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On the transverse indentation moduli of high-performance KM2 single fibers using a curved area function

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Abstract

Nanoindentation of single microscale fibers is a challenging task due to the dimensional similarity of the probing instruments to the single-fiber cross sections. Algorithms customarily used in nanoindentation equipment assume that the indentation occurs in flat surfaces, thus simplifying the local geometry and approximating material properties in curved specimens. A modified Curved Area Function (mCAF) is developed using finite element analysis and tested using nanoindentation measurements of high-performance single microfibers. The mCAF accounts for the dimensions and curvature in the transverse direction of the cylindrical microfiber in conjunction with the contact depth and the impression of the indented area. The transverse direction indentation modulus of a \(12\,\upmu \hbox {m}\) of \(\hbox {Kevlar}^{\textregistered }\) KM2 fiber was estimated as \(7.76\, \pm \,0.22\) GPa. The computational results were corroborated with experimental measurements performed on KM2 single fibers and agreed with literature findings that assumed minor differences in testing equipment, area analysis, and projected surface area. Two geometry-related coefficients \( C_{0}\) and \(C_{1}\) were determined that facilitate simulation of fiber nanoindentations with diameters of \(d = 7, 15, 30, 40,\) and \(50\,\upmu \hbox {m}\) with indentation depths up to, and including, \(2\,\upmu \hbox {m}\). The mCAF provided a narrow measurement error of \(\pm \,0.22\) GPa (2.8%) when compared to published studies using the semi-infinite plane approximation, reinforcing the suitability of the developed model.

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References

  1. Bencomo-Cisneros, J.A., Tejeda-Ochoa, A., García-Estrada, J.A., Herrera-Ramírez, C.A., Hurtado-Macías, A., Martínez-Sánchez, R., Herrera-Ramírez, J.M.: Characterization of Kevlar-29 fibers by tensile tests and nanoindentation. J. Alloys Compd. 536, S456–S459 (2012)

    Article  Google Scholar 

  2. Bunsell, A.R.: The tensile and fatigue behaviour of Kevlar-49 (PRD-49) fibre. J. Mater. Sci. 10, 1300–1308 (1975)

    Article  Google Scholar 

  3. Hadley, D.W., Ward, I.M., Ward, J.: The transverse compression of anisotropic fiber monofilaments. Proc. R. Soc. A 285, 275–286 (1965)

    Google Scholar 

  4. Pinnock, P.R., Ward, I.M., Wolfe, J.M.: The compression of anisotropic fiber monofilaments II. Proc. R. Soc. A 291, 267–278 (1966)

    Google Scholar 

  5. Rector, J.H., Slaman, M., Verdoold, R., Iannuzzi, D., Beekmans, S.V.: Optimization of the batch production of silicon fiber-top MEMS devices. J. Micromech. Microeng. 27, 1–10 (2017)

    Article  Google Scholar 

  6. Swadener, J.G., George, E.P., Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681–694 (2002)

    Article  Google Scholar 

  7. Poon, B., Rittel, D., Ravichandran, G.: An analysis of nanoindentation in linearly elastic solids. Int. J. Solids Struct. 45, 6018–6033 (2008)

    Article  Google Scholar 

  8. Bhushan, B.: Depth-sensing nanoindentation measurement techniques and applications. Microsyst. Technol. 23, 1595–1649 (2017)

    Article  Google Scholar 

  9. Wierenga, P.E., Franken, A.J.J.: Ultramicroindentation apparatus for the mechanical characterization of thin films. J. Appl. Phys. 55, 4244–4247 (1984)

    Article  Google Scholar 

  10. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564–1583 (1992)

    Article  Google Scholar 

  11. Doerner, M.F., Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1(4), 601–609 (1986)

    Article  Google Scholar 

  12. Garrido Maneiro, M.A., Rodríguez, J.: Pile-up effect on nanoindentation tests with spherical-conical tips. Scr. Mater. 52, 593–598 (2005)

    Article  Google Scholar 

  13. Sargent, P.M., Page, T.F.: The possible effect of elastic recovery on the microhardness of anisotropic materials. Scr. Metall. 15, 245–250 (1981)

    Article  Google Scholar 

  14. Kalman, D.P., Merrill, R.L., Wagner, N.J., Wetzel, E.D.: Effect of particle hardness on the penetration behavior of fabrics intercalated with dry particles and concentrated particle-fluid suspensions. ACS Appl. Mater. Interfaces 1, 2602–2612 (2009)

    Article  Google Scholar 

  15. Decker, M.J., Egres, R.G., Wetzel, E.D., Wagner, N.J.: Low velocity ballistic properties of shear thickening fluid (STF)-fabric composites. In: Proceedings of 22nd International Symposium International Symposium on Ballistics, pp. 18–25 (2005)

  16. Riekel, C., Davies, R.J.: Applications of synchrotron radiation micro-focus techniques to the study of polymer and biopolymer fibers. Curr. Opin. Colloid Interface Sci. 9, 396–403 (2005)

    Article  Google Scholar 

  17. Li, S.F.Y., McGhie, A.J., Tang, S.L.: Comparative study of the internal structures of Kevlar and spider silk by atomic force microscopy. J. Vac. Sci. Technol. A 12, 1891–1894 (1994)

    Article  Google Scholar 

  18. Gindl, W., Schöberl, T.: The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements. Compos. Part A 35, 1345–1349 (2004)

    Article  Google Scholar 

  19. Vlassak, J.J., Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, 1223–1245 (1994)

    Article  Google Scholar 

  20. Pharr, G.M., Herbert, E.G., Gao, Y.: The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40, 271–292 (2010)

    Article  Google Scholar 

  21. Ghanbari, S., Bahr, D.F.: An energy-based nanoindentation method to assess localized residual stresses and mechanical properties on shot-peened materials. J. Mater. Res. 34(7), 1121–1129 (2019)

    Article  Google Scholar 

  22. Cheng, M., Chen, W., Weerasooriya, T.: Mechanical Properties of Kevlar®KM2 Single Fiber. J. Eng. Mater. Technol. 127, 197–203 (2005)

    Article  Google Scholar 

  23. Deteresa, S.J., Allen, S.R., Farris, R.J., Porter, R.S.: Compressive and torsional behaviour of Kevlar 49 fibre. J. Mater. Sci. 19, 57–72 (1984)

    Article  Google Scholar 

  24. McAllister, Q.P., Gillespie Jr., J.W., VanLandingham, M.R.: Evaluation of the three-dimensional properties of Kevlar across length scales. J. Mater. Res. 27(14), 1824–1837 (2012)

    Article  Google Scholar 

  25. McAllister, Q.P., Gillespie Jr., J.W., VanLandingham, M.R.: Nonlinear indentation of fibers. J. Mater. Res. 27(1), 197–213 (2012)

    Article  Google Scholar 

  26. Cole, D.P., Strawhecker, K.E.: An improved instrumented indentation technique for single microfibers. J. Mater. Res. 29(9), 1104–1112 (2014)

    Article  Google Scholar 

  27. Kawabata, S.: Measurement of the transverse mechanical properties of high-performance fibres. J. Text. Inst. 81, 432–447 (1990)

    Article  Google Scholar 

  28. Leal, A.A., Deitzel, J.M., Gillespie Jr., J.W.: Compressive strength analysis for high performance fibers with different modulus in tension and compression. J. Compos. Mater. 43, 661–674 (2009)

    Article  Google Scholar 

  29. Singletary, J., Davis, H., Ramasubramanian, M.K., Knoff, W.: The transverse compression of PPTA fibers Part I Single fiber transverse compression testing. J. Mater. Sci. 35, 573–581 (2000)

    Article  Google Scholar 

  30. Singletary, J., Davis, H., Song, Y., Ramasubramanian, M.K., Knoff, W.: The transverse compression of PPTA fibers Part II Fiber transverse structure. J. Mater. Sci. 35, 583–592 (2000)

    Article  Google Scholar 

  31. Raju, H., Pelegri, A.A.: Experimental investigation of transverse mechanical properties of high-performance Kevlar KM2 single fiber. In: ASME 2017 International Mechanical Engineering Congress and Exposition V014T11A045 (2017)

  32. Li, X., Bhushan, B.: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48, 11–36 (2002)

    Article  Google Scholar 

  33. Pharr, G.M., Strader, J.H., Oliver, W.C.: Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res. 24, 653–666 (2009)

    Article  Google Scholar 

  34. Hanson, M.T.: The elastic field for conical indentation including sliding friction for transverse isotropy. J. Appl. Mech. 59, S123–S130 (1992)

    Article  Google Scholar 

  35. Hanson, M.T.: The elastic field for spherical Hertzian contact including sliding friction for transverse isotropy. J. Tribol. 114, 606–611 (1992)

    Article  Google Scholar 

  36. Chicot, D., Yetna N’Jock, M., Puchi-Cabrera, E.S., Iost, A., Staia, M.H., Louis, G., Bouscarrat, G., Aumaitre, R.: A contact area function for Berkovich nanoindentation: application to hardness determination of a TiHfCN thin film. Thin Solid Films 558, 259–266 (2014)

    Article  Google Scholar 

  37. Sakharova, N.A., Fernandes, J.V., Antunes, J.M., Oliveira, M.C.: Comparison between Berkovich, Vickers and conical indentation tests: a three-dimensional numerical simulation study. Int. J. Solids Struct. 46, 1095–1104 (2009)

    Article  Google Scholar 

  38. Briscoe, B.J., Fiori, L., Pelillo, E.: Nano-indentation of polymeric surfaces. J. Phys. D Appl. Phys. 31, 2395–2405 (1998)

    Article  Google Scholar 

  39. Wang, J.S., Zheng, X.J., Zheng, H., Zhu, Z., Song, S.T.: Evaluation of the substrate effect on indentation behavior of film/substrate system. Appl. Surf. Sci. 256, 5998–6002 (2010)

    Article  Google Scholar 

  40. Jiang, W.G., Su, J.J., Feng, X.Q.: Effect of surface roughness on nanoindentation test of thin films. Eng. Fract. Mech. 75, 4965–4972 (2008)

    Article  Google Scholar 

  41. Nano Test Vantage User Manual, Indenter Area Function, Micro Materials Ltd Excellence in Nano-mechanics

  42. Sahin, K., Clawson, J.K., Singletary, J., Horner, S., Zheng, J., Pelegri, A.A., Chasiotis, I.: Limiting role of crystalline domain orientation on the modulus and strength of aramid fibers. Polymer 140, 96–106 (2018)

    Article  Google Scholar 

  43. Swadener, J.G., Pharr, G.M.: Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution. Philos. Mag. A 81, 447–466 (2001)

    Article  Google Scholar 

Download references

Acknowledgements

The authors kindly acknowledge the financial support of PEO Soldier of the United States Army Contract W91CRB-12-P-0047 P00003 to perform this research.

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  1. Mechanical and Aerospace Engineering Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, NJ, 08854-8058, USA

    Prashanth Turla, Hinal Patel & Assimina A. Pelegri

  2. Trumpf Inc., 2601 US-130, Cranbury, NJ, 08512, USA

    Prashanth Turla

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  1. Prashanth Turla
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Correspondence to Assimina A. Pelegri.

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Turla, P., Patel, H. & Pelegri, A.A. On the transverse indentation moduli of high-performance KM2 single fibers using a curved area function. Acta Mech 231, 2113–2124 (2020). https://doi.org/10.1007/s00707-020-02645-3

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