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Needs to impart appropriate elasticity and high toughness to viscoelasticpolymer materials are ubiquitous in industries such as concerning automobilesand medical devices. One of the major problems to overcome for toughening iscatastrophic failure linked to a velocity jump, i.e., a sharp transition in thevelocity of crack propagation occurred in a narrow range of the applied load.However, its physical origin has remained an enigma despite previous studiesover 35 years. Here, we propose an exactly solvable model that exhibits thevelocity jump incorporating linear viscoelasticity with a cutoff length for acontinuum description. With the exact solution, we elucidate the physicalorigin of the velocity jump: it emerges from a dynamic glass transition in thevicinity of the propagating crack tip. We further quantify the velocity jumptogether with slow- and fast-velocity regimes of crack propagation, which wouldstimulate the development of tough polymer materials.

Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids