Abstract
Some problems on the fracture of bodies containing interacting cracks under the action of forces directed along the cracks planes are discussed. Given are the descriptions of two non-classical failure mechanisms—the fracture of materials with initial (residual) stresses acting along cracks and the fracture of compressed bodies under the action of forces directed in parallel to the planes containing cracks. We use a unified approach to investigate the abovementioned fracture mechanisms within the framework of the linearized solid mechanics. Problems on unbounded pre-stressed bodies containing coaxial penny-shaped cracks located in the neighboring parallel planes and semi-infinite pre-stressed bodies with cracks located near the surfaces of the bodies are solved. Several types of loads on the crack faces in additional to the initial stresses, viz., normal separation, transverse shear, and longitudinal shear are considered. Corresponding non-homogeneous boundary value problems were reduced to paired (dual) integral equations and then to resolving Fredholm integral equations of the second kind, which permit an efficient numerical investigation. The influence of residual stresses on stress intensity factors is analyzed for some types of materials, namely, highly elastic materials and composites. Some mechanical effects associated with the interaction of cracks with each other or with the boundary of the body are also studied. The effects of a “resonance” nature are revealed when the compressive initial stresses approach the values corresponding to the local buckling of the material in the cracks vicinity, which, according to the unified approach mentioned, makes it possible to determine the critical (limiting) loading parameters during compression of bodies along parallel cracks. The dependences of these critical loading parameters on geometric parameters of the problems, as well as materials mechanical characteristics, were investigated.
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Bogdanov, V., Guz, A., Nazarenko, V. (2023). Fracture of Materials Loaded Along Cracks: Approach and Results. In: Guz, A.N., Altenbach, H., Bogdanov, V., Nazarenko, V.M. (eds) Advances in Mechanics. Advanced Structured Materials, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-031-37313-8_4
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