scholarly journals Theoretical Transient Analysis of the Interaction Between a Dynamically Propagating In-Plane Crack and Traction-Free Boundaries

1997 ◽  
Vol 64 (4) ◽  
pp. 819-827 ◽  
Author(s):  
Chwan-Huei Tsai ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Dynamic Stress ◽  
Fundamental Solutions ◽  
Transform Domain ◽  
Free Boundaries ◽  
Reflected Waves ◽  
Transient Solutions ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient response of a propagating in-plane crack interacting with half-plane boundaries is investigated in detail. The reflected waves which are generated from traction-free boundaries will interact with the propagating crack and make the problem extremely difficult to analyze. The complete transient solutions are constructed by superimposing fundamental solutions in the Laplace transform domain. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or the propagating crack faces. We focus our attention on the determination of the dynamic stress intensity factor. The dynamic stress intensity factors of a propagating crack in a configuration with boundaries and subjected to dynamic loadings are obtained in an explicit closed form. The transient solutions obtained in this study are in agreement with the experimental results from the literature. Some interesting phenomena observed in the published experimental works are also identified and discussed. It is concluded that the reflected waves generated from the boundary parallel to the crack have much stronger influence on the propagating crack than those generated from the boundary perpendicular to the crack. When the reflected waves generated from the boundary parallel to the crack return to the moving crack tip, the stress intensity factor will increase rapidly.

Transient Analysis of a Propagating In-Plane Crack in a Finite Geometry Body Subjected to Static Loadings

1997 ◽  
Vol 64 (3) ◽  
pp. 620-628 ◽  
Author(s):  
Chwan-Huei Tsai ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Transform Domain ◽  
Free Boundaries ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Reflected Waves ◽  
The Laplace Transform

In this study, a cracked body with finite boundaries subjected to static loading and the crack propagating with a constant speed are analyzed. The interaction of the propagating crack with reflected waves generated from traction-free boundaries is investigated in detail. The methodology for constructing the scattered field by superimposing the fundamental solution in the Laplace transform domain is proposed. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or a crack. The dynamic stress intensity factors of a propagating crack induced from the interaction with the first few reflected waves generated from the traction-free boundary are obtained in an explicit closed form. The analytical solutions of dynamic stress intensity factors are compared with available numerical and experimental results and the agreement is quite good. We find one thing very interesting: the dynamic stress intensity factor for a long time period is a universal function of the instantaneous extending rate of a crack tip times the static stress intensity factor for an equivalent stationary crack for the finite strip problem. It was also found that the reflected waves generated from free boundaries always increase the stress intensity factor, and the influence from reflected waves generated from the boundary, which is perpendicular to the crack, are weaker than those generated from the boundary, which is parallel to the crack.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

scholarly journals Exact transient full–field analysis of a finite crack subjected to dynamic anti–plane concentrated loadings in anisotropic materials

2005 ◽  
Vol 461 (2054) ◽  
pp. 509-539 ◽  
Author(s):  
Yi-Shyong Ing ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity ◽  
Crack Tip ◽  
Fundamental Solutions ◽  
Shear Stresses ◽  
Transform Domain ◽  
Intensity Factors ◽  
Full Field ◽  
Transient Solutions ◽  
The Laplace Transform ◽  
Finite Crack

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 factor are obtained by using the Cagniard–de Hoop method of Laplace inversion and are expressed in explicitly compact formulations. The solutions have accounted for the contributions of all diffracted waves generated from two crack tips. Numerical results for the time history of shear stresses and stress–intensity factors during the transient process are calculated based on analytical solutions and are discussed in detail. The transient solutions of stresses have been shown to approach the corresponding static values after the first eight waves have passed the field point. The dynamic stress–intensity factor will reach a maximum value when the incident wave arrives at the crack tip, and remain constant before the first diffracted wave generated from the other crack tip arrives, and then will oscillate near the static value. A simple explicit expression of the dynamic overshoot for stress–intensity factors is derived as a function of the location for applied loadings, the crack length and material constants.

Transient Analysis of a Subsonic Propagating Interface Crack Subjected to Antiplane Dynamic Loading in Dissimilar Isotropic Materials

1997 ◽  
Vol 64 (3) ◽  
pp. 546-556 ◽  
Author(s):  
Yi-Shyong Ing ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Transform Domain ◽  
Full Field ◽  
Shear Wave Speed ◽  
The Laplace Transform ◽  
Crack Faces

In this study, the transient stress fields and the dynamic stress intensity factor of a semi-infinite antiplane crack propagating along the interface between two different media are analyzed in detail. The crack is initially at rest and, at a certain instant, is subjected to an antiplane uniformly distributed loading on the stationary crack faces. After some delay time, the crack begins to move along the interface with a constant velocity, which is less than the smaller of the shear wave speed of these two materials. A new fundamental solution is proposed in this study, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The exact full-field solutions and the stress intensity factor are found in the time domain by using the Cagniard-de Hoop method (de Hoop, 1958) of Laplace inversion. The near-tip fields are also obtained from the reduction of the full-field solutions. Numerical results for the dynamically extending crack are evaluated in detail. The region of the stress singular field dominated in the transient process is also discussed.

The Dynamic Stress Intensity Factor Due to Arbitrary Screw Dislocation Motion

1983 ◽  
Vol 50 (2) ◽  
pp. 383-389 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Wave ◽  
Screw Dislocation ◽  
Dynamic Stress ◽  
Critical Level ◽  
Dynamic Stress Intensity Factor ◽  
Dislocation Motion ◽  
Crack Edge

The dynamic stress intensity factor for a stationary semi-infinite crack due to the motion of a screw dislocation is obtained analytically. The dislocation position, orientation, and speed are largely arbitrary. However, a dislocation traveling toward the crack surface is assumed to arrest upon arrival. It is found that discontinuities in speed and a nonsmooth path may cause discontinuities in the intensity factor and that dislocation arrest at any point causes the intensity factor to instantaneously assume a static value. Morever, explicit dependence on speed and orientation vanish when the dislocation moves directly toward or away from the crack edge. The results are applied to antiplane shear wave diffraction at the crack edge. For an incident step-stress plane wave, a stationary dislocation near the crack tip can either accelerate or delay attainment of a critical level of stress intensity, depending on the relative orientation of the crack, the dislocation, and the plane wave. However, if the incident wave also triggers dislocation motion, then the delaying effect is diminished and the acceleration is accentuated.

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