Approximate stress intensity factor for an embedded elliptical crack near two parallel free surfaces

Kobayashi, A. S.; Ziv, M.; Hall, L. R.

doi:10.1007/bf00186746

Cited by 33 publications

(5 citation statements)

References 4 publications

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“…Reference (8) gives an approximate analytical solution for an eccentrically cracked centre notched plate. The analysis of this case is difficult by the present approximate method because the inclusion of bending stresses on the two ligaments results in a statically indeterminate stress system and the only solution possible is assuming constant stresses over each section.…”

Section: Eccentric Centre Crackmentioning

confidence: 99%

Calculation of the strain-energy release rates of cracked plates by an approximate method

Williams

Isherwood

1968

Journal of Strain Analysis

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A method for the approximate calculation of strain-energy release rates for finite plates is proposed in terms of a mean stress. Solutions are compared with those cases for which analytical and numerical solutions exist and good agreement is obtained. The method is then applied to the general case of a plate with unequal cracks and a non-axial load and to a finite rotating disc with a central hole.

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Section: Eccentric Centre Crackmentioning

confidence: 99%

Calculation of the strain-energy release rates of cracked plates by an approximate method

Williams

Isherwood

1968

Journal of Strain Analysis

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“…Several works were carried out for an infinite solid. They are the tension [1,2,3] and the shear [4] of coplanar elliptical cracks, the tension [5] of an infinite row of parallel penny-shaped cracks, the tension [5] and the torsion [6] of a pair of parallel circular cracks and so on. Some results are also available for semi-infinite solids on the tension [7] and the bending [8] of two coplanar semi-elliptical surface cracks.…”

Section: Introductionmentioning

confidence: 99%

Two parallel elliptical cracks in an infinite solid subjected to tension

et al. 1985

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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 boundary 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.

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“…Using this simplification, Kobayashi, and Moss [7] estimated the correction factor for the deep surface flaw. The front surface correction was based on available solutions [9,10] and the back surface correction was estimated using the approximate solution of two coplanar elliptical flaws in an infinite solid subjected to uniform tension [11 ]. Smith and Alavi solved numerically the problems of a circular crack embedded in a halfspace [12] and a part circular surface flaw in a halfspace [1311 Thresher and Smith [14] extended the work of Smith and Alavi to solve the problem of a part-circular crack in a plate and obtained the back surface correction for the stress intensity 1) Numbers in brackets designate referents at end of paper.…”

Section: Introductionmentioning

confidence: 99%

Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid

1973

Self Cite

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A B S T R A C TStress intensity factors for an embedded elliptical crack approaching the free surface of the semi-infinite solid that is subjected to uniform tension perpendicular to the plane of crack are presented in a nondimensional form for various crack aspect ratios and crack distances from the free surface. Stress intensity factors are determined numerically using an alternating technique with two solutions. The first solution involves an elliptical crack in a solid and subjected to normal loading expressible in a polynomial of x and y. The second solution involves stresses in the half space due to prescribed normal and shear stresses on the surface. Effect of the Poisson's ratio on these stress intensity factors is also investigated. Stress intensity factors for a semi-elliptical surface crack in a finite thickness plate are then estimated in a nondimensional form for various crack aspect ratios and crack depth to plate thickness ratios. Nomenclature~b suitable harmonic stress function = ~f= o ~ffi 0 ~ij; i+j < 3 2,/a, v ellipsoidal coordinates a semi-major axis of ellipse b semi-minor axis of ellipse h distance from the free surface to the center of ellipse or plate thickness X 2 y2 z2 co(s) 1 a2+s bZ+s s Q(s) s(a 2 + s)(b 2 + s) r/ Poisson's ratio G shear modulus u~ incomplete elliptic integral of the first l~ind K(k) complete elliptic integral of the first kind E(ul) incomplete elliptic integral of the second kind E(k) complete elliptic integral of the second kind snu. cnul, dnux, dcut, cdut, ndu~, ncul, sdu~ = Jacobian elliptic functions k, k' modulus and complimentary modulus of Jacobian elliptic functions, respectively 0 K~e with k 2 = (1 -b2/a 2)angle in the parametric equations of ellipse, x = a cos 0; y = b sin 0 90 °-0 i.e., x = a sin t, y = b cos fl opening mode stress intensity factor stress intensity factor for an elliptical crack embedded in an elastic solid

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Approximate stress intensity factor for an embedded elliptical crack near two parallel free surfaces

Cited by 33 publications

References 4 publications

Calculation of the strain-energy release rates of cracked plates by an approximate method

Calculation of the strain-energy release rates of cracked plates by an approximate method

Two parallel elliptical cracks in an infinite solid subjected to tension

Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid

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