Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote mode III uniform load and concentrated load

2011

Commun. Theor. Phys.

Self Cite

The electro-elastic interaction between a piezoelectric screw dislocation and an elliptical piezoelectric inhomogeneity, which contains an electrically conductive confocal elliptical rigid core under remote anti-plane shear stresses and in-plane electrical load is dealt with. The analytical solutions to the elastic field and the electric field, the interfacial stress fields of inhomogeneity and matrix under longitudinal shear and the image force acting on the dislocation are derived by means of complex method. The effect of material properties and geometric configurations of the rigid core on interfacial stresses generated by a remote uniform load, rigid core and material electroelastic properties on the image force is discussed.

“…The conclusion is in agreement with the results in Refs. [13] and [14]. The influence of the piezoelectric coefficients is smaller than that of the shear modulus.…”

Section: Numerical Results and Discussionmentioning

confidence: 95%

“…Noting that U 2 is a constant on the boundary L 2 , and using Eqs. (2), ( 5), (11), (13), and ( 14), yields…”

Section: Solution Of Problemmentioning

confidence: 99%

A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

Jiang

Xie

2011

Commun. Theor. Phys.

Self Cite

“…For anti-plane problems, the anti-plane displacement w along z-direction, the stress components in Cartesian coordinates form ( xz τ , yz τ ) can be written as follows in ζ -plane [6][7] ( ) Re ( ), ( )…”

Section: Problem Statements and Basic Equationsmentioning

confidence: 99%

Interaction between a Screw Dislocation Located in Strained Reinforcement Layer and a Lip-Shaped Crack

2012

AMM

The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

“…The existence of various non-conventional cracks will lead to stress concentration due to elastic mismatch, so an effective method to reduce this is applying a reinforcement layer bonded to crack faces with appropriate geometry and material property. Chao, Lu and Chen [5] obtained the analytical solution for a reinforcement layer bound to an elliptic hole under a remote uniform load using a new analytical method which is different from the standard Muskhelishvili complex potential functions; Liu and Xie [6] obtained the stress field of lip-shaped crack tip with a strained reinforcement layer bonded under a remote uniform load and a concentrated load.…”

Section: Introductionmentioning

confidence: 99%

A Screw Dislocation Interacting with a Lip-Shaped Crack Bonded by a Strained Reinforcement Layer under Remote Longitudinal Shear Load

2012

AMR

The interaction between a screw dislocation and a reinforced lip-shaped crack embedded in an infinite matrix subjected to a remote longitudinal shear load is investigated in this paper. By combining the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and Riemann boundary problem, the problem is reduced to solve an elementary complex potentials equation. The general expressions of complex function in the matrix and the reinforcement layer are derived explicitly in series form for the case when the screw dislocation is located in the matrix. The image force acting on the screw dislocation and the stress intensity factor are also calculated. Some numerical results are provided to discuss the effects of dislocation position, material parameters, geometric configurations and eigenstrain on the image force.