Transition failure stress in a chain of brittle elastic beads under impact

• When a chain of brittle grains is impacted, the first or second grain fails first.
• Failure first appears in the top section of the brittle grains under impact.
• There exists a transition failure stress in a chain of brittle grains when impacted.

High strain rate experiments of chains of glass beads under impact loading demonstrate that first failure develops in either the first or second glass bead, depending on the impact velocity and associated stress propagation. Motivated by this notion of ‘transition failure stress’ we present a series of three-dimensional dynamic simulations of a 10 brittle elastic beads chain under impact of a stiffer elastic bar using the material point method (MPM). The numerical simulation results show that, as observed in the experiments, failure would first form in either the first or second closest brittle elastic bead to the impacting bar, depending on the parametric ratio between an impact-induced maximum tensile stress to fracture strength. Further non-dimensional analysis by varying materials and system parameters in the simulations suggests that this transition failure stress exists universally in brittle materials under impact loading.