Experimental Mechanics

, Volume 57, Issue 7, pp 1027–1035 | Cite as

Local Mechanical Behavior of Steel Exposed to Nonlinear Harmonic Oscillation

  • D. P. ColeEmail author
  • E. M. Habtour
  • T. Sano
  • S. J. Fudger
  • S. M. Grendahl
  • A. Dasgupta


The local mechanical behavior of fatigued steel specimens was probed using nanoindentation. High-carbon steel cantilevers were exposed to nonlinear harmonic oscillation. The indentation modulus on the beam surface and plastic work during indentation decreased as a function of cycles, which was attributed to grain fragmentation and reorientation as well as the continuous reduction in inherent energy dissipation capacity of the material. X-ray diffraction, electron backscatter diffraction, and atomic force microscopy were used to characterize this microstructural evolution during early stages of the beam fatigue life, which altered 1) the local mechanical properties and 2) the global structural dynamic response. The results provide insight into fatigue damage precursors and provides a framework for connecting materials evolution with nonlinear structural dynamics.


Nanoindentation Fatigue Nondestructive testing Damage precursor Nonlinear vibration 



Authors wish to thank Chris Kube and Volker Weiss for useful discussions during the course of this work.


  1. 1.
    Farrar C, Worden K (2007) An introduction to structural health monitoring. Phil Trans R Soc A 365:303–315Google Scholar
  2. 2.
    Pohl J, Willberg C, Gabbert U, Mook G (2012) Experimental and theoretical analysis of lamb wave generation by piezoceramic actuators for structural health monitoring. Exp Mech 52:429–438Google Scholar
  3. 3.
    Kersemans M, Martens A, Lammens N, Van Den Abeele K, Degrieck J, Zastavnik F, Pyl L, Sol H, Van Paepegem W (2014) Identification of the elastic properties of isotropic and orthotropic thin-plate materials with the pulsed ultrasonic polar scan. Exp Mech 54:1121–1132Google Scholar
  4. 4.
    Kube C, Turner J (2015) Acoustic nonlinearity parameters for transversely isotropic polycrystalline materials. J Acoust Soc Am 137:3272–3280Google Scholar
  5. 5.
    Habtour E, Cole DP, Riddick JC, Weiss V, Robeson M, Sridharan R, Dasgupta A (2016) Struct Control Health Monit. doi: Scholar
  6. 6.
    Habtour E, Cole DP, Stanton SC, Sridharan R, Dasgupta A (2016) Damage precursor detection for structures subjected to rotational base vibration. Intl J Nonlinear Mech 82:49–58Google Scholar
  7. 7.
    Pang C, Yu M, Zhang XM, Gupta AK, Bryden KM (2012) Multifunctional optical MEMS sensor platform with heterogeneous fiber optic Fabry-Pérot sensors for wireless sensor networks. Sensor Actuat A-Phys 188:471–480Google Scholar
  8. 8.
    Sangid MD (2013) The physics of fatigue crack initiation. Int J Fatigue 57:58–72Google Scholar
  9. 9.
    Shih CC, Ho NJ, Huang HL (2010) The effects of grain boundary on dislocation development for cyclically deformed IF steel. Mater Sci Eng A 527:7247–7251Google Scholar
  10. 10.
    Basinksi ZS, Basinksi SJ (1992) Fundamental aspects of low-amplitude cyclic deformation in face-centered cubic crystals. Prog Mater Sci 36:89–148Google Scholar
  11. 11.
    Alankar A, Field DP, Raabe D (2014) Plastic anisotropy of electro-deposited pure α-iron with sharp crystallographic <111>// texture innormal direction: Analysis by an explicitly dislocation-based crystal plasticity model. Int J Plasticity 52:18–32Google Scholar
  12. 12.
    Mughrabi H, Herz K, Stark X (1976) The effect of strain-rate on the cyclic deformation properties of α-iron single crystals. Acta Metall Mater 24:659–668Google Scholar
  13. 13.
    Mughrabi H, Herz K, Stark X (1981) Cyclic deformation and fatigue behavior of α-iron mono- and polycrystals. Int J Fracture 17:193–220Google Scholar
  14. 14.
    Pai PF, Nayfeh AH (1990) Non-linear non-planar oscillations of a cantilever beam under lateral base excitations. Intl J Nonlinear Mech 25:455–474Google Scholar
  15. 15.
    Crespo Da Silva MRM, Zaretzky CL (1994) Nonlinear flexural-flexural-torsional interactions in beams including the effect of torsional dynamics. I: Primary resonance. Nonlinear Dyn 5:3–23Google Scholar
  16. 16.
    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacementsensing indentation experiments. J Mater Res 7(6):1564–1583Google Scholar
  17. 17.
    Xu ZH, Li X (2005) Influence of equi-biaxial residual stress on unloading behaviour of nanoindentation. Acta Mater 53:1913–1919Google Scholar
  18. 18.
    Lee YH, Kwon D (2003) Measurement of residual-stress effect by nanoindentation on elastically strained (100) W. Scripta Mater 49:459–465Google Scholar
  19. 19.
    Odegard GM, Gates TS, Herring HM (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45:130–136Google Scholar
  20. 20.
    Huang G, Lu H (2007) Measurements of two independent viscoelastic functions by nanoindentation. Exp Mech 47:87–98Google Scholar
  21. 21.
    Cole DP, Bruck HA, Roytburd AL (2009) Nanomechanical characterisation of graded NiTi films fabricated through diffusion modification. Strain 45:232–237Google Scholar
  22. 22.
    Cole DP, Strawhecker KE (2014) An improved instrumented indentation technique for single microfibers. J Mater Res 29:1104–1112Google Scholar
  23. 23.
    Jakes JE, Frihart CR, Beecher JF, Moon RJ, Stone DS (2008) Experimental method to account for structural compliance in nanoindentation measurements. J Mater Res 23(4):1113–1127Google Scholar
  24. 24.
    Cole DP, Riddick JC, Jaim HMI, Strawhecker KE, Zander NE (2016) Interfacial mechanical behavior of 3D printed ABS. J Appl Polym Sci 133:43671Google Scholar
  25. 25.
    Giannakopoulos AE, Suresh S (1999) Determination of elastoplastic properties by instrumented sharp indentation. Scripta Mater 40:1191–1198Google Scholar
  26. 26.
    Ye D, Xu H, Feng X, Xu Y, Xiao L (2016) Depth-sensing indentation-based studies of surface mechanical behavior and fatigue damageevolution of an austenitic stainless steel subjected to cyclic straining. Mater Sci Eng A 650:38–51Google Scholar
  27. 27.
    Shigley JE, Mischke CR (2001) Mechanical engineering design. McGraw-Hill, BostonGoogle Scholar
  28. 28.
    Jang J (2009) Estimation of residual stress by instrumented indentation: A review. J Ceram Process Res 10:391–400Google Scholar
  29. 29.
    Adams JJ, Agosta DS, Leisure RG, Ledbetter H (2006) Elastic constants of monocrystal iron from 3 to 500 K. J Appl Phys 100:113530-1–113530-7Google Scholar
  30. 30.
    Johnson KL (1970) The correlation of indentation experiments. J Mech Phys Solids 18:115–126Google Scholar
  31. 31.
    Johnson KL (1985) Contact mechanics. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  32. 32.
    Kumar V, Miller JK, Rhoads JF (2011) Nonlinear parametric amplification and attenuation in a base-excited cantilever beam. J Sound Vib 330:5401–5409Google Scholar
  33. 33.
    Mura T (1987) Micromechanics of defects in solids. Martinus Nijhoff Publishers, DordrechtCrossRefzbMATHGoogle Scholar
  34. 34.
    Allix O, Hild F (2002) Continuum damage mechanics of materials and structures. Elsevier, AmsterdamCrossRefGoogle Scholar
  35. 35.
    Lifshitz R, Kenig E, Cross MC (2012) Fluctuating nonlinear oscillators. Oxford Univ Press, OxfordGoogle Scholar
  36. 36.
    Villanueva LG, Karabalin RB, Matheny MH, Chi D, Sader JE, Roukes ML (2013) Nonlinearity in nanomechanical cantilevers. Phys Rev B 87:024304Google Scholar
  37. 37.
    Zavodney LD, Nayfeh AH (1989) The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: Theory and experiment. Intl J Nonlinear Mech 24(2):105–125Google Scholar
  38. 38.
    Yu S, He S, Li W (2010) Theoretical and experimental studies of beam bimorph piezoelectric power harvesters. J Mech Mater Struct 5(3):427–445Google Scholar

Copyright information

© Society for Experimental Mechanics (outside the USA) 2017

Authors and Affiliations

  • D. P. Cole
    • 1
    Email author
  • E. M. Habtour
    • 1
  • T. Sano
    • 2
  • S. J. Fudger
    • 2
  • S. M. Grendahl
    • 2
  • A. Dasgupta
    • 3
  1. 1.U.S. Army Research Laboratory - Vehicle Technology DirectorateAberdeen Proving GroundUSA
  2. 2.U.S. Army Research Laboratory - Weapons and Materials Research DirectorateAberdeen Proving GroundUSA
  3. 3.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA

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