Boundary layer analysis of plane strain shear cracks propagating steadily on an impermeable plane in an elastic diffusive solid

Abstract

Matched asymptotic expansions are used to examine the stress and pore pressure fields near the tip of a plane strain shear (mode II) crack propagating on an impermeable plane in a linear elastic diffusive solid. For propagation speeds V that are large compared with c/ l, where c is the diffusivity and l is the crack-length, boundary layers are required at the crack-tip and on the line ahead of the crack. The latter is required to meet the condition of no flow across this plan; in contrast, for propagation on a permeable. plane, a boundary layer is required on the crack faces behind the tip. As for the permeable plane, the solution in the crack-tip boundary layer reveals that the stress field near the crack-tip has the form of the usual linear elastic field with a stress intensity factor [ (1 − v u (1 − v) ]K (c), where K (e) is the stress intensity factor of the outer elastic field, v is the Poisson's ratio governing slow (drained) deformation, and v u ⩾ v is the Poisson's ratio governing rapid (undrained) deformation. Thus. coupling between deformation and fluid diffusion reduces the local value of the stress intensity factor and. hence, stabilizes against rapid propagation. For the permeable plane, the pore pressure goes to zero as the crack-tip is approached along any ray. In contrast, for the impermeable plane, a closed-form solution for the pore pressure in the cracktip boundary layer reveals that the pore pressure at the crack-tip is non-zero, but bounded.