Yi-Shyong Ing

Dynamic fracture analysis of a finite crack subjected to an incident horizontally polarized shear wave

The transient response for diffraction of an incident horizontally polarized shear wave by a finite crack in an unbounded elastic solid is investigated in this study. In analyzing this problem, an infinite number of diffracted waves generated by two crack tips must be taken into account that will make the analysis extremely difficult. An alternative methodology different from the conventional superposition method is used to construct the reflected and diffracted fields. The complete 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 (in the Laplace transform domain) traction and screw dislocation on the crack faces and along the crack tip line, respectively. The exact transient closed form solutions of dynamic stress intensity factor for two crack tips are obtained and expressed in very simple and compact formulations. Each term in the formulations has its own physical meaning. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted waves. Numerical results of both tips for different incident angles are evaluated which indicate that the dynamic stress intensity factors will oscillate near the correspondent static values after the first three waves have passed the specified crack tip. Some discrepancies of the numerical results compared with available solutions are discussed in detail.

Transient dislocation emission from a crack tip

Abstract Transient nature of dislocation emission from a crack tip gives a new twist to the study of brittle-to-ductile transition. In a class of materials, only the dislocations traveling at high speed may escape from the crack tip. The nucleation of a fast moving dislocation, however, requires a higher level of activation energy, as supported by many experimental data. The present paper explores this scenario under the restriction that the dislocation moves along the crack extension plane. Fundamental solutions of moving dislocations are derived, and which provide the drag forces on the dislocations and the shielding to the crack tip. Nucleation of a fast moving dislocation is examined under the Peierls–Nabarro theory. Incremental dislocation flux is created continuously from the crack tip, and moves away at a constant speed. At a judgmental time of dislocation emission, the displacement jump relates to the holding force along the crack extension plane by a periodic inter-planar potential, and the singular stress induced by the transient and rate-dependent displacement jump negates the original crack tip singularity. A dynamic overshoot calculation under quasi-steady assumption provides an escape velocity of dislocations. To achieve it, extra activation energy is required for the transient dislocation nucleation and that reduces the dislocation nucleation rate along the crack front. When compared with the rate-insensitive process of cleavage, the transient dislocation emission process allows us to predict the rate dependency of the brittle versus ductile behavior of materials.

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

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.

Transient Analysis of Dynamic Crack Propagation With Boundary Effect

In this study, a dynamic antiplane crack propagation with constant velocity in a configuration with boundary is investigated in detail. The reflected cylindrical waves which are generated from the free boundary 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 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 Cagniards method for Laplace inversion is used to obtain the transient solution in time domain. Numerical results of dynamic stress intensity factors for the propagation crack are evaluated in detail.

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

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.

Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

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 Cagniards 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.

Dynamic Crack Propagation in Piezoelectric Materials Subjected to Dynamic Body Forces for Vacuum Boundary

The problem of a semi-infinite propagating crack in the piezoelectric material subjected to a dynamic anti-plane concentrated body force is investigated in the present study. It is assumed that between the growing crack surfaces there is a permeable vacuum free space, in which the electrostatic potential is nonzero. It is noted that this problem has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener-Hopf techniques [1] is not applicable. This paper proposes a new fundamental solution for propagating crack in the piezoelectric material and the transient response of the propagating crack is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution represents the responses of applying exponentially distributed loadings in the Laplace transform domain on the propagating crack surface. Exact analytical transient solutions for the dynamic stress intensity factor and the dynamic electric displacement intensity factor are obtained by using the Cagniard-de Hoop method [2,3] of Laplace inversion and are expressed in explicit forms. Finally, numerical results based on analytical solutions are calculated and are discussed in detail.

Theoretical simulations of a propagating crack subjected to in-plane stress wave loading by caustic method

The optical method of caustics for measuring the dynamic stress intensity factor in a transient process is investigated in this study. The transient full-field solutions of a propagating crack contained in an infinite medium subjected to step-stress wave and ramp-stress wave loadings are used to establish the exact equations of the initial and caustic curves. The results of the stress intensity factor obtained from the caustic method are compared with theoretical predictions and some experiments. The results demonstrate that a significant deviation can occur in the determination of the dynamic stress intensity factor from shadow spot measurements. The factors, such as screen distance, magnitude of loading, crack speed and rising time which can influence the accuracy of the experimental measurements are discussed in detail. In addition, the valid region of the dynamic stress singular field for the propagating crack is discussed in detail and it gives a better understanding of the appropriate region of measurements for investigators.

Dynamic full‐field analysis of a surface crack subjected to an antiplane moving loading

Abstract In this study, the transient full‐field solution of a surface crack subjected to a dynamic anti‐plane moving loading is investigated. The solution is 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 dislocations on the crack faces and along the crack tip line, respectively. The exact transient solutions of shear stresses and displacement are obtained and expressed in compact formulations. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted and reflected waves. Numerical calculations for both moving and stationary loading cases are evaluated and discussed in detail. The results indicate that the stresses will approach steady‐state or static solutions after the first few waves have passed through the receiver.

Transient analysis of crack in composite layered medium subjected to dynamic loadings

A semi-infinite crack in a layered medium subjected to antiplane dynamic loading is investigated. In analyzing this problem, the fact that the reflections and diffractions of stress waves by the interface boundary and by the crack will generate an infinite number of waves must be taken into account. A useful fundamental solution is proposed, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the application of exponentially distributed traction (in the Laplace transform domain) on the crack faces. Cagniards method for Laplace inversion is used to obtain the transient solution in time domain. The final formulations for the stress intensity factor are expressed explicitly and the dynamic effect of each wave is presented in a closed form. The results are valid for an infinite number of waves that are scattered from the crack tip and reflected by the interface. Numerical calculations of dynamic stress intensity factors are evaluated and discussed in detail.