圆柱平压头压电陶瓷压痕过程中接触应力和电场的奇异性

采用有限元方法，针对横观各向同性压电材料进行轴对称纳米压痕的机电耦合响应数值仿真。结果表明：当压入过程中不施加预设电压，压痕载荷与压痕位移之间呈线性关系；导电压头上电势与压痕位移也呈现相似关系，压头边缘附近的接触应力和电场存在奇异性，且二者均随压头下固体厚度呈指数变化。通过对不同压痕深度和材料厚度下，从压头内部到接触边缘向应力、法向电势和切向电势分布情况的拟合公式得到了不同压电材料厚度下电场和应力场的奇异常数，并对其变化规律进行了分析。

Singularities of Contact Stress and Electric Field During Indentation of Piezoelectric Ceramics by Cylindrical, Flat Indenter

The finite element method (FEM) was used to simulate and to verify the axisymmetric nanoindentation response of a transversely isotropic piezoelectric ceramics by a conductive rigid flat indenter from half-space to thin film. The cylindrical, flat indenter without prescribed electric force was adopted to mechanically load the piezoelectric ceramics. The results show that the linear relationship between indentation load and indentation displacement is obtained. And the same relationship is obtained between electric potential and indentation displacement. In addition, resultant mechanoelectrical responses were analyzed. The simulation results indicate that the contact stress and electric field exhibit singularities round the edge of the indenter. Both stress and electric field singularities vary exponentially with respect to the thickness of the solids under the indenter. At the same time, the normal stress and electric potential distributions of the direct piezoelectric effects are given. Through the fitting formula of the normal stress, normal electric potential and tangential electric potential from the indentation interior to the contact edge under different indentation depths, the singular constants of electric field and stress field under different thickness of piezoelectric ceramics are proposed, and their variation rules are analyzed.