An Enhanced Viscoplastic Constitutive Model for Semi-Solid Materials to Analyze Shear Localization

Subject Areas : Engineering

M.H Sheikh-Ansari ¹ (Faculty of Materials Science and Engineering, K.N. Toosi University of Technology, Tehran, Iran)
M Aghaie-Khafri ² (Faculty of Materials Science and Engineering, K.N. Toosi University of Technology, Tehran, Iran)

Received: 2018-08-05 Accepted : 2018-10-05 Published : 2018-12-30

Keywords: Semi-Solid, Viscoplastic model, Shear band, Perturbation growth, Dilatancy,

Abstract :

Semi-solid materials undergo strain localization and shear band formation as a result of granular nature of semi-solid deformation. In the present study, to analyze the shear localization, a unified viscoplastic constitutive model was developed for the homogeneous flow. Then, a linearized analysis of the stability performed by examining the necessary condition for the perturbation growth. For this purpose, a shear layer model was considered to analyze the perturbation growth and subsequent instability. The perturbation analysis revealed that the failure mode in semi-solid materials is diffused with long wave length regime, rather than to be localized and exhibiting short wave length regime. Moreover, decreasing the solid skeleton has a retarding effect on the perturbation growth and localization at low and modest strain rates. The performed analysis showed that the localization analysis results in a new interpretation for the micro-mechanisms of the semi-solid deformation. The constitutive model was fairly well correlated with the experimental results.

References:

[1] Kang C.G., Choi J.S., Kim K.H., 1999, The effect of strain rate on macroscopic behaviour in the compression forming of semi-solid aluminium alloy, Journal of Materials Processing Technology 88: 159-168.
[2] Atkinson H.V., 2005, Modelling the semisolid processing of metallic alloys, Progress in Materials Science 50: 341-412.
[3] Koeune R., Ponthot J.P., 2008, A one-phase thermomechanical constitutive model for the numerical simulation of semi-solid thixoforming, International Journal of Material Forming 1: 1007-1010.
[4] Bayoumi M.A., Negm M.I., El-Gohry A.M., 2009, Microstructure and mechanical properties of extruded Al–Si alloy (A356) in the semi-solid state, Materials & Design 30: 4469-4477.
[5] Favier V., Atkinson H.V., 2011, Micromechanical modelling of the elastic–viscoplastic response of metallic alloys under rapid compression in the semi-solid state, Acta Materialia 59: 1271-1280.
[6] Gourlay C.M., Dahle A.K., 2007, Dilatant shear bands in solidifying metals, Nature 445: 70-73.
[7] Gourlay C.M., Dahle A.K., Nagira T., Nakatsuka N., Nogita K., Uesugi K., 2011, Granular deformation mechanisms in semi-solid alloys, Acta Materialia 59: 4933-4943.
[8] Fonseca J., O’Sullivan C., Nagira T., Yasuda H., Gourlay C.M., 2013, In situ study of granular micromechanics in semi-solid carbon steels, Acta Materialia 61: 4169-4179.
[9] Kareh K.M., O’Sullivan C., Nagira T., Yasuda H., Gourlay C.M., 2017, Dilatancy in semi-solid steels at high solid fraction, Acta Materialia 125: 187-195.
[10] Meylan B., Terzi S., Gourlay C.M., Suéry M., Dahle A.K., 2010, Development of shear bands during deformation of partially solid alloys, Scripta Materialia 63: 1185-1188.
[11] Montassar S., Buhan P., 2006, Some general results on the stability and flow failure of rigid viscoplastic structures, Mechanics Research Communications 33: 63-71.
[12] Hu X.G., Zhu Q., Atkinson H.V., Lu H.X., Zhang F., Dong H.B., 2017, A time-dependent power law viscosity model and its application in modelling semi-solid die casting of 319s alloy, Acta Materialia 124: 410-420.
[13] Rudnicki J.W., Rice J.R.,1975, Conditions for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids 23: 371-394.
[14] Vardoulakis I., 1977, Sensitivity analysis of the shear band bifurcation solution in the biaxial test on sand samples, Mechanics Research Communications 4: 171-177.
[15] Bai Y.L., 1982, Thermo-plastic instability in simple shear, Journal of the Mechanics and Physics of Solids 30: 195-207.
[16] Anand L., 1987, Onset of shear localization in viscoplastic solids, Journal of the Mechanics and Physics of Solids 35: 407-429.
[17] Desoyer T., Hanus J.L., Keryvin V., 1998, An instability condition of the deformation process in elasto-(visco)-non-linear materials, Mechanics Research Communications 25: 437-442.
[18] Aghaie-Khafri M., Mahmudi R., 2005, The effect of preheating on the formability of an Al–Fe–Si alloy sheet, Journal of Material Processing and Technology 169: 38-43.
[19] Aghaie-Khafri M., Mahmudi R., 2005, Optimizing homogenization parameters for better stretch formability in an Al-Mn-Mg alloy sheet, Materials Science and Engineering A 399: 173-180.
[20] Sheikh-Ansari M.H., Aghaie-Khafri M., 2017, Predicting flow localization in semi-solid deformation, International Journal of Material Forming 11: 165-173.
[21] Terzaghi K.V., 1936, The shearing resistance of saturated soils, Proc 1st ICSMFE 1: 54-56.
[22] Nguyen T.G., Favier D., Suery M., 1994, Theoretical and experimental study of the isothermal mechanical behaviour of alloys in the semi-solid state, International Journal of Plasticity 10: 663-693.
[23] Martin C.L., Brown S.B., Favier D., Suéry M., 1995, Shear deformation of high solid fraction (>0.60) semi-solid Sn-Pb under various structures, Materials Science and Engineering: A 202: 112-122.