Dynamic fracture analysis of a finite crack subjected to an incident horizontally polarized shear wave (original) (raw)
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International journal of fracture, 1996
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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An exact transient closed-form solution for a semi-infinite crack subjected to a timedependent concentrated force is obtained in this study. The total wave field is due to the effect of this point source and the scattering of the incident waves by the crack tip. An alternative methodology for constructing the reflected and diffracted field is proposed, which proves both powerful and efficient in solving complicated dynamic crack problems. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem. The waves reflected by the traction-free crack surface and diffracted from the crack tip can be constructed by superimposing this fundamental solution. The superposition is performed in the Laplace transform domain. Numerical results for the time history of stresses and stress intensity factors during the transient process are obtained and compared with the corresponding static values. It is shown that the field solution wi...
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International Journal of Fracture, 1992
To gain insight into the phenomenon of the interaction of stress waves with material defects and the linkage of two cracks, the transient response of two semi-infinite inclined cracks subjected to dynamic loading is examined. The solutions are obtained by the linear superposition of fundamental solutions in the Laplace transform domain. The fundamental solution is the exponentially distributed traction on crack faces proposed by Tsai and Ma [-1]. The exact closed form solutions of stress intensity factor histories for these two inclined cracks subjected to incident plane waves and diffracted waves are obtained explicitly. These solutions are valid for the time interval from initial loading until the first wave scattered at one crack tip returns to the same crack tip after being diffracted by another crack tip. The result shows that the contribution of diffracted waves to stress intensity factors is much less than the incident waves. The probable crack propagation direction is predicted from the fracture criterion of maximum circumferential tensile stress. The linkage of these two cracks is also investigated in detail.
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The problem considered here is the antiplane response of an elastic solid containing a half-plane crack subjected to suddenly applied concentrated point forces acting at a finite distance from the crack tip. A fundamental solution for the dynamic dislocation is obtained to construct the dynamic fracture problem containing a characteristic length. Attention is focused on the time-dependent full-field solutions of stresses and stress intensity factor. It is found that at the instant that the first shear wave reaches the crack tip, the stress intensity factor jumps from zero to the appropriate static value. The stresses will take on the appropriate static value instantaneously upon arrival of the shear wave diffracted from the crack tip, and this static value is thereafter maintained. The dynamic stress intensity factor of a kinked crack from this stationary semi-infinite crack after the arrival of shear wave is obtained in an explicit form as a function of the kinked crack velocity, t...
Exact transient analysis of an anti-plane semi-infinite crack subjected to dynamic body forces
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Exact transient closed form solutions for a stationary semi-infinite crack subjected to a suddenly applied anti-plane dynamic body force are obtained in this study. An alternative methodology different from the conventional superposition method is used to construct the re.flected and diffracted fields. The waves reflected from the traction free crack surface and diffracted by the crack tip are constructed by superimposing a fundamental solution. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem and the superposition is performed in the Laplace transform domain. Numerical results of the transient stresses are obtained and compared with the corresponding static values. It is shown that the transient solution will approach the static value after the diffracted wave has passed.
Dynamic fracture analysis of an inclined subsurface crack subjected to dynamic moving loadings
International Journal of Fracture, 1996
The transient response of a half-space containing a subsurface inclined semi-infinite crack excited by a dynamic moving antiplane loading on the surface of the half-space is investigated in this study. The solutions of dynamic stress intensity factors are derived for all load speeds (subsonic and supersonic) and are determined by superposition of a proposed fundamental solution in the Laplace transform domain. The fundamental problem is the problem of applying an exponentially distributed traction in the Laplace transform domain on crack faces. The method of analysis is based on integral transform techniques and the Wiener-Hopf technique. The exact closed form transient solutions of dynamic stress intensity factors are expressed in very compact formulations in this study. These solutions are valid for an infinite length of time and have accounted for all the contributions of infinitely many waves. Numerical results of the transient stress intensity factor are obtained and the results of the limit case of zero load speed is compared with the corresponding static values.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
In this study, the elastodynamic full–field response of a finite crack in an anisotropic material subjected to a dynamic anti–plane concentrated loading with Heaviside–function time dependence is investigated. A linear coordinate transformation is introduced to simplify the problem. The linear coordinate transformation reduces the anisotropic finite–crack problem to an equivalent isotropic problem. An alternative methodology, different from the conventional superposition method, is developed to construct the reflected and diffracted wave fields. The transient solutions are determined by superposition of two proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are the problems for applying exponentially distributed traction and displacement on the crack faces and along the crack–tip line in the Laplace transform domain, respectively. Exact analytical transient solutions for dynamic shear stresses, displacement and stress–intensity facto...
International Journal of Fracture, 2000
The transient elastodynamic response of a transversely isotropic material containing a semi-infinite crack under uniform impact loading on the faces is examined. The crack lies in a principle plane of the material, but the crack front does not coincide with a principle direction. Rather, the crack front is at an angle to a principle direction and thus the problem becomes more three-dimensional in nature. Three loading modes are considered, i.e., opening, in-plane shear and anti-plane shear. The solutions for the stress intensity factor history around the crack tip are found. Laplace and Fourier transforms together with the Wiener-Hopf technique are employed to solve the equations of motion directly. The asymptotic expression of stress near the crack tip leads to a closed-form solution for the dynamic stress intensity factor for each loading mode. It is found that the stress intensity factors are proportional to the square root of time as expected. Results given here converge to know...
Engineering, 2010
Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the boundary conditions are reduced to six simultaneous integral equations. To solve these equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in those series are solved using the Schmidt method such that the conditions inside the cracks are satisfied. Numerical calculations are carried out for some crack configurations.