Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half plane

Meccanica ◽  
2009 ◽  
Vol 44 (5) ◽  
pp. 519-534 ◽  
Author(s):  
Wei-Hung Hsu ◽  
Ching-Hwei Chue
Keyword(s):  
Half Plane ◽  
Mode Iii ◽  
Arbitrarily Oriented Crack

Elastic cloaking for a periodic distribution of parallel finite cracks

2021 ◽  
Vol 477 (2249) ◽  
pp. 20200997
Author(s):  
Ping Yang ◽  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Mode Iii ◽  
Original Design ◽  
Periodic Distribution ◽  
Wavy Interface ◽  
Cauchy Singular Integral ◽  
Periodic Cracks ◽  
The Right

We achieve elastic cloaking for a periodic distribution of an infinite number of parallel finite mode III cracks by means of the complex variable method and the theory of Cauchy singular integral equations. The cloaking bimaterial structure is composed of an undisturbed uniformly stressed left half-plane perfectly bonded via a wavy interface to the right half-plane which contains periodic cracks. The original design of the wavy interface and the positions of the periodic cracks are ultimately reduced to the solution of a Cauchy singular integral equation which can be solved numerically.

Mode-III Stress Intensity Factors of an Arbitrarily Oriented Crack Crossing Interface in a Layered Structure

2013 ◽  
Vol 29 (4) ◽  
pp. 643-651 ◽  
Author(s):  
C. K. Chao ◽  
L. M. Lu
Keyword(s):  
Stress Intensity ◽  
Layered Structure ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Linear Interpolation ◽  
Plane Elasticity ◽  
Intensity Factors ◽  
Mode Iii ◽  
Line Segments ◽  
Arbitrarily Oriented Crack

ABSTRACTThe problem of a layered structure containing an arbitrarily oriented crack crossing the interface in anti-plane elasticity is considered in this paper. The fundamental solution of displacements and stresses is obtained in a series form via the method of analytical continuation in conjunction with the alternating technique. A dislocation distribution along the prospective site of a crack is used to model a crack crossing the interface and the singular integral equations with logarithmic singular kernels for a line crack are then established. The crack is approximated by several line segments and the linear interpolation equation with undetermined coefficients was applied for the dislocation function along line segments. Once the undetermined dislocation coefficients are solved, the mode-III stress intensity factors KIII at two crack tips can be obtained for various crack inclinations with different material property combinations. All the numerical results are checked to achieve a good approximation that demonstrates the accuracy and the efficiency of the proposed method.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

2017 ◽  
Vol 28 (19) ◽  
pp. 2823-2834 ◽  
Author(s):  
Mojtaba Ayatollahi ◽  
Mojtaba Mahmoudi Monfared ◽  
Mahsa Nourazar
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Field Intensity ◽  
Electric Displacement ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Mode Iii ◽  
Singular Stress ◽  
Field Intensity Factors

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

Anti-Plane Interaction between a Crack and an Elliptically Cylindrical Layered Media

2013 ◽  
Vol 29 (1) ◽  
pp. 85-93 ◽  
Author(s):  
C.K. Chao ◽  
A. Wikarta
Keyword(s):  
Stress Intensity ◽  
Screw Dislocation ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Layered Media ◽  
Infinite Matrix ◽  
Intensity Factors ◽  
Mode Iii ◽  
Plane Interaction ◽  
Arbitrarily Oriented Crack

AbstractAnti-plane interaction of an elliptically cylindrical layered media with an arbitrarily oriented crack embedded in an infinite matrix, intermediate layer, or inner inclusion under a remote uniform shear load is considered in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation in the inclusions and the matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack can easily be obtained by using the screw dislocation solutions as the Green's function together with the principle superposition. The stress intensity factors, which can properly reflect the interaction between a crack and an elliptically cylindrical layered media, are then obtained numerically in terms of the values of the dislocation density functions of the integral equations. The effects of material property combinations and geometric parameters on the normalized mode-III stress intensity factors are discussed in detail and shown in graphic form.

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