Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures

Abstract A kinetic equation for the shearing rates on slip systems based on the thermally activated theory for plastic flow is formulated, and an evolution equation for slip system deformation resistances is developed. These constitutive functions are incorporated in a model for elasto-viscoplasticity of face-centered-cubic (f.c.c.) single crystals. For polycrystalline materials, the classical Taylor assumption is invoked. This constitutive model has been implemented in a finite element program to facilitate simulations of quasi-static as well as dynamic non-homogeneous deformations of polycrystalline f.c.c. materials. The material parameters in the model have been calibrated against existing experimental data for aluminum. The improved physical description for plastic flow and hardening evolution, enables the constitutive model to reproduce the macroscopic stress–strain response in aluminum up to large strains (≈100%), for a wide range of strain-rates (10 −3 – 10 2 s −1 ), and a wide range of low homologous temperatures (77– 298 K ). Important strain-rate-history and temperature-history effects on the strain-hardening behavior of aluminum are shown to be well represented by the constitutive model.

[1]  U. S. Lindholm Some experiments with the split hopkinson pressure bar , 1964 .

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

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

[4]  J. Klepaczko Thermally activated flow and strain rate history effects for some polycrystalline f.c.c. metals , 1975 .

[5]  R. P. Carreker,et al.  Tensile deformation of aluminum as a function of temperature, strain rate, and grain size , 1957 .

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

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

[8]  Herbert F. Wang,et al.  Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook , 1971 .

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

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

[11]  U. F. Kocks,et al.  Application of polycrystal plasticity to sheet forming , 1994 .

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

[13]  P. E. Senseny,et al.  Experiments on Strain Rate History and Temperature Effects During the Plastic Deformation of Close-Packed Metals , 1978 .

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

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

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

[17]  J. Klepaczko Strain rate history effects for polycrystalline aluminium and theory of intersections , 1968 .

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

[19]  L. Anand,et al.  Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[20]  U. F. Kocks Laws for Work-Hardening and Low-Temperature Creep , 1976 .

[21]  J. Duffy The Dynamic Plastic Deformation of Metals: A Review , 1982 .

[22]  S. Balasubramanian Polycrystalline plasticity : application to deformation processing of lightweight metals , 1998 .

[23]  Lallit Anand,et al.  Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum , 1998 .

[24]  J. D. Campbell,et al.  The behaviour of materials subjected to dynamic incremental shear loading , 1970 .

[25]  J. E. Dorn,et al.  The Effect of Thermal-Mechanical History on the Strain Hardening of Metals, , 1948 .

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

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

[28]  Lallit Anand,et al.  Macroscopic shape change and evolution of crystallographic texture in pre-textured FCC metals , 1994 .

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

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

[31]  A. Cottrell,et al.  Effects of temperature on the plastic properties of aluminium crystals , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

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

[33]  A. Argon,et al.  Forest Dislocation Intersections in Stage I Deformation of Copper Single Crystals , 1979 .

[34]  K. S. Havner,et al.  Finite Plastic Deformation of Crystalline Solids , 1992 .

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