Exact Transient Full-Field Analysis of an Antiplane Subsurface Crack Subjected to Dynamic Impact Loading

1994 ◽  
Vol 61 (3) ◽  
pp. 649-655 ◽  
Author(s):  
Chien-Ching Ma ◽  
Szu-Kuzi Chen
Keyword(s):  
Fundamental Solution ◽  
Half Space ◽  
Observation Point ◽  
Field Analysis ◽  
Full Field ◽  
Transient Solutions ◽  
Diffracted Waves ◽  
The Laplace Transform ◽  
Long Time ◽  
Close Form

The transient problem of a half-space containing a subsurface inclined semi-infinite crack subjected to dynamic antiplane loading on the boundary of the half-space has been investigated to gain insight into the phenomenon of the interaction of stress waves with material defects. The solutions are determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution is the exponentially distributed traction on crack faces. The exact close-form transient solutions of stresses and displacement are obtained in this study. These solutions are valid for an infinitely long time and have accounted for the contributions of incident, reflected, and diffracted waves. Numerical results of the transient stresses are obtained and compared with the corresponding static values. The transient solution has been shown to approach the static value after the first few diffracted waves generated from the crack tip have passed the observation point.

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.

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.

scholarly journals Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

2019 ◽  
Vol 24 (1) ◽  
pp. 26 ◽  
Author(s):  
Sergey Davydov ◽  
Andrei Zemskov ◽  
Elena Akhmetova
Keyword(s):  
Half Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Local Equilibrium ◽  
Linear Equations ◽  
Integral Form ◽  
External Effects ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
The Laplace Transform

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes.

Exact Solutions for Unsteady Magnetohydrodynamic Oscillatory Flow of a Maxwell Fluid in a Porous Medium

2013 ◽  
Vol 68 (10-11) ◽  
pp. 635-645 ◽  
Author(s):  
Ilyas Khan ◽  
Farhad Ali ◽  
Sharidan Shafie ◽  
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Transform Method ◽  
Transient Solutions ◽  
The Laplace Transform ◽  
Porous Half Space ◽  
The Given ◽  
Steady State Solutions

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and transient velocities are plotted and discussed. It is found that for a large value of the time t, the transient solutions disappear, and the motion is described by the corresponding steady-state solutions.

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