Characterization of elastic modulus and hardness of brittle solids by instrumented indentation  

利用仪器化压入表征脆性固体的弹性模量和硬度

作　　者：Zhitong Xu Ming Liu Jianghong Gong 徐智通;刘明;龚江宏

机构地区：[1]Fujian Provincial Key Laboratory of Terahertz Functional Devices and Intelligent Sensing,School of Mechanical Engineering and Automation,Fuzhou University,Fuzhou 350108,China [2]State Key Laboratory of New Ceramics and Fine Processing,School of Materials Science and Engineering,Tsinghua University,Beijing 100084,China

出　　处：《Acta Mechanica Sinica》2025年第1期141-162,共22页力学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China (Grant No.51705082);Fujian Provincial Minjiang Scholar Program (Grant No.0020-510759);Qishan Sholar program in Fuzhou University (Grant No.0020-650289);Fuzhou University Testing Fund of precious apparatus (Grant No.2023T018).

摘　　要：The reduced elastic modulus Er and indentation hardness HIT of various brittle solids including ceramics,semiconductors,glasses,single crystals,and laser material were evaluated using nanoindentation.Various analysis procedures were compared such as Oliver&Pharr and nominal hardness-based methods,which require area function of the indenter,and other methods based on energy,displacement,contact depth,and contact stiffness,which do not require calibration of the indenter.Elastic recovery of the imprint by the Knoop indenter was also utilized to evaluate elastic moduli of brittle solids.Expressions relating HIT/Er and dimensionless nanoindentation variables(e.g.,the ratio of elastic work over total work and the ratio of permanent displacement over maximum displacement)are found to be nonlinear rather than linear for brittle solids.The plastic hardness Hp of brittle solids(except traditional glasses)extracted based on Er is found to be proportional to E_(r)√H_(IT).利用纳米压入测试了各种脆性固体(比如:陶瓷、半导体、玻璃、单晶和激光材料)的缩减弹性模量Er和压入硬度HIT,比较了各种分析方法:一些方法需要压头的面积函数,比如Oliver&Pharr(OP)方法和基于名义硬度的方法;另外一些方法不需要校准压头,比如基于能量、位移、接触深度和接触硬度的方法.努氏压头下压痕的弹性恢复也被用于评估脆性固体材料的弹性模量.对于脆性固体,HIT/Er与纳米压入无量纲特征量(如弹性功与总功之比、残余位移与最大位移之比)之间的关系是非线性的,而不是线性的.对于脆性固体(传统玻璃除外),根据Er计算的塑性硬度Hp与E_(r)√H_(IT)成正比.

关 键 词：Brittle solids NANOINDENTATION Elastic modulus HARDNESS Elastic recovery of Knoop imprint 

分 类 号：TG115[金属学及工艺—物理冶金]