Stress distribution, crack shape and energy for a penny-shaped crack in a plate of finite thickness

Tsai, Y. M.

doi:10.1016/0013-7944(72)90085-9

Cited by 10 publications

(6 citation statements)

References 8 publications

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“…The first expression on the right-hand side of (18) is exactly the same as that for a static crack in an infinite solid [7]. The second and third terms on the right-hand side of (18) are apparently due to the effect of stress waves.…”

Section: (2)mentioning

confidence: 83%

“…The second and third terms on the right-hand side of (18) are apparently due to the effect of stress waves. If the same operations as those used [7] are applied to (18), an integral equation for the unknown w (r) is obtained as In terms of the known value of a=, the unknown function w(r) is to be determined from (18).…”

Section: (2)mentioning

confidence: 99%

“…The expression (23) is the same as that for a static crack and clearly indicates the operations applied over (18) [7]. If w (r) is solved from (22) and substituted in (18), the normal stress distribution tr~(r, t) can be obtained from (18).…”

Section: Ii= If " T3 T V °Dzds Sm(s¢) Fo Jo [Sci(t-o]mentioning

confidence: 99%

“…To obtain the solution, a method of successive approximation is used [7,11]. To obtain the solution, a method of successive approximation is used [7,11].…”

Section: Crack Of Constant Speedmentioning

confidence: 99%

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Exact stress distribution, crack shape and energy for a running penny-shaped crack in an infinite elastic solid

Tsai¹

1973

Int J Fract

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The integral solutions for an axisymmetrical crack propagating at arbitrary speed in an infinite elastic solid are obtained as sums of associated static solutions and stress-waves integrals. For a circular crack running at a constant speed, exact dynamic solutions for crack shape and stress distribution with singularities in the crack plane are obtained in closed forms easily comparable to associated static solutions. The dynamic solution reduces to the static solution at zero crack speed and deviates at speed other than zero. Deviation between dynamic and static solutions is governed by dynamic correction factors which are nondimensional functions of Poisson's ratio and the ratio between crack speed and shear-wave speed. Values of these dynamic factors are obtained for large range of crack speed and deviation can clearly be determined from the results obtained. Exact expressions for dynamic stress-intensity factor and energy functions are also obtained in terms of crack speed.

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Section: (2)mentioning

confidence: 83%

Section: (2)mentioning

confidence: 99%

Section: Ii= If " T3 T V °Dzds Sm(s¢) Fo Jo [Sci(t-o]mentioning

confidence: 99%

“…To obtain the solution, a method of successive approximation is used [7,11]. To obtain the solution, a method of successive approximation is used [7,11].…”

Section: Crack Of Constant Speedmentioning

confidence: 99%

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Exact stress distribution, crack shape and energy for a running penny-shaped crack in an infinite elastic solid

Tsai¹

1973

Int J Fract

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“…where the COD derivatives can be taken from Equation (12) and the e HI ( M ) terms can be computed by the following equations:…”

Section: The Numerical Green's Functionmentioning

confidence: 99%

The 3-D BEM implementation of a numerical Green's function for fracture mechanics applications

Castor

Telles

2000

Int. J. Numer. Meth. Engng.

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SUMMARYThe use of Green's functions has been considered a powerful technique in the solution of fracture mechanics problems by the boundary element method (BEM). Closed-form expressions for Green's function components, however, have only been available for few simple 2-D crack geometry applications and require complex variable theory. The present authors have recently introduced an alternative numerical procedure to compute the Green's function components that produced BEM results for 2-D general geometry multiple crack problems, including static and dynamic applications. This technique is not restricted to 2-D problems and the computational aspects of the 3-D implementation of the numerical Green's function approach are now discussed, including examples.

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Dugdale‐model for a ring‐shaped crack in a transtropic thick walled cylinder

Uyaner

2004

Z Angew Math Mech

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In this study, a problem of a ring‐shaped crack contained in an infinitely long thick‐walled cylinder is considered. The problem is formulated for a transtropic (transversely isotropic) material by using integral transform technique under uniform load. The governing elasticity equation for the transtropic axisymmetric problem in cylindrical co‐ordinates was obtained in terms of a Love type stress function. Hankel and Fourier transforms were applied on the stress function because of the geometry of the configuration and boundary conditions. The stress function was expressed in terms of the governing equation. Using the boundary conditions, the problem reduced to a singular integral equation. This singular integral equation is solved by using the Gaussian Quadrature. Then the stress intensity factor at the crack tip was determined. The plastic zone widths are obtained by using the Dugdale model. The plastic zone widths are plotted for various ring‐shaped crack sizes and transtropic materials.

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Stress distribution, crack shape and energy for a penny-shaped crack in a plate of finite thickness

Cited by 10 publications

References 8 publications

Exact stress distribution, crack shape and energy for a running penny-shaped crack in an infinite elastic solid

Exact stress distribution, crack shape and energy for a running penny-shaped crack in an infinite elastic solid

The 3-D BEM implementation of a numerical Green's function for fracture mechanics applications

Dugdale‐model for a ring‐shaped crack in a transtropic thick walled cylinder

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