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