Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev-Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Introduction. Fracture mechanics is still one of the most intensively developing branches of solid mechanics, which is primarily due to its great practical importance for the quantitative assessment of critical loads for materials and structures with cracks. However, some problems in this area are yet to be completely resolved. Among them are the effect of initial (residual) stresses on the stress-strain state of materials and compression of cracked bodies. That researchers are interested in such problems is evidenced by the great many recent publications on the subject (see, e.g., [11, 16-18, 23, 26]).Of special interest are cases where prestresses (or compressive forces) act along crack surfaces. According to [5,7,8,16,17], such are nonclassical problems of fracture mechanics because they cannot be solved within the framework of classical linear fracture mechanics. The reason is that according to the linear theory of elasticity, the load components parallel to the crack planes do not appear in the expressions for the stress intensity factors and crack opening displacements and, hence, cannot be allowed for in classical failure criteria such as Griffiths-Irwin or critical crack opening.To solve problems of fracture mechanics for bodies with initial stresses acting along cracks, the papers [2, 4, 5] proposed an approach based on the three-dimensional linearized theory of elasticity and a brittle-failure criterion analogous to the Griffiths-Irwin criterion. This approach made it possible to solve some static and dynamic problems (mainly for single cracks in an unbounded material) and reveal new mechanical effects of prestresses (see [5,6,13,16,20,24] for reviews of relevant studies).In [3,7], local buckling near cracks was considered a failure mechanism in materials compressed by forces parallel to crack planes. Relevant problems were formulated and solved within the framework of the three-dimensional linearized theory of stability of deformable bodies [14,15] (see [7,12,18] for a review of studies based on the approach for homogeneous and composite materials in a continuum formulation). There are also a few recent results obtained using a piecewise-homogeneous medium to model a material containing and compressed along parallel interfacial plane cracks [19].What these two approaches to nonclassical problems of fracture mechanics (fracture of prestressed materials and bodies compressed along cracks) have ...

Approaches of linearized solid mechanics are used to solve the axisymmetric problem of interaction of a periodic set of coaxial penny-shaped mode II cracks in an unbounded prestressed material. Two nonclassical fracture mechanisms are considered: fracture of a body with prestresses parallel to the crack plane and fracture of a body compressed along cracks. The fracture parameters for hyperelastic materials with elastic potentials of different types are calculated and their dependence on the loading conditions, the mechanical characteristics of the materials, and the geometrical parameters of the problem is studied Keywords: fracture, initial stresses, stress intensity factor, penny-shaped crack, hyperelastic material Introduction. Problems of fracture mechanics of materials with initial (or residual) stresses and fracture of bodies compressed along cracks that cannot be solved in the classical way are of practical importance. Relevant results are analyzed in detail in [6-8, 10, 11, 13-20, 23]. For example, the approaches based on linearized elasticity theory proposed in [2-5, 12, 13] were used in [11] to solve the three-dimensional axisymmetric problem of the fracture of an unbounded prestressed elastic body with a periodic set of parallel coaxial penny-shaped mode I cracks.In support of [11], we will solve the three-dimensional spatial problem of the stress-strain state of an elastic prestressed body with a periodic set of coaxial mode II penny-shaped cracks. We will derive expressions for the stress intensity factors in the neighborhood of the cracks. The influence of prestresses and the interaction of the cracks on the stress intensity factors will be numerically analyzed for some types of hyperelastic materials.Moreover, we will use the integrated approach of [11] to problems of the fracture of materials having prestresses parallel to the crack plane or compressed along the cracks to determine the critical compressive loads acting along a periodic set of parallel coaxial cracks and causing antisymmetric (flexural) local loss of stability (the critical compressive loads causing symmetric local loss of stability near cracks were determined in [11]). These critical loads will be calculated as the initial compressive stresses that cause resonance-like changes in the stress intensity factors near a periodic set of coaxial mode II cracks.

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