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1

Moving semi-infinite mode-III crack inside the semi-infinite elastic media

Mandal Palas

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 3

649--659

EN

The problem of a semi-infinite moving mode-III crack inside a semi-infinite isotropic half- -space is considered. The crack is located between a semi-infinite elastic medium and a layer whose distance from the surface to crack depth is h. Initially, Fourier transformation and inverse Fourier transformation are applied to transfer the governing boundary value problem to the well-known Wiener-Hopf equation. The purpose of this problem is to obtain the analytical solution of Stress Intensity Factor (SIF) and Crack Opening Displacement (COD) at the neighbourhood of the crack tip. In numerical Section, I have discussed the variation of parameters (crack velocity, layer distance h from the surface to crack depth) to show the effect of these parametric values on the graphs of SIF and COD where the material properties (density, shear modulus) were fixed.

2

Extended finite element numerical analysis of scale effect in notched glass fiber reinforced epoxy composite

Abdellah M. Y., Alsoufi M. S., Hassan M. K., Ghulman H. A., Mohamed A. F.

Archive of Mechanical Engineering

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2015

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Vol. LXII, nr 2

217--236

EN

Nominal strength reduction in cross ply laminates of [0/90]2s is observed in tensile tests of glass fiber composite laminates having central open hole of diameters varying from 2 to 10 mm. This is well known as the size effect. The extended finite element method (XFEM) is implemented to simulate the fracture process and size effect (scale effect) in the glass fiber reinforced polymer laminates weakened by holes or notches. The analysis shows that XFEM results are in good agreement with the experimental results specifying nominal strength and in good agreement with the analytical results based on the cohesive zone model specifying crack opening displacement and the fracture process zone length.

PL

Zmniejszenie nominalnej wytrzymałości laminatu warstwowego z poprzecznym ułożeniem włókien typu [0/90]2s jest obserwowane dla naprężeń rozciągających w laminatach kompozytowych z włóknem szklanym mających centralny otwór o średnicy od 2 do 10 mm. Jest to dobrze znany efekt rozmiaru (efekt skali). Rozszerzona analiza metodą elementów skończonych (XFEM) została zastosowana w celu symulacji procesu pękania i efektu skali w polimerowych laminatach z włóknem szklanym osłabionych obecnością karbu lub otworu. W pracy wykazano, że wyniki metody XFEM dotyczące wytrzymałości nominalnej są zgodne z danymi eksperymentalnymi, dobrze zgadzają sią z wynikami analitycznymi opartymi na modelu strefy spójnej i pozwalają określić przemieszczenie otworu szczeliny i długość strefy procesu pęknięcia.

3

Model for a piezoelectric strip of crack arrest subjected to Mode-I loadings

Bhargava R.R., Setia A.

Archives of Computational Materials Science and Surface Engineering

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2009

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Vol. 1, nr 1

5-12

EN

Purpose: In the present paper a crack arrest model is proposed for an infinitely long narrow poled piezoelectric strip embedded with a centrally situated finite hairline straight crack. Design/methodology/approach: The ceramic of the strip is assumed to be mechanically brittle and electrically ductile. Combined mechanical and electrical loads applied at the edge of the strip open the rims of the crack in mode-I deformations. Consequently a yield zone protrudes ahead of each tip of the crack. Under small scale yielding the yield zone are assumed to lie on the line segment along the axis of the crack. To arrest the crack from further opening the rims of the yield zones are subjected to normal, cohesive quadratically varying yield point stress. Two cases are considered: Case-I the edges of the strip are subjected to in-plane normal and in-plane electrical displacement and in Case-II the in-plane stresses and in-plane electrical field are applied on the edges of the strip. In each case problem is solved using Fourier transform method which finally reduces to the solution of integral equation. Findings: Analytic expressions are derived for stress intensity factor, yield zone, crack opening displacement, crack growth rate, variation of these quantities with respect to affecting parameters viz. width of the strip, yield zone length, crack length, material constants for different ceramics have been plotted. Research limitations/implications: The material of the strip is assumed mechanically brittle and electrically ductile consequently mechanically singularity is encountered first. The investigations in this paper are carried at this level. Also the crack yielding under the loads is considered small scale hence the yield zone is assumed to be lying on the line segment ahead of the crack. Practical implications: Piezoelectric ceramics are widely used as sensors and actuators, this necessity prompts the fracture study on such ceramics under different loading conditions. Originality/value: The paper gives an assessment of the quadratically varying load required to be prescribed on yield zones so as to arrest the opening of the crack. The investigations are useful to smart material design technology where sensors and actuators are manufactured.

4

Crack arrest model for a piezoelectric strip subjected to Mode-I loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 22, nr 2

19-22

EN

Purpose: The present paper aims at proposing a crack arrest model for an infinitely long narrow, poled ceramic strip weakened by a finite hairline straight crack when the edges of the strip are subjected to combined mechanical and electrical loads. Design/methodology/approach: (Model) As a consequence of loads the rims of crack open forming a yield zone ahead of each tip of the crack. To arrest the crack from further opening the rims of the yield zones are subjected to normal cohesive quadratically varying yield point stress. Two cases are presented when edges of the strip are subjected to: Case-I-in-plane stresses and electrical displacement or Case-II-in-plane stresses and in-plane electric field. Problems are solved using Fourier integral transform method. Findings: The stress intensity factor, yield zone length, crack opening displacement, crack growth rate have been calculated. Their variation with respect to affecting parameters viz. yield zone length, width of the strip, material constant, electrical and mechanical loads has been depicted graphically. Research limitations/implications: The material of the strip is assumed mechanically brittle and electrically ductile consequently mechanically singularity is encountered first. The investigations in this paper are carried at this level. Also the crack yielding under the loads is considered small scale hence the yield zone is assumed to be lying on the line segment ahead of the crack. Practical implications: Piezoelectric ceramics are widely used as sensors and actuators, this necessity prompts the fracture study on such ceramics under difference loading conditions. Originality/value: The paper gives an assessment of the quadratically varying load required to be prescribed on yield zones so as to arrest the opening of the crack. The investigations are useful to smart material design technology where sensors and actuators are manufactured.

5

Crack arrest model for a piezoelectric strip subjected to Mode-I loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

|

Vol. 20, nr 1-2

215-218

EN

Purpose: The present paper aims at proposing a crack arrest model for an infinitely long narrow, poled ceramic strip weakened by a finite hairline straight crack when the edges of the strip are subjected to combined mechanical and electrical loads. Design/methodology/approach: (Model) As a consequence of loads the rims of crack open forming a yield zone ahead of each tip of the crack. To arrest the crack from further opening the rims of the yield zones are subjected to normal cohesive quadratically varying yield point stress. Two cases are presented when edges of the strip are subjected to: Case-I-in-plane stresses and electrical displacement or Case-II-in-plane stresses and in-plane electric field. Problems are solved using Fourier integral transform method. Findings: The stress intensity factor, yield zone length, crack opening displacement, crack growth rate have been calculated. Their variation with respect to affecting parameters viz. yield zone length, width of the strip, material constant, electrical and mechanical loads has been depicted graphically. Research limitations/implications: The material of the strip is assumed mechanically brittle and electrically ductile consequently mechanically singularity is encountered first. The investigations in this paper are carried at this level. Also the crack yielding under the loads is considered small scale hence the yield zone is assumed to be lying on the line segment ahead of the crack. Practical implications: Piezoelectric ceramics are widely used as sensors and actuators, this necessity prompts the fracture study on such ceramics under different loading conditions. Originality/value: The paper gives an assessment of the quadratically varying load required to be prescribed on yield zones so as to arrest the opening of the crack. The investigations are useful to smart material design technology where sensors and actuators are manufactured.

6

Eksperymentalne określenie krzywej podatności dla płaskiej próbki z karbem krawędziowym (SEC)

Bukowski L., Kłysz S.

Prace Naukowe Instytutu Technicznego Wojsk Lotniczych. Technika Lotnicza

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2003

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nr 16

23-31

PL

W pracy przedstawiono wyniki pomiarów i obliczeń, których celem było wyznaczenie postaci krzywej podatności - zależności długości pęknięcia od podatności próbki - dla płaskiej próbki z pojedynczym karbem krawędziowym (Single Edge Crack specimen). Dla próbki tej znane są zależności współczynnika intensywności naprężeń i rozwarcia pęknięcia zmęczeniowego od długości pęknięcia, natomiast postać funkcji podatności nie jest powszechnie publikowana i znana.

7

A pair of equal collinear interfacial cracks between bonded dissimilar fixed isotropic layers

Das S.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 2

167-175

EN

The problem of a pair of equal collinear Griffith cracks propagating with constant velocity under antiplane shear stress at the interface of two bonded dissimilar fixed isotropic layers has been considered. The method of Fourier transforms is employed and the problem is reduced to the solution of a singular integral equation, which has finally been solved numerically by using Chebyshev polynomials. The stress intensity factors at the crack tips and the crack opening displacement have been calculated numerically for some particular cases and displayed graphically.

8

Three interfacial Griffith cracks between bonded dissimilar elastic media

Das S.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 1

133-149

EN

The paper deals with three collinear Griffith cracks propagating with constant velocity under antiplane shear stress at the interface of an elastic layer of finite thickness h and a semi-infinite half plane of different elastic properties. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips and crack opening displacements are obtained for large h. The graphical plots of these results are also presented for some particular cases.

9

The influence of cracks on the mechanical behaviour of particulate MMCs: an experimental study

Kourkoulis S. K.

Archives of Mechanics

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2001

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Vol. 53, nr 4-5

439-456

EN

The deterioration of the mechanical properties of particulate Metal Matrix Composites (MMCs) caused by macroscopic cracks is studied, experimentally, in comparison to the behaviour of the respective matrix alloys. Two Al-based MMCs, reinforced with fine SiC particles, extensively used in aerospace engineering, are employed. The study is focused on the influence of cracks on the fracture strength of MMCs and on the variation of the critical Crack Opening Displacement (COD) versus the inclination of the crack with respect to the loading direction. The role of the plastic anisotropy induced during manufacturing is also investigated.