刚性球压头与压电半空间的接触问题再探  

Reconsideration of Contact Problem between Rigid Spherical Indenter and Piezoelectric Half-Space

作　　者：陈聪[1] 陈伟球[1] 

机构地区：[1]浙江大学工程力学系,杭州310027

出　　处：《力学季刊》2011年第3期307-314,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10725210)项目

摘　　要：压痕技术被广泛用于新型材料的性能测定,因此相关理论的建立就显得十分重要。在压电材料的压痕理论中对球形或锥形压头的压入分析的已有结果并不完全一致,本文为此重新考察了刚性球形压头与横观各向同性压电材料的接触问题。研究发现在处理接触边缘应力奇异性时,存在着两类不同的处理方式:一类假设接触边缘不存在由压头位移引起的应力奇异性,而另一类则假设不存在由压头位移和压头上作用的电势共同引起的应力奇异性。这两类不同的处理方式给出了不同的接触半径,并将影响压入过程中荷载-压入深度关系以及压电半空间内电弹性场的分布。结合算例,进行了对比分析。Indentation technique has been widely used to characterize material behavior of new-type materials,and hence it is very important to establish the underlying theory for material characterization.The available theoretical results for the indentation of a piezoelectric material with a spherical or conical indenter are however not consistent.The contact problem of a rigid spherical indenter was reconsidered in contact with a transversely isotropic half-space.It was found that there are two different treatments regarding the stress singularity at the contact edge： One assumes that the singularity of mechanical stress at the contact edge induced by the indentation displacement only vanishes,and the other assumes that there is entirely no stress singularity at the contact edge under a combined action of indentation displacement and electric potential prescribed on the conducting indenter.The two treatments lead to apparently different formulae for the contact radius,and will affect the relation between the applied load and indentation displacement as well as the elastoelectric field distribution in the piezoelectric half-space.The numerical example was considered and the comparison was made between the results obtained under the two assumptions.

关 键 词：压电材料 压痕理论 球压头 接触半径 应力奇异性 

分 类 号：O343.3[理学—固体力学]