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 ...
