Scale effect of explosive destruction of spherical vessels: Dynamic crack propagation and branching

• Proposed a damage model considering the material imperfection and rate dependent failure criterion, to account for explosively destruction.
• FSI (Fluid Structure Interaction) simulation indicated that the elastic-plastic response of structure subjected to explosive loading has no scale effect when the damage model is not considered. However numerical crack analysis clearly shows the proposed damage model can well explain the cause of fracture and fragments of structures, as well as the transient crack propagation and branching process.
• Provides a method to assessment the permissible load and corresponding extent of damage of explosively loaded structure, also the scale law was quantitatively acquired.

Scale effect was repeatedly founded in Explosion containment vessels (ECVs) that with an increment of scale factor, the relative weight (the ratio of explosive destruction charge to the weight of vessel) decreased drastically. Also a reduction of the amount of deformation before failure and an increase in the tendency to the brittle failure were observed in large size structures. Though the scale effect was believed relevant with crack propagation energy and is decisive to the ultimate strength of explosively loaded structures, there's still no satisfying mechanism had been obtained in the past decades. In this paper, a numerical method combining with a phenomenological failure criterion was presented to re-examine the scale effect problems, where a failure criterion fully considering strain rate softening was implanted into the finite element code to account for the explosive destruction of the vessel. FSI (Fluid Structure Interaction) simulation and crack analysis covering the different scale factor from 1 to 10 were conducted, and the dynamical crack propagation and branching process was clearly revealed, which illuminates the cause of fracture and fragments of vessels, as well as the scale law of destruction charge. It was concluded that strain rate softening becomes more significant with an increase of strain rate, which leads to a rapid destruction in a very narrow region even the plastic deformation is too late to occur in the rest parts of the material, thus the brittle fracture mode was presented. The approach illustrated in this paper also provides an effective way to assessment the limit load of ECVs, which is helpful to prevent catastrophic brittle and quasi-brittle failure of the vessels.