An instrumented indentation method for evaluating the effect of hydrostatic pressure on the yield strength of solid poly
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Yihui Feng State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Donghui Wen and Taihua Zhanga) College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China (Received 9 June 2014; accepted 14 October 2014)
The yield behavior of solid polymers may be influenced by the hydrostatic pressure, strain rate, and temperature. In the present work, we focus on evaluating the effect of hydrostatic pressure on the yield strength by instrumented indentation. Using dimensional analysis and finite element analysis, two analytical expressions were derived to relate the indentation data to the plastic properties, and a method for extracting the coefficient of internal friction which reflects the effect of hydrostatic pressure on the yield strength was established. Applications were illustrated on polypropylene (PP), polycarbonate (PC), and unplasticized polyvinyl chloride (UPVC). The coefficient of internal friction determined by this indentation method is 0.20 6 0.02 for PP, 0.07 6 0.01 for PC, and 0.10 6 0.01 for UPVC, which are in good agreement with the values reported in the literature. This demonstrates the proposed indentation method which is useful to evaluate the effect of hydrostatic pressure on the yield strength of solid polymers.
I. INTRODUCTION
The yield behavior of solid polymers is sensitive to hydrostatic pressure. It is evident that the von Mises’ and Tresca’s yield criteria, which were formulated by assuming that the yielding is independent of hydrostatic pressure, are inapplicable to polymers. Previous studies1–6 have shown that the yield strength increases approximately linearly with the hydrostatic pressure. The Drucker–Prager7 yield criterion which takes into account the linear dependence of the yield strength on hydrostatic pressure is usually adopted and is shown below: ry0 þ kP ¼ 0 ; f rij ¼ r ð1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi [ ð3=2Þsij sij is the effective stress; ry0 is the where r yield strength under the pure shear deformation; k is the coefficient of internal friction, which reflects the effect of the hydrostatic pressure on the yield strength; P [ rii/3 is the hydrostatic pressure. To evaluate the effect of hydrostatic pressure on the yield strength, uniaxial tension or compression at various hydrostatic pressures was carried out to determine the coefficient of internal friction, k, for bulk polymers.1,8–10 However, with the development a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2014.330 J. Mater. Res., Vol. 29, No. 24, Dec 28, 2014
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of micromachining process, polymeric moldings and structures become smaller and smaller. The conventional testing techniques face great challenges when applied to such products due to the difficulty of specimen preparation. Consequently, there is an increasing demand for new techniques to evaluate the effect of hydrostatic pressure on the yield strength for small
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