Skip to main content

A Masing-Type Modelling Concept for Cyclic Plasticity at Elevated Temperature

  • Chapter
  • First Online:
Advanced Materials Modelling for Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 19))

  • 2297 Accesses

Abstract

Classical plasticity models commonly apply a yield surface concept for the formulation of elastic-plastic constitutive behaviour. This inherently implies a discontinuous transition between the elastic and plastic deformation regime. In the absence of a direct physical interpretation, the identification of the model parameters is further strongly affected by the adopted elastic modulus and yield stress. A continuous Masing-type model formulation is suggested that effectively represents the continuous elastic-plastic behaviour of a low-alloy steel (2CrMoNiWV). The small number of four model parameters allows for a straight-forward parameter identification due to their direct interpretability both in the stress–strain characteristic and on the physical basis of the Masing approach. In particular, a significant correlation has been found between three of the model parameters and the sub-grain size and dislocation density evolutions upon low-cycle fatigue loading. The adopted approach suggests potential for a future physically motivated modelling concept for the simulation of cyclic plasticity.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

  1. Mughrabi, H.: Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals. Acta Metall Mater. 31(9), 1367–1379 (1983)

    Google Scholar 

  2. Chaboche, J.-L.: A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 11(8), 991–1005 (2008)

    Google Scholar 

  3. Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D.D., Bieler, T.R., Raabe, D.: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modelling: theory, experiments, applications. Acta Mater. 58, 1152–1211 (2010)

    Article  CAS  Google Scholar 

  4. Ottoson, N.S., Ristinmaa, M.: The Mechanics of Constitutive Modelling. Elsevier Ltd, Oxford (2005)

    Google Scholar 

  5. Masing, G.: Zur Heyn’schen Theorie der Verfestigung der Metalle durch verborgene elastische Spannungen. Wiss Veröffentlichung aus dem Siemens-Konzern 3, 231–239 (1923)

    Google Scholar 

  6. Afanas’ev, N.N.: Statistical theory of fatigue strength of metals (in Russian: Statisticheskaia teoriia ustalostnoi prochnosti metallov). Azv Akad Nauk SSSR (1953)

    Google Scholar 

  7. Iwan, W.D.: A distributed element model for hysteresis and its steady-state dynamic response. ASME J. Appl. Mech. 33(4), 893–900 (1966)

    Google Scholar 

  8. Polák, J., Fardoun, F., Degallaix, S.: Analysis of the hysteresis loop in stainless steels—I. Austenitic and ferritic steels. Mater. Sci. Eng. A 297, 144–153 (2001)

    Article  Google Scholar 

  9. Christ, H.-J.: Wechselverformung von Metallen—Zyklisches Spannungs-Dehnungs-Verhalten und Mikrostruktur. In: Ilschner, B. (ed.) Werkstoff-Forschung und -Technik. Springer, Berlin (1991)

    Google Scholar 

  10. Chiang, D.-Y., Beck, J.L.: A new class of distributed-element models for cyclic plasticity—I. Theory and application. Int. J. Solids Struct. 31(4), 469–484 (1994)

    Google Scholar 

  11. Skelton, R., Maier, H., Christ, H.-J.: The Bauschinger effect, masing model and the Ramberg-Osgood relation for cyclic deformation in metals. Mater. Sci. Eng. A 238(2), 377–390 (1997)

    Google Scholar 

  12. Mayer, T., Mazza, E., Holdsworth, S.R.: A continuous Masing approach for a physically motivated formulation of temperature and strain rate dependent plasticity. Int. J. Pres. Ves. Pip. doi:10.1016/j.ijpvp.2012.11.001 (2012)

  13. Mayer, T., Mazza, E., Holdsworth, S.R.: Parameter evolution in a continuous masing approach for cyclic plasticity and its physical interpretation. Mech. Mater. doi:10.1016/j.mechmat.2012.10.014 (2012)

  14. Polák, J., Klesnil, M.: The hysteresis loop—1. A statistical theory. Fatigue Eng. Mater. 5, 19–32 (1982)

    Article  Google Scholar 

  15. Mayer, T., Balogh, L., Solenthaler, C., Müller-Gubler, E., Holdsworth, S.R.: Dislocation density and sub-grain size evolution of 2CrMoNiWV during low cycle fatigue at elevated temperatures. Acta Mater. 60, 2485–2496 (2012)

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The financial support by the Swiss Competence Centre for Materials Science and Technology (CCMX-MERU), ABB Turbo-Generators, ALSTOM and Swissnuclear is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Mayer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mayer, T., Mazza, E., Holdsworth, S.R. (2013). A Masing-Type Modelling Concept for Cyclic Plasticity at Elevated Temperature. In: Altenbach, H., Kruch, S. (eds) Advanced Materials Modelling for Structures. Advanced Structured Materials, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35167-9_24

Download citation

Publish with us

Policies and ethics