Comparison between high and low strain-rate deformation of tantalum
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I. INTRODUCTION
THE mechanical properties of a material depend on its internal microstructure, and changes in these mechanical properties result from corresponding changes in the microstructure. In most materials, the microstructure continuously changes during deformation, causing the stress required for further deformation to change. This, in turn, results in work hardening. The microstructure here refers to the grain size, distribution of second-phase particles or precipitates, and distribution and density of dislocations. One common microstructure parameter used is the dislocation density. With dislocation density as the microstructural parameter, the shear stress on a slip plane can be written as [1] t 5 t ( r,g˙ ,T ) ˙ where r is the dislocation density, g is the shear strain rate on that slip plane, and T is the temperature. The stress required to overcome a given microstructure at 0 K, referred to as the mechanical threshold stress, can also be used as a microstructural parameter.[1,2] The microstructure can evolve differently for different loading conditions, that is, for differ˙ ent values of g and T. This results in different flow stresses ˙ at different g (or T ) at a given strain. Strain is not a state variable, and the variation of the stress with strain only has meaning if the initial microstructure at 0 strain is known, and there is a concurrent knowledge of microstructure evolution as a function of strain path. Previous researchers have attempted to describe the flow stress of materials using the concept of dislocation density as a microstructural parameter.[1,3–7] The resistance to deformation can be due to: (1) dislocations overcoming periodic lattice potentials; (2) dislocations RAJEEV KAPOOR, Visiting Scientist, Bhabha Atomic Research Centre, Mumbai, India 40085, was formerly with the Center of Excellence for Advanced Materials, University of California, San Diego. SIA NEMAT-NASSER, Professor, is with the Center of Excellence for Advanced Materials, University of California, San Diego, La Jolla, CA 92093-0416. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees. METALLURGICAL AND MATERIALS TRANSACTIONS A
interacting with other dislocations; (3) dislocations interacting with solute atoms; (4) dislocations overcoming the long-range elastic stress field caused by grain boundaries, precipitates, dislocation forests, and other defects; and (5) dislocations overcoming the viscous drag, in the course of their motion. A moving dislocation encounters some or all of these obstacles. Obstacles that can be overcome with assistance from thermal energy are called thermal (shortrange) barriers. Obstacles that cannot be overcome by thermal energy are called athermal (long-range) barriers. Viscous drag may be present depending on the temperature and stre
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