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Predicting flow localization in semi-solid deformation

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Abstract

A new analytical instability criterion based on a finite deformation continuum analysis was developed to identify the condition associated with the unstable flow during the semi-solid deformation. The proposed criterion can be used to calculate the onset of strain localization. Strain localization causes the formation of liquid channels, which is the characteristic of an inhomogeneous deformation. The results indicate that strain localization increases with decreasing rate sensitivity and increases with increasing solid fraction. Considering the formability of alloys in the semi-solid state, the critical value of the solid fraction was determined according to the critical value of the localization parameter. The results obtained are in favorable agreement with the results from the experimental data for AA7075 and AA2014 aluminum alloy.

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Abbreviations

A 0, A 1 :

Two functions of the solid fraction which defined according to the relations proposed by Zavaliangos (1998)

A(E, G):

Thermodynamic driving force

b :

a constant for a certain liquid fraction denoting the destruction rate of the solid skeleton

c :

Cohesion degree

c init :

Initial value of the cohesion degree

D p :

Plastic stretching rate

E :

Strain tensor

f s :

Solid fraction

f c :

Percolation threshold

f crit s :

Critical solid fraction corresponding to α = 5

G :

Deformation gradient

L :

Velocity gradient

m :

Strain-rate sensitivity parameter

α :

Localization parameter

α cr :

Critical value of localization parameter

γ :

Norm of velocity gradient

\( {\overset{.}{\varepsilon}}_0,{\sigma}_0 \) :

Material parameters (reference strain rate and deformation resistance, respectively)

\( {\overset{.}{\varepsilon}}_e \) :

effective rate of deformation

Δε peak :

Width of the downward part of the peak

ξ :

Viscoplastic dissipation function

Ψ :

Helmholtz potential function

ϕ :

Viscoplastic potential

σ e :

von Mises stress

References

  1. Atkinson HV, Burke K, Vaneetveld G (2008) Recrystallisation in the semi-solid state in 7075 aluminium alloy. Int J Mater Form 1:973–976. doi:10.1007/s12289-008-0220-z

    Article  Google Scholar 

  2. Bayoumi MA, Negm MI, El-Gohry AM (2009) Microstructure and mechanical properties of extruded Al–Si alloy (A356) in the semi-solid state. Mater Des 30:4469–4477. doi:10.1016/j.matdes.2008.11.025

    Article  Google Scholar 

  3. Baadjou R, Knauf F, Hirt G (2009) Semi-solid forging and joining of steel components and their properties. Int J Mater Form 2:741–744. doi:10.1007/s12289-009-0510-0

    Article  Google Scholar 

  4. Rogal Ł, Dutkiewicz J, Atkinson HV et al (2013) Characterization of semi-solid processing of aluminium alloy 7075 with Sc and Zr additions. Mater Sci Eng A 580:362–373. doi:10.1016/j.msea.2013.04.078

    Article  Google Scholar 

  5. Chen Y, Zhang L, Liu W et al (2016) Preparation of Mg–Nd–Zn–(Zr) alloys semisolid slurry by electromagnetic stirring. Mater Des 95:398–409. doi:10.1016/j.matdes.2016.01.131

    Article  Google Scholar 

  6. Chen G, Lin F, Yao S et al (2016) Constitutive behavior of aluminum alloy in a wide temperature range from warm to semi-solid regions. J Alloys Compd 674:26–36. doi:10.1016/j.jallcom.2016.02.254

    Article  Google Scholar 

  7. Koeune R, Ponthot J-P (2008) A one-phase thermomechanical constitutive model for the numerical simulation of semi-solid thixoforming. Int J Mater Form 1:1007–1010. doi:10.1007/s12289-008-0228-4

    Article  Google Scholar 

  8. Koeune R, Ponthot JP (2014) A one phase thermomechanical model for the numerical simulation of semi-solid material behavior. Application to thixoforming. Int J Plast 58:120–153. doi:10.1016/j.ijplas.2014.01.004

    Article  Google Scholar 

  9. Spencer DB, Mehrabian R, Flemings MC (1972) Rheological behavior of Sn-15 pct Pb in the crystallization range. Metall Trans 3:1925–1932. doi:10.1007/BF02642580

    Article  Google Scholar 

  10. Tzimas E, Zavaliangos A (2000) Evolution of near-equiaxed microstructure in the semisolid state. Mater Sci Eng A 289:228–240. doi:10.1016/S0921-5093(00)00908-4

    Article  Google Scholar 

  11. Atkinson HV (2005) Modelling the semisolid processing of metallic alloys. Prog Mater Sci 50:341–412. doi:10.1016/j.pmatsci.2004.04.003

    Article  Google Scholar 

  12. Liu TY, Atkinson HV, Kapranos P et al (2003) Rapid compression of aluminum alloys and its relationship to thixoformability. Metall Mater Trans A 34:1545–1554. doi:10.1007/s11661-003-0266-y

    Article  Google Scholar 

  13. Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23:371–394. doi:10.1016/0022-5096(75)90001-0

    Article  Google Scholar 

  14. Kareh KM, Lee PD, Atwood RC et al (2014) Revealing the micromechanisms behind semi-solid metal deformation with time-resolved X-ray tomography. Nat Commun 5:1–7

    Article  Google Scholar 

  15. Cai B, Karagadde S, Yuan L et al (2014) In situ synchrotron tomographic quantification of granular and intragranular deformation during semi-solid compression of an equiaxed dendritic Al–Cu alloy. Acta Mater 76:371–380. doi:10.1016/j.actamat.2014.05.035

    Article  Google Scholar 

  16. Cai B, Lee PD, Karagadde S et al (2016) Time-resolved synchrotron tomographic quantification of deformation during indentation of an equiaxed semi-solid granular alloy. Acta Mater 105:338–346. doi:10.1016/j.actamat.2015.11.028

    Article  Google Scholar 

  17. Gourlay CM, Meylan B, Dahle AK (2008) Shear mechanisms at 0–50% solid during equiaxed dendritic solidification of an AZ91 magnesium alloy. Acta Mater 56:3403–3413. doi:10.1016/j.actamat.2008.03.020

    Article  Google Scholar 

  18. Meylan B, Terzi S, Gourlay CM et al (2010) Development of shear bands during deformation of partially solid alloys. Scr Mater 63:1185–1188. doi:10.1016/j.scriptamat.2010.08.032

    Article  Google Scholar 

  19. DE Freitas ER, Ferrante M (2001) Rheological behaviour and deformation characteristics of a commercial and a laboratory-cast Al-4%Cu alloy in the semi-solid state. Acta Mater 49:3839–3847. doi:10.1016/S1359-6454(01)00239-7

    Article  Google Scholar 

  20. Tzimas E, Zavaliangos A (1999) Mechanical behavior of alloys with equiaxed microstructure in the semisolid state at high solid content. Acta Mater 47:517–528. doi:10.1016/S1359-6454(98)00356-5

    Article  Google Scholar 

  21. Gourlay CM, Dahle AK (2007) Dilatant shear bands in solidifying metals. Nature 445:70–73

    Article  Google Scholar 

  22. Suery M, Flemings MC (1982) Effect of strain rate on deformation behavior of semi-solid dendritic alloys. Metall Trans A 13:1809–1819. doi:10.1007/BF02647837

    Article  Google Scholar 

  23. Zavaliangos A (1998) Modeling of the mechanical behavior of semisolid metallic alloys at high volume fractions of solid. Int J Mech Sci 40:1029–1041. doi:10.1016/S0020-7403(98)00011-3

    Article  MATH  Google Scholar 

  24. Ziegler H (1963) Some extremum principles in irreversible thermodynamics with application to continuum mechanics. Prog Solids Mech 4:93–193

    Google Scholar 

  25. Rajagopal K, Srinivasa AR (1998) Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings. Int J Plast 14:945–967. doi:10.1016/S0749-6419(98)00037-0

    Article  MATH  Google Scholar 

  26. Rajagopal K, Srinivasa AR (1998) Mechanics of the inelastic behavior of materials. Part II: inelastic response. Int J Plast 14:969–995. doi:10.1016/S0749-6419(98)00041-2

    Article  MATH  Google Scholar 

  27. Srinivasa AR (2010) Application of the maximum rate of dissipation criterion to dilatant, pressure dependent plasticity models. Int J Eng Sci 48:1590–1603. doi:10.1016/j.ijengsci.2010.09.010

    Article  MathSciNet  MATH  Google Scholar 

  28. Semiatin SL, Lahoti GD (1981) Deformation and unstable flow in hot forging of Ti-6Ai-2Sn-4Zr-2Mo-0.1Si. Metall Trans A 12:1705–1717. doi:10.1007/BF02643753

    Article  Google Scholar 

  29. Jonas JJ, Holt RA, Coleman CE (1976) Plastic stability in tension and compression. Acta Metall 24:911–918. doi:10.1016/0001-6160(76)90039-0

    Article  Google Scholar 

  30. Pan J, Saje M, Needleman A (1983) Localization of deformation in rate sensitive porous plastic solids. Int J Fract 21:261–278. doi:10.1007/BF00942345

    Article  Google Scholar 

  31. Xu X-P, Needleman A (1992) The influence of nucleation criterion on shear localization in rate-sensitive porous plastic solids. Int J Plast 8:315–330. doi:10.1016/0749-6419(92)90052-E

    Article  Google Scholar 

  32. Binesh B, Aghaie-Khafri M (2015) Microstructure and texture characterization of 7075 Al alloy during the SIMA process. Mater Charact 106:390–403. doi:10.1016/j.matchar.2015.06.013

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, 1999143344, Tehran, Iran

    M. H. Sheikh Ansari & M. Aghaie-Khafri

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  1. M. H. Sheikh Ansari
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Correspondence to M. Aghaie-Khafri.

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Ansari, M.H.S., Aghaie-Khafri, M. Predicting flow localization in semi-solid deformation. Int J Mater Form 11, 165–173 (2018). https://doi.org/10.1007/s12289-017-1339-6

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