Abstract :
A crack is steadily running in an elastic
isotropic fluid-saturated porous solid at an intersonic
constant speed c. The crack tip speeds of interest are
bounded belowby the slower between the slowlongitudinal
wave-speed and the shear wave-speed, and above
by the fast longitudinal wave-speed. Biot’s theory of
poroelasticity with inertia forces governs the motion
of the mixture. The poroelastic moduli depend on the
porosity, and the complete range of porosities n ∈ [0, 1]
is investigated. Solids are obtained as the limit case
n = 0, and the continuity of the energy release rate as
the porosity vanishes is addressed. Three characteristic
regions in the plane (n, c) are delineated, depending
on the relative order of the body wave-speeds. Mode
II loading conditions are considered, with a permeable
crack surface. Cracks with and without process zones
are envisaged. In each region, the analytical solution to
a Riemann-Hilbert problem provides the stress, pore
pressure and velocity fields near the tip of the crack. For
subsonic propagation, the asymptotic crack tip fields
are known to be continuous in the body [Loret and
Radi (2001) J Mech Phys Solids 49(5):995-1020]. Incontrast, for intersonic crack propagation without a
process zone, the asymptotic stress and pore pressure
might display a discontinuity across two or four symmetric
rays emanating from themoving crack tip. Under
Mode II loading condition, the singularity exponent
for energetically admissible tip speeds turns out to be
weaker than 1/2, except at a special point and along
special curves of the (n, c)-plane. The introduction of
a finite length process zone is required so that 1. the
energy release rate at the crack tip is strictly positive
and finite; 2. the relative sliding of the crack surfaces
has the same direction as the applied loading. The presence
of the process zone is shown to wipe out possible
first order discontinuities.
