A closed-form solution is provided for the stress, pore pressure and displacement fields near the tip of a crack, steadily running in an elastic fluid-saturated porous solid at crack tip speed ranging between the faster longitudinal wave-speed and the lower between the longitudinal Biot second wave-speed and the shear wave-speed. Mode I and Mode II loading conditions with permeable crack surfaces have been considered. The Biot theory of poroelasticity with inertia forces is assumed to govern the motion of the medium. At variance with the subsonic case where the crack tip fields are continuous in the body, for intersonic crack propagation, the stress and pore pressure fields display a strong discontinuity (shock wave) across two or four symmetric rays emanating from the moving crack tip. The obtained solution also reveals that favorable velocity regimes, occurring with crack face displacements in agreement with the sign of the tractions ahead of the crack tip, exist under both Mode I and Mode II loading conditions. The singularity of the stress and pore pressure fields predicted for these favorable regimes turns out to be weaker than the square-root singularity which characterizes the subsonic case. The introduction of a finite length cohesive zone allows to obtain an energy release rate at the crack tip that does not vanish, unlike for a point size process zone.
展开▼
