功能梯度压电/压磁双材料的周期界面裂纹问题

Periodic Interfacial Cracks in a Functionally Graded Piezoelectric/Piezomagnetic Bimaterials

研究反平面载荷作用下压电/压磁双材料的周期界面裂纹问题,压电/压磁双材料由有限厚度的功能梯度压电层和功能梯度压磁层粘结而成.为便于分析,假设压电层和压磁层的材料性质沿着裂纹的法线方向呈指数变化,基于分离变量和Hilbert核奇异积分方程方法,获得应力强度因子的数值解.数值算例讨论层厚、周期带长度、梯度参数以及材料参数变动等对应力强度因子的影响。结果发现层厚以及裂纹间距的增大会降低裂纹尖端应力强度因子,梯度参数的改变对应力强度因子也有显著的影响.材料参数变动的讨论发现弹性参数的变动对应力强度因子影响最大,其次为电参数,磁参数的变动对应力强度因子影响最小。

The periodic collinear interfacial cracks contained in a layered piezoelectric/piezomagnetic bima- terials was considered theoretically. The piezoelectric/piezomagnetic bimaterials contain a functionally graded piezoelectric layer of finite thickness and a functionally graded piezomagnetic layer of finite thick- ness. Variables separation and dislocation density functions were employed to reduce the mixed-boundary value problem to a singular integral equation of Hilbert kernel, which was solved numerically by standard Lobatto-Chebyshev quadrature technique. The effects of the gradient parameter and the thickness of lay- ers, the crack spacing, and the material constants on the stress intensity factor were discussed and yield- ing some main conclusions as follows： （a） in order to reduce the SIF, the length of periodic area and the thickness of layers should be larger; （b） there is a strong interference between the stress fields around cracks when the gradient parameter changes; and （c） the influences of the elastic parameters and electric parameters on the SIF is more sensitive than the influences of the magnetic parameters on the SIF.