科研之友
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摘要
In this paper a first order perturbation analysis is carried out on a symmetrically perturbed non-ideal crack for three kinds of electric boundary conditions, namely permeable, impermeable and conducting crack boundary condition. By using the extended Stroh formula, the two-domain problems are reduced to standard Riemann-Hilbert problems, and the singular integral equations of the internal electric field inside the permeable crack are solved. The stress and electric intensity factors (SEIFs) are determined to the first order of accuracy. The results indicate that for a symmetrically perturbed non-ideal crack the electro-mechanical loading at infinity does not affect the first order solution for the mode I intensity factor for general piezoelectric materials. The energy release rate and the SEIFs are determined by remote mechanical loads only and the perturbation effect on the SEIFs and energy release rate is small. The electric field distribution inside crack is constant for the zeroth order solution and quadratic for the first order solution, which is different from the constant electric field distribution for an ideal permeable crack. The internal electric concentration near the crack tip caused by the perturbation reveals that the dielectric inside the crack probably breaks down before the matrix does when the matrix is subjected to a not too high electro-mechanical load at infinity. The SEIFs and the energy release rate are also given for the non-ideal crack under the impermeable and conducting electric boundary condition respectively. For all three kinds of electric boundary conditions, the lateral stresses sigma (infinity)(11), sigma (infinity)(13) have no contribution to the SEIFs to the first order of accuracy.
- 出版日期2001-10
- 单位上海交通大学
