Abstract
A simple method for measuring the Young's modulus of thermoplastic polymers at the nanoscale is proposed. Nanoindentation tests have been carried out on three polymers (ABS, PET and PP) using the Berkovich indenter tip. The elasticity moduli obtained from the reduced moduli thanks to the slope of the initial part of the discharge curve were greater than the real moduli of these polymers. For this, a simple method is proposed to minimize the error made on the determination of the modulus which is based on the calculation of several stiffnesses between 10 and 98% of the maximum load on the experimental unloading curve. The results show that the calculated moduli at a load less than 50% of the maximum load were close to the macroscopic moduli and the effect of viscosity was minimized. In the end, the elastic Young's modulus obtained by our approach is in very good agreement with the result of the tensile tests.
Similar content being viewed by others
References
V. Králík and J. Němeček, Comparison of Nanoindentation Techniques for Local Mechanical Quantification of Aluminium Alloy, Mater. Sci. Eng. A, 2014, 618, p 118.
A.P. Silva, F. Booth, L. Garrido, E. Aglietti, P. Pena, and C. Baudín, Young’s Modulus and Hardness of Multiphase CaZrO3-MgO Ceramics by Micro and Nanoindentation, J. Eur. Ceram. Soc., 2018, 38, p 2194.
W.C. Oliver and G.M. Pharr, Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology, J. Mater. Res., 2004, 19, p 3.
B. Bhushan, Nanomechanical properties of solid surfaces and thin films, Handbook of Micro/Nano Tribology. B. Bhushan Ed., CRC Press, Boca Raton, 1999
S. Yang, Y.W. Zhang, and K.Y. Zeng, Analysis of Nanoindentation Creep for Polymeric Materials, J. Appl. Phys., 2004, 95, p 3655.
D. Tranchida, S. Piccarolo, J. Loos, and A. Alexeev, Mechanical Characterization of Polymers on a Nanometer Scale through Nanoindentation: A Sudy on Pile-up and Vscoelasticity, Macromolecules, 2007, 40, p 1259.
M. Hardiman, T.J. Vaughan, and C.T. McCarthy, The Effects of Pile-up, Viscoelasticity and Hydrostatic Stress on Polymer Matrix Nanoindentation, Polym. Test., 2016, 52, p 157.
T. Jin, X. Niu, G. Xiao, Z. Wang, Z. Zhou, G. Yuan et al., Effects of Experimental Variables on PMMA Nano-indentation Measurements, Polym. Test., 2015, 41, p 1.
X.D. Hou and N.M. Jennett, Defining the Limits to Long-term Nano-indentation Creep Measurement of Viscoelastic Materials, Polym. Test., 2018, 70, p 297.
B.J. Briscoe, L. Fiori, and E. Pelillo, Nano-indentation of Polymeric Surfaces, J. Phys. D: Appl. Phys., 1998, 31, p 2395.
Y.T. Cheng and C.M. Cheng, Relationships Between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Conical Indentation in Linear Viscoelastic Solids, J. Mater. Res., 2005, 20, p 1046.
K. Geng, F. Yang, and E.A. Grulke, Nanoindentation of Submicron Polymeric Coating Systems, Mater. Sci. Eng. A, 2008, 479, p 157.
I.N. Sneddon, The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile, Int. J. Eng. Sci., 1965, 3, p 47.
J.C. Hay, A. Bolshakov, and G.M. Pharr, A Critical Examination of the Fundamental Relations used in the Analysis of Nanoindentation Data, J. Mater. Res., 1999, 14, p 2296.
R.B. King, Elastic Analysis of Some Punch Problems for Layered Medium, Int. J. Solids. Struct., 1987, 23, p 1657.
A. Bolshakov and G.M. Pharr, Influences of Pile-up on the Measurement of Mechanical Properties by Load and Depth Sensing Indentation Techniques, J. Mater. Res., 1998, 13, p 1049.
G. Feng and A.H.W. Ngan, Effects of Creep and Thermal Drift on Modulus Measurement Using Depth-sensing Indentation, J. Mater. Res., 2002, 17, p 660.
T. Chudoba and F. Richter, Investigation of Creep Behaviour Under Load During Indentation Experiments and its Influence on Hardness and Modulus Results, Surf. Coat. Technol., 2001, 148, p 191.
M. Sakai and S. Shimizu, Indentation Rheometry for Glass-forming Materials, J. Non-Cryst. Solids., 2001, 282, p 236.
S.A.S. Asif and J.B. Pethica, Nanoindentation Creep of Single-crystal Tungsten and Gallium Arsenide, Philos. Mag. A, 1997, 76, p 1105.
B.D. Beake and G.J. Leggett, Nanoindentation and Nanoscratch Testing of Uniaxially and Biaxially Drawn Polyethylene Terephthalate) Film, Polymer, 2002, 43, p 319.
M.S. Bobji and S.K. Biswas, Deconvolution of Hardness from Data Obtained from Nanoindentation of Rough Surfaces, J. Mater. Res., 1999, 14(6), p 2259.
X. Li and B. Bhushan, A Review of Nanoindentation Continuous Stiffness Measurement Technique and its Applications, Mater. Charact., 2002, 48, p 11.
I.M. Low, Effects of Load and Time on the Hardness of a Viscoelastic Polymer, Mater. Res. Bull., 1998, 33, p 1753.
T.K. Harris, E.J. Brookes, and R. Daniel, The Application of the Soft Impressor Technique to Problems of the Measurement of Creep in Covalent Materials, Int. J. Refract. Met. Hard Mater., 1999, 17, p 33.
S.A. Syed Asif and J.B. Pethica, in Thin Films: Stresses and Mechanical Properties VI, In: W.W. Gerberich, H. Gao, J-E. Sundgren, and S.P. Baker (Eds.), Materials Research Society Symposium Proceedings, vol. 436 (Pittsburgh, PA, 1996), p 201.
A.A. Elmustafa and D.S. Stone, Indentation Size Effect in Polycrystalline F.C.C. Metals, Acta. Mater., 2002, 50, p 3641.
M. Sakai, S. Shimizu, N. Miyajima, Y. Tanabe, and E. Yasuda, Viscoelastic Indentation on Iodine-treated Coal Tar Pitch, Carbon, 2001, 39, p 605.
B.N. Lucas and W.C. Oliver, Indentation Power-law Creep of High-purity Indium, Metall. Mater. Trans. A, 1999, 30, p 601.
T.Y. Tsui and G.M. Pharr, Substrate Effects on Nanoindentation Mechanical Property Measurement of Soft Films on Hard Substrates, J. Mater. Res., 1999, 14, p 292.
J.L. Loubet, J.M. Georges, and J. Meille, Nanoindentation Techniques in Materials Science and Engineering, ASTM, Philadelphia, 1986.
G. Hochstetter, A. Jimenez, and J.L. Loubet, Strain-rate Effects on Hardness of Glassy Polymers in the Nanoscale Range: Comparison Between Quasi-static and Continuous Stiffness Measurements, J. Macromol. Sci. B: Phys., 1999, 38, p 681.
W.C. Oliver and G.M.J. Pharr, An Improved Technique for Determining Hardness and Elastic Modulus Using: Load and Displacement Sensing Indentation, J. Mater. Res., 1992, 7, p 1564.
ASTM D638–14, Standard Test Method for Tensile Properties of Plastics, ASTM International, West Conshohocken, 2014.
A. Menyhárd, P. Suba, Z.S. László, H.M. Fekete, Á.O. Mester, Z.S. Horváth, G.Y. Vörö, J. Varga, and J. Móczó, Direct Correlation Between Modulus and the Crystalline Structure in Isotactic Polypropylene, Express Polym. Lett., 2015, 9(3), p 308–320.
D. W. van der Meer, Structure-Property Relationships in Isotactic Polypropylene. Ph.D. thesis. University of Twente (2003)
A.N. Gaduan, L. Solhi, E. Kontturi, and K.Y. Lee, From Micro to Nano: Polypropylene Composites Reinforced with TEMPO-oxidised Cellulose of Different Fibre Widths, Cellulose, 2021, 28(5), p 2947–2963.
J. Giró-Paloma, J.J. Roab, A.M.D. Pascualc, E. Florese, M. Martíneza, J.M. Chimenosa, and A.I. Fernándeza, Depth-sensing Indentation Applied to Polymers: A Comparison Between Standard Methods of Analysis in Relation to the Nature of the Materials, Eur. Polym. J., 2013, 49, p 4047.
D. Tranchida, S. Piccarolo, and M. Soliman, Nanoscale Mechanical Characterization of Polymers by AFM Nanoindentations: Critical Approach to the Elastic Characterization, Macromolecules, 2006, 39, p 4547.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mokhtari, A., Tala-Ighil, N. & Masmoudi, Y.A. Nanoindentation to Determine Young’s Modulus for Thermoplastic Polymers. J. of Materi Eng and Perform 31, 2715–2722 (2022). https://doi.org/10.1007/s11665-021-06386-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11665-021-06386-9