The Higher Order Mechanical and Electric Fields for Arbitrarily Oriented Crack with the Physical Weak-Discontinuity

2014 ◽  
Vol 602-605 ◽  
pp. 283-286
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Electric Fields ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for anti-plane crack oblique to the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The crack is oriented in arbitrary direction. The crack surfaces are assumed to be electrically impermeable. The material properties of FGPMs are assumed to be linear functions with their gradient direction perpendicular to the interface. By using the eigen-expansion method, the high order crack tip stress and electric displacement fields are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 1015 ◽  
pp. 97-100
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Ying Chen
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

The Crack Tip Fields for Anti-Plane Crack in FGPM of x Linear Function

2014 ◽  
Vol 1015 ◽  
pp. 93-96
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Jin Cai Huang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Electric Displacement ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Plane Crack ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack tip fields for an anti-plane crack in functionally graded piezoelectric materials (FGPMs) under mechanical and electrical loadings are studied. Different from previous analyses, all material properties of FGPMs are assumed to be linear functions of x parallel to the crack. The boundary conditions on crack surfaces are assumed to be the stress free and electrically impermeable. By using the eigen-expansion method, the problem is reduced to solving the system of ordinary differential equations. The higher order stress and electric displacement crack tip fields for FGPMs are obtained by solving the ordinary differential equations.

The Crack Tip Fields for Anti-Plane Interfacial Crack between Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 989-994 ◽  
pp. 719-722
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Intensity Factor ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Expansion Method ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Functionally Graded Piezoelectric Materials ◽  
Electric Displacement Intensity Factor

The problem of an anti-plane crack situated in the interface of functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) is considered under the impermeable assumption of crack surfaces. The mechanical and electrical properties of the FGPMs are assumed to be exponential functions of y perpendicular to the crack. The higher order crack tip stress and electric displacement fields for FGPMs and HPMs are obtained by the eigen-expansion method. The stress intensity factor and electric displacement intensity factor are obtained explicitly.

The Higher Order Crack-Tip Fields for Anti-Plane Crack in Exponential Functionally Graded Piezoelectric Materials

2014 ◽  
Vol 989-994 ◽  
pp. 1212-1215
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Shi Min Li
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Expansion Method ◽  
Elastic Stiffness ◽  
Functionally Graded ◽  
Plane Crack ◽  
Displacement Fields ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

The near-tip fields of an anti-plane crack in functionally graded piezoelectric materials (FGPMs) are investigated. To make the analysis tractable as usual, the elastic stiffness, piezoelectric parameter, and dielectric permittivity of FGPMs are assumed to be exponential functions of x parallel to the crack. The boundary conditions on crack surfaces are assumed to be the stress free and electrically impermeable. The high order crack tip stress and electric displacement fields are obtained by the eigen-expansion method. This study possesses fundamental significance as Williams’ solution to homogeneous materials.

The Higher Order Crack Tip Fields for Anti-Plane Crack in Linear Functionally Graded Piezoelectric Materials

2014 ◽  
Vol 989-994 ◽  
pp. 715-718
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Shi Min Li
Keyword(s):  
Material Properties ◽  
Piezoelectric Materials ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Crack Tip Field ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

The crack tip field in functionally graded piezoelectric materials (FGPMs) under mechanical and electrical loadings is studied. Different from previous analyses, all material properties of the functionally graded piezoelectric materials are assumed to be linear function of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. Similar to the Williams’ solution of homogeneous elastic materials, the higher order crack tip fields of FGPMs are obtained by the eigen-expansion method.

Interaction Integrals for Fracture Analysis of Functionally Graded Piezoelectric Materials

2008 ◽  
Author(s):  
B. N. Rao
Keyword(s):  
Piezoelectric Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Piezoelectric Medium ◽  
Intensity Factors ◽  
Interaction Integral ◽  
Functionally Graded Piezoelectric Materials ◽  
Electric Displacement Intensity Factor ◽  
Functionally Graded Piezoelectric ◽  
Asymptotic Fields

This paper presents domain form of interaction integrals based on three independent formulations for computation of stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials. Conservation integrals of J–type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields. Each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of an example.

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