Possible cohesive fracture path leading to the rapidest failure of ductile materials under dynamic tension

Abstract

Fracture velocity for a solid undergoing high-rate plastic flow with an internal fracture depends on a cohesive fracture path at a fracture point and momentum transport process from the surrounding medium to a fracture point. Assuming a more complex nonlinear relationship between fracture cohesion and fracture opening displacement, fracture evolution under different damage models, critical fracture time, Mott wave propagation distance, and analytical or numerical solutions of the average size of fragments are derived in this study. A step-like cohesive fracture path leads to the quickest fracture process, with the step stress on the fracture point being 2/3 of its strength, while maintaining constant fracture strength and energy among all conceivable cohesive fracture paths. For a wide range of loading strain rates, the damage time had a minimum value regardless of the damage evolution path selected for material failure for various damage models. Results obtained in this study based on the principle of rapidest unloading provide a reference to study the intrinsic damage mechanisms in fracture processes.