摘要
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。
Based on the mechanics of piezoelectric composites,by introducing an appropriate numerical conformal mapping function and using the Stroh-type formula and the complex variable function method,the anti-plane problem of two asymmetric cracks emanating from a regular hexagonal hole in piezoelectric composites was investigated.Firstly,the governing equations of the anti-plane problem of piezoelectric composites were derived from the constitutive equations and the mechanical-electrical equilibrium equations.Combined with the residue theorem and Cauchy integral formula,the analytical expressions of the field intensity factors and energy release rate at the crack tip were obtained under the condition of electrically impermeable and electrically permeable boundaries.Numerical examples were provided to analyze the influences of the hole side length,crack geometry size and mechanical/electric loads on equivalent field intensity factor and energy release rate.The results show that,the increase of the size of regular hexagonal hole and the length of cracks lead to the increase of the equivalent field intensity factor.Under the electrically impermeable and electrically permeable boundaries,the energy release rate increases with the increases of the size of regular hexagonal hole,the length of crack and the mechanical load.Under the electrically impermeable boundary condition,the electric displacements can both promote and restrain the crack growth,but the electric displacements have no effect on the crack growth under the electrically permeable boundary.
作者
徐燕
杨娟
XU Yan;YANG Juan(Xinhua College,Ningxia University,Yinchuan 750021,China;School of Preparatory Education for Nationalities,Ningxia University,Yinchuan 750002,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)
出处
《科学技术与工程》
北大核心
2021年第12期4778-4784,共7页
Science Technology and Engineering
基金
国家自然科学基金(12062022,42064004,11762016,11762017)
宁夏自然科学基金(2020AAC03061,2020AAC03057)
宁夏高等学校科学研究项目(NGY2020013)
宁夏回族自治区2019年数学与应用数学一流专业。
关键词
压电复合材料
正六边形孔边裂纹
复变函数方法
场强度因子
能量释放率
piezoelectric composite
regular hexagonal hole edge crack
complex variable function method
field intensity factor
energy release rate
