压电材料平面裂纹问题的强度因子和能量释放率

在压电材料平面问题复变函数形式的通解的基础上，推导了裂纹问题的应力强度因子和电位移强度因子（统称为强度因子）的一般表达式。提出了用裂纹面上的位移和电势来推算强度因子的方法，并用有限元实施计算。以无限大压电介质中的Ⅰ型（即张开型）裂纹问题为例，将有限元计算结果与解析解做了比较。进一步又计算了含有边界裂纹的紧凑拉伸试件以及三点弯曲试件的强度因子、能量释放率和断裂荷载，与已有的试验结果作了比较，并对以机械能释放率为判据的断裂准则进行了讨论。

Intensity Factors and Energy Release Rates for Planar Fracture Problems in Piezoelectric Media

With the use of the general solution of the planar problems in piezoelectric media by means of complex variable functions,the expressions of stress intensity factors and electric displacement intensity factors are formulated.A method for determination of intensity factors using displacement and potential on the crack faces is presented.In the case of an infinitely large piezoelectric medium with a central crack subjected to a remote uniform tension and a remote uniform electric field,the numerical solutions of the intensity factors are obtained using finite element method and compared with the analytical solutions.Furthermore,intensity factors,energy release rates and fracture loads are calculated for piezoelectric specimens of compact tension and three point bending.Results are compared with experimental data.Finally,the fracture criterion based on the mechanical energy release rate is discussed.