New test specimens derivable from cores are proposed by the senior author. The specimen is semicircular in shape with an edge crack, subjected to three-point bending. For mode I fracture, the edge crack is cut perpendicular to the bottom edge. Kinematics of mode I specimen have been investigated. For mixed modes I and II, the edge crack is cut at an angle (other than 90") with the bottom edge. The specimen can be prepared from typical rock, concrete, or other cores with very little machining. It is especially adaptable to small, compact specimens requiring duplicate samples. The effect of crack length on the normalized stress intensity factor for the proposed geometry is investigated by finite elements. The fracture load is obtained by compressing the specimen to failure. As an example, the mode I fracture toughness is determined for oil shales (transversely isotropic materials) using compliance, energy and other methods. It is observed that data derived from the proposed specimen compare favorably with published data using conventional specimens, and that the independent methods in obtaining stress intensity factors and fracture toughness agree well with each other. Size effects are also investigated.
NOTATION
Crack length or major axis of a conic-section Modulus of elasticity Shear modulus Mode I stress intensity factor Mode I fracture toughness Normalized mode I stress intensity factor [Kr/(oO&)]; o. = P/(2&) Mode II stress intensity factor Mode II fracture toughness Normalized mode II stress intensity factor [K,,/(q&%)] (3 -4~) for plane strain and (3 -v)/( 1 + V) for plane stress Mode I geometrical correction factor Mode II geometrical correction factor Polar coordinates Applied load Specimen radius Specimen thickness Half span Displacements along and normal to the crack, respectively Relative crack surface displacements Displacements in x and y directions, respectively Cartesian coordinates Angle of crack measured from verticai line Poisson's ratio Uniform tensile stress remote from a crack Normal tensile stress in the region of a crack Shear stress in the region of an inclined crack