A B S T R A C T
A tentative analysis of an unstable shear crack propagating axially in the wall of a long pipe under gas pressure is developed. Six processes known to be associated with crack propagation are treated numerically: (1) axial decompression of the gas, (2) bulging of the pipe wall, (3) radial decompression of the gas, (4) local stress and strain intensification at the crack tip, (5) plastic deformation, and (6) ductile cracking. The treatment is quasi-static; dynamic effects in the pipe wall are ignored. Because the numerical descriptions included in the model are approximate and incomplete, several variants of the basic model are examined. The response of the model is evaluated for different line pressures, geometries, and material properties and compared with full-scale test data for 100% shear cracks. A wide range of speeds can be calculated for the limits within which the system parameters are specified including the speeds observed in practice. The bulging and decompression characteristics of the model cause the crack speed to be relatively insensitive to line pressure. Yet the calculated crack speeds are influenced by yield strength and toughness of the material. The model does not provide for nonaxial crack paths, nor does it adequately describe crack-arrest possibilities. The paper represents the first step in the analysis of a complex problem. * Argentine Atomic Energy Commission. ** When the axial propagation speed of a crack is comparable to or exceeds the speed of decompression, then the crack front does not experience a pressure loss. Since the hoop and bending stresses that drive the crack are largely maintained in this case, the "fast" crack tends to produce a long failure. In contrast, the "slow" crack---one that lags far behind the decompression event--experiences the loss of pressure in the line. This can reduce the driving force for cracking sufficiently to produce crack arrest. * These estimates are derived from the calculations discussed in subsequent sections. ** Considerable uncertainly must be placed on this comparison because the circumferential weld failed before the arrival of the axial fracture. This, of course, would affect the way in which the pipe op'ned up. *** This is a simplified, two-dimensional view of what is properly a three-dimensional problem. Int. Journ. of Fracture, 9 (1973) 209-222 * This means that K, increases with crack speed because it depends on the flow stress (Equations (11), (12) and (13)): Kc ~-{/h ~ c OD * [~ + (a~/Ax) F V] }~.