An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory
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摘要: 基于偶应力理论，研究了刚性绝缘球压头与横观各向同性压电半空间尺度依赖的轴对称接触问题. 利用Hankel积分变换和积分最小二乘法，获得了接触压力. 讨论了特征材料长度对接触压力分布、接触半径和压痕深度的影响. 结果表明，基于偶应力理论获得的接触压力结果明显大于经典结果.Abstract: Based on the couple stress theory, the axisymmetric contact problem between a rigid insulating spherical punch and a transversely isotropic piezoelectric half-space was studied. With the Hankel integral transform and the integral least squares approach, the analytical solutions of the contact pressure were obtained. The effects of the characteristic material length on the contact pressure distribution, the contact radius and the indentation depth were discussed. The results indicate that, the contact pressure obtained based on the couple-stress theory is significantly greater than the classical results.
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Key words:
- axisymmetric contact /
- piezoelectric material /
- size effect /
- couple stress theory
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图 1 球压头与压电半空间尺度依赖的轴对称接触
Figure 1. Size-dependent axisymmetric contact between the spherical punch and the piezoelectric half-space
图 3 特征材料长度对接触压力分布的影响
Figure 3. The effects of the characteristic material length on the contact pressure distribution
图 4 法向加载F对最大接触压力的影响
Figure 4. The effects of normal loading F on the maximum contact pressure
图 6 特征材料长度对p(r)/pc(r)的影响
Figure 6. The effects of the characteristic material length on p(r)/pc(r)
图 7 特征材料长度对a/ac，p0/p0c，δ/δc的影响
Figure 7. The effects of the characteristic material length on a/ac, p0/p0c, δ/δc
C11/GPa C12/GPa C13/GPa C33/GPa C44/GPa e13/(C/m2) e33/(C/m2) e15/(C/m2) PZT-4 139 77.8 74.3 115 25.6 -5.2 15.1 12.7 BaTiO3 150 6.6 6.6 14.6 4.4 -17.3 17.5 11.4 ε11/(10－10·C/(V·m)) ε33/(10－10·C/(V·m)) f21/(10－11·Pa－1) PZT-4 64.61 56.2 1.772 8 BaTiO3 98.7 112 1.376 6 
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表 2 接触半径a的收敛性分析
Table 2. Convergence analysis of contact radius a
M 2 3 4 a/μm 23.671 23.665 23.665
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