Modified method for continuous stiffness measurement
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Jen Fin Lina) Department of Mechanical Engineering, Center for Micro/Nano Science and Technology, and Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung University, Tainan, Taiwan 701, Republic of China (Received 1 July 2008; accepted 5 September 2008)
This study proposes a method developed to simultaneously solve contact hardness and reduced modulus by loading and unloading coefficients together with the inclined angle of an indenter. The ratios of the applied load to the squared slopes of load–depth curves during loading and unloading processes were used to determine loading and unloading coefficients. The values of the contact area estimated by the present method were found to be precise for a variety of materials. Compared to the reduced modulus, errors due to underestimated contact area were found more significant in the evaluation of contact hardness.
I. INTRODUCTION
Because of their high resolution in load, position, and displacement, nanoindentation techniques have become a means for determining materials’ mechanical properties, such as Young’s modulus (E) and contact hardness (HC). These methods were originally applied to bulk, homogeneous materials;1–5 however, they have also been directly applied to determining composite mechanical properties of film/substrate systems.6–10 Much attention has been focused on the analysis of the unloading curve to obtain the contact area for the determination of hardness and Young’s modulus. Most procedures are based on the Oliver–Pharr method,1 which determines the contact area through an unloading tangent, together with the known area function. Standard specimens, such as fused quartz, are used to calibrate the area function of an indenter. Usually, measurement for properties exhibited at different depths requires a series of experiments. With quantitative accuracy and high repeatability, the continuous stiffness measurement (CSM) technique has been developed to obtain a series of hardness and modulus results by one indent.6 The CSM method usually applies an exponential type load, maintaining a constant strain rate, with a small amplitude oscillation on the specimen. The depth response is measured at the same frequency corresponding to the applied oscillating load, and the resulting phase lag can be obtained. Continuous measurements of contact stiffness are performed throughout a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0087 J. Mater. Res., Vol. 24, No. 3, Mar 2009
the loading process. The values of the support spring stiffness, load frame stiffness, damping, and mass of the indenter column are known a priori. Then the experimental results of oscillating load and depth amplitudes, phase lag, and oscillating frequency can be used to determine the contact stiffness. Therefore, continuous results of (contact) hardness and (storage) modulus can be evaluated by following the Oliver–Pharr method. The obtained Young’s modulus and contact hardness have been reported to be precise when compare
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