Spatial Problems of the Fracture of Materials Loaded Along Cracks (Review)

Abstract

The results of solving spatial problems of the fracture of cracked materials under loads acting along cracks are reviewed. A combined approach based on the three-dimensional linearized solid mechanics is used to analyze two nonclassical brittle-fracture mechanisms: (i) fracture of materials with initial stresses acting along cracks and (ii) fracture of materials compressed along parallel cracks. The results of solving nonaxisymmetric and axisymmetric problems for the most typical cases of arrangement of cracks relative to each other and to the boundaries of prestressed bodies are generalized. In the linearized theory, stresses and displacements are expressed in terms of harmonic potential functions. The Hankel transform is used to reduce problems for interacting cracks to the Fredholm equations of the second kind. This approach allows solving problems in a universal general form for compressible or incompressible, isotropic or transversely isotropic homogeneous elastic bodies with an arbitrary elastic potential using the theories of finite and small initial deformations and specifying the material model only at the stage of numerical solution of the general governing equations. New mechanical effects associated with the influence of the initial stresses and crack interaction on the asymptotic distribution of stresses and displacements near the crack tips are analyzed. Resonant effects occurring as the initial compressive stresses tend to the level at which local buckling of the material occurs near the crack are detected. This allows using the combined approach to determine the critical loads for bodies compressed along cracks. Conclusions on the behavior of the stress intensity factors and critical compressive loads with variation in the geometrical and material parameters are drawn