Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

Akbarov, S. D.; Yahnioğlu, Nazmiye; Turan, Arzu

doi:10.1023/b:mocm.0000039747.47634.69

Cited by 5 publications

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“…[38] This method allows taking into consideration the real singularities of the solution at the ends of the integration interval. Considering that the distances from the crack tips to the short edge of the semi-strip are big enough, there are no fixed singularities in the kernels of the SSIE (20). With regard to it, the functions̃( ),̃1( ),̃2( ) are expanded in series by the Chebyshev polynomials of the second kind ( )…”

Section: Casementioning

confidence: 99%

“…These expressions are substituted into the SSIE (20), and the standard scheme of the orthogonal polynomials' method is realized. During it, the spectral correspondence [38] is used.…”

Section: Casementioning

confidence: 99%

“…The problem for an infinite strip with a crack was solved with the help of three-dimensional lineralized elasticity methods in [20], SIF were calculated by the energetic method. The problem for a stressed crack in an infinite strip was solved in [21] with the help of the superposition method and solutions for three problems: a stressed crack in a infinite plane, a first main problem of elasticity for a infinite homogeneous strip and an infinite strip which is free from stress.…”

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The investigation of semi‐strip's stress state with a longitudinal crack

Vaysfeld

Zhuravlova

2020

Z Angew Math Mech

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The article is dedicated to the investigation of the stress state of a semi-strip weakened by a longitudinal crack. Two statements of the problem are considered. The integral Fourier transform is applied directly to the initial problem. The discontinuous boundary problem which is formulated in vector form is solved with the help of the matrix differential calculation and the Green's matrix-function's discontinuous properties. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). This system is solved by two methods regarding to the conditions at the semi-strip's short edge. The orthogonal polynomials method is used when the semi-strip is loaded at the center of its short edge, and the special generalized scheme, which allows consideration of fixed singularities, this is applied when the whole semi-strip's short edge is loaded. The stress intensity factors (SIF) are investigated for the two cases. K E Y W O R D Sfixed singularity, Green's function, longitudinal crack, semi-strip, singular integral equations INTRODUCTIONThe elasticity problem for a semi-strip with a longitudinal crack is a model problem. Its solving is important both for the development of theoretical methods and for the practical demand of engineering problems.The problems of elastic strips and semi-strips weakened by cracks have been solved by many methods: with the help of harmonic functions, simple and double layer potentials, integral transformations, asymptotic methods and others.The mixed elasticity problems were solved in [1]. Elastodynamic analysis of multiple crack problem in 3-D bi-materials was made in [2]. A new type of cracks adding to Griffith-Irwin cracks was investigated in [3]. In the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations. A finite elastic wedge-shaped thick plate was considered in [4].The problem about determining the thermal stress in a thermoelastic strip with a collinear array of cracks which are parallel to the strip's sides was considered in [5]. The solving of the Duhamel-Neumann equation was constructed with the help of harmonic functions. The solving of the problem for the infinite strip with a semi-infinite crack was reduced to solving of singular integral equation by the use of simple layer and double layer potentials in [6]. The method for the elastic strip which is weakened by cracks and holes was proposed in [7]. The solution of this problem was reduced to singular integral equation with the help of complex potentials.The plane problem about the interfacial crack between the elastic strip and the elastic semi-plane from another material was solved in [8]. The regular asymptotic method was applied for the solving of the system of integral equations for the displacements' jumps. This method is efficient when the crack is sufficiently narrow. Two configurations of modeling of an interfacial crack with parallel free boundaries were investigated in [9]: a crack in the semi-plane...

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Section: Casementioning

confidence: 99%

“…These expressions are substituted into the SSIE (20), and the standard scheme of the orthogonal polynomials' method is realized. During it, the spectral correspondence [38] is used.…”

Section: Casementioning

confidence: 99%

mentioning

confidence: 99%

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The investigation of semi‐strip's stress state with a longitudinal crack

Vaysfeld

Zhuravlova

2020

Z Angew Math Mech

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“…Different approaches were applied for stress estimation in infinite strips with cracks. SIFs were calculated for the infinite strip with a crack with the help of the energetic method in [7]. The crack's spreading in the infinity strip was considered in [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Investigation of the stress state of the elastic semi-strip with a transverse crack

Reut

Vaysfeld

Zhuravlova

2019

Theoretical and Applied Fracture Mechanics

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“…5b, are calculated in a well-known manner after the completion of the solution procedure. Thus, the paper [15] investigates the evolution of the infinitesimal initial imperfection defined by (24) and (25) employing the approach developed in [1,18,22,23,69]. In this case, the time (force) at which this initial imperfection starts increasing indefinitely is taken as the critical time (force) for a viscoelastic (elastic) plate.…”

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confidence: 99%

Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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Investigations of viscoelastic composite materials and structural members carried out using the TDLTSDB and initial-imperfection method are reviewed. The investigations address the internal and surface loss of stability of layered and fibrous composites, the loss of stability of plates, and the delamination (buckling) of plates with cracks. Each of these problems is reviewed separately. New areas of further research are proposed. The review focuses on the investigations carried out by the author and his students Keywords: buckling, crack, delamination, plate, instability, viscoelastic composite material 1. Introduction. As in [33,[41][42][43][44][45] and many other publications, by three-dimensional instability problems will be understood here instability problems investigated employing the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB). The investigations regarding the construction of the TDLTSDB are detailed in the paper [46] and in the monographs [33,[41][42][43]45]. It was noted there that the tendencies to construct the theory, which allows us (i) to describe the buckling phenomenon for a well-defined three-dimensional stress-strain state and (ii) to obtain reliable data on the critical parameters for thin-walled and massive structural elements, contributed to the creation of the TDLTSDB. Historically, the TDLTSDB began to be developed in the first half of the 20th century, and the basic TDLTSDB relations were obtained in [30, 31-33, 35, 38, 45, 63, 71-73, 80, 84, 85] using either a strict and exact approach based on the linearization of the exact and strict relations of the nonlinear three-dimensional theory or an approximate approach based on a physical and, in part, linearization of certain relations. Development and detailed analyses of the results from these investigations were presented in the monographs [41,42,45].In the second half of the 20th century, the main attention of researchers was focused on the solution to separate classes of TDLTSDB problems. At the same time, general aspects of the TDLTSDB were also developed. It should be noted that the results of these studies were the subject of many monographs such as [41][42][43][44][45] and were reviewed in many papers such as [28,46,47,49,52,55,56,58].It follows from the search of the foregoing and other numerous inquiries that the TDLTSDB was mainly applied to analyze the stability of structural members made of time-independent materials. Moreover, these investigations used the bifurcation (Euler) approach. The Euler approach is known to be generally unsuitable for investigating instability problems for structural elements made of time-dependent materials and subjected to external static loading. This is why a dynamic investigation method was suggested in [40,45] to examine these problems. Note that this method represents the sought quantities with a multiplier exp(iWt) and determines the critical parameters of the problems from the requirement ImW = 0. However, if the dynamic investigation method is applied with...

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Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

Cited by 5 publications

References 4 publications

The investigation of semi‐strip's stress state with a longitudinal crack

The investigation of semi‐strip's stress state with a longitudinal crack

Investigation of the stress state of the elastic semi-strip with a transverse crack

Three-dimensional instability problems for viscoelastic composite materials and structural members

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