Comparative analysis of mechanisms of 3-D brittle crack growth in compression

Abstract

Pre-existing 3-D defects are common and ubiquitous elements of microstructures in heterogeneous and brittle materials like rocks. It is well believed that brittle fractures are due to the initiation and subsequent growth of cracks from pre-existing defects. Therefore, a thorough knowledge of 3-D crack growth under different loading conditions (mainly in the compressive stress field) is necessary to understand the macroscopic constitutive behaviour of rocks, i.e. the pronounced nonlinearity of rock deformation and ultimate failure modes. The current paper reviews experimental preparation, techniques, and experimental results of 3-D crack growth (both from the studies of 3-D surface crack and 3-D internal crack). In addition, potential factors which may influence the experimental outcomes of crack growth process are discussed. The current findings are: the main feature of 3-D crack growth in uniaxial compression is wrapping of the formed wing cracks around the initial crack, and the same can be found from the wings produced from an initial spherical pore. The crack interaction in uniaxial compression is found when the initial cracks are close to each other and located on a line normal to the loading axis, in which their combined stress field creates a new crack surface extensively growing up to the sample ends causing splitting. For 3-D surface crack growth in uniaxial compression, the results depend upon the depth of the initial crack penetration as compared to the sample thickness: with large depth of penetration the subsequent crack pattern resembles that of 2-D tests (with a through initial crack), with small depth – 3-D tests. In 3-D crack growth, the intermediate principal stress suppresses wing wrapping enabling extensive crack growth up to the sample ends. The same phenomenon is also observed for wing cracks emanating from an initial spherical pore. The thresholds of the biaxial load ratio for the extensive 3-D crack growth are quite low: in the case of an initial penny-shape crack inclined at 30° to the major principal stress axis, the intermediate principal stress should only exceed 5.7% of the major principal stress. For an initial spherical pore the threshold is somewhat higher – 8.5%, but still small. Numerical modelling studies of 3-D crack growth face challenges related to the determination of the direction of crack growth in 3-D as well as the considerable computational resources required for the modelling of extensive crack growth.