Evaluation of the three-dimensional properties of Kevlar across length scales


In this study, nanoindentation was utilized to measure the local, three-dimensional properties of Kevlar 49 and Kevlar KM2 on the length scales of the fiber microstructure. First, atomic force microscopy-based methods were used to explore the extent of property changes with respect to radial position in the fibers’ axial and hoop planes. From these measurements, no significant change in response was found for Kevlar 49 fibers, consistent with transverse isotropy. However, a reduced stiffness “shell” region (up to;300–350 nm thick) was observed for KM2 fibers. Instrumented indentation was then used to evaluate fiber response with respect to orientation and contact size and establish a critical contact size above which the response is independent of indenter size (i.e., “homogeneous” behavior). A previously proposed analytical method for indentation of a transversely isotropic material was used to estimate the local material properties of the Kevlar fibers from the measured homogeneous response.

This is a preview of subscription content, access via your institution.

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7
FIG. 8
FIG. 9
FIG. 10
FIG. 11
FIG. 12
FIG. 13
FIG. 14
FIG. 15
FIG. 16
FIG. 17


  1. 1.

    D.P. Kalman, R.L. Merrill, N.J. Wagner, and E.D. Wetzel: 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 (2009).

    CAS  Article  Google Scholar 

  2. 2.

    M.J. Decker, R.G. Egres, E.D. Wetzel, and N.J. Wagner: Low-velocity ballistic properties of shear thickening fluid (STF)-fabric composites, In Proceedings of the 22nd International Symposium on Ballistics: Terminal Ballistics, W. Flis and B. Scott, eds, Vancouver, Canada, 2005).

    Google Scholar 

  3. 3.

    M.J. Decker, C.J Halbach, C.H. Nam, N.J. Wagner, and E.D. Wetzel: Stab resistance of shear thickening fluid (STF)-treated fabrics. Compos. Sci. Technol. 367, 565 (2007).

    Article  CAS  Google Scholar 

  4. 4.

    C. Riekel, M.C. Garcia Gutierrez, A. Gourrier, and S. Roth: Recent synchrotron radiation microdiffraction experiments on polymer and biopolymer fibers. Anal. Bioanal. Chem. 275, 594 (2003).

    Article  CAS  Google Scholar 

  5. 5.

    C. Riekel and R.J. Davies: Applications of synchrotron radiationmicrofocus techniques to the study of polymer and biopolymer fibers. Curr. Opin. Colloid Interface Sci. 9, 396 (2005).

    CAS  Article  Google Scholar 

  6. 6.

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

    CAS  Article  Google Scholar 

  7. 7.

    M. Panar, P. Avakian, R.C. Blume, K.H. Gardner, T.D. Gierke, and H.H. Yang: Morphology of poly(p-phenylene terephthalamide) fibers. J. Polym. Sci. Part B: Polym. Phys. 21, 1955 (1983).

    CAS  Google Scholar 

  8. 8.

    Y. Rao, A.J. Waddon, and R.J. Farris: The evolution of structure and properties in poly(p-phenylene terephthalamide) fibers. Polymer 42, 5925 (2001).

    CAS  Article  Google Scholar 

  9. 9.

    D. Snetivy, G.J. Vancso, and G.C. Rutledge: Atomic force microscopy of polymer crystals. 6. Molecular imaging and study of polymorphism in poly(p-phenyleneterephthalamide) fibers. Macromolecules 25, 7037 (1992).

    CAS  Article  Google Scholar 

  10. 10.

    K.G. Lee, R. Barton Jr, and J.M. Schultz: Structure and property development in poly(p-phenylene terephthalamide) during heat treatment under tension. J. Polym. Sci., Part B: Polym. Phys. 33, 1 (1995).

    Article  Google Scholar 

  11. 11.

    M. Cheng, W.N. Chen, and T. Weerasooriya: Mechanical properties of Kevlar® KM2 single fiber. J. Eng. Mater. Technol. 127, 197 (2005).

    CAS  Article  Google Scholar 

  12. 12.

    S.J. Deteresa, S.R. Allen, R.J. Farris, and R.S. Porter: Compressive and torsional behavior of Kevlar 49 fiber. J. Mater. Sci. 19, 57 (1984).

    CAS  Article  Google Scholar 

  13. 13.

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

    CAS  Article  Google Scholar 

  14. 14.

    A.A Leal, J.M. Deitzel, and J.W. Gillespie Jr: Assessment of compressive properties of high-performance organic fibers. Compos. Sci. Technol. 67, 2786 (2007).

    CAS  Article  Google Scholar 

  15. 15.

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

    CAS  Article  Google Scholar 

  16. 16.

    J. Singletary, H. Davis, M.K. Ramasubramanian, W. Knoff, and M. Toney: The transverse compression of PPTA fibers part II: Fiber transverse structure. J. Mater. Sci. 35, 583 (2000).

    CAS  Article  Google Scholar 

  17. 17.

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

    CAS  Article  Google Scholar 

  18. 18.

    C.L. Tsai and I.M. Daniel: Determination of shear modulus of single fibers. Exp. Mech. 39, 284 (1999).

    Article  Google Scholar 

  19. 19.

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

    CAS  Article  Google Scholar 

  20. 20.

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

    CAS  Article  Google Scholar 

  21. 21.

    J.E. Jakes and D.S. Stone: The edge effect in nanoindentation. Philos. Mag. 91, 1387 (2011).

    CAS  Article  Google Scholar 

  22. 22.

    J.E. Jakes, C.R. Frihart, J.F. Beecher, R.J. Moon, and D.S. Stone: Experimental method to account for structural compliance in nanoindentation measurements. J. Mater. Res. 23, 1113 (2008).

    CAS  Article  Google Scholar 

  23. 23.

    D.M. Ebenstein and K.J. Wahl: Anisotropic nanomechanical properties of Nephila clavipes dragline silk. J. Mater. Res. 21, 2035 (2006).

    CAS  Article  Google Scholar 

  24. 24.

    W. Gindl and T. Schoberl: The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements. Composites Part A 35, 1345 (2004).

    Article  Google Scholar 

  25. 25.

    W. Gindl, H.S. Gupta, T. Schoberl, H.C. Lichtenegger, and P. Fratzl: Mechanical properties of spruce wood cell walls by nanoindentation. Appl. Phys. A 79, 2069 (2004).

    CAS  Article  Google Scholar 

  26. 26.

    A. Delafargue and F.J. Ulm: Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters. Int. J. Solids. Struct. 41, 7351 (2004).

    Article  Google Scholar 

  27. 27.

    H.A. Elliot: Axially symmetric stress distributions in aeolotropic hexagonal crystals. The problem of the plane and related problems. Math. Proc. Cambridge Philos. Soc. 45, 621 (1949).

    Article  Google Scholar 

  28. 28.

    H.A. Elliot: Three dimensional stress distributions in hexagonal aeolotropic crystals. Math. Proc. Cambridge Philos. Soc. 44, 522 (1948).

    Article  Google Scholar 

  29. 29.

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

    Article  Google Scholar 

  30. 30.

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

    Article  Google Scholar 

  31. 31.

    J.J. Vlassak and W.D. Nix: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 8, 1223 (1994).

    Article  Google Scholar 

  32. 32.

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

    CAS  Article  Google Scholar 

  33. 33.

    J.J. Vlassak, M. Ciavarella, J.R. Barber, and X. Wang: The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, 1701 (2003).

    Article  Google Scholar 

  34. 34.

    J.G. Swadener, J.Y. Rho, and G.M. Pharr: Effects of anisotropy on elastic modulus measured by nanoindentation in human tibial cortical bone. J. Biomed. Mater. Res. 57, 108 (2001).

    CAS  Article  Google Scholar 

  35. 35.

    D.L. Languerand, H. Zhang, N.S. Murthy, K.T. Ramesh, and F. Sansoz: Inelastic behavior and fracture of high-modulus polymeric fiber bundles at high strain-rates. Mater. Sci. Eng. A 500, 216 (2009).

    Article  CAS  Google Scholar 

  36. 36.

    J.F. Graham, C. McCague, O.L. Warren, and P.R. Norton: Spatially resolved nanomechanical properties of Kevlar ® fibers. Polymer 41, 4761 (2000).

    CAS  Article  Google Scholar 

  37. 37.

    U. Rabe, K. Janser, and W. Arnold: Vibrations of free and surface coupled atomic force microscope cantilever: Theory and experiment. Rev. Sci. Instrum. 61, 3281 (1996).

    Article  Google Scholar 

  38. 38.

    G. Stan and R.F. Cook: Mapping the elastic properties of granular Au films by contact resonance atomic force microscopy. Nanotechnology 19, 235701 (2008).

    CAS  Article  Google Scholar 

  39. 39.

    G. Stan, S.W. King, and R.F. Cook: Elastic modulus of low-k dielectric thin films measured by load-dependent contact-resonance atomic force microscopy. J. Mater. Res. 24, 2960 (2009).

    CAS  Article  Google Scholar 

  40. 40.

    G. Stan, C.V. Ciobanu, P.M. Parthangal, and R.F. Cook: Diameter-dependent radial and tangential elastic moduli of ZnO nanowires. Nano Lett. 7, 3691 (2007).

    CAS  Article  Google Scholar 

  41. 41.

    G. Stan, C.V. Ciobanu, T.P. Thayer, G.T. Wang, J.R. Creighton, K.P. Purushotham, L.A. Bendersky, and R.F. Cook: Elastic moduli of faceted aluminum nitride nanotubes measured by contact resonance atomic force microscopy. Nanotechnology. 20, 035706 (2009).

    CAS  Article  Google Scholar 

  42. 42.

    G. Stan, S. Krylyuk, A.V. Davydov, and R.F. Cook: Compressive stress effect on the radial elastic modulus of oxidized Si nanowires. Nano Lett. 10, 2031 (2010).

    CAS  Article  Google Scholar 

  43. 43.

    M.R. VanLandingham, S.H. McKnight, G.R. Palmese, R.F. Eduljee, J.W. Gillespie Jr, and R.L. McCullough: Relating elastic modulus to indentation response using atomic force microscopy. J. Mater. Sci. Lett. 16, 117 (1997).

    CAS  Article  Google Scholar 

  44. 44.

    M.R. VanLandingham, R.R. Dagastine, R.F. Eduljee, R.L. McCullough, and J.W. Gillespie Jr: Characterization of nanoscale property variations in polymer composite systems: 1. Experimental results. Composites Part A 30, 75 (1999).

    Article  Google Scholar 

  45. 45.

    M.R. VanLandingham, S.H. McKnight, G.R. Palmese, J.R. Elings, X. Huang, T.A. Bogetti, R.F. Eduljee, and J.W. Gillespie: Nanoscale indentation of polymer systems using the atomic force microscope. J. Adhes. 64, 31 (1997).

    CAS  Article  Google Scholar 

  46. 46.

    M.R. VanLandingham, J.S. Villarrubia, W.F. Guthrie, and G.F. Meyers: Nanoindentation of polymers: An overview. Macromol. Symp. 167, 15 (2001).

    CAS  Article  Google Scholar 

  47. 47.

    E.P.S. Tan and C.T. Lim: Nanoindentation study of nanofibers. Appl. Phys. Lett. 87, 123106 (2005).

    Article  CAS  Google Scholar 

  48. 48.

    J. Domke and M. Radmacher: Measuring the elastic properties of thin polymer films with the atomic force microscope. Langmuir 14, 3320 (1998).

    CAS  Article  Google Scholar 

  49. 49.

    X. Li, H. Gao, C.J. Murphy, and K.K. Caswell: Nanoindentation of silver nanowires. Nano Lett. 3, 1495 (2003).

    CAS  Article  Google Scholar 

  50. 50.

    M.S. Bischel, M.R. VanLandingham, R.F. Eduljee, J.W. Gillespie Jr, and J.M. Schultz: On the use of nanoscale indentation with the AFM in the identification of phases in blends in linear low density polyethylene and high-density polyethylene. J. Mater. Sci. 35, 221 (2000).

    CAS  Article  Google Scholar 

  51. 51.

    K. Tai, D. Ming, S. Suresh, A. Palazoglu, and C. Ortiz: Nanoscale heterogeneity promotes energy dissipation in bone. Nat. Mater. 6, 454 (2007).

    CAS  Article  Google Scholar 

  52. 52.

    XP User’s Manual. V.16. (Agilent Technologies, Santa Clara, CA, 2002).

  53. 53.

    M.C.G. Jones, E. Lara-Curzio, A. Kopper, and D.C. Martin: The lateral deformation of cross-linkable PPXTA. J. Mater. Sci. 32, 2855 (1997).

    CAS  Article  Google Scholar 

Download references


QM and JWG gratefully acknowledge sponsorship by the Army Research Laboratory under cooperative agreement W911NF-06-2-0011. The views and conclusions contained in this paper should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes not withstanding any copyright notation herein.

The authors wish to thank Dr. Gheorghe Stan for his efforts in obtaining the CR-AFM results. The authors would also like to thank Dr. Kenneth Strawhecker for useful discussions in data interpretation and Dr. Joseph Deitzel for help in formulating a proper mounting system.

Author information



Corresponding author

Correspondence to John W. Gillespie Jr.

Appendix Definition of Elastic Stiffness Constants, Cij

Appendix Definition of Elastic Stiffness Constants, Cij

Equations (A1)(A6) define the shorthand used for the elastic constants in Eqs. (4)(6):

$${C_{aa}} = {C_{aaaa}},$$
$${C_{rr}} = {C_{rrrr}},$$
$${C_{ra}} = {C_{rraa}} = {C_{aarr,}}$$
$${C_{r{{\theta }}}} = {C_{rr{{\theta \theta }}}},$$
$${C_{ar}} = {\left( {{C_{rr}}{C_{aa}}} \right)^{1/2}},$$

Equations (A7)(A12) define the elastic constants, Cij, in terms of the material properties:

$${C_{aa}} - \frac{{{E_{aa}}\left( {1 - v_{{\text{r}\theta }}^2} \right.}}{\Delta }$$
$${C_{rr}} = \frac{{{E_{rr}}\left( {1 - \frac{{{E_{rr}}}}{{{E_{aa}}}}v_{ar}^2} \right)}}{\Delta },$$
$${C_{ra}} = \frac{{\left( {{v_{ar}} + {v_{ar}}{v_{r{{\theta }}}}} \right){E_{rr}}}}{\Delta },$$
$${C_{r{{\theta }}}} = \frac{{\left( {{v_{r{{\theta }}}} + \frac{{{E_{rr}}}}{{{E_{aa}}}}v_{ar}^2} \right){E_{rr}}}}{\Delta },$$
$${C_{rara}} = {G_{ar}},$$
$$\Delta = 1 - 2\frac{{{E_{rr}}}}{{{E_{rr}}}}v_{ar}^2 - v_{r{{\theta }}}^2 - 2\frac{{{E_{rr}}}}{{{E_{aa}}}}v_{ar}^2{v_{r{{\theta }}}},$$

Rights and permissions

Reprints and Permissions

About this article

Cite this article

McAllister, Q.P., Gillespie, J.W. & VanLandingham, M.R. Evaluation of the three-dimensional properties of Kevlar across length scales. Journal of Materials Research 27, 1824–1837 (2012). https://doi.org/10.1557/jmr.2012.80

Download citation