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.



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References
Russell AM, Chumbley LS, Tian Y (2000) Deformation processed metal–metal composites. Adv Eng Mater 2:11–22
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
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
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
Frommeyer G, Wassermann G (1975) Microstructure and anomalous mechanical properties of in situ-produced silver–copper composite wires. Acta Metall 23:1353–1360
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
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
Xu K, Russell AM (2004) Texture–strength relationships in a deformation processed Al–Sn metal–metal composite. Mater Sci Eng A 373:99–106
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
Funkenbusch PD, Courtney TH (1985) On the strength of heavily cold worked in situ composites. Acta Metall 33:913–922
Funkenbusch PD, Lee JK, Courtney TH (1987) Ductile two-phase alloys: prediction of strengthening at high strains. Met Trans A 18:1249–1256
Funkenbusch PD, Courtney TH (1989) On the role of interphase barrier and substructural strengthening in deformation processed composite materials. Scr Metall 23:1719–1724
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
Brinckmann S, Siegmund T, Huang Y (2006) A dislocation density based strain gradient model. Int J Plast 22:1784–1797
Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42:475–487
Stolken JS, Evans AG (1998) A microbend test method for measuring the plasticity length scale. Acta Mater 46:5109–5115
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
Lloyd DJ (1994) Particle reinforced aluminium and magnesium matrix composites. Int Mater Rev 39:1–23
Abu Al-Rub RK, Voyiadjis GZ (2006) A physically based gradient plasticity theory. Int J Plast 22:654–684
Gao H, Huang Y, Nix WD, Hutchinson JW (1999) Mechanism-based strain gradient plasticity—I. Theory. J Mech Phys Solids 47:1239–1263
Lubliner J (1990) Plasticity theory, 1st edn. Macmillan Publishing Company, New York
Nye J (1953) Some geometrical relations in dislocated crystals. Acta Metall 1:153–162
Ashby MF (1970) The deformation of plastically non-homogeneous materials. Philos Mag 21:399–424
Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324
Fleck NA, Hutchinson JW (2001) A reformulation of strain gradient plasticity. J Mech Phys Solids 49:2245–2271
Nix WD, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425
Gao H, Huang Y (2001) Taylor-based nonlocal theory of plasticity. Int J Solid Struct 38:2615–2637
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
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
Dieter GE, Kuhn HA, Semiatin SL (2003) Handbook of workability and process design, 2nd edn. ASM International, Materials Park
Zamiri A et al (2006) On mechanical properties of the superconducting niobium. Mater Sci Eng A 435–436:658–665
http://www.matweb.com/. Accessed 22 Mar 2013
Bechtold JH (1955) Tensile properties of annealed tantalum at low temperatures. Acta Metall 3:249–254
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
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
Rodak K, Radwański K, Molak R (2011) Microstructure and mechanical properties of aluminum processed by multi-axial compression. Solid State Phenom 176:21–28
Welsch G, Boyer RF, Collings EW (1994) Materials properties handbook: titanium alloys, 1st edn. ASM International, Materials Park
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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.
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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
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DOI: https://doi.org/10.1007/s10853-013-7982-5


