Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum

Abstract Strain-rate and temperature-dependent constitutive equations for polycrystalline metals which are capable of modeling the initial and evolving anisotropy in ductile metallic materials owing to the evolution of crystallographic texture are reviewed and then specialized to reproduce the recently published stress-strain response of commercially pure b.c.c. tantalum for strains up to 60%, at strain rates from quasi-static to 30,000 s −1 , and temperatures from −200 to 525 °C (Hoge and Mukherjee, 1977; Vecchio, 1994; Nemat-Nasser and Isaacs, 1996). The constitutive equations have been implemented in a finite element program, and the computational capability is used to simulate the evolution of crystallographic texture in simple compression, plane-strain compression, and torsion under quasi-static conditions. A comparison of the predictions against corresponding experiments shows that the crystal plasticity-based model predicts the texture evolution and the macroscopic stress-strain curves satisfactorily. The computational capability is also used to simulate the dynamic Taylor rod-impact tests performed by Ting (1992) on pre-textured tantalum cylinders. The numerical simulations reasonably reproduce the final length and the ovalized macroscopic shape of the impact end of the cylinders observed in the experiments.

[1]  Alan Needleman,et al.  An analysis of nonuniform and localized deformation in ductile single crystals , 1982 .

[2]  W. Spitzig,et al.  Three-stage hardening in tantalum single crystals. , 1965 .

[3]  James R. Rice,et al.  Strain localization in ductile single crystals , 1977 .

[4]  C. Teodosiu,et al.  A theory of finite elastoviscoplasticity of single crystals , 1976 .

[5]  D. Raabe,et al.  Rolling and Recrystallization Textures of BCC Steels , 1991 .

[6]  K. G. Hoge,et al.  The temperature and strain rate dependence of the flow stress of tantalum , 1977 .

[7]  P. Kumar,et al.  Correlating microstructure and texture in cold-rolled Ta ingot , 1989 .

[8]  E. Orowan,et al.  Problems of plastic gliding , 1940 .

[9]  S. Nemat-Nasser,et al.  Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and TaW alloys , 1997 .

[10]  B. Mordike,et al.  Three-stage hardening in tantalum deformed in compression , 1967 .

[11]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[12]  P. Dawson,et al.  Texture Development During Wire Drawing , 1990 .

[13]  Lallit Anand,et al.  The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture , 1994 .

[14]  Ronald W. Armstrong,et al.  Description of tantalum deformation behavior by dislocation mechanics based constitutive relations , 1990 .

[15]  A. Argon.  CHAPTER 21 – MECHANICAL PROPERTIES OF SINGLE-PHASE CRYSTALLINE MEDIA: DEFORMATION AT LOW TEMPERATURES , 1996 .

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

[17]  J. Rice,et al.  Constitutive analysis of elastic-plastic crystals at arbitrary strain , 1972 .

[18]  Lallit Anand,et al.  Single crystal and polycrystal elasto-viscoplasticity: Application to earing in cup drawing of F.C.C. materials , 1996 .

[19]  D. Hull,et al.  The yield of polycrystalline tantalum , 1962 .

[20]  Paul R. Dawson,et al.  On modeling the development of crystallographic texture in bulk forming processes , 1989 .

[21]  L. Anand,et al.  An internal variable constitutive model for hot working of metals , 1989 .

[22]  C. Vold,et al.  Effect of processing variables on texture and texture gradients in tantalum , 1991 .

[23]  J. Mandel.  Thermodynamics and Plasticity , 1973 .

[24]  L. Anand,et al.  Crystallographic texture evolution in bulk deformation processing of FCC metals , 1992 .

[25]  John L. Bassani,et al.  Plastic flow of crystals , 1993 .

[26]  G. Gray,et al.  Constitutive behavior of tantalum and tantalum-tungsten alloys , 1996 .

[27]  U. F. Kocks.  Thermodynamics and kinetics of slip , 1975 .

[28]  H. Conrad.  Thermally activated deformation of metals , 1964 .

[29]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[30]  J. Hutchinson.  Plastic deformation of b.c.c. polycrystals , 1964 .

[31]  R. Pick,et al.  Dynamic-loading-induced damage in tantalum and Armco iron , 1993 .

[32]  John W. Cell,et al.  Stephen Timoshenko-60th Anniversary Volume , 1940 .

[33]  J. H. Bechtold.  Tensile properties of annealed tantalum at low temperatures , 1955 .

[34]  R. Asaro,et al.  Overview no. 42 Texture development and strain hardening in rate dependent polycrystals , 1985 .