Details

Autor(en) / Beteiligte

• Bogdanov, Viacheslav L
• Guz, Aleksander N
• Nazarenko, Vladimir M

Titel

Two-Dimensional Problems on the Fracture of Bodies Under Compression Along Cracks

Ist Teil von

• Fracture of Materials Under Compression Along Cracks, 2020, Vol.138, p.149-248

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• This chapter focuses on plane problems of the fracture mechanics of bodies with cracks under uniaxial compression along the planes of cracks location. The general solutions of the two-dimensional linearized problems at uniform subcritical states presented in Chap. 2 are specified; in particular, for equal and non-equal roots of the characteristic equation the representation of displacements and stresses is presented in terms of both the complex potentials introduced and harmonic potential functions. The first form of representing the general solutions of plane linearized functions is oriented towards using the methods of the theory of functions of a complex variable, the other—towards employing the integral transformation methods. It should be noted that the representations of stresses and displacements in terms of complex potentials in the case of equal roots (when initial stresses are absent) turn into Kolosov–Muskhelishvili representation, widely used in the linear theory of elasticity [43] for the isotropic body, and in the case of non-equal roots—into Lekhnitsky representation [42] for the orthotropic body. General solutions of plane linearized problems are constructed in a single (unified) form for various models of compressible and incompressible materials (non-linearly elastic, elastoplastic and composite ones) for the theory of large initial strains and the variants of the theory of small initial strains. The specification of material model is only necessary at the stage of numerical investigation of the resolving equations obtained in the unified form. In the case of elastoplastic bodies, the generalized concept of continuous loading is additionally involved; it allows the changes of the unloading zones in the process of the stability loss of material near cracks to be neglected. This chapter investigates problems on the compression of the bodies containing isolated cracks and the arrays of coplanar (located in the same plane) cracks. It also examines problems on the most typical geometric configurations of crack arrays in the bodies, in terms of evaluating the effect of cracks interaction among themselves and with the boundary surfaces of the bodies on the fracture parameters. The patterns of the effect of problem geometries and physico-mechanical properties of the materials on those fracture parameters under compression have been revealed. In particular, it has been shown that the account for the interaction of the cracks located in the neighboring parallel planes or the mutual effect of a near-surface crack and the boundary surface of the body can lead to a reduction in the value of the compression strength by an order of magnitude or more as compared to the respective ultimate strength of the compressed body containing a single isolated crack. A part of the results presented in [15, 16, 19, 20, 22–28, 30–33, 35, 36, 44, 45, 48] are used in this chapter.