Skip to main content
SpringerLink
Log in

Indentation Fatigue Mechanics

  • Reference work entry
  • First Online:
Handbook of Nonlocal Continuum Mechanics for Materials and Structures

  • 1848 Accesses

Abstract

Instrumented indentation has been widely used in the determination of mechanical properties of materials due to its fast, simple, precise, and nondestructive merits over the past few years. In this chapter, we will present an emerging indentation technique, referred to as indentation fatigue, where a fatigue load is applied on a sample via a flat punch indenter, and establish the framework of mechanics of indentation fatigue to extract fatigue properties of materials. Through extensive experimental, theoretical, and computational investigations, we demonstrate a similarity between the indentation fatigue depth propagation and the fatigue crack growth, and propose an indentation fatigue depth propagation law and indentation fatigue strength law to describe indentation fatigue-induced deformation and failure of materials, respectively. This study provides an alternative approach for determining fatigue properties, as well as for studying the fatigue mechanisms of materials, especially for materials that are not available or feasible for conventional fatigue tests.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 799.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state. Int. J. Plast. 16, 225–240 (2000)

    Article  MATH  Google Scholar 

  • D.H. Alsem, O.N. Pierron, E.A. Stach, C.L. Muhlstein, R.O. Ritchie, Mechanisms for fatigue of Micron-scale silicon structural films. Adv. Eng. Mater. 9, 15–30 (2007)

    Article  Google Scholar 

  • D.H. Alsem, C.L. Muhlstein, E.A. Stach, R.O. Ritchie, Further considerations on the high-cycle fatigue of micron-scale polycrystalline silicon. Scr. Mater. 59, 931–935 (2008)

    Article  Google Scholar 

  • S.A.S. Asif, K.J. Wahl, R.J. Colton, Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer. Rev. Sci. Instrum. 70, 2408–2413 (1999)

    Article  Google Scholar 

  • X. Baoxing, Y. Zhufeng, C. Xi, Characterization of strain rate sensitivity and activation volume using the indentation relaxation test. J. Phys. D. Appl. Phys. 43, 245401 (2010)

    Article  Google Scholar 

  • O.H. Basquin, The exponential law of endurance tests. Proc. Am. Soc. Test. Mater. 10, 625–630 (1910)

    Google Scholar 

  • J.A. Berr’ıos, D.G. Teer, E.S. Puchi-Cabrera, Fatigue properties of a 316L stainless steel coated with different TiNx deposits. Surf. Coat. Technol. 148, 179–190 (2001)

    Article  Google Scholar 

  • T. S., Bhat, Indentation Analysis of Transversely Isotropic Materials, PhD thesis, Stony Brook University, Stony Brook, 2012

    Google Scholar 

  • S. Bhowmick, J.J. Meléndez-Martínez, B.R. Lawn, Bulk silicon is susceptible to fatigue. Appl. Phys. Lett. 91, 201902 (2007)

    Article  Google Scholar 

  • L.P. Borrego, J.M. Ferreira, J.M. Pinho da Cruz, J.M. Costa, Evaluation of overload effects on fatigue crack growth and closure. Eng. Fract. Mech. 70, 1379–1397 (2003)

    Article  Google Scholar 

  • J.L. Bucaille, S. Stauss, E. Felder, J. Michler, Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater. 51, 1663–1678 (2003)

    Article  Google Scholar 

  • P. Cavaliere, Cyclic deformation of ultra-fine and nanocrystalline metals through nanoindentation: Similarities with crack propagation. Procedia Eng. 2, 213–222 (2010)

    Article  Google Scholar 

  • J.L. Chaboche, D. Nouailhas, Constitutive modeling of ratchetting effects—part I: experimental facts and properties of the classical models. J. Eng. Mater. Technol. 111, 384–392 (1989a)

    Article  Google Scholar 

  • J.L. Chaboche, D. Nouailhas, Constitutive modeling of ratchetting effects—part II: possibilities of some additional kinematic rules. J. Eng. Mater. Technol. 111, 409–416 (1989b)

    Article  Google Scholar 

  • E.P. Chan, Y. Hu, P.M. Johnson, Z. Suo, C.M. Stafford, Spherical indentation testing of poroelastic relaxations in thin hydrogel layers. Soft Matter 8, 1492–1498 (2012)

    Article  Google Scholar 

  • X. Chen, N. Ogasawara, M. Zhao, N. Chiba, On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials. J. Mech. Phys. Solids 55, 1618–1660 (2007)

    Article  MATH  Google Scholar 

  • R. Chen, Y.C. Lu, F. Yang, G.P. Tandon, G.A. Schoeppner, Impression creep of PMR-15 resin at elevated temperatures. Polym. Eng. Sci. 50, 209–213 (2010)

    Article  Google Scholar 

  • Y.T. Cheng, C.M. Cheng, Scaling approach to conical indentation in elastic-plastic solids with work hardening. J. Appl. Phys. 84, 1284–1291 (1998)

    Article  Google Scholar 

  • Y.T. Cheng, C.M. Cheng, Scaling relationships in indentation of power-law creep solids using self-similar indenters. Philos. Mag. Lett. 811, 9–16 (2001)

    Article  Google Scholar 

  • Y.T. Cheng, C.M. Cheng, Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91–149 (2004)

    Article  Google Scholar 

  • S.N.G. Chu, J.C.M. Li, Impression creep; a new creep test. J. Mater. Sci. 12, 2200–2208 (1977)

    Article  Google Scholar 

  • S.N.G. Chu, J.C.M. Li, Localized stress relaxation by impression testing. Mater. Sci. Eng. 45, 167–171 (1980a)

    Article  Google Scholar 

  • S.N.G. Chu, J.C.M. Li, Delayed retardation of overloading effects in impression fatigue. J. Eng. Mater. Technol. 102, 337–340 (1980b)

    Article  Google Scholar 

  • T. Connolley, P.E. McHugh, M. Bruzzi, A review of deformation and fatigue of metals at small size scales. Fatigue Fract. Eng. Mater. Struct. 28, 1119–1152 (2005)

    Article  Google Scholar 

  • G. Contreras, C. Fajardo, J.A. BerrõÂos, A. Pertuz, J. Chitty, H. Hintermann, E.S. Puchi, Fatigue properties of an AISI 1045 steel coated with an electroless Ni-P deposit. Thin Solid Films 355–356, 480–486 (1999)

    Article  Google Scholar 

  • J.A. D’ıaz, M. Passarelli, J.A. Berr’ıos, E.S. Puchi-Cabrera, Fatigue behavior of a 4340 steel coated with an electroless Ni-P deposit. Surf. Coat. Technol. 149, 45–56 (2002)

    Article  Google Scholar 

  • M. Dao, N. Chollacoop, K.J. VanVliet, T.A. Venkatesh, S. Suresh, Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899–3918 (2001)

    Article  Google Scholar 

  • R.H. Dauskardt, M.R. James, J.R. Porter, R.O. Ritchie, Cyclic fatigue-crack growth in SiC-whiskerreinforced alumina ceramic composite: Long and small-crack behavior. J. Am. Ceram. Soc. 75, 759–771 (1992)

    Article  Google Scholar 

  • P. Delobelle, P. Robinet, L. Bocher, Experimental study and phenomenological modelization of ratchet under uniaxial and biaxial loading on an austenitic stainless steel. Int. J. Plast. 11, 295–330 (1995)

    Article  Google Scholar 

  • J.-H. Dirks, E. Parle, D. Taylor, Fatigue of insect cuticle. J. Exp. Biol. 216, 1924–1927 (2013)

    Article  Google Scholar 

  • Y. Estrin, A. Vinogradov, Fatigue behaviour of light alloys with ultrafine grain structure produced by severe plastic deformation: an overview. Int. J. Fatigue 32, 898–907 (2010)

    Article  Google Scholar 

  • A.C. Fischer-Cripps, Nanoindentation (Spring-Verlag, New York, 2000)

    Google Scholar 

  • N.A. Fleck, R.A. Smith, Fatigue life prediction of a structural steel under service loading. Int. J. Fatigue 6, 203–210 (1984)

    Article  Google Scholar 

  • F. Guiberteau, N.P. Padture, H. Cai, B.R. Lawn, Indentation fatigue: a simple cyclic hertzian test for measuring damage accumulation in polycrystalline ceramics. Philos. Mag. A 68, 1003–1016 (1993)

    Article  Google Scholar 

  • R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials (Wiley, Oxford, 1995)

    Google Scholar 

  • R. Hill, The Mathematical Theory of Plasticity (Oxford University Press, 1998)

    Google Scholar 

  • H.-W. Höppel, H. Mughrabi, A. Vinogradov, Bulk Nanostructured Materials (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2009), pp. 481–500

    Google Scholar 

  • Y. Hu, E.P. Chan, J.J. Vlassak, Z. Suo, Poroelastic relaxation indentation of thin layers of gels. J. Appl. Phys. 110, 086103 (2011)

    Article  Google Scholar 

  • H.L. Huang, N.J. Ho, The model of crack propagation in polycrystalline copper at various propagating rates. Mater. Sci. Eng. A 279, 254–260 (2000)

    Article  Google Scholar 

  • H.L. Huang, N.J. Ho, The observation of dislocation reversal in front of crack tips of polycrystalline copper after reducing maximum load. Mater. Sci. Eng. A 345, 215–222 (2003)

    Article  Google Scholar 

  • Y. Jiang, P. Kurath, Characteristics of the Armstrong-Frederick type plasticity models. Int. J. Plast. 12, 387–415 (1996)

    Article  MATH  Google Scholar 

  • P. Jiang, T. Zhang, Y. Feng, R. Yang, N. Liang, Determination of plastic properties by instrumented spherical indentation: expanding cavity model and similarity solution approach. J. Mater. Res. 24, 1045–1053 (2009)

    Article  Google Scholar 

  • K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985)

    Google Scholar 

  • P. Kaszynski, E. Ghorbel, D. Marquis, An experimental study of ratchetting during indentation of 316L stainless steel. J. Eng. Mater. Technol. 120, 218–223 (1998)

    Article  Google Scholar 

  • R. Kumar, A. Kumar, S. Kumar, Delay effects in fatigue crack propagation. Int. J. Press. Vessel. Pip. 67, 1–5 (1996)

    Article  Google Scholar 

  • H. Lan, T.A. Venkatesh, Determination of the elastic and plastic properties of materials through instrumented indentation with reduced sensitivity. Acta Mater. 55, 2025–2041 (2007)

    Article  Google Scholar 

  • B. Lawn, R. Wilshaw, Indentation fracture: principles and applications. J. Mater. Sci. 10, 1049–1081 (1975)

    Article  Google Scholar 

  • C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)

    Article  Google Scholar 

  • J.H. Lee, T. Kim, H. Lee, A study on robust indentation techniques to evaluate elastic–plastic properties of metals. Int. J. Solids Struct. 47, 647–664 (2010)

    Article  MATH  Google Scholar 

  • J.C.M. Li, Impression creep and other localized tests. Mater. Sci. Eng. A 322, 23–42 (2002)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • J.C.M. Li, S.N.G. Chu, Impression fatigue. Scr. Metall. 13, 1021–1026 (1979)

    Article  Google Scholar 

  • W.B. Li, J.L. Henshall, R.M. Hooper, K.E. Easterling, The mechanisms of indentation creep. Acta Metall. Mater. 39, 3099–3110 (1991)

    Article  Google Scholar 

  • X. Li, H. Gao, C.J. Murphy, K.K. Caswell, Nanoindentation of silver nanowires. Nano Lett. 3, 1495–1498 (2003)

    Article  Google Scholar 

  • P. Li, Q. Liao, S. Yang, X. Bai, Y. Huang, X. Yan, Z. Zhang, S. Liu, P. Lin, Z. Kang, Y. Zhang, In situ transmission electron microscopy investigation on fatigue behavior of single ZnO wires under high-cycle strain. Nano Lett. 14, 480–485 (2014)

    Article  Google Scholar 

  • S.Y. Liu, I.W. Chen, Fatigue of yttria-stabilized zirconia - I. Fatigue damage, fracture origins and lifetime prediction. J. Am. Ceram. Soc. 74, 1197–1205 (1991)

    Article  Google Scholar 

  • S.J. Lloyd, A. Castellero, F. Giuliani, Y. Long, K.K. McLaughlin, J.M. Molina-Aldareguia, N.A. Stelmashenko, L.J. Vandeperre, W.J. Clegg, Observations of nanoindents via cross-sectional transmission electron microscopy: a survey of deformation mechanisms. Proc. R. Soc. A 461, 2521–2543 (2005)

    Article  Google Scholar 

  • J.L. Loubet, W.C. Oliver, B.N. Lucas, Measurement of the loss tangent of low-density polyethylene with a nanoindentation technique. J. Mater. Res. 15, 1195–1198 (2000)

    Article  Google Scholar 

  • J. Luo, K. Dahmen, P.K. Liaw, Y. Shi, Low-cycle fatigue of metallic glass nanowires. Acta Mater. 87, 225–232 (2015)

    Article  Google Scholar 

  • D. Mclean, Mechanical Properties of Metals (Wiley Press, New Jersey, 1965)

    Google Scholar 

  • P. Miranzo, J.S. Moya, Elastic/plastic indentation in ceramics: a fracture toughness determination method. Ceram. Int. 10, 147–152 (1984)

    Article  Google Scholar 

  • J.C. Moosbrugger, D.J. Morrison, Nonlinear kinematic hardening rule parameters – direct determination from completely reversed proportional cycling. Int. J. Plast. 13, 633–668 (1997)

    Article  MATH  Google Scholar 

  • K.A. Nibur, D.F. Bahr, Identifying slip systems around indentations in FCC metals. Scr. Mater. 49, 1055–1060 (2003)

    Article  Google Scholar 

  • J.D. Nowak, K.A. Rzepiejewska-Malyska, R.C. Major, O.L. Warren, J. Michler, In-situ nanoindentation in the SEM. Mater. Today 12(Supplement 1), 44–45 (2010)

    Article  Google Scholar 

  • N. Ohno, J. Wang, On modelling of kinematic hardening for ratcheting behaviour. Nucl. Eng. Des. 153, 205–212 (1995)

    Article  Google Scholar 

  • W.C. Oliver, G.M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20 (2004)

    Article  Google Scholar 

  • E.S. Puchi-Cabrera, F. Mat’ınez, I. Herrera, J.A. Berr’ios, S. Dixit, D. Bhat, On the fatigue behavior of an AISI 316L stainless steel coated with a PVD TiN deposit. Surf. Coat. Technol. 182, 276–286 (2004)

    Article  Google Scholar 

  • G.D. Quinn, R.C. Bradt, On the Vickers indentation fracture toughness test. J. Am. Ceram. Soc. 90, 673–680 (2007)

    Article  Google Scholar 

  • Y. Rao, R.J. Farris, Fatigue and creep of high-performance fibers: deformation mechanics and failure criteria. Int. J. Fatigue 30, 793–799 (2008)

    Article  Google Scholar 

  • R.O. Ritchie, Influence of microstructure on near-threshold fatigue crack propagation in ultra-high strength steel. Met. Sci. 11, 368–381 (1977)

    Article  Google Scholar 

  • R.O. Ritchie, Mechanisms of fatigue-crack propagation in ductile and brittle solids. Int. J. Fract. 100, 55–83 (1999)

    Article  Google Scholar 

  • K. Sadananda, A.K. Vasudevan, Fatigue crack growth mechanisms in steels. Int. J. Fatigue 25, 899–914 (2003)

    Article  Google Scholar 

  • S. Sakaguchi, N. Murayama, Y. Kodama, & F. Wakai, in Fracture Mechanics of Ceramics: Fracture Fundamentals, High-Temperature Deformation, Damage, and Design, eds. by R. C. Bradt, D. P. H. Hasselman, D. Munz, M. Sakai, V. Ya Shevchenko (Springer US, 1992), pp. 509–521

    Google Scholar 

  • I.N. Sneddon, The relationship between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47–57 (1965)

    Article  MATH  Google Scholar 

  • D.S. Stone, J.E. Jakes, J. Puthoff, A.A. Elmustafa, Analysis of indentation creep. J. Mater. Res. 25, 611–621 (2010)

    Article  Google Scholar 

  • B. Storakers, P.L. Larsson, On Brinell and Boussinesq indentation of creeping solids. J. Mech. Phys. Solids 42, 307–332 (1994)

    Article  MATH  Google Scholar 

  • S. Suresh, Fatigue of materials (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  • B. Taljat, G.M. Pharr, Development of pile-up during spherical indentation of elastic-plastic solids. Int. J. Soilds Struct. 41, 3891–3904 (2004)

    Article  MATH  Google Scholar 

  • Y. Tang, A. Yonezu, N. Ogasawara, N. Chiba, X. Chen, On radial crack and half-penny crack induced by Vickers indentation. Proc. R. Soc. A: Math. Phys. Eng. Sci. 464, 2967–2984 (2008)

    Article  Google Scholar 

  • J. Tang, J. Li, J.J. Vlassak, Z. Suo, Fatigue fracture of hydrogels. Extreme Mech. Lett. 10, 24–31 (2017)

    Article  Google Scholar 

  • S.H. Teoh, Fatigue of biomaterials: a review. Int. J. Fatigue 22, 825–837 (2000)

    Article  Google Scholar 

  • V. Tvergaard, Overload effects in fatigue crack growth by crack-tip blunting. Int. J. Fatigue 27, 1389–1397 (2005)

    Article  MATH  Google Scholar 

  • O.L. Warren, Z. Shan, S.A.S. Asif, E.A. Stach, J.W. Morris Jr., A.M. Minor, In situ nanoindentation in the TEM. Mater. Today 10, 59–60 (2007)

    Article  Google Scholar 

  • P.J. Wei, Y.C. Wang, J.F. Lin, Retardation of cyclic indentation creep exhibited in metal alloys. J. Mater. Res. 23, 2650–2656 (2008)

    Article  Google Scholar 

  • Z. Xia, W.A. Curtin, B.W. Sheldon, A new method to evaluate the fracture toughness of thin films. Acta Mater. 52, 3507–3517 (2004)

    Article  Google Scholar 

  • B. Xu, X. Chen, Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test. J. Mater. Res. 25, 2297–2307 (2010)

    Article  Google Scholar 

  • B. Xu, Z. Yue, Study of the ratcheting by the indentation fatigue method with a flat cylindrical indenter: part I. Experimental study. J. Mater. Res. 21(7), 1793–1797 (2006)

    Article  Google Scholar 

  • B. Xu, Z. Yue, Study of the ratcheting by the indentation fatigue method with a flat cylindrical indenter: part II. Finite element simulation. J. Mater. Res. 22, 186–192 (2007)

    Article  Google Scholar 

  • B. Xu, B. Zhao, Z. Yue, Investigation of residual stress by the indentation method with the flat cylindrical indenter. J. Mater. Eng. Perform. 15, 299–305 (2006)

    Article  Google Scholar 

  • B. Xu, Z. Yue, J. Wang, Indentation fatigue behaviour of polycrystalline copper. Mech. Mater. 39(12), 1066–1080 (2007a)

    Article  Google Scholar 

  • B. Xu, X. Wang, Z. Yue, Indentation behavior of polycrystalline copper under fatigue peak overloading. J. Mater. Res. 22, 1585–1592 (2007b)

    Article  Google Scholar 

  • B.X. Xu, X.M. Wang, B. Zhao, Z.F. Yue, Study of crystallographic creep parameters of nickel-based single crystal superalloys by indentation method. Mater. Sci. Eng. A 478, 187–194 (2008a)

    Article  Google Scholar 

  • B.X. Xu, X.M. Wang, Z.F. Yue, Determination of the internal stress and dislocation velocity stress exponent with indentation stress relaxation test. J. Mater. Res. 23, 2486–2490 (2008b)

    Article  Google Scholar 

  • B. Xu, Z. Yue, X. Chen, An indentation fatigue depth propagation law. Scr. Mater. 60(10), 854–857 (2009)

    Article  Google Scholar 

  • B. Xu, Z. Yue, X. Chen, Numerical investigation of indentation fatigue on copper polycrystalline. J. Mater. Res. 24(3), 1007–1015 (2009)

    Google Scholar 

  • B.X. Xu, A. Yonezu, X. Chen, An indentation fatigue strength law. Philos. Mag. Lett. 90(5), 313–322 (2010)

    Article  Google Scholar 

  • F. Yang, J.C.M. Li, Impression creep by an annular punch. Mech. Mater. 21, 89–97 (1995)

    Article  Google Scholar 

  • F. Yang, J.C.M. Li, Impression test – a review. Mater. Sci. Eng. R. Rep 74, 233–253 (2013)

    Article  Google Scholar 

  • W. Yang, S. Mao, J. Yang, T. Shang, H. Song, J. Mabon, W. Swiech, J.R. Vance, Z. Yue, S.J. Dillon, H. Xu, B. Xu, Large-deformation and high-strength amorphous porous carbon nanospheres. Sci. Rep. 6, 24187 (2016)

    Article  Google Scholar 

  • A. Yonezu, B. Xu, X. Chen, Indentation induced lateral crack in ceramics with surface hardening. Mater. Sci. Eng. A 507, 226–235 (2009)

    Article  Google Scholar 

  • A. Yonezu, B. Xu, X. Chen, An experimental methodology for characterizing fracture of hard thin films under cyclic contact loading. Thin Solid Films 8, 2082–2089 (2010)

    Article  Google Scholar 

  • N. Zaafarani, D. Raabe, F. Roters, S. Zaefferer, On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56, 31–42 (2008)

    Article  Google Scholar 

  • Y. Zhu, C. Ke, H.D. Espinosa, Experimental techniques for the mechanical characterization of one-dimensional nanostructures. Exp. Mech. 47, 7 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, USA

    Baoxing Xu

  2. Department of Earth and Environmental Engineering, Columbia Nanomechanics Research Center, Columbia University, New York, NY, USA

    Xi Chen

  3. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, Shaanxi, China

    Zhufeng Yue

Authors
  1. Baoxing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhufeng Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baoxing Xu .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    George Z. Voyiadjis

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Xu, B., Chen, X., Yue, Z. (2019). Indentation Fatigue Mechanics. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-58729-5_25

Download citation

Publish with us

Policies and ethics

Search

Navigation