Nonclassical Problem Of Fracture Mechanics Research Articles

On General List of References to the Monograph “Eight Non-Classical Problems of Fracture Mechanics”

On General List of References to the Monograph “Eight Non-Classical Problems of Fracture Mechanics”

Investigation of the Fracture of a Semibounded Body Compressed Along a Near-Surface Interface Crack

We consider the problem of compression of a piecewise homogeneous half plane by forces directed along a near-surface crack located on the interface of two materials. This problem belongs to the class of nonclassical problems of fracture mechanics because, for the analyzed loading scheme, the stressstrain state realized in the body is homogeneous and the corresponding expressions for stresses and displacements in the vicinity of the crack do not contain singular components. Due to the fact that the stress intensity factors are equal to zero, for the analyzed problem, the classical Griffith–Irwin fracture criteria are inapplicable. In the indicated situation, the onset of crack propagation is associated with the local loss of stability of the equilibrium state of a part of the material located in the region adjacent to the crack. By using the approaches of the three-dimensional linearized theory of stability of deformable bodies, we propose a mathematical statement of the problem and an approach to its investigation. By using the representations of stresses and displacements in terms of complex potentials, we analyze the case where the roots of the corresponding characteristic equation are identical for each material.

Fracture of a Semi-Bounded Composite Material with a Near-Surface Penny-Shaped Crack under Compression

The nonclassical problem of fracture mechanics for a near-surface crack is solved in the case of small distances between the free surface and the crack plane. The problem is axisymmetric for a penny-shaped crack. A numerical study for a composite material is carried out as an example.

Nonclassical Problems of Fracture/Failure Mechanics: on the Occasion of the 50th Anniversary of the Research (Review)

The main results of research on some nonclassical problems of fracture/failure mechanics are analyzed. These results have been obtained by the author and his followers at the Department of Dynamics and Stability of Continua of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials; it is published in Prikladnaya Mekhanika (55, No. 3, 2019). The third part is Other Nonclassical Problems of Fracture/Failure Mechanics; it is published in Prikladnaya Mekhanika (55, No. 4, 2019).

Three-Dimensional Problems in the Dynamic Fracture Mechanics of Materials with Interface Cracks (Review)

Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed

Fracture of a material compressed along a periodic set of closely spaced cracks

A nonclassical problem of fracture mechanics for a body with a periodic set of closely spaced cracks is solved. In the case of equal roots of the characteristic equations, an axisymmetric problem is considered. Materials with harmonic and Bartenev–Khazanovich potentials are analyzed numerically. The numerical results are presented in the form of tables and graphs and analyzed

Fracture of a half-space compressed along a penny-shaped crack located at a short distance from the surface

Non-classical problems of fracture mechanics for a half-space with a crack located at a short distance from the free surface are solved. An axisymmetric problem for a penny-shaped crack is considered. A numerical analysis is performed for materials with harmonic and Bartenev–Khazanovich potentials in the case of unequal roots of the characteristic equation. This case is similar in mathematical structure of the equations to the case of equal roots in the classical theory of isotropic elasticity. The numerical results are tabulated and analyzed

Fracture of a material compressed along a crack located at a short distance from the free surface

A nonclassical problem of fracture mechanics for a compressed material with a crack located at a short distance from the free surface is solved. The axisymmetric case for a circular crack is examined. Numerical results (critical stresses corresponding to the initial stage of fracture) for the Treloar material are discussed as an example

The effect of the interaction of cracks in orthotropic layered materials under compressive loading

The non-classical problem of fracture mechanics of composites compressed along the layers with interfacial cracks is analysed. The statement of the problem is based on the model of piecewise homogeneous medium, the most accurate within the framework of the mechanics of deformable bodies as applied to composites. The condition of plane strain state is examined. The layers are modelled by a transversally isotropic material (a matrix reinforced by continuous parallel fibres). The frictionless Hertzian contact of the crack faces is considered. The complex fracture mechanics problem is solved using the finite-element analysis. The shear mode of stability loss is studied. The results are obtained for the typical dispositions of cracks. It was found that the interacting crack faces, the crack length and the mutual position of cracks influence the critical strain in the composite.

On Some Nonclassical Problems of Fracture Mechanics Taking into Account the Stresses Along Cracks

The paper reports on the results from analysis of some nonclassical fracture problems that allow for stresses along cracks. The results have been obtained by the author and his collaborators at the Institute of Mechanics (Kiev) since 1980

Description and Study of Some Nonclassical Problems of Fracture Mechanics and Related Mechanisms

Some nonclassical problems of fracture mechanics that have been analyzed by the author and his collaborators at the Institute of Mechanics (Kiev) during the past thirty years are considered in brief

On nonclassical problems and mechanisms of fracture mechanics and its description

As was mentioned in the introduction, in this article, in a brief form (as an annotation), information on some results obtained in nonclassical problems of fracture mechanics obtained by the author and his co-author at the Institute of Mechanics of the Ukrainian Academy of Sciences is presented. Along with the above results, at the Institute of Mechanics of the Ukrainian Academy of Sciences other results on nonclassical problems of fracture mechanics were also obtained; information on these results may be partially obtained from the four-volume (in 5 books) monograph [14]. Additional information on the mechanics of composite materials, obtained by scientific workers at the Institute of Mechanics of the Ukrainian Academy of Sciences, may be obtained from the three volume monograph [13]. It should be noted that investigations on nonclassical problems of fracture mechanics in parallel with the Institute of Mechanics of the Ukrainian Academy of Sciences are also carried out in other scientific centers. The research described in this publication was made possible in part by Grant No. K4F100 from the Joint Fund of the Government of Ukraine and the International Science Foundation.