A modified Johnson–Cook constitutive model for Mg–Gd–Y alloy extended to a wide range of temperatures

Abstract In this paper, a new phenomenological and empirically based constitutive model was proposed to change the temperature term in the original Johnson–Cook constitutive model. The new model can be used to describe or predict the stress–strain relation of the metals deformed over a wide range of temperatures even though the current temperatures were lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar technique, the material constants in the new model can be experimentally determined using isothermal and adiabatic stress–strain curves at different strain rates and temperatures. Good agreement is obtained between the predicted and the experimental stress–strain curves for a hot-extruded Mg–10Gd–2Y–0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures were lower than the reference temperature.

[1]  Xiaoming He,et al.  A method to predict flow stress considering dynamic recrystallization during hot deformation , 2008 .

[2]  D. Agard,et al.  Microtubule nucleation by γ-tubulin complexes , 2011, Nature Reviews Molecular Cell Biology.

[3]  R. Armstrong,et al.  Dislocation-mechanics-based constitutive relations for material dynamics calculations , 1987 .

[4]  L. Parashkevova,et al.  Thermomechanical modelling of hot extrusion of Al-alloys, followed by cooling on the press , 2006 .

[5]  S. Kamado,et al.  Creep properties of Mg-Gd-Y-Zr alloys , 2001 .

[6]  M. Meyers,et al.  High-strain, high-strain-rate behavior of tantalum , 1995 .

[7]  William K. Rule,et al.  A revised form for the Johnson-Cook strength model , 1998 .

[8]  Yang Wang,et al.  A constitutive description of tensile behavior for brass over a wide range of strain rates , 2004 .

[9]  Christian Krempaszky,et al.  3-D FEM-simulation of hot forming processes for the production of a connecting rod , 2006 .

[10]  Zhihua Yang,et al.  Microstructures of extruded Mg–12Gd–1Zn–0.5Zr and Mg–12Gd–4Y–1Zn–0.5Zr alloys , 2007 .

[11]  Y. Lin,et al.  A new mathematical model for predicting flow stress of typical high-strength alloy steel at elevated high temperature , 2010 .

[12]  Zhong Yang,et al.  Plastic deformation and dynamic recrystallization behaviors of Mg–5Gd–4Y–0.5Zn–0.5Zr alloy , 2008 .

[13]  E. El-Magd,et al.  Characterization, modelling and simulation of deformation and fracture behaviour of the light-weight wrought alloys under high strain rate loading , 2006 .

[14]  S. R. Bodner,et al.  Constitutive Equations for Elastic-Viscoplastic Strain-Hardening Materials , 1975 .

[15]  T. Ohkubo,et al.  Effect of Zn additions on the age-hardening of Mg-2.0gd-1.2Y-0.2Zr alloys , 2007 .

[16]  A. K. Bhaduri,et al.  A comparative study on Johnson Cook, modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behaviour in modified 9Cr–1Mo steel , 2009 .

[17]  U. F. Kocks,et al.  A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable , 1988 .

[18]  S. Kamado,et al.  Alloy Development of High Toughness Mg-Gd-Y-Zn-Zr Alloys , 2006 .

[19]  C. J. Smithells,et al.  Smithells metals reference book , 1949 .