SpringerLink
Log in

Development of an Energy-Based Experimental Method for Estimation of Fatigue Crack Evolution in Titanium Alloys

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

This paper presents an experimental study of energy dissipation caused by fatigue crack growth in Grade 2 titanium and titanium alloys Ti-1.1Al-0.9Mn and Ti-4.6Al-1.77V using the original heat flux method. It is shown that significant structural changes occur in the material under plastic deformation, leading to internal energy evolution. As is known, a large part of the deformation energy is dissipated as heat. The developed method allows high-accuracy measurements of the heat flux caused by plastic zone development at the crack tip directly in the fatigue experiment. Simultaneous measurements of the crack length and displacements in the stress concentration zone allow estimating the energy balance of the tested specimens. Analysis of the obtained data confirms that the stored strain energy reflecting the structural state of the material can be used as a fracture criterion. Based on the heat flux data, a kinetic equation is derived for predicting the rate of fatigue crack growth under Paris’s law by the energy dissipation rate.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Thailand)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. Paris, P.C. and Erdogan, F.J., A Critical Analysis of Crack Propagation Laws, J. Basic Eng. Trans ASME, 1963, vol. 85, pp. 528–534. https://doi.org/10.1115/1.3656900

    Article  CAS  Google Scholar 

  2. Jones, R., Molent, L., and Pitt, S., Similitude and the Paris Crack Growth Law, Int. J. Fatigue, 2008, vol. 30, pp. 1873–1880. https://doi.org/10.1016/j.ijfatigue.2008.01.016

    Article  CAS  Google Scholar 

  3. Iino, Y., Fatigue Crack Propagation Work Coefficient—A Material Constant Giving Degree of Resistance to Fatigue Crack Growth, Eng. Fract. Mech., 1979, vol. 12, pp. 279–299. https://doi.org/10.1016/0013-7944(79)90120-6

    Article  CAS  Google Scholar 

  4. Fedorov, V.V., Kinetics of Damage and Fracture of Solids, Tashkent: Fan, 1985.

  5. Ivanova, V.S. and Terentyev, V.F., Nature of Metal Fatigue, Moscow: Metallurgiya, 1975.

  6. Kasimov, B.M., Muminov, M.R., and Shin, I.G., Determination of Latent Strain Energy Based on Thermodynamic Relationships during Finishing and Strengthening Treatment, in Proc. of the 54th International Scientific and Technical Conference of Teachers and Students, 2 vols., Vitebsk: Educational Institution VSTU, 2021, pp. 283–285.

  7. Shchipachev, A.M., Thermodynamic Theory of Strength: Prediction of High-Cycle Fatigue of Metals, Ufa: Ufa Technological Institute of Service, 1998.

  8. Arutyunyan, A.R. and Arutyunyan, R.A., Fatigue Criterion Based on the Concept of Latent Strain Energy, Fiz. Mezomekh., 2010, vol. 13, no. 2, pp. 31–39.

    Google Scholar 

  9. Arutyunyan, A.R. and Arutyunyan, R.A., Energy Approach to the Solution of the High-Cycle Fatigue Problem, Vest. Nizhegorod. Univer. Lobachevskogo, 2011, no. 4-4, pp. 1359–1360.

    Google Scholar 

  10. Structural Levels of Plastic Deformation and Fracture, Panin, V.E., Ed., Novosibirsk: Nauka, 1990.

  11. Shchipachev, A.M. and Poyarkova, E.V., Influence of Fatigue Damage on Hardness and Internal Energy Storage in Metals, Mashinostr. Materialoved. Termich. Obrab. Met., 2007, vol. 9, no. 6(24), pp. 152–157.

    Google Scholar 

  12. Bezyazychnii, V.F., Drapkin, B.M., Prokofiev, M.A., and Timofeev, M.V., Study of Strain Energy Stored in Metal during Ball Indentation, Zavod. Lab., 2005, vol. 71, no. 4, pp. 32–35.

    Google Scholar 

  13. Bolshanina, M.A. and Panin, V.E., Latent Strain Energy, in Research in Solid State Physics, Moscow: Publ. House of the USSR Academy of Sciences, 1957, pp. 193–234.

  14. Bever, M.B., Holt, D.L., and Titchener, A.L., The Stored Energy of Cold Work, Progr. Mater. Sci., 1973, vol. 17, pp. 5–177. https://doi.org/10.1016/0079-6425(73)90001-7

    Article  Google Scholar 

  15. Mason, J.J., Rosakis, A.J., and Ravichandran, G., On the Strain and Strain Rate Dependence of the Fraction of Plastic Work Converted to Heat: An Experimental Study Using High Speed Infrared Detectors and the Kolsky Bar, Mech. Mater., 1994, vol. 17, no. 2–3, pp. 135–145. https://doi.org/10.1016/0167-6636(94)90054-X

    Article  Google Scholar 

  16. Rittel, D., On the Conversion of Plastic Work to Heat during High Strain Rate Deformation of Glassy Polymers, Mech. Mater., 1999, vol. 31, no. 2, pp. 131–139. https://doi.org/10.1016/S0167-6636(98)00063-5

    Article  ADS  Google Scholar 

  17. Hodowany, J., Ravichandran, G., Rosakis, A.J., and Rosakis, P., Partition of Plastic Work into Heat and Stored Energy in Metals, Exp. Mech., 2000, vol. 40, no. 2, pp. 113–123. https://doi.org/10.1007/BF02325036

    Article  CAS  Google Scholar 

  18. Rittel, D., Zhang, L.H., and Osovski, S., The Dependence of the Taylor–Quinney Coefficient on the Dynamic Loading Mode, J. Mech. Phys. Solids, 2017, vol. 107, pp. 96–114. https://doi.org/10.1016/j.jmps.2017.06.016

    Article  CAS  ADS  Google Scholar 

  19. Neto, D.M., Simões, V.M., Oliveira, M.C., Alves, J.L., Laurent, H., Oudriss, A., and Menezes, L.F., Experimental and Numerical Analysis of the Heat Generated by Plastic Deformation in Quasi-Static Uniaxial Tensile Tests, Mech. Mater., 2020, vol. 146, p. 103398. https://doi.org/10.1016/j.mechmat.2020.103398

    Article  Google Scholar 

  20. Plekhov, O.A., Energy Dissipation and Storage during Plastic Deformation and Fracture of Metals (Experimental and Theoretical Research), in Proc. of XII All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics, Ufa, August 19–24, 2019, 4 vols., Ufa: Bashkir State University, 2019, vol. 3, pp. 32–35.

  21. Taylor, G.I. and Quinney, H., The Latent Energy Remaining in a Metal after Cold Working, Proc. R. Soc. Lond., 1934, pp. 307–326. https://doi.org/10.1098/rspa.1934.0004

  22. Dæhli, L.E.B., Johnsen, J., Berstad, T., Børvik, T., and Hopperstad, O.S., An Experimental-Numerical Study on the Evolution of the Taylor–Quinney Coefficient with Plastic Deformation in Metals, Mech. Mater., 2023, vol. 179, p. 104605. https://doi.org/10.1016/j.mechmat.2023.104605

    Article  Google Scholar 

  23. Kostina, A.A., Plekhov, O.A., and Venkatraman, B., Use of Stored Strain Energy in Numerical Modeling of Fracture of Steel Structures, Vestn. Samar. Gos. Univer. Ser. Fiz.-Mat. Nauk, 2016, vol. 20, no. 4, pp. 656–674. http://dx.doi.org/10.14498/vsgtu1518

    Article  Google Scholar 

  24. Chudnovsky, A. and Moet, A., Thermodynamics of Translational Crack Layer Propagation, J. Mater. Sci., 1985, vol. 20, pp. 630–635.

    Article  ADS  Google Scholar 

  25. Wang, X.G., Ran, H.R., Jiang, C., and Fang, Q.H., An Energy Dissipation-Based Fatigue Crack Growth Model, Int. J. Fatigue, 2018, vol. 114, pp. 167–176. https://doi.org/10.1016/j.ijfatigue.2018.05.018

    Article  CAS  Google Scholar 

  26. Vshivkov, A., Iziumova, A., Zakharov, A., Shlyannikov, V., and Plekhov, O., The Experimental and Theoretical Study of Heat Dissipation at Fatigue Crack Tip under Biaxial Loading, Theor. Appl. Fract. Mech., 2019, vol. 103, p. 102308. https://doi.org/10.1016/j.tafmec.2019.102308

    Article  CAS  Google Scholar 

  27. Vshivkov, A.N., Iziumova, A.Yu., Panteleev, I.A., Ilinykh, A.V., Wildemann, V.E., and Plekhov, O.A., The Study of a Fatigue Crack Propagation in Titanium Grade 2 Using Analysis of Energy Dissipation and Acoustic Emission Data, Eng. Fract. Mech., 2019, vol. 210, pp. 312–319. https://doi.org/10.1016/j.engfracmech.2018.05.012

    Article  Google Scholar 

  28. Kozhevnikova, M.E., An Analytical Approach to the Evaluation of Energy Dissipation at the Fatigue Crack Tip, Fiz. Mezomekh., 2020, vol. 23, no. 3, pp. 93–106. https://doi.org/10.24411/1683-805X-2020-13009

    Article  Google Scholar 

  29. Meneghetti, G. and Ricotta, M., A Heat Energy Dissipation Approach to Elastic-Plastic Fatigue Crack Propagation, Theor. Appl. Fract. Mech., 2020, vol. 105, p. 102405. https://doi.org/10.1016/j.tafmec.2019.102405

    Article  CAS  Google Scholar 

  30. Quan, H. and Alderliesten, R.C., The energy dissipation during fatigue crack growth in metallic materials, Eng. Fract. Mech., 2022, vol. 269, p. 108567. https://doi.org/10.1016/j.engfracmech.2022.108567

    Article  Google Scholar 

  31. Vshivkov, A.N., Prokhorov, A.E., Plekhov, O.A., Ber, J., and Batsal, Zh.-K., Patent 2603939 RF, IPC G01N 3/32 (2006.01), Method for Determining Crack Growth Rate in the Sample and Device for Its Implementation, Byul. FSIS (Rospatent), 2016, no. 34. https://new.fips.ru/Archive/PAT/2016FULL/2016.12.10/Index_ru.htm

  32. Illarionov, A.G. and Popov, A.A., Technological and Operational Properties of Titanium Alloys: Textbook, Yekaterinburg: Ural Univ. Publ. House, 2014. https://elar.urfu.ru/bitstream/10995/28698/1/978-5-7996-1096-8_2014.pdf

  33. Moiseev, V.N., Titanium in Russia, Met Sci. Heat Treat., 2005, no. 8. https://viam.ru/sites/default/files/scipub/2005/2005-204293.pdf

  34. Vshivkov, A., Iziumova, A., and Plekhov, O., Experimental Study of Heat Dissipation at the Crack Tip during Fatigue Crack Propagation, Fratt. Integr. Strutt., 2016, vol. 35, pp. 131–137. https://doi.org/10.3221/IGF-ESIS.35.16

    Article  Google Scholar 

  35. Gachegova, E.A., Sikhamov, R., Ventzke, V., Kashaev, N., and Plekhov, O.A., Influence of Laser Shock Peening on Low- and High-Cycle Fatigue of an OT4-0 Titanium Alloy, J. Appl. Mech. Tech. Phys., 2022, vol. 63, no. 2, pp. 335–342.

    Article  CAS  ADS  Google Scholar 

  36. Pavlenko, D.V., Tkach, D.V., and Greshta, V.L., Deformation Behavior and Endurance of VT1-0 Alloy with a Submicrocrystalline Structure, Vest. Dvigatelestr., 2011, no. 1, pp. 125–131.

    Google Scholar 

  37. Naidenkin, E.V., Kolomeets, N.P., Ratochka, I.V., Kaminskii, P.P., and Sharkeev, Yu.P., PT-3V Titanium Alloy with Ultradisperse Structure for Waveguides of High-Amplitude Acoustic Systems, Vopr. Materialoved., 2009, no. 4, pp. 15–19.

    Google Scholar 

  38. Rice, J.R., Mechanics of Crack Tip Deformation and Extension by Fatigue, ASTM. Spec. Tech. Publ., 1966, vol. 415, pp. 247–311. https://doi.org/10.1520/STP47234S

    Article  Google Scholar 

  39. Klevtsov, G.V., Plastic Zone Patterns Formed at the Crack Tip under Various Loading and X-Ray Diagnostics of Fracture, Vest. Orenburgsk. Gos. Univ., 2006, vol. 2, no. 1, pp. 81–88.

    Google Scholar 

  40. Klevtsov, G.V., Botvina, L.R., Klevtsova, N.A., and Limar, L.V., Diagnostics of Fracture of Metal Materials and Structures, Moscow: MISiS, 2007.

  41. Klevtsov, G.V., Botvina, L.R., Klevtsova, N.A., Valiev, R.Z., and Pigaleva, I.N., Determination of Fatigue Failure Parameters from the Depth of Plastic Zones Beneath the Fracture Surface, Phys. Mesomech., 2023, vol. 26, no. 1, pp. 1–6. https://doi.org/10.1134/S1029959923010010

    Article  Google Scholar 

  42. Raju, K.N., An Energy Balance Criterion for Crack Growth under Fatigue Loading from Considerations of Energy of Plastic Deformation, Int. J. Fract. Mech., 1972, vol. 8, pp. 1–14.

    Article  Google Scholar 

  43. Vshivkov, A., Iziumova, A., Yarullin, R., Shlyannikov, V., and Plekhov, O., Experimental and Theoretical Analysis of Heat Flux at Fatigue Crack Tip under Mixed Mode Loading, Proc. Struct. Integr., 2019, vol. 18, pp. 608–615. https://doi.org/10.1016/j.prostr.2019.08.206

    Article  Google Scholar 

Download references

Funding

The experimental part of the work was supported by Russian Science Foundation grant No. 22-79-10168. Data analysis and estimation of stored energy were carried out within the government statement of work for the Institute of Continuous Media Mechanics UB RAS, a branch of the Perm Federal Research Center UB RAS (research line AAAA-A19-119013090021-5).

Author information

Authors and Affiliations

  1. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, 614013, Perm, Russia

    A. Yu. Iziumova, A. N. Vshivkov & O. A. Plekhov

Authors
  1. A. Yu. Iziumova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Vshivkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. A. Plekhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Iziumova.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher's Note. Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iziumova, A.Y., Vshivkov, A.N. & Plekhov, O.A. Development of an Energy-Based Experimental Method for Estimation of Fatigue Crack Evolution in Titanium Alloys. Phys Mesomech 27, 41–48 (2024). https://doi.org/10.1134/S1029959924010041

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959924010041

Keywords:

Search

Navigation