Diffraction of SH-Waves by an Edge Crack

1979 ◽  
Vol 46 (1) ◽  
pp. 101-106 ◽  
Author(s):  
S. K. Datta
Keyword(s):  
Stress Intensity Factor ◽  
Nondestructive Evaluation ◽  
Edge Crack ◽  
Dynamic Stress ◽  
Near Field ◽  
Dynamic Stress Intensity Factor ◽  
Antiplane Shear ◽  
Far Field ◽  
Sh Wave ◽  
Sh Waves

Diffraction of an antiplane shear (SH-) wave by an edge crack in a semi-infinite elastic medium is studied here. Asymptotic expansions for the scattered field both near and far from the crack are obtained for the case when the wavelength is large compared to the length of the crack. Near-field expansion is used to compute the dynamic stress-intensity factor at the tip of the crack. Also, the far-field expansion gives the scattered displacement amplitude, which is useful in ultrasonic nondestructive evaluation.

Dynamic Analysis of Antiplane Crack under SH-Waves in the Functionally Graded Materials

2007 ◽  
Vol 353-358 ◽  
pp. 38-41
Author(s):  
Xin Gang Li ◽  
Cheng Jin ◽  
Li Zhang ◽  
Da Yong Chu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Infinite Plate ◽  
Functionally Graded ◽  
Graded Materials ◽  
Sh Waves

In this paper, the behavior of a finite crack in an infinite plate of functionally graded materials (FGM) with free boundary subjected to SH-waves is considered. To make the analysis tractable, it is assumed that the material properties vary exponentially with the thickness direction and the problem is transformed into a dual integrated equation with the method of integral transform. The dynamic stress intensity factor is obtained using Schmidt method. The numerical examples are presented to demonstrate this numerical technique for SH-waves propagating in FGM plate. Finally the number of the waves, the gradient parameter of FGM and the angle of the incidence upon the dynamic stress intensity factor are also given.

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 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.

Fracture Dynamics of a Mode III Moving Crack Impacted by Elastic Wave in Functionally Graded Materials

2010 ◽  
Vol 105-106 ◽  
pp. 683-686
Author(s):  
Xin Gang Li ◽  
Zhen Qing Wang ◽  
Nian Chun Lü
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Sh Waves

The dynamic stress field under the SH-waves at the moving crack tip of functionally graded materials is analyzed, and the influences of parameters such as graded parameter, crack velocity, the angle of the incidence and the number of the waves on dynamic stress intensity factor are also studied. Due to the same time factor of scattering wave and incident wave, the scattering model of the crack tip can be constructed by making use of the displacement function of harmonic load in the infinite plane. The dual integral equation of moving crack problem subjected to SH-waves is obtained through Fourier transform with the help of the exponent model of the shear modulus and density, then have some process on the even and odd term of the integral kernel. The displacement is expanded into series form using Jacobi Polynomial, and then the semi-analytic and numerical solutions of dynamic stress intensity factor are derived with Schmidt method.

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 on Periodic Cracks in an Infinite Plane of Piezoelectric/Piezomagnic Composite Materials

2012 ◽  
Vol 166-169 ◽  
pp. 3364-3368
Author(s):  
Wei Shi ◽  
Li Xia Ma
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Composite Materials ◽  
Piezoelectric Materials ◽  
Infinite Plane ◽  
Sh Wave ◽  
Scattering Problems ◽  
Sh Waves ◽  
Periodic Cracks ◽  
The Fourier Transform

In this paper, the scattering problems of SH waves on periodic cracks in an infinite of piezoelectric/piezomagnic composite materials bonded to an infinite of homogeneous piezoelectric materials is investigated, the Fourier transform techniques are used to reduce the problem to the solution of Hilbert singular integral equation, the latter is solved by Lobotto-Chebyshev and Gauss integral equation, at last, numerical results showed the effect of the frequency of wave, sizes and so on upon the normalized stress intensity factor.

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