Toughness heterogeneity induced shielding effect of a bi-wing hydraulic crack in plane strain state

Abstract

Hydraulic cracks can be found in many areas, such as oil and gas exploration, carbon dioxide storage, geothermal development, and magma flow path prediction. From the analyses on symmetrical bi-wing cracks growth, it is known that the difficulties lie in the stress singularities in the solid and the fracturing fluid, the incompatibility of boundary conditions at the moving crack tip and the dominated regime transition. Furthermore, hydraulic cracks in heterogeneous solids can be asymmetric due to fracture toughness heterogeneity. In this paper, the fracture toughness induced asymmetrical crack growth, i.e. the shielding effect, is studied. Based on the investigation of symmetrical bi-wing cracks, a simplified mechanical model is established for an asymmetrical bi-wing hydraulic crack. Boundary integral method is used to derive the crack opening and the stress intensity factors on both crack tips. The model is mathematically expressed as an integro-differential equation set. Using the scaling analysis, the model is demonstrated to be self-similar under the assumption that the crack propagates steadily, and the self-similar solution is obtained using a high-precision numerical method. Shielding effect of fracture toughness difference on the crack wing length is studied under different dominated regimes. At last, it is demonstrated that the crack can become symmetric if the fracture toughness difference vanishes from non-zero values. The results of this paper will be useful in the understanding of multiple hydraulic crack growths and the validation of numerical simulations.