The M-integral for calculating intensity factors of an impermeable crack in a piezoelectric material

2008 ◽  
Vol 75 (5) ◽  
pp. 901-925 ◽  
Author(s):  
Leslie Banks-Sills ◽  
Yael Motola ◽  
Lucy Shemesh
Keyword(s):  
Piezoelectric Material ◽  
Intensity Factors ◽  
Impermeable Crack ◽  
M Integral

Three-Dimensional Electroelastic Analysis of a Piezoelectric Material With a Penny-Shaped Dielectric Crack

2004 ◽  
Vol 71 (6) ◽  
pp. 866-878 ◽  
Author(s):  
Xian-Fang Li ◽  
Kang Yong Lee
Keyword(s):  
Boundary Conditions ◽  
Piezoelectric Material ◽  
Field Intensity ◽  
Three Dimensional ◽  
Intensity Factors ◽  
Elementary Functions ◽  
Dual Integral Equations ◽  
Electroelastic Field ◽  
Field Intensity Factors ◽  
Dielectric Crack

Previous studies assumed that a crack is either impermeable or permeable, which are actually two limiting cases of a dielectric crack. This paper considers the electroelastic problem of a three-dimensional transversely isotropic piezoelectric material with a penny-shaped dielectric crack perpendicular to the poling axis. Using electric boundary conditions controlled by the boundaries of an opening crack, the electric displacements at the crack surfaces are determined. The Hankel transform technique is employed to reduce the considered problem to dual integral equations. By solving resulting equations, the results are presented for the case of remote uniform loading, and explicit expressions for the electroelastic field at any point in the entire piezoelectric body are given in terms of elementary functions. Moreover, the distribution of asymptotic field around the crack front and field intensity factors are determined. Numerical results for a cracked PZT-5H ceramic are evaluated to examine the influence of the dielectric permittivity of the crack interior on the field intensity factors, indicating that the electric boundary conditions at the crack surfaces play an important role in determining electroelastic field induced by a crack, and that the results are overestimated for an impermeable crack, and underestimated for a permeable crack.

Full Form of the Near Tip Field for the Interface Crack between a Piezoelectric Material and a Thin Electrode

2005 ◽  
Vol 492-493 ◽  
pp. 261-266 ◽  
Author(s):  
Christoph Häusler ◽  
Herbert Balke
Keyword(s):  
Numerical Calculation ◽  
Piezoelectric Material ◽  
Interface Crack ◽  
Extrapolation Method ◽  
Linear Extrapolation ◽  
Intensity Factors ◽  
Interfacial Cracks ◽  
Full Form ◽  
Field Intensity Factors ◽  
Thin Electrode

The Hilbert problems and their solutions of the near tip field for the permeable and the impermeable electrode-ceramic interfacial cracks are derived with the aid of the modified Stroh formalism. In addition, a linear extrapolation method for numerical calculation of field intensity factors is given. This extrapolation method is based on a special combination of the field quantities.

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