Transient stress intensity factors for a finite crack in an elastic solid caused by a dilatational wave

Thau, Stephen A.; Lu, Tsin-Hwei

doi:10.1016/0020-7683(71)90090-4

Cited by 133 publications

(24 citation statements)

References 7 publications

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“…Let us consider the problem of a mode I central crack in an infinite body, which was discussed in [19][20] with analytical methods. A numerical modelling of this problem can be found in [21], The problem is shown in Fig.…”

Section: -{Bx)2( -Coscos Fj) ± Ibxcos ^ Cos ^Yjl{\ -Cos^cos T])mentioning

confidence: 99%

Improved bicharacteristic schemes for two-dimensional elastodynamic equations

Lin¹,

Ballmann²

1995

Quart. Appl. Math.

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Abstract. Several authors have used explicit numerical schemes of bicharacteristics to solve the system of hyperbolic partial differential equations describing the two-dimensional propagation of stress waves in elastic solids. However, their numerical approaches differ slightly, which results in different limits of the CFL number for stable solutions and in different defects of numerical accuracy near singular points like, e.g., a numerically caused cutting trace emanating from a crack tip. After reviewing the different approaches, some techniques are presented to set up stable explicit schemes with CFL number up to the limiting values 1 for the fastest mode. Finally, the schemes are applied to the crack problem of a shock loaded body, where the main reasons for the appearance of a cutting trace become apparent.

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Section: -{Bx)2( -Coscos Fj) ± Ibxcos ^ Cos ^Yjl{\ -Cos^cos T])mentioning

confidence: 99%

Improved bicharacteristic schemes for two-dimensional elastodynamic equations

Lin¹,

Ballmann²

1995

Quart. Appl. Math.

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“…Later, Sih et al [8] examined the corresponding Mode I and Mode II stress intensity factors for a crack in an infinite elastic medium. Thau and Lu [9] used the Wiener-Hopf method to solve the dynamic transient problem for a crack in an infinite medium. Their solutions are exact from the instant when the incident stress wave arrives at a crack end until a diffracted P wave reaches the opposite crack end, is rediffracted, and then returns to the original edge.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stress intensity factors around three parallel cracks in an infinite medium during a passage of impact normal stresses

Itou

2015

Acta Mech

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This study investigates the perpendicular impingement of a normal shock stress wave on three parallel cracks in an infinite medium. The cracks are placed so that two upper collinear cracks are parallel to a lower crack. Using Fourier and Laplace transform techniques, the boundary conditions are reduced to four simultaneous integral equations. In the Laplace domain, the differences in the displacements inside the cracks are expanded in a series of functions that have zero value outside the cracks. The Schmidt method is used to solve the unknown coefficients in the series such that the conditions inside the cracks are satisfied. The stress intensity factors are defined in the Laplace domain, and these are inversed using the numerical method. The stress intensity factors are calculated numerically for some crack configurations.

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“…Than and Lu [5], following the work of Kostrov [6] and Flitman [7], treated the analogous transient problem of diffraction of an arbitrary plane dilatational wave by a finite crack in an infinite elastic solid. Their results are exact only at the time interval in which the dilatational wave has traveled the length of the crack twice.…”

Section: Introductionmentioning

confidence: 99%

“…A thoroughsummary of the application of the main direct methods of analysis for transient problem in dynamic fracture for elastic or inelastic problems has been given by Freund [19]. Freund [19] has suggested an alternate approach based on the aforementioned moving dislocation solution to examine the same finite-crack problem which had been solved by Thau and Lu [5]. In practice, however, the alternate approach provides a solution which is valid for the same time range as before.…”

Section: Introductionmentioning

confidence: 99%

Transient response of a finite crack subjected to dynamic anti-plane loading

Ing

1996

Int J Fract

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In this study, the transient response of a finite crack in an elastic solid subjected to dynamic antiplane loading is investigated. Two specific loading situations, a body force near the finite crack and a concentrated point loading applied on the crack face, are analyzed in detail. In analyzing this problem, an infinite number of diffracted waves generated by two crack tips must be taken into account which will make the analysis extremely difficult. The solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are the problems for applying exponentially distributed traction and screw dislocation to the crack faces and along the crack-tip line respectively. Exact transient closed-form solutions for the dynamic stress intensity factor are obtained and expressed in very simple and compact formulations. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted waves. Numerical calculations for the two problems are evaluated and results indicate that the dynamic stress intensity factors will oscillate near the corresponding static values after the first three waves have passed through the specified crack tip.

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Transient stress intensity factors for a finite crack in an elastic solid caused by a dilatational wave

Cited by 133 publications

References 7 publications

Improved bicharacteristic schemes for two-dimensional elastodynamic equations

Improved bicharacteristic schemes for two-dimensional elastodynamic equations

Dynamic stress intensity factors around three parallel cracks in an infinite medium during a passage of impact normal stresses

Transient response of a finite crack subjected to dynamic anti-plane loading

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