The effect of inertia on tensile ductility
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INTRODUCTION
THE estimation of tensile ductility has been studied from a variety of theoretical perspectives, including those involving plastic-instability and flow-localization (necking) concepts. The earliest analysis describing the onset of instability in uniaxial tension was conducted by ConsidEre, ~j according to whom instability occurs at the load maximum, where the load increment caused by strain hardening is equal to the load decrement caused by geometrical softening. However, Consid6re's criterion is only valid for a rate-independent material. For this material, necking and failure follow rapidly after the maximum load is attained. For materials that exhibit rate-dependent behavior, on the other hand, the extensive analytical and experimental investigations of Hart t2j and others t3-26j indicate that strain-rate sensitivity delays the onset of instability pertaining to rate-independent materials and induces postuniform elongation, leading to an enhancement of tensile ductility. For such materials, several criteria for predicting the onset of instability have been proposed, and relationships between the failure strain, er, and material parameters (the strain-hardening exponent, n, and strainrate-sensitivity index, m) have been established. Although it has been commonly accepted that m is unimportant prior to the maximum load and n is unimportant after the maximum load, 1271 a detailed, twodimensional finite element analysis of the sheet tensile test t22j has revealed that the total elongation, er, is strongly affected by both n and m. Furthermore, it has been of interest to note that for the given n and m values, the strain distribution and necking behavior of ratedependent materials, which obey power-law strain-rate sensitivity, are independent of the strain rate under quasi-static and isothermal conditions, t2~,28'291 Although the influence of strain rate on tensile instability and necking has been extensively studied, the XIAOYU HU, Postdoctoral Researcher, ROBERT H. WAGONER, Professor, and GLENN S. DAEHN, Associate Professor, Department of Materials Science and Engineering, and SOMNATH GHOSH, Assistant Professor, Department of Engineering Mechanics, are with The Ohio State University, Columbus, OH 43210. Manuscript submitted June 21, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
strain rates employed in these investigations were typically limited to low values. When materials deform at low rates, the variation of the material velocity with time is small. In these cases, the material acceleration and the propagation of plastic waves are negligible, so that quasi-static equilibrium can be assumed. The development of strain gradients during such tests relies only on the static axial-force equilibrium at any cross section of the gage length. A tensile test at high strain rates must be distinguished from a test at low strain rates by the fact that inertia becomes significant. In this case, a dynamic-equilibrium condition should be satisfied. Experimentally, an improvement of tensile ductility at hig
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