Scattering of SH Wave by an Interacting Mode III Crack and a Circular Cavity in Half Space

2007 ◽  
Vol 348-349 ◽  
pp. 861-864 ◽  
Author(s):  
Zai Lin Yang ◽  
Zhi Gang Chen ◽  
Dian Kui Liu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Arbitrary Point ◽  
Circular Cavity ◽  
Sh Wave ◽  
Mode Iii

Scattering of SH wave by an elastic half space with a circular cavity 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 the fundamental solution of the displacement field for a half space with a circular cavity impacted by an out-plane harmonic line source loading at an arbitrary point in half space. 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 cavity 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.

Far Field Solution of SH-Wave Scattered by a Circular Cavity and a Mode III Crack in Half Space

2008 ◽  
Vol 385-387 ◽  
pp. 157-160 ◽  
Author(s):  
Bai Tao Sun ◽  
Pei Lei Yan ◽  
Zai Lin Yang
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Far Field ◽  
Circular Cavity ◽  
Sh Wave ◽  
Field Solution ◽  
Displacement Mode ◽  
Arbitrary Position

Based on Green’s function, complex function and multi-polar coordinate system, the far field solution of SH wave scattered by an elastic half space with a circular cavity and a crack at an arbitrary position and orientation is investigated. First, a suitable Green’s function is constructed, which is the fundamental solution of the displacement field for a half space with a circular cavity subjected to an out-plane time-harmonic line force at an arbitrary position in half space. Second, by means of crack-division technique, a crack with any location and orientation can be constructed in the region of the half space. The displacement field and stress field are established in the situation of coexistence of circular cavity and crack. At last expressions of far field, such as displacement mode of scattering wave are deduced. Some examples and numerical results are illustrated. The influences of the combination of different media parameters on solutions of far field are discussed.

Dynamics of a Mode III Crack Impacted by Elastic Wave in Half Space with a Removable Rigid Cylindrical Inclusion

2006 ◽  
Vol 324-325 ◽  
pp. 679-682 ◽  
Author(s):  
Zai Lin Yang ◽  
Dian Kui Liu ◽  
Xiao Lang Lv
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Complex Function ◽  
Elastic Half Space ◽  
Cylindrical Inclusion ◽  
Sh Wave ◽  
Mode Iii ◽  
Scattering Wave ◽  
Moving Coordinate

Scattering of SH wave by a crack is studied in elastic half space with a removable rigid cylindrical inclusion by Green’s function, complex function and moving coordinate method. In half space, firstly the scattering wave function of removable rigid cylindrical inclusion is constructed; next a suitable Green’s function is solved for present problem, then using crack-division to make a crack. Thus the solution of problem can be obtained. Numerical examples are provided and discussed.

The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

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 Response of Circular Lining Structure and Multiple Cracks in Half Space under Impact Loading

2009 ◽  
Vol 417-418 ◽  
pp. 713-716
Author(s):  
Zai Lin Yang ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Dynamic Response ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Impact Loading ◽  
Complex Function ◽  
Polar Coordinates ◽  
Multiple Cracks ◽  
Sh Wave ◽  
Lining Structure

The dynamic response of a circular lining structure and multiple cracks in an elastic half space while bearing impact loading is studied in this paper. This problem can be seen as the problem of defending of blast. The methods of Green's function, complex function and multi-polar coordinates are used here. First, the scattering wave which satisfies the condition of stress free on the ground surface of half-space containing a shallow-embedded circular lining structure impacted by incident SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack or multiple cracks in any position and direction can be constructed by Green's function and 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 cracks, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. The interaction of inclusion and two cracks is chosen as numerical examples finally. According to nu-merical examples, the influences of different parameters on DSIF are discussed.

Interaction of Elliptical Inclusion and Crack in Half-Space under SH-Waves

2012 ◽  
Vol 525-526 ◽  
pp. 345-348
Author(s):  
Zai Lin Yang ◽  
Hua Nan Xu ◽  
Bao Ping Hei ◽  
Yong Yang
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Polar Coordinates ◽  
Arbitrary Length ◽  
Sh Waves ◽  
Elliptical Inclusion

The methods of Green's function, complex function and multi-polar coordinates are applied here to report interaction of an elliptical inclusion and a crack in half-space under incident SH-waves. Based on the symmetry of SH-waves scattering, the "conformal mapping" technology was developed to construct a suitable Green's function, a fundamental solution to the displacement field for the elastic half space containing elliptical inclusion while bearing out-plane line source load at arbitrary point, for creating a beeline crack with arbitrary length at any position combined with crack-division technology. The displacement field and stress field were then deduced while the inclusion coexists with the crack Lastly, numerical examples are presented to discuss the dependence of dynamic stress concentration factor (DSCF) around the elastic inclusion on different parameters.

Interaction of SH-Wave on Multiple Linear Cracks near Shallow-Embedded Structure

2011 ◽  
Vol 488-489 ◽  
pp. 440-443
Author(s):  
Zai Lin Yang ◽  
Hua Nan Xu ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Complex Function ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Polar Coordinates ◽  
Multiple Cracks ◽  
Sh Wave ◽  
Lining Structure

The surface displacement of a circular lining structure and multiple cracks in an elastic half space by incident SH-wave is studied in this paper based on the methods of Green's function, complex function and multi-polar coordinates. Firstly, we construct a suitable Green’s function which indicates a fundamental solution to the displacement field for an elastic half space possessing a circular lining structure and cracks while bearing out-plane harmonic line loads at arbitrary point. Then using the method of crack-division, a crack is created. Thus expressions of displacement and stress field are established at the existence of the structure and the cracks. Finally, the interaction of inclusion and two cracks is chosen as numerical examples and the influences of different parameters on the surface displacement are discussed.

Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

2012 ◽  
Vol 28 (1) ◽  
pp. 143-151 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi ◽  
J. Y. Tian
Keyword(s):  
Free Boundary ◽  
Dynamic Analysis ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Interfacial Crack ◽  
Circular Inclusion ◽  
Wave Number ◽  
Complex Method ◽  
Sh Wave

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

Lattice statics of interfaces and interfacial cracks in bimaterial solids

1992 ◽  
Vol 7 (4) ◽  
pp. 1018-1028 ◽  
Author(s):  
V.K. Tewary ◽  
Robb Thomson
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Nearest Neighbor ◽  
Interfacial Crack ◽  
Continuum Theory ◽  
Two Phase ◽  
Lattice Statics ◽  
Interfacial Cracks

A method for calculating lattice statics Green's function is described for a bimaterial lattice or a bicrystal containing a plane interface. The method involves creation of two half space lattices containing free surfaces and then joining them to form a bicrystal. The two half space lattices may have different structures as in a two-phase bicrystal or may be of the same type but joined at different orientations to form a grain boundary interface. The method is quite general but, in this paper, has been applied only to a simple model bicrystal formed by two simple cubic lattices with nearest neighbor interactions. The bimaterial Green's function is modified to account for an interfacial crack that is used to calculate the displacement field due to an applied external force. It is found that the displacement field, as calculated by using the lattice theory, does not have the unphysical oscillations predicted by the continuum theory.

Sign in / Sign up

Export Citation Format

Share Document