Skip to main content
Log in

A dislocation-based, strain–gradient–plasticity strengthening model for deformation processed metal–metal composites

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

Deformation processed metal–metal composites (DMMCs) are high-strength, high-electrical conductivity composites developed by severe plastic deformation of two ductile metal phases. The extraordinarily high strength of DMMCs is underestimated using the rule of mixture (or volumetric weighted average) of conventionally work-hardened metals. In this article, a dislocation-density-based, strain–gradient–plasticity model is proposed to relate the strain-gradient effect with the geometrically necessary dislocations emanating from the interface to better predict the strength of DMMCs. The model prediction was compared with the experimental findings of Cu–Nb, Cu–Ta, and Al–Ti DMMC systems to verify the applicability of the new model. The results show that this model predicts the strength of DMMCs better than the rule-of-mixture model. The strain-gradient effect, responsible for the exceptionally high strength of heavily cold worked DMMCs, is dominant at large deformation strain since its characteristic microstructure length is comparable with the intrinsic material length.

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

Access this article

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Russell AM, Chumbley LS, Tian Y (2000) Deformation processed metal–metal composites. Adv Eng Mater 2:11–22

    Article  Google Scholar 

  2. Bevk J, Harbison JP, Bell JL (1978) Anomalous increase in strength of in situ formed Cu–Nb multifilamentary composites. J Appl Phys 49:6031–6038

    Article  Google Scholar 

  3. Spitzig WA, Krotz PD (1988) Comparison of the strengths and microstructures of Cu-20 % Ta and Cu-20 % Nb in situ composites. Acta Metall 36:1709–1715

    Article  Google Scholar 

  4. Biselli C, Morris DG (1994) Microstructure and strength of Cu–Fe in situ composites obtained from prealloyed Cu–Fe powders. Acta Metal Mater 42:163–176

    Article  Google Scholar 

  5. Frommeyer G, Wassermann G (1975) Microstructure and anomalous mechanical properties of in situ-produced silver–copper composite wires. Acta Metall 23:1353–1360

    Article  Google Scholar 

  6. Russell AM, Lund T, Chumbley LS, Laabs FA, Keehner LL, Harringa JL (1999) A high-strength, high-conductivity Al–Ti deformation processed metal metal matrix composite. Compos A 30:239–247

    Article  Google Scholar 

  7. Xu K, Russell AM, Chumbley LS, Laabs FC et al (1999) Characterization of strength and microstructure in deformation processed Al–Mg composites. J Mater Sci 34:5955–5959

    Article  Google Scholar 

  8. Xu K, Russell AM (2004) Texture–strength relationships in a deformation processed Al–Sn metal–metal composite. Mater Sci Eng A 373:99–106

    Article  Google Scholar 

  9. Spitzig WA, Pelton AR, Laabs FC (1987) Characterization of the strength and microstructure of heavily cold worked Cu–Nb composites. Acta Metall 35:2427–2442

    Article  Google Scholar 

  10. Funkenbusch PD, Courtney TH (1985) On the strength of heavily cold worked in situ composites. Acta Metall 33:913–922

    Article  Google Scholar 

  11. Funkenbusch PD, Lee JK, Courtney TH (1987) Ductile two-phase alloys: prediction of strengthening at high strains. Met Trans A 18:1249–1256

    Article  Google Scholar 

  12. Funkenbusch PD, Courtney TH (1989) On the role of interphase barrier and substructural strengthening in deformation processed composite materials. Scr Metall 23:1719–1724

    Article  Google Scholar 

  13. Raabe D, Hangen U (1995) Introduction of a modified linear rule of mixtures for the modeling of the yield strength of heavily wire drawn in situ composites. Comp Sci Tech 55:57–61

    Article  Google Scholar 

  14. Brinckmann S, Siegmund T, Huang Y (2006) A dislocation density based strain gradient model. Int J Plast 22:1784–1797

    Article  Google Scholar 

  15. Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42:475–487

    Article  Google Scholar 

  16. Stolken JS, Evans AG (1998) A microbend test method for measuring the plasticity length scale. Acta Mater 46:5109–5115

    Article  Google Scholar 

  17. De Guzmana MS, Neubauera G, Flinna P, Nix WD (1993) The role of indentation depth on the measured hardness of materials. Mater Res Symp Proc 308:613–618

    Article  Google Scholar 

  18. Lloyd DJ (1994) Particle reinforced aluminium and magnesium matrix composites. Int Mater Rev 39:1–23

    Google Scholar 

  19. Abu Al-Rub RK, Voyiadjis GZ (2006) A physically based gradient plasticity theory. Int J Plast 22:654–684

    Article  Google Scholar 

  20. Gao H, Huang Y, Nix WD, Hutchinson JW (1999) Mechanism-based strain gradient plasticity—I. Theory. J Mech Phys Solids 47:1239–1263

    Article  Google Scholar 

  21. Lubliner J (1990) Plasticity theory, 1st edn. Macmillan Publishing Company, New York

    Google Scholar 

  22. Nye J (1953) Some geometrical relations in dislocated crystals. Acta Metall 1:153–162

    Article  Google Scholar 

  23. Ashby MF (1970) The deformation of plastically non-homogeneous materials. Philos Mag 21:399–424

    Article  Google Scholar 

  24. Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324

    Google Scholar 

  25. Fleck NA, Hutchinson JW (2001) A reformulation of strain gradient plasticity. J Mech Phys Solids 49:2245–2271

    Article  Google Scholar 

  26. Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425

    Article  Google Scholar 

  27. Gao H, Huang Y (2001) Taylor-based nonlocal theory of plasticity. Int J Solid Struct 38:2615–2637

    Article  Google Scholar 

  28. Trybus CL, Spitzig WA (1989) Characterization of the strength and microstructural evolution of a heavily cold rolled Cu-20% Nb composite. Acta Metall 37:1971–1981

    Article  Google Scholar 

  29. Spitzig WA, Krotz PD, Chumbley LS, Downing HL, Verhoeven JD (1988) Effect of temperature on the mechanical properties and microstructures of in situ formed Cu–Nb and Cu–Ta composites. Mater Res Soc Symp Proc 120:45–50

    Article  Google Scholar 

  30. Dieter GE, Kuhn HA, Semiatin SL (2003) Handbook of workability and process design, 2nd edn. ASM International, Materials Park

    Google Scholar 

  31. Zamiri A et al (2006) On mechanical properties of the superconducting niobium. Mater Sci Eng A 435–436:658–665

    Article  Google Scholar 

  32. http://www.matweb.com/. Accessed 22 Mar 2013

  33. Bechtold JH (1955) Tensile properties of annealed tantalum at low temperatures. Acta Metall 3:249–254

    Article  Google Scholar 

  34. Trybus CL, Chumbley LS, Spitzig WA, Verhoeven JD (1989) Problems in evaluating the dislocation densities in heavily deformed Cu–Nb composites. Ultramicroscopy 30:315–320

    Article  Google Scholar 

  35. Tian L, Kim H, Anderson I, Russell AM (2013) The microstructure-strength relationship in a deformation processed Al–Ca composite. Mater Sci Eng A 570:106–113

    Article  Google Scholar 

  36. Rodak K, Radwański K, Molak R (2011) Microstructure and mechanical properties of aluminum processed by multi-axial compression. Solid State Phenom 176:21–28

    Article  Google Scholar 

  37. Welsch G, Boyer RF, Collings EW (1994) Materials properties handbook: titanium alloys, 1st edn. ASM International, Materials Park

    Google Scholar 

Download references

Acknowledgements

The authors appreciate the financial support of the Iowa State University Research Foundation, the Electric Power Research Center of Iowa State University, and the Department of Energy through Ames Laboratory contract no. DE-AC02-07CH11358.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Liang Tian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, L., Russell, A. & Anderson, I. A dislocation-based, strain–gradient–plasticity strengthening model for deformation processed metal–metal composites. J Mater Sci 49, 2787–2794 (2014). https://doi.org/10.1007/s10853-013-7982-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1007/s10853-013-7982-5

Keywords