压电复合材料中正六边形孔边裂纹反平面问题

基于压电复合材料力学,通过引入合适的数值保角映射函数,运用Stroh公式和复变函数方法,研究了压电复合材料中含正六边形孔边两不对称裂纹的反平面问题.首先由压电复合材料反平面问题的本构方程和力-电平衡方程推导出其控制方程,结合留数定理和Cauchy积分公式,求解出电不可通和电可通边界条件下裂纹尖端场强度因子和能量释放率的解析表达式.数值算例分析了正六边形的孔洞边长、裂纹几何尺寸以及机电载荷对等效场强度因子和能量释放率的影响规律.研究结果表明:正六边形孔洞边长和裂纹长度的增加会导致等效场强度因子的增大;在电不可通和电可通边界条件下,能量释放率随着正六边形的边长、裂纹的长度和机械载荷的增加而增加.在电不可通边界条件下电位移既可以促进又可以抑制裂纹的扩展,而在电可通边界条件下电位移对裂纹扩展没有影响.

The Anti-Plane Problem of Regular Hexagonal Hole Edge Crack in Piezoelectric Composites

By using Stroh-type formulism and complex variable function theory and by introducing an appropriate numerical conformal mapping function , the antiplane problem of double cracks originnating from a regular hexagonal hole in piezoelectric composites was investigated in this paper. Based on the governing equation of the two-dimensional antiplane problem of piezoelectric elastomers, the analytical expressions of the field intensity factor and energy release rate at the crack tip under the condition of electrically impermeable and electrically permeable boundary were determined by using the residue theorem and Cauchy integral formula.The effects of the side length, crack length, mechanical load and electrical load on crack propagation and energy release rate were analyzed by numerical examples.