Skip to main content

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 46))

  • 348 Accesses

Abstract

Internal stresses in multiphase materials fluctuate because of differential thermoelastic and plastic properties of components. Due to the random microstructure of most multiphase materials, the internal stresses become random quantities, too. We present a direct statistical method which describes the internal fields (stress, elastic strain, thermal strain, plastic strain) by probability distributions which are derived using a maximum entropy formalism. One obtains Gaussian distributions where mean value, spread, and correlation depend on easily accessible quantities (volume fractions, phase properties). The theory is applied to two-phase composites, and the results are compared with some experimental observations.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tvergaard, V.: Effect of thermally induced residual stresses on the failure of a whisker-reinforced metal, Mech.Mater., 11 (1991) 149–61.

    Article  Google Scholar 

  2. Shen, Y.-L., Finot, M, Needleman, A. and Suresh, S.: Effective plastic response of two-phase composites, Acta metall.mater., 43 (1995) 1701–1722.

    Article  Google Scholar 

  3. Kreher, W. and Pompe, W.: Field fluctuations in a heterogeneous elastic material — an information theory approach, J.Mech.Phys.Solids, 33 (1985) 419–45.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Kreher, W.: Internal stresses and relations between the effective thermoelastic properties of stochastic solids —some exact solutions, Z.angew.Math.Mech, 68 (1988) 147–54.

    Article  MATH  Google Scholar 

  5. Jaynes, E.T.: Where do we stand on maximum entropy?. In: R.D. Levine and M. Tribus (Eds.), The maximum entropy formalism, MIT press, Cambridge (USA), 1978, pp. 15–118.

    Google Scholar 

  6. Buck, B. and Macaulay, V.A. (Eds.): Maximum entropy in action, Oxford University Press, Oxford, 1991.

    Google Scholar 

  7. Kreher, W. and Pompe, W.: Internal stresses in heterogeneous solids, Physical research, Volume 9, Akademie Verlag, Berlin, 1989.

    Google Scholar 

  8. Bock, H., Hoffmann, H., Blumenauer, H.: Mechanische Eigenschaften von Wolframkarbid-Kobalt-Legierungen, die Technik 31 (1976) 47–51.

    Google Scholar 

  9. Allais, L., Bornert, M., Bretheau, T. and Caldemaison, D.: Experimental characterization of the local strain field in a heterogeneous elastoplastic material, Acta metall.mater., 42 (1994) 3865–3880.

    Article  Google Scholar 

  10. Bomert, M., Herve, E., Stolz, C. and Zaoui, A.: Self-consistent approaches and strain heterogeneities in two-phase elastoplastic materials. Appl.Mech.Rev., 47 (1994) S66–S76.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this paper

Cite this paper

Kreher, W.S. (1996). Statistical Theory of Microplasticity of Two-Phase Composites. In: Pineau, A., Zaoui, A. (eds) IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials. Solid Mechanics and its Applications, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1756-9_45

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1756-9_45

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7285-4

  • Online ISBN: 978-94-009-1756-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics