermore, we conclude that although brittle HMX crystals may not sustain extensive plastic deformation, the contribution of plasticity to the fracture toughness is not negligible, and the anisotropy of the plastic deformation should not be neglected.