Self-calibration of area function for mechanical property determination with nanoindentation tests
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Self-calibration of area function for mechanical property determination with nanoindentation tests Jianghong Gong1,*
, Bin Deng2, Haipeng Qiu3, and Danyu Jiang4
1
State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China 2 Department of the Prosthodontics, The General Hospital of Chinese PLA, Beijing 100853, China 3 AVIC Composite Technology Center, Beijing 101300, China 4 State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Shanghai 200050, China
Received: 7 May 2020
ABSTRACT
Accepted: 22 July 2020
Determination of mechanical properties with nanoindentation tests needs a knowledge of contact area, which is characterized with an area function. In the current methods, typically the Oliver–Pharr method, the area function is usually calibrated with the reference materials prior to practical tests. However, the accuracy and applicability of such a pre-calibrated area function have been questioned in many studies by considering the difference between the indentation response of the real test sample and that of the reference material. In order to overcome this problem, a simple method was proposed in the present study to calibrate area function and extract mechanical properties simultaneously with the same load–displacement curve. Due to the self-calibration, rather than precalibration, nature of this new method, the resultant area function may accurately reflect the response of the test material to nanoindentation. Analyses of the nanoindentation data measured on several typical materials, including glass, metal and ceramic, confirmed that reasonable values of Young’s modulus and hardness can be extracted with this new method.
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Springer Science+Business
Media, LLC, part of Springer Nature 2020
Introduction Nanoindentation technique has been widely carried out for the determination of Young’s modulus and hardness for various types of materials [1–9], including metals, glasses, ceramics and polymers. Handling Editor: Nathan Mara.
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https://doi.org/10.1007/s10853-020-05167-4
The most commonly used method for analyzing nanoindentation data to extract mechanical properties was established by Oliver and Pharr [1]. The Oliver–Pharr (OP) method starts with the analysis of the unloading portion of the experimentally recorded
J Mater Sci
load–displacement (P–h) curve according to a power law: P ¼ a ð h hf Þ m
ð1Þ
where P is the load, h is the displacement, and a, m and hf are empirically determined fitting parameters. Specially, hf is considered as the final displacement after complete unloading. Once the parameters a, m and hf are obtained, the contact stiffness, SOP, corresponding to the peak load Pmax, can be calculated by differentiating Eq. 1 at the maximum displacement, h = hmax, i.e., dP ¼ amðhmax hf Þm1 ð2Þ SOP ¼ dh h¼hmax and the contact depth hc can be calculated with [1]: hc ¼ hmax e
Pmax SOP
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