压电陶瓷中圆币形裂纹在横向剪力下的机－电耦合行为

MECHANICAL-ELECTRIC COUPLING BEHAVIOUR OF A PENNY-SHAPE CRACK IN PIEZOELECTRIC CERAMICS SUBJECTED TO LATERAL SHEARING FORCE

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。

The field equations for three-dimensional problems in transversely isotropicpiezoelectric medium may be reduced to four second order linear partial differential equa-tions,in which the elastic displacement components and electric potential functions areunknowns.In this paper,expressions for displacement components and electric potentialfunctions are derived by using four harmonic functions,they form the so-called general solu-tions of the field equations for three-dimensional problems.As an example,a penny-shapecrack subjected to laterally distributed shearing forces is solved and analytic expressions forthe crack-tip stress and electric displacement fields are obtained. It is found that the crack-tip fields,stress and electric displacement intensity factors have obvious mechanical-electriccoupling behaviour,and the stress and electric displacement components at crack tip haver￣(-1/2) singularity.