Basic solution of a mode-I permeable crack in functionally graded piezoelectric materials

2009 ◽  
Vol 5 (2-3) ◽  
pp. 63-78
Author(s):  
Jun Liang
Keyword(s):  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Mode I ◽  
Basic Solution ◽  
Permeable Crack ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

Investigation of the critical states of dielectric cracks in functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2110) ◽  
pp. 3187-3207
Author(s):  
Zhi Yan ◽  
Liying Jiang
Keyword(s):  
Crack Length ◽  
Critical State ◽  
Fourier Transforms ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Crack Model ◽  
Permeable Crack ◽  
Critical States ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

A critical state for electromechanical loads that determines when the traditional impermeable (or permeable) crack model serves as the upper or the lower bound of the dielectric crack model, first proposed for homogeneous piezoelectric materials, is studied further for functionally graded piezoelectric materials (FGPMs) in the current work. The analytical formulations of a single crack and two interacting cracks in the FGPMs are derived by using Fourier transforms, and the resulting integral equations are solved with Chebyshev polynomials. Numerical simulations are conducted to show the effect of crack length, positions of two interacting cracks and material gradient of FGPMs at this critical state. Interesting results show that the combination of the material gradient and the crack length α a plays an important role in determining this critical state. Our solutions also reveal there may exist several critical states for two interacting cracks in the FGPMs.

The fracture behaviour of functionally graded piezoelectric materials containing collinear dielectric cracks

2009 ◽  
Vol 465 (2106) ◽  
pp. 1779-1798 ◽  
Author(s):  
Zhi Yan ◽  
Liying Jiang ◽  
John R. Dryden
Keyword(s):  
Fourier Transforms ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Dielectric Constants ◽  
Crack Model ◽  
Permeable Crack ◽  
Electric Boundary Condition ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric ◽  
Dielectric Crack

In this paper, the problem of two collinear cracks in functionally graded piezoelectric materials (FGPMs) under in-plane electromechanical loads is examined. The elastic, piezoelectric and dielectric constants of the FGPMs are assumed to vary continuously in space. The theoretical formulations are derived by using Fourier transforms and the resulting singular integral equations are solved with Chebyshev polynomials. A dielectric crack model with deformation-dependent electric boundary condition is adopted in the fracture analysis of FGPMs. Numerical simulations are made to show the effect of the dielectric medium, the material gradient and the geometry of interacting cracks upon the fracture parameters at crack tips. A critical state for applied electromechanical loading is identified, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound of the current dielectric crack model.

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