Interaction of a penny-shaped crack with an elliptic crack
TL;DR: In this paper, the authors solved the three-dimensional problem of crack-microcrack interaction in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity.
Abstract: Three-dimensional problem of crack-microcrack interaction is solved. Both the crack and microcrack are embedded in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity. One of the cracks is circular while the other is elliptic and they are coplanar and are positioned in such a way that the axis of the elliptic crack passes through the centre of the circular crack. A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem. A series of transformations first reduce them to a quadruplet infinite system of equations. A series solution is finally obtained in terms of crack separation parameter β which depends on the separation of the crack microcrack centre. Analytical expression for the stress intensity factors have been obtained up to the order β6. Numerical values of the interaction effect have been computed for and results show that interaction effects fluctuate from shielding to amplification depending on the location of each crack with respect to the other and crack tip spacing as well as the aspect ratio of the elliptic crack. The short range interaction can play a dominant role in the prediction of crack microcrack propagation.
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TL;DR: In this paper, a set of joints within granite of the South Bohemian Pluton exposed in the Borsov Quarry, southeast of Prague in the Czech Republic, were investigated.
Abstract: This study relates to jointing in granite that took place in the crust before uplift, thus offering an insight into paleo–fracture processes. Our investigation reveals a unique set of joints within granite of the South Bohemian Pluton exposed in the Borsov Quarry, southeast of Prague in the Czech Republic. These joints occur in close proximity and exhibit a great variety of fracture-surface morphologies. The joints in the Borsov granite may be divided into four groups based on fractographic features: (1) partial mirror planes without fringes, (2) mirror planes rimmed by en echelon fringes, (3) complex en echelon fringes, and (4) hackled fringes. On the basis of theoretical, experimental, and fractographic data obtained in outcrops, we have constructed a curve for the change in crack velocity V as a function of the stress-intensity factor K I, and we have plotted the various joints in the Borsov granite on this curve. The spread of the joints along the curve indicates that the joints terminated under widely different physical conditions, possibly responding to repeated extensional events and different fracture mechanisms. Hence, a new quantitative method of joint classification is introduced.
Such a great variety of fractographic features is unknown from joint sets that occur in a single quarry in sedimentary rock, because their formation always relates to a particular fracture mechanism. We argue that the joints in the Borsov granite formed before uplift in a fluid-enriched environment, while the granite responded to diverse, local effective-stress conditions.
45 citations
TL;DR: In this article, the interaction of a pair of outer cracks on a central crack situated at the interface of two dissimilar orthotropic half-planes has been investigated and the mixed boundary value problem is reduced to solving a pair simultaneous singular integral equations which have finally been solved numerically by using Jacobi polynomials.
Abstract: The paper deals with the interaction of a pair of outer cracks on a central crack situated at the interface of two dissimilar orthotropic half-planes. The mixed boundary value problem is reduced to solving a pair of simultaneous singular integral equations which have finally been solved numerically by using Jacobi polynomials. The analytical expressions for stress intensity factors at the central crack tip and the expression of the strain energy release rate have been derived for general loading. Numerical values of the interaction effects of the outer cracks on the central crack have been calculated through stress magnification factors. It is seen that the interaction effects are either shielding or amplification depending on the size of the outer cracks and their spacing from the central crack.
15 citations
TL;DR: In this paper, the Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result.
Abstract: We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic layer of finite thickness 2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have 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 are obtained for large h. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the layer.
9 citations
Cites background from "Interaction of a penny-shaped crack..."
...The interaction between the elliptic cracks has been studied by Roy and Saha [15] and Murakami and Nishitani [12], and others....
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...The interaction between the elliptic cracks has been studied by Roy and Saha [15] and Murakami and Nishitani [12], and others....
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...[15] A. Roy and T. K. Saha, Interaction of a penny-shaped crack with an elliptic crack, Internat....
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06 Dec 2019
TL;DR: Linear and Non-Linear Deformations of Elastic Solids as discussed by the authors aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics.
Abstract: Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.
5 citations
TL;DR: In this article, the same integral equation method has been used to solve the title problem of equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al.
Abstract: The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter β
i
up to the order β
5
,(i=1,2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289–313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.
4 citations
Cites methods from "Interaction of a penny-shaped crack..."
...The perturbation technique used earlier (see Roy and Chatterjee, 1994; Roy and Saha, 1995; Saha et al., 1999) has been used again to solve the integral equations....
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...The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method....
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References
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TL;DR: In this paper, the interaction between a main crack and two-dimensional microcracks surrounding the main-crack tip can be simplified by using a point-source representation for the micro-cracks and a selfconsistent scheme to determine the strength of these point sources.
Abstract: It is noted that calculations of the interaction between a main crack and two-dimensional microcracks surrounding the main-crack tip can be considerably simplified by using a point-source representation for the microcracks and a self-consistent scheme to determine the strength of these point sources The procedure is illustrated by a detailed analysis for two basic configurations: (i) a single microcrack of arbitrary orientation near a main crack which is subjected to combined mode I and mode II loading; (ii) two microcracks symmetrically disposed about a main crack which is subjected to purely mode I loading By comparing the result for configuration (i) with the exact result which is available for the special case of a collinear microcrack, it is found that the point-source representation for that case is accurate to within 5 percent over the range 0
160 citations
TL;DR: In this paper, the analysis of stress intensity factors of a semi-infinite body with an elliptical or semi-elliptical crack subject to tension is presented, where the authors focus on the stress intensity factor of the body with respect to tension.
Abstract: This paper is concerned with the analysis of stress intensity factors of a semi-infinite body with an elliptical or a semi-elliptical crack subject to tension.
111 citations
TL;DR: In this paper, the collinear periodical array of microcracks ahead of a semi-infinite crack (macrocrack) is considered, and a close form solution in terms of complex stress potentials is given, assuming that a remote, macro-scale, stress intensity factor is given.
Abstract: The collinear periodical array of microcracks ahead of a semi-infinite crack (macrocrack) is considered. A close form solution in terms of complex stress potentials is given, assuming that a remote, macroscale, stress intensity factor is given. The exact solution of the interaction of a macrocrack with a single microcrack is given.
105 citations
TL;DR: In this paper, the tension of an infinite solid containing two parallel elliptical cracks located in staggered positions is analyzed based on the body force method, in which symmetric and antisymmetric type body forces are distributed over the crack surfaces and their densities are determined from the bondary conditions.
Abstract: This paper is concerned with the tension of an infinite solid containing two parallel elliptical cracks located in staggered positions. The analysis is based on the body force method, in which symmetric and antisymmetric type body forces are distributed over the crack surfaces and their densities are determined from the bondary conditions. Numerical calculations are performed for a wide range of the parameters, and the effects of the shapes and the relative locations of the cracks on the stress intensity factors are examined. Convenient empirical formulae of the stress intensity factors are also proposed for some important cases.
46 citations
TL;DR: In this article, the 3D interactions of a crack front with arrays of penny-shaped microcracks are considered, and the authors extend the analysis of 2D crack-microcracks interactions to 3D configurations.
Abstract: Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks are considered. The work extends the earlier analysis of 2-D crack-microcrack interactions to the 3-D configurations.
45 citations