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Title: Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks

Abstract

We consider two types of nonclassical fracture mechanisms, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and the fracture of solids under compression along parallel cracks. To investigate nonaxisymmetric and axisymmetric problems for infinite solids containing two parallel coaxial cracks or a periodic set of coaxial parallel cracks, we use a combined analytic-numerical method within the framework of the three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements in the linearized theory via harmonic potential functions. With the use of the integral Fourier–Hankel transformations, the problems are reduced to the solution of Fredholm integral equations of the second kind. This approach allows us to investigate problems in a unified general form for compressible and noncompressible homogeneous isotropic or transversely isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only in the stage of numerical analysis of the resolving equations obtained in the general form. The effects of initial stresses on the stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversely isotropic elastic bodies). The “resonance-like” effects are revealed when compressivemore » initial stresses reach the values corresponding to the local loss of stability of the material in the vicinity of cracks, which, according to the indicated combined method, allows one to determine the critical (limiting) load parameters under the conditions of compression of the body along the cracks. The conclusions concerning the dependences of the stress intensity factors and critical (limiting) parameters of compression on the geometric parameters of the problems are formulated as well as concerning the dependences on physical and mechanical characteristics of the materials.« less

Authors:
;  [1]
  1. Timoshenko Institute of Mechanics, Ukrainian National Academy of Science (Ukraine)
Publication Date:
OSTI Identifier:
22771557
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 229; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 42 ENGINEERING; AXIAL SYMMETRY; COMPRESSION; CRACKS; FOURIER TRANSFORMATION; FRACTURES; HARMONIC POTENTIAL; NUMERICAL ANALYSIS; PERIODICITY; PHYSICAL PROPERTIES; STRESS INTENSITY FACTORS; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Bogdanov, V. L., and Nazarenko, V. M.. Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3667-6.
Bogdanov, V. L., & Nazarenko, V. M.. Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks. United States. doi:10.1007/S10958-018-3667-6.
Bogdanov, V. L., and Nazarenko, V. M.. Thu . "Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks". United States. doi:10.1007/S10958-018-3667-6.
@article{osti_22771557,
title = {Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks},
author = {Bogdanov, V. L. and Nazarenko, V. M.},
abstractNote = {We consider two types of nonclassical fracture mechanisms, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and the fracture of solids under compression along parallel cracks. To investigate nonaxisymmetric and axisymmetric problems for infinite solids containing two parallel coaxial cracks or a periodic set of coaxial parallel cracks, we use a combined analytic-numerical method within the framework of the three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements in the linearized theory via harmonic potential functions. With the use of the integral Fourier–Hankel transformations, the problems are reduced to the solution of Fredholm integral equations of the second kind. This approach allows us to investigate problems in a unified general form for compressible and noncompressible homogeneous isotropic or transversely isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only in the stage of numerical analysis of the resolving equations obtained in the general form. The effects of initial stresses on the stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversely isotropic elastic bodies). The “resonance-like” effects are revealed when compressive initial stresses reach the values corresponding to the local loss of stability of the material in the vicinity of cracks, which, according to the indicated combined method, allows one to determine the critical (limiting) load parameters under the conditions of compression of the body along the cracks. The conclusions concerning the dependences of the stress intensity factors and critical (limiting) parameters of compression on the geometric parameters of the problems are formulated as well as concerning the dependences on physical and mechanical characteristics of the materials.},
doi = {10.1007/S10958-018-3667-6},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 2,
volume = 229,
place = {United States},
year = {2018},
month = {2}
}