Physically-Based Single and Polycrystal Plasticity Models and their Experimental Verification

Abstract

Physically-based constitutive relations for single crystals are formulated on the basis of slip-induced plastic deformation, and the accompanying elastic lattice distortion. The slip is produced through the motion of dislocations. Due account is taken of the crystal structure and the barriers which the dislocations must overcome in their motion through the lattice. A slip model that directly accounts for both the temperature- and strain-rate effects, is presented. The short- and long-range barriers that the dislocations must overcome in their motion are identified. The hardening issue, associated with the long-range athermal resistance to the motion of the dislocations, is examined. Illustrative physically-based models of the flow stress associated with slip, are developed. Explicit results for bcc and fcc crystals are produced, taking into account the temperature, strain rate, and the long-range hardening effects. As an illustration, explicit results for a commercially pure tantalum (bcc), and OFHC copper (fcc), are given. Using the results of novel experiments, performed to obtain the isothermal and adiabatic stress-strain relations of a number of polycrystalline metals over broad ranges of the strain-rates and temperatures, the resulting constitutive relations are verified. The references listed at the end of this paper provide the necessary background data for the modeling and the corresponding experimental assessment.