On the origin of indentation size effects and depth dependent mechanical properties of elastic polymers
-
Chung-Souk Han
,
Seyed H.R. Sanei
Abstract
Indentation size effects have been observed in both polymers and metals but, unlike in metals, the origin of size effects in polymers is not well understood. To clarify the role of second order gradients of displacements, a model polymer is examined with spherical and Berkovich tips at probing depths between 5 and 25 μm. Applying different theories to determine the elastic modulus, it is found that with a pyramidal tip, the elastic modulus increases with decreasing indentation depth, while tests with the spherical tip yielded essentially constant values for the elastic modulus independent of indentation depth. The differences between these tips are attributed to second order displacement gradients, as they remain essentially constant with a spherical tip while they increase in magnitude with decreasing indentation depth applying a Berkovich tip.
Acknowledgments
The material of this article is based on work supported by the U.S. National Science Foundation under Grants No. 1102764 and No. 1126860.
References
[1] Lim YY, Chaudhri MM. Mech. Mater. 2006, 38, 1213–1228.10.1016/j.mechmat.2006.04.006Search in Google Scholar
[2] Charitidis C. Indust. Eng. Chem. Res. 2011, 50, 565–570.10.1021/ie100099gSearch in Google Scholar
[3] Khun NW, Cheng HKF, Li L, Liu E. J. Polym. Eng. 2014, 35, 367–376.10.1515/polyeng-2013-0241Search in Google Scholar
[4] Huang CC, Wei MK, Harmon JP, Lee S. J. Mater. Res. 2012, 27, 2746–2751.10.1557/jmr.2012.30Search in Google Scholar
[5] Schilde C, Kwade A. J. Mater. Res. 2012, 27, 672–684.10.1557/jmr.2011.440Search in Google Scholar
[6] Swadener JG, George EP, Pharr GM. J. Mech. Phys. Sol. 2002, 50, 681–694.10.1016/S0022-5096(01)00103-XSearch in Google Scholar
[7] Tymiak NI, Kramer DE, Bahr DF, Wyrobek TJ, Gerberich WW. Acta Mater. 2001, 49, 1021–1034.10.1016/S1359-6454(00)00378-5Search in Google Scholar
[8] Durst K, Göken M, Pharr GM. J. Phys. D: Appl. Phys. 2008, 41, 074005.10.1088/0022-3727/41/7/074005Search in Google Scholar
[9] Shen L, Liu T, Lv P. Polym. Test. 2005, 24, 746–749.10.1016/j.polymertesting.2005.04.004Search in Google Scholar
[10] Chong ACM, Lam DCC. J. Mater. Res. 1999, 14, 4103–4110.10.1557/JMR.1999.0554Search in Google Scholar
[11] Zhang TY, Xu WH. J. Mater. Res. 2002, 17, 1715–1720.10.1557/JMR.2002.0254Search in Google Scholar
[12] Tatiraju RVS, Han CS. J. Mech. Mater. Struct. 2010, 5, 277–288.10.2140/jomms.2010.5.277Search in Google Scholar
[13] Briscoe BJ, Fiori L, Pelillo E. J. Phys. D: Appl. Phys. 1998, 31, 2395–2405.10.1088/0022-3727/31/19/006Search in Google Scholar
[14] Fleck NA, Muller GM, Ashby MF, Hutchinson JW. Acta Metal. Mater. 1994, 42, 475–487.10.1016/0956-7151(94)90502-9Search in Google Scholar
[15] Nix WD, Gao H. J. Mech. Phys. Sol. 1998, 46, 411–425.10.1016/S0022-5096(97)00086-0Search in Google Scholar
[16] Han CS, Ma A, Roters F, Raabe D. Int. J. Plast. 2007, 23, 690–710.10.1016/j.ijplas.2006.08.003Search in Google Scholar
[17] Lee MG, Han CS. Comp. Mech. 2012, 49, 171–183.10.1007/s00466-011-0637-ySearch in Google Scholar
[18] Lam DCC, Yang F, Chong ACM, Wang J, Tong P. J. Mech. Phys. Sol. 2003, 51, 1477–1508.10.1016/S0022-5096(03)00053-XSearch in Google Scholar
[19] Wrucke A, Han CS, Majumdar P. J. Appl. Polym. Sci. 2013, 128, 258–264.10.1002/app.38161Search in Google Scholar
[20] Alisafaei F, Han CS, Sanei SHR. Polym. Test. 2013, 32, 1220–1228.10.1016/j.polymertesting.2013.07.013Search in Google Scholar
[21] Nikolov S, Han CS, Raabe D. Int. J. Sol. Struc. 2007, 44, 1582–1592. Corrigendum: Int. J. Sol. Struc. 2007, 44, 7713.10.1016/j.ijsolstr.2007.07.006Search in Google Scholar
[22] Han CS, Nikolov S. J. Mater. Res. 2007, 22, 1662–1672.10.1557/JMR.2007.0197Search in Google Scholar
[23] Garg N, Han CS. Comp. Mech. 2013, 52, 709–720.10.1007/s00466-013-0842-ySearch in Google Scholar
[24] Han CS. Mater. Sci. Eng. A 2010, 527, 619–624.10.1016/j.msea.2009.08.033Search in Google Scholar
[25] Kim S, Torkelson JM. Macromolecules 2011, 44, 4546–4553.10.1021/ma200617jSearch in Google Scholar
[26] Priestley RD, Ellison CJ, Broadbelt LJ, Torkelson JM. Science 2005, 309, 456–459.10.1126/science.1112217Search in Google Scholar PubMed
[27] Alisafaei F, Han CS, Lakhera N. Polym. Test. 2014, 40, 70–78.10.1016/j.polymertesting.2014.08.012Search in Google Scholar
[28] Johnson KL. Contact Mechanics, Cambridge University Press, Cambridge, UK, 1987.Search in Google Scholar
[29] Johnson KL, Kendall K, Roberts AD. Proc. R. Soc. A 1971, 324, 301–313.10.1098/rspa.1971.0141Search in Google Scholar
[30] Oliver WC, Pharr GM. J. Mater. Res. 1992, 7, 1564–1583.10.1557/JMR.1992.1564Search in Google Scholar
[31] Sneddon IN. Int. J. Eng. Sci. 1965, 3, 47–57.10.1016/0020-7225(65)90019-4Search in Google Scholar
[32] Derjaguin BV, Muller VM, Toporov YP. J. Coll. Interf. Sci. 1975, 53, 314–326.10.1016/0021-9797(75)90018-1Search in Google Scholar
[33] Maugis D. J. Coll. Interf. Sci. 1992, 150, 243–269.10.1016/0021-9797(92)90285-TSearch in Google Scholar
[34] Ebenstein DM. J. Mat. Res. 2011, 26, 1026–1035.10.1557/jmr.2011.42Search in Google Scholar
[35] Carrillo F, Gupta S, Balooch M, Marshall SJ, Marshall GW, Pruitt L, Puttlitz CM. J. Mat. Res. 2005, 20, 2820–2830. Erratum in J. Mat. Res. 21, 535.10.1557/JMR.2005.0354Search in Google Scholar
[36] Cao YF, Yang DH, Soboyejoy W. J. Mater. Res. 2005, 20, 2004–2011.10.1557/JMR.2005.0256Search in Google Scholar
[37] Chin P, McCullough RL, Wu WL. J. Adhesion 2005, 64, 145–160.10.1080/00218469708010536Search in Google Scholar
[38] Kröner E, Paretkar DR, McMeeting RM, Arzt E. J. Adhesion 2011, 87, 447–465.10.1080/00218464.2011.575317Search in Google Scholar
[39] Ebenstein DM, Wahl KJ. J. Coll. Interf. Sci. 2006, 298, 652–662.10.1016/j.jcis.2005.12.062Search in Google Scholar
[40] Gupta S, Carillo F, Li C, Pruitt L, Puttlitz C. Mater. Lett. 2007, 61, 448–451.10.1016/j.matlet.2006.04.078Search in Google Scholar
[41] Muller VM, Yushchenko VS, Derjaguin BV. J. Coll. Interf. Sci. 1980, 77, 91–101.10.1016/0021-9797(80)90419-1Search in Google Scholar
[42] Kaufman JD, Klapperich CM. J. Mech. Beh. Biomed. Mater. 2009, 2, 312–317.10.1016/j.jmbbm.2008.08.004Search in Google Scholar
[43] Chin P. The characterization of polymer-solid adhesion. Ph.D. dissertation, University of Delaware, Newark, Delaware, 1996.Search in Google Scholar
[44] Chin P, McCullough RL, Wu WL. J. Adhesion 1997, 64, 145–160.10.1080/00218469708010536Search in Google Scholar
[45] Vaenkatesan V, Li Z, Vellinga WP, de Jeu WH. Polymer 2006, 47, 8317–8325.10.1016/j.polymer.2006.09.037Search in Google Scholar
[46] ISO14577-1 Metallic materials – Instrumented indentation test for hardness and materials parameters – Part 1: test method. International Organization for Standardization, 2002, Geneva, Switzerland.Search in Google Scholar
©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Review
- Development of biomaterial surfaces with and without microbial nanosegments
- Original articles
- Performance and field implementation of a new fracturing fluid consisting of hydrophobically associating polyacrylamide and anionic surfactant
- Enhancing electrical and tribological properties of poly(methyl methacrylate) matrix nanocomposite films by co-incorporation of multiwalled carbon nanotubes and silicon dioxide microparticles
- The effect of two commercial melt strength enhancer additives on the thermal, rheological and morphological properties of polylactide
- Preparation and characterization of reactive liquid rubbers toughened epoxy-clay hybrid nanocomposites
- Catalytic growth of multi-walled carbon nanotubes using NiFe2O4 nanoparticles and incorporation into epoxy matrix for enhanced mechanical properties
- Enhanced carbon dioxide separation by polyethersulfone (PES) mixed matrix membranes deposited with clay
- Excellent durability of epoxy modified mortars in corrosive environments
- Engineering of silver nanoparticle fabricated poly (N-isopropylacrylamide-co-acrylic acid) microgels for rapid catalytic reduction of nitrobenzene
- High efficiency fabrication of ultrahigh molecular weight polyethylene submicron filaments/sheets by flash-spinning
- On the origin of indentation size effects and depth dependent mechanical properties of elastic polymers
Articles in the same Issue
- Frontmatter
- Review
- Development of biomaterial surfaces with and without microbial nanosegments
- Original articles
- Performance and field implementation of a new fracturing fluid consisting of hydrophobically associating polyacrylamide and anionic surfactant
- Enhancing electrical and tribological properties of poly(methyl methacrylate) matrix nanocomposite films by co-incorporation of multiwalled carbon nanotubes and silicon dioxide microparticles
- The effect of two commercial melt strength enhancer additives on the thermal, rheological and morphological properties of polylactide
- Preparation and characterization of reactive liquid rubbers toughened epoxy-clay hybrid nanocomposites
- Catalytic growth of multi-walled carbon nanotubes using NiFe2O4 nanoparticles and incorporation into epoxy matrix for enhanced mechanical properties
- Enhanced carbon dioxide separation by polyethersulfone (PES) mixed matrix membranes deposited with clay
- Excellent durability of epoxy modified mortars in corrosive environments
- Engineering of silver nanoparticle fabricated poly (N-isopropylacrylamide-co-acrylic acid) microgels for rapid catalytic reduction of nitrobenzene
- High efficiency fabrication of ultrahigh molecular weight polyethylene submicron filaments/sheets by flash-spinning
- On the origin of indentation size effects and depth dependent mechanical properties of elastic polymers
