Abstract
Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r −1/2) singularity.
Similar content being viewed by others
References
Deeg WF. The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. PhD Thesis, Stanford University, 1980
Pak YE. Crack extension force in a piezoelectric material.J Appl Mech, 1992, 57(3): 647–653
Sosa HA and Pak YE. Three-dimensional eigenfunction analysis of a crack in a piezoelectric material.Int J Solids Structures, 1990, 26(1): 1–15
Senddon IN, Fourier Transforms. New York: McGraw-Hill, 1951
Senddon IN and Lowengrub M. Crack Problems in the Classical Theory of Elasticity. New York: John Wiley and Sons, 1969
Author information
Authors and Affiliations
Additional information
The project supported by the Natural Science Foundation of Shaanxi Province, China
Rights and permissions
About this article
Cite this article
Zikun, W. Penny-shaped crack in transversely isotropic piezoelectric materials. Acta Mech Sinica 10, 49–60 (1994). https://doi.org/10.1007/BF02487657
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487657