Plane strain fracture in poroelastic media

Abstract

The effect of fully coupled poroelasticity on an impulsively loaded crack in plane strain is investigated. A formally exact solution for a semi-infinite crack in a linear, isotropic, poroelastic medium with a prescribed internal stress is considered; the solution is obtained using Laplace and Fourier transforms in time and space respectively and then using the Wiener-Hopf technique to solve the resulting functional equations. The stress intensity factor is found as a function of the Laplace variable s and is evaluated explicitly for small times and numerically for all times. The problem of a finite length crack embedded in a poroelastic medium under uniform impulsively applied tension at infinity is solved using the method of matched asymptotic expansions for small times. The formal solution for a steadily propagating semi-infinite crack under tension is outlined, the crack-tip fields are examined and the crack-tip stress intensity factors are found as functions of the crack velocity. Analytical solutions for the pore pressure and stress ahead of the crack are obtained and their relevance to the retardation of fracture discussed. The results extend the range of possible solutions of the fully coupled poroelastic equations to mixed boundary-value problems in fracture mechanics. These are fundamental to the study of the interaction between a diffusing pore fluid and the solid elastic skeleton. In particular, time dependent solutions to the symmetric problems of impulsive loadings and explicit solutions to the steady problems are considered.