Scattering of SH Wave by a Cylindrical Inclusion and a Semi-Cylindrical Hollow Near Vertical Interface Crack in the Bi-Material Half Space

2016 ◽  
Vol 33 (5) ◽  
pp. 619-629 ◽  
Author(s):  
H. Qi ◽  
X.-M. Zhang ◽  
H.-Y. Cheng ◽  
M. Xiang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Concentration ◽  
Half Space ◽  
Function Method ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Cylindrical Inclusion ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Scattering of SH-Wave by a Circular Inclusion Near the Interfacial Cracks in the Piezoelectric Bi-Material Half-Space

2017 ◽  
Vol 34 (3) ◽  
pp. 337-347 ◽  
Author(s):  
H. Qi ◽  
X. M. Zhang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Function Method ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Inclusion ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor ◽  
Interfacial Cracks ◽  
Vertical Boundary

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a circular inclusion near the two symmetrically permeable interfacial cracks in the piezoelectric bi-material half -space is considered to obtain the steady state response. Firstly, by means of the image method, the essential function of Green's function is constructed, which satisfies the stress free and electric insulation conditions on the horizontal boundaries in a right-angle space including a circular inclusion and bearing a harmonic out-plane line source force on the vertical boundary. Secondly, the bi-material media is divided into two parts along the vertical boundary. According to continuity condition, the first kind of Fredholm integral equations containing undetermined anti-plane forces are established by “the conjunction method” and “the crack-division technology”, then the integral equations are reduced to the algebraic equations including finite items by effective truncation. Finally, the dynamic stress concentration factor around the edge of circular inclusion and dynamic stress intensity factor at the crack tip are calculated, then the influences of the frequency of incident wave, the length of crack, the position of the crack, the position of circular inclusion, etc. on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Scattering of Sh-Wave by Cylindrical Inclusion Near Interface in Bi-Material Half-Space

2011 ◽  
Vol 27 (1) ◽  
pp. 37-45 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Green's Function ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

ABSTRACTGreen's function and complex function methods are used here to investigate the problem of the scattering of SH-wave by a cylindrical inclusion near interface in bi-material half-space. Firstly, Green's function was constructed which was an essential solution of displacement field for an elastic right-angle space possessing a cylindrical inclusion while bearing out-of-plane harmonic line source load at any point of its vertical boundary. Secondly, the bi-material media was divided into two parts along the vertical interface using the idea of interface “conjunction”, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on surface. Finally, some examples for dynamic stress concentration factor of the cylindrical elastic inclusion are given. Numerical results show that dynamic stress concentration factor is influenced by interfaces, free boundary and combination of different media parameters.

Dynamic Analysis for a Subsurface Elastic Cylindrical Inclusion with a Semi- Cylindrical Hill Impacted by SH-Wave

2011 ◽  
Vol 199-200 ◽  
pp. 945-948
Author(s):  
Xiao Lang Lv ◽  
Dian Kui Liu
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Dynamic Stress ◽  
Scattered Wave ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor ◽  
Variable Function

An analytic method is developed for dynamic stress concentration of a subsurface elastic cylindrical inclusion below a semi-cylindrical hill under SH-wave. And the dynamic stress concentration factor (DSCF) is given by complex variable function. During the solution, a standing wave and scattered wave displacement functions are constructed in different parts respectively. All of these displacement functions should satisfy the boundary conditions of each part. Employed to the boundary conditions around the elastic cylindrical inclusion, a series of infinite algebraic equations about the problem can be obtained. The calculating results of DSCF around the elastic cylindrical inclusion are plotted to show the effects of some parameters on DSCF.

Dynamic Stress Intensity Problem of SH-Wave by Double Linear Cracks near a Circular Hole

2008 ◽  
Vol 385-387 ◽  
pp. 105-108 ◽  
Author(s):  
Hong Liang Li ◽  
Hong Li ◽  
Yong Yang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Green’S Function ◽  
Circular Hole ◽  
Green's Function ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Elastic Space ◽  
Sh Wave

In mechanical engineering, circular hole is used widely in structure design. When the structure is overloaded or the load is changed regularly, cracks emerge and spread. Based on the former study of dynamic stress concentration problem of SH wave by a crack originating at a circular hole edge, in this paper, the method of Green’s function is used to investigate the problem of dynamic stress intensity problem of double linear cracks near a circular hole impacted by incident SH-wave. The train of thought for this problem is that: Firstly, a Green’s function is constructed for the problem, which is a fundamental solution of displacement field for an elastic space possessing a circular hole and a linear crack while bearing out-of-plane harmonic line source force at any point; Secondly, in terms of the solution of SH-wave’s scattering by an elastic space with a circular hole and a linear crack, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the second crack is in existent actually, we called this process “crack-division”; Finally, the expressions of the dynamic stress intensity factor(DSIF) of the cracks are given when the circular hole and double linear crack exist at the same time. Then, by using the expressions, an example was provided to show the effect of circular hole and cracks on the dynamic stress intensity factor of the cracks.

Scattering of SH-Waves and Dynamic Stress Intensity Factor by an Interacting Mode III Crack and a Lining Structure in Half Space

2008 ◽  
Vol 385-387 ◽  
pp. 273-276
Author(s):  
Zai Lin Yang ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Lining Structure

Scattering of SH wave by an elastic half space with a lining structure and a crack in any position and direction is studied with Green’s function, complex function and multi-polar coordinate method. First, a suitable Green’s function is constructed, which is a fundamental solution to the displacement field for the elastic space possessing circular lining structure while bearing out-of-plane harmonic line source load at arbitrary point. Then a crack in any position and direction is constructed by means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular lining structure and crack, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. According to numerical examples, the influences of different parameters on DSIF are 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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