Rupture and Damage at Dilatant Geological Interfaces

The work discusses the processes that can be present at fractures and defects at geological interfaces. The introductory comment clearly indicates that the computational approaches offer the most appropriate methods for examining complex contact problems at geomaterial interfaces. There are, however, certain types of contact problems that are amenable to analytical treatment. The paper examines the problem of a circular dilatant-frictional patch located at an otherwise frictionless interface. The dilatancy processes are induced at the circular patch by the relative shear of the elastic regions. The paper presents a mathematical approach for the study of the problem where results from the solution of integral equations applicable for the internal indentation of a penny-shaped crack by a rigid inclusion and the internal pressurization of an annular crack are combined with a work-dissipation relationship to examine the mechanics of the interactions at the dilatant zone.

Eccentric annular crack under general nonuniform internal pressure

For a better approximation of ring-shaped and toroidal cracks, a new eccentric annular crack model is proposed and an analytical approach for determination of the corresponding stress intensity factors is given. The crack is subjected to arbitrary mode I loading. A rigorous solution is provided by mapping the eccentric annular crack to a concentric annular crack. The analysis leads to two decoupled Fredholm integral equations of the second kind. For the sake of verification, the problem of a conventional annular crack is examined. Furthermore, for various crack configurations of an eccentric annular crack under uniform tension, the stress intensity factors pertaining to the inner and outer crack edges are delineated in dimensionless plots.

Evaluation of Threshold Condition of Interior Annular Crack Growth in Gigacycle Regime

Gigacycle fatigue properties with interior-induced failure of three high strength steels under different loading conditions were investigated, and an experimental-theoretical method is proposed to quantitatively evaluate the threshold condition of interior crack growth. The entire growth process consists of small crack growth within fine granular area (FGA), stable long crack growth outside of FGA within fish-eye and unstable crack growth outside of fish-eye. Based on the comparison between evaluated and experimental results, the validity of method is verified.