Displacement Consideration for a Ductile Propagating Fracture in Line Pipe

To date, the technically complex problem of arriving at an analysis for a running shear fracture in a gas-transmission line pipe has been primarily viewed by investigators in terms of an energy balance that involves empirical correlations of data. In contrast, in the present paper, the problem is reviewed in terms of the forces, masses, and time involved in the fracturing event and the resultant accelerations, velocities, and displacements with respect to (1) the forces driving the crack, (2) the pipe-wall ductility resisting the driving forces, and (3) the manner in which the crack arrests. Special attention is given to the effects of backfill on these events. On the bases of the data available, it is proposed that the displacements developed by the driving force are the result of the acceleration developed by the pressure acting on the flaps behind the crack. The driving force developed by the flaps results in forces which open the crack. For a constant velocity of propagation, the time for this flap displacement corresponds to the time for the pipe-wall thinning at the crack tip, which is controlled by the pipe-wall ductility. Thus, pipe-wall ductility can limit the speed of the crack. At a low crack speed, sufficient radial displacement of the flaps behind the crack occurs to cause the crack to turn in a helical path and arrest. Finally, the backfill significantly decreases the driving force and thus reduces the pipe-wall ductility necessary for arrest. Therefore, considerations of the displacements which occur during a propagating shear fracture indicate that the time and forces required for thinning the material at the crack tip, which is essentially governed by the ductility of the pipe wall, limit the speed of the crack.