非均匀铁弹畴变对离面极化压电陶瓷应力强度因子的影响研究

The Effect of Non-Uniform Ferroelastic Fomain Switching on the Stress Intensity Factor of Piezoelectric Ceramic in Anti-Plane Poling

基于文献中报道的试验结果,本文考虑非均匀的畴变过程区,它包含一个位于中心的饱和区和环绕饱和区的渐变区.为了描述外加应力引起的部分铁弹畴变,本文采用一个显式的基于最小能量原理的非均匀畴变准则.考虑离面极化的压电陶瓷,假设其初始极化矢量平行于离面方向.畴变后的电畴位于面内,具体方位由最大释放功来确定.基于非均匀畴变准则,本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布.并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响.结果表明:(1)静止裂纹尖端处的畴变减小了材料的起裂强度;(2)准静态稳态裂纹附近的畴变增加了材料的断裂强度.且理论预测的R曲线渐近值与试验结果定量吻合.

Based on experimental observations of papers by others researchers, this paper considers a non-uniform process zone,which consists of a saturated core and a transitional annulus. To depict the effective degree of domain reorientation induced by mechanical load, we adopt an explicit switching criterion based on the principle of minimum energy. For simplicity, it is assumed that initial polarization vector of piezoelectric ceramic in anti-plane poling is parallel to x3-axis of a rectangular coordinate system.The switched polarization lies in the plane of Ox1 x2, its definite orientation is determined on the principle of releasing the maximum mechanical work. Via the non-uniform switching criterion, the switch zone geometry and contour of volume fraction are depicted.And the effect of ferroelastic domain switching on crack-tip stress intensity are investigated for two special cracks: a stationary crack and a quasi-static steady-state growing crack. Theoretical results indicate that(1) the switching zone around a stationary crack lowers the initial fracture strength of ceramic;(2) the switching zone around a steady-state growing crack increases the material’s fracture toughness. Specially, the predicted asymptote of R-curve is in complete agreement with experimental result quantitatively.