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 slow longitudinal wave-speed and the shear wave-speed, and above by the fast longitudinal wave-speed. Biot’s theory ofporoelasticity 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, dependingon 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]. In contrast, 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.

Mode II intersonic crack propagation in poroelastic media / B., Loret; Radi, Enrico. - In: INTERNATIONAL JOURNAL OF FRACTURE. - ISSN 0376-9429. - STAMPA. - 147:1-4(2007), pp. 235-267. (Intervento presentato al convegno ISDMM 2007 - 3rd International Symposium on Defect and Material Mechanics tenutosi a Aussois, France nel 25-29/03/2007) [10.1007/s10704-007-9169-z].

Mode II intersonic crack propagation in poroelastic media

RADI, Enrico
2007

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 slow longitudinal wave-speed and the shear wave-speed, and above by the fast longitudinal wave-speed. Biot’s theory ofporoelasticity 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, dependingon 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]. In contrast, 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.
2007
ISDMM 2007 - 3rd International Symposium on Defect and Material Mechanics
Aussois, France
25-29/03/2007
147
235
267
B., Loret; Radi, Enrico
Mode II intersonic crack propagation in poroelastic media / B., Loret; Radi, Enrico. - In: INTERNATIONAL JOURNAL OF FRACTURE. - ISSN 0376-9429. - STAMPA. - 147:1-4(2007), pp. 235-267. (Intervento presentato al convegno ISDMM 2007 - 3rd International Symposium on Defect and Material Mechanics tenutosi a Aussois, France nel 25-29/03/2007) [10.1007/s10704-007-9169-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/466501
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