Stress analysis near the tips of a transverse crack in an elastic semi-strip

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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“…The stress intensity factors for two cases can be found as,

\begin{matrix} K_{I -} = \sum_{k = 0}^{2 N - 1} s_{k}^{1} \frac{\sqrt{π (b_{1} - b_{0})} (n + 1) {((), - 1)}^{k}}{\sqrt{2}}, K_{I +} = \sum_{k = 0}^{2 N - 1} s_{k}^{1} \frac{\sqrt{π (b_{1} - b_{0})} (n + 1)}{\sqrt{2}} \\ K_{I I -} = \sum_{k = 0}^{2 N - 1} s_{k}^{2} \frac{\sqrt{π (b_{1} - b_{0})} (n + 1) {((), - 1)}^{k}}{\sqrt{2}}, K_{I I +} = \sum_{k = 0}^{2 N - 1} s_{k}^{2} \frac{\sqrt{π (b_{1} - b_{0})} (n + 1)}{\sqrt{2}} \end{matrix}

…”

Section: The Stress Intensity Factorsmentioning

confidence: 99%

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

Vaysfeld

Zhuravlova

2020

Z Angew Math Mech

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“…     are expanded in the series by the Chebyshev polynomials of the second type [24]      …”

Section: The Solving Of the Singular Integral Equationsmentioning

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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“…Besides, Alshamma and Jassim [7] confirmed all parameters of the Paris Law in the experiment and found the crack growth speed through the experiment and analysis. On the basis of the previous studies, the investigation on crack growth and fracture is in the ascendant in recent years [8][9][10][11][12], and the main progress is described as follows: Lei [13] takes 2024-T4 aluminum alloy as the investigation object and uses the finite element method to investigate the influence rule and mechanism of overload condition on the change trend of subsequent fatigue crack growth rate (da/ dN). For the problem of crack propagation in a plate with a single hole central crack, Zhang and Wang [14] introduced a new Z fracture criterion which can well predict the crack propagating direction of mode I crack in carbon-fiber reinforced composite laminates and proposed new concepts of in-plane average strain, in-plane dilatational strain energy density factor, and reciprocal characteristic function.…”

Section: Introductionmentioning

confidence: 99%

SVR Prediction Algorithm for Crack Propagation of Aviation Aluminum Alloy

Chang

Wang

Zhu

et al. 2020

Journal of Mathematics

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Aluminum alloy material is an important component material in the safe flight of aircraft. It is very important and necessary to predict the fatigue crack growth between holes of aviation aluminum alloy materials. At present, the investigation on the prediction of the cracks between two holes and multiholes is a key problem to be solved. Due to the fact that the fatigue crack growth test of aluminum alloy plate with two or three holes was carried out by the MTS fatigue testing machine, the crack length growth data under different test conditions were obtained. In this paper, support vector regression (SVR) was used to fit the crack data, and the parameters of SVR are optimized by the grid search algorithm at the same time. And then the model of SVR to predict the crack length was established. Discussion on the results shows that the prediction model is effective. Furthermore, the crack growth between three holes was predicted accurately through the model of the crack law between two holes under the same load form.

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Stress analysis near the tips of a transverse crack in an elastic semi-strip

Cited by 7 publications

References 27 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

SVR Prediction Algorithm for Crack Propagation of Aviation Aluminum Alloy

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