The equation of dynamic crack growth

Rapid crack propagation along pressurized pipelines has resulted in a number of failures involving fatalities. In some cases, cracks have run for several miles before stopping. Given the catastrophic nature of this kind of failure, pipes must be designed to resist rapid crack propagation. The equation of motion of a dynamic crack remains one of the most important and fundamental issues in dynamic fracture mechanics. When the crack motion is understood, pipes can be designed to resist the crack driving force.;The equation of dynamic crack growth is typically based on Griffith's energy criterion Gdyn = 2gamma, namely that all of the energy released in a propagating crack is absorbed into the newly formed surfaces. Given the discrepancy between this equation and experimental results, the principle of least action is proposed as an alternative criterion or dynamic crack growth. The variational problem is formulated in terms of the dynamic energy release rate and the volume of elastic excitation resulting from the crack motion. The differential equation of motion of the physical system is derived in terms of crack speed and crack length. The resulting equation is examined with respect to both the limiting case and experimental data.