压电压磁复合材料中正六边形孔边裂纹的反平面断裂问题

Anti-Plane Fracture Problem of a Regular Hexagonal Hole with Radial Edge Cracks in Piezoelectric/Piezomagnetic Composites

基于线性磁电弹性理论,利用Schwarz-Christoffel(CS)变换技术和Stroth公式,首次系统研究了压电压磁复合材料中含带两个不对称裂纹的正六边形孔口问题在部分渗透磁电边界条件下的解析解.当忽略磁场时,磁电非渗透裂纹和磁电渗透裂纹两种极端情况下的解析解答可退化为文献已有研究结果.数值结果揭示了正六边形孔口尺寸、裂纹长度以及力电载荷和磁载荷对能量释放率的影响规律.研究结果表明:减小孔口边长和裂纹长度可以提高材料的可靠性;机械载荷总是促进裂纹扩展;在磁电非渗透和磁电部分渗透边界条件下,负电场和负磁场会延缓裂纹的扩展,而正电场可以增强或阻碍裂纹的扩展,这取决于所施加的电场和磁场的强度以及机械载荷的水平;在磁电渗透边界条件下,电场和磁场对裂纹的扩展没有影响.

Based on the linear theory of magnetoelectroelasticity,using the Schwarz-Christoffel transformation technique and Stroh-type formula,the analytical solutions of the regular hexagonal hole problems with asymmetry cracks in magnetoelectroelastic materials under the partially magnetoelectrically permeable boundary condition were systematically investigated for the first time.When the magnetic field was ignored,the analytical solutions of the two extreme cases of the magnetoelectric impermeable crack and the magnetoelectric permeable crack can be degraded to the existing results in the literature.In addition,the numerical results reveal the influences of the regular hexagonal hole size,the crack length and the applied mechanical-electric-magnetic loads on the energy release rate.It shows that the reliability of the material can be improved by reducing the edge length of the hole and the crack length,and the mechanical loads always promote crack propagation.Under the impermeable boundary condition and partial permeable boundary condition,the negative electric field and negative magnetic field can delay the crack propagation,while the positive electric field can enhance or hinder the crack propagation,depending on the intensity of the applied electric/magnetic field and the level of mechanical load.However,the electric field and magnetic field have no effect on the crack propagation under the magnetoelectrically permeable boundary condition.