Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review)

Guz, A. N.

doi:10.1007/s10778-014-0609-y

Cited by 50 publications

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References 101 publications

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“…The general solution of the system of ordinary differential equations (20), (21) can be obtained using the standard method of variation of constants:…”

Section: Formulation Of and Solutionmentioning

confidence: 99%

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Modeling the Radiation of Ultrasonic Waves by a Unit Source of Acoustic Emission Noise

Petrishchev

Trushko

2015

Int Appl Mech

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The generation of radial Lamb waves by a system of volume and surface loads acting within a finite region of an isotropic elastic plate is studied. General solutions are used to model the emission of ultrasonic waves in an isotropic plate by a unit source of acoustic emission noise of two model configurations: linear and point. It is established that the results for a pulsating linear source are in qualitative agreement with Torwick's solution to the physically equivalent problem of the emission of Lamb waves by a longitudinal harmonic force acting at the end of a half-strip. The generation of Lamb waves in a plate by a point source is modeled to asses how effectively the energy of elastic vibrations is extracted from the source and is transferred through the plate by different modes and at different frequencies Keywords: acoustic emission, Lamb waves, nondestructive testing Introduction. Of many nondestructive testing methods, the acoustic-emission method has recently become more and more popular. This method has the following considerable advantages. First, the method is applied not to detect current damage, but to predict, by analyzing test data, the development of damage depending on the operating conditions. Such a prediction does not assume conducting external calculations or invoking the structure design and operation history [11]. Second, unlike the active methods in which the parameters of radiation are a factor that affects, to some extent, the test data, the "primary source" in this method is a defect [9]. Third, the diagnostic process does not require constant active participation of the personnel after installation and setting of the diagnostic system. Moreover, during diagnostics, the personnel and the analytical data processing units of the system can be far from the object, which is important in case of risk of an emergency [1,11]. The method is most frequently used for continuous monitoring usually for a rather long time, sometimes for the entire service life.Experimental research has reliably established a relationship between the spectral and energy characteristics of acoustic emission noise and the scales of the deformation processes in materials [2,3,9,11,14,16,19,20,25,27]. Moreover, the current understanding of fracture mechanics [10,17,[21][22][23] allows us to provide a well-founded (to some extent) physical interpretation for this relationship.An experimentally proved fact is that the acoustic-emission method can be used to measure stresses (strains) in a material, detect various defects, determine their coordinates, assess the danger of defects, and solve other problems of structural assessment. These methods have not, however, been applied in practice at a level appropriate to their real capabilities. This is due to their relative novelty and some unclear aspects of the acoustic-emission theory such as the mechanism of delivery of energy from a source of acoustic emission noise along structural elements as waveguides to an electroacoustic transducer detecting ultrasonic waves. A featur...

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“…The general solution of the system of ordinary differential equations (20), (21) can be obtained using the standard method of variation of constants:…”

Section: Formulation Of and Solutionmentioning

confidence: 99%

“…Moreover, the current understanding of fracture mechanics [10,17,[21][22][23] allows us to provide a well-founded (to some extent) physical interpretation for this relationship.…”

mentioning

confidence: 99%

Modeling the Radiation of Ultrasonic Waves by a Unit Source of Acoustic Emission Noise

Petrishchev

Trushko

2015

Int Appl Mech

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“…As an efficient method for the investigation of the problems of fracture mechanics of materials for bodies with cracks [2,3,12], we can mention the Wiener-Hopf technique [7]. In the present work, by using this technique, we construct the exact solution of a plane static problem of the theory of elasticity for a piecewise homogeneous isotropic elastic body with small-scale interface shear cracks near the angular point of the interface.…”

Section: Introductionmentioning

confidence: 99%

Influence of Interface Shear Cracks Located Near the Angular Point of the Interface in a Bi-Homogeneous Body on the Stress State Formed in the Vicinity of this Point

Назаренко

Kipnis

2022

J Math Sci

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Within the framework of the hypothesis of plane deformation, we consider a piecewise homogeneous isotropic elastic body with interface shear cracks near the angular point of the interface. The exact solution of the corresponding problem of the theory of elasticity for a wedge-shaped body is constructed by the Wiener-Hopf method. On the basis of the constructed solution, we analyze the behavior of stresses in the vicinity of the angular point.

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“…Fundamental areas of fracture mechanics are problems of the fracture of materials compressed along cracks [5,8,10,13,14] and dynamic problems for homogeneous and composite materials with cracks [6,7,12].…”

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confidence: 99%

Necking Near a Crack Tip in a Plate: a Plane Problem

Khoroshun

2015

Int Appl Mech

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The nonlinear plane problem of the tension of a plate with a crack and a neck at the crack tip is solved. The stress-strain curve is assumed piecewise-linear with a constant bulk modulus. By applying the Fourier transform and discretization, the problem is reduced to a system of nonlinear algebraic equations. The distribution of the neck depth near the crack tip and the effect of nonlinearity on the crack-tip opening displacement are studied Introduction. The primary task of fracture mechanics is to analyze the stress-strain state near a crack and to establish criteria and laws governing its growth [2,9,23]. It is quite obvious that the adequate solution of this problem is possible based on a comprehensive study of the physics of the phenomenon and accompanying processes, a rigorous formulation of a chosen mathematical model describing the phenomenon, and the exact solution of the corresponding equations. Simplifications in the formulation of the mathematical model and analytic or numerical problem-solving methods may substantially distort the description of the real situation.Problems and criteria of fracture mechanics are known [12, 13] to be classical and nonclassical. The former include problems of tension or shear near cracks provided that deformation behavior does not change sharply before fracture. Failure criteria in the former case are formulated for quantities describing the stress-strain state at the crack tip.Nonclassical problems of fracture mechanics involve search for new failure mechanisms that can then be used to solve certain classes of problems. Fundamental areas of fracture mechanics are problems of the fracture of materials compressed along cracks [5,8,10,13,14] and dynamic problems for homogeneous and composite materials with cracks [6,7,12].Unlike most problems in mechanics where the strength of a body is assessed by comparing the maximum stresses or strains to their ultimate levels for a certain material, the calculated stresses and strains at the crack tip in linear fracture mechanics are infinite, which eliminates the possibility of using this procedure and creates formulational and computational difficulties [2]. Therefore, classical fracture mechanics was developed by formulating alternative concepts and approaches based on additional simplifying assumptions on the stress distribution and failure mechanism at the crack tip. These approaches are known as energy-, stress-, and strain-based failure criteria [2].Griffith's energy criterion for brittle fracture [11] and its modification for quasibrittle fracture by Orowan and Irwin [15,22] are considered fundamental failure criteria in classical fracture mechanics. These criteria are based on the assumption of balance between the elastic strain energy released as the crack grows and either the increment of the surface energy in the case of brittle fracture or the energy dissipated in the plastic zone at the crack tip in the case of qusibrittle fracture. This assumption cannot be considered correct because the increment of surface energy equ...

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Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review)

Cited by 50 publications

References 101 publications

Modeling the Radiation of Ultrasonic Waves by a Unit Source of Acoustic Emission Noise

Modeling the Radiation of Ultrasonic Waves by a Unit Source of Acoustic Emission Noise

Influence of Interface Shear Cracks Located Near the Angular Point of the Interface in a Bi-Homogeneous Body on the Stress State Formed in the Vicinity of this Point

Necking Near a Crack Tip in a Plate: a Plane Problem

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