Brittle and Quasi-Brittle Fracture of Geomaterials with Circular Hole in Nonuniform Compression
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Brittle and Quasi-Brittle Fracture of Geomaterials with Circular Hole in Nonuniform Compression S. V. Suknev Chersky Institute of Mining of the North, Siberian Branch, Russian Academy of Sciences, Yakutsk, 677980 Russia e-mail: [email protected] Received February 17, 2020 Revised February 18, 2020 Accepted April 10, 2020 Abstract—The author studies the influence exerted by the boundary conditions and diameter of a circular hole on tensile fracture initiation in brittle and quasi-brittle geomaterials subjected to nonuniform compression with regard to the size effect. The calculation of the critical stress uses the modified nonlocal and gradient fracture criteria. The calculation results are compared with the experimental data. The developed criteria allow taking into account the size effect when the size of the stress concentration zone is varied by changing both geometry and boundary conditions of the stress raiser. Keywords: Brittle fracture, quasi-brittle fracture, geomaterials, size effect, hole, stress gradient, nonlocal fracture criteria. DOI: 10.1134/S1062739120026625
INTRODUCTION
Mechanical properties of geomaterials are susceptible to size effects which are specifically strong in the conditions of stress concentration at openings, cavities and mine excavations when typical size of a stress heterogeneity is comparable with sizes of structural constituents of a material. Strength estimation and fracture prediction in structurally nonuniform materials uses nonlocal and gradient models with a structural parameter [1–9]. Widely used nonlocal fracture criteria implement methods and approaches of the theory of critical distances [10–15]. The keystone is the idea on a pre-fracture zone formation in a material. Local stresses in this zone undergo re-distribution, while the material beyond this zone experiences elastic deformation up to fracture. A common feature of the nonlocal criteria is the internal size d 0 introduced as a structural characteristic of a material, which enables description of the size effect inherent in all structurally nonuniform materials. Then, it becomes possible to predict fracture beginning by varying the stress concentration zone size Le . In physical modeling of fracture in materials with stress raisers [16–22], variation in Le was carried out as the change in geometry or shape of a stress raiser (a hole, a cut) at the unaltered boundary conditions. The study [23] into tensile fractures in samples with circular holes with different diameters under uniform and nonuniform compression points at the high influence of stress distribution along a fracture growth path governed by the boundary conditions. Under unvaried boundary condition, tensile fracture initiation
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