Investigation of Beam Specimen Geometries under Four-Point Asymmetric Bending for Shear Mode Fracture Toughness Measurements of Rocks

Abstract:

Four-point asymmetric bending beam geometry can conveniently be used in shear mode fracture testing of rock and concrete-like materials. Stress intensity factors are computed by contour integration procedure embedded in a finite element program package. To achieve pure shear mode state, loading configuration and parameters are varied in models of rectangular beams. Beam depth is varied as 40, 50, and 60 millimeters. Initial crack length/beam depth ratio (a/W) is varied between 0.15 and 0.60. Pure shear conditions at crack are generated by changing asymmetric loading spans at upper and lower boundaries of the beam geometry. Computations showed that as beam depth was increased, mode II stress intensity factor decreased. Mathematical relations for pure shear mode stress intensity factor were proposed with varying asymmetric loading span and a/W to assure pure shear mode state at crack front. Proper loading and beam geometric conditions were identified for pure mode II fracture toughness K_IIc testing. From four-point asymmetric bending tests on Ankara andesite, average mode II fracture toughness value was found as 0.61 MPavm. Results of shear mode fracture toughness tests showed that variation of beam depth had no significant effect on mode II fracture toughness of beam type rock specimens.

Introduction

Shear type (mode II) loading state is still an active subject of interest in fracture mechanics. Although, numerous test methods have been suggested (Rao et al., 2003, Awaji and Sato, 1978, Atkinson, 1982, Fowell and Xu, 1993)[1-4] to measure mode II fracture toughness K_IIc of rocks, common opinion in this respect is not well-established yet.

Mode II fracture toughness tests aim to measure resistance of a crack to propagate due to in plane shear stress acting on it. Mode II fracture toughness of rocks appears in practical problems of rock mechanics such as hydraulic fracturing (Daneshy, 1974, Hubbert and Willis, 1957), rock cutting (Hood and Roxborough, 1992, Xu, 1993), and rock burst mechanism investigations (Salamon 1963, Cook 1965, Zipf and Heasley, 1990).

In geotechnical applications, rock medium is usually under the effect of compressive forces as a result of overburden stress. This increases the importance of shear mode crack formation and propagation under pure shear mode or under mixed mode loading involving compressive-shear state over the crack.