Simulation of the hot-tension test under cavitating conditions
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I.
INTRODUCTION
THE tension test is the oldest and most common mechanical test used to assess the plastic flow response of metals. Because of its simplicity, it is often used to obtain insight into material behavior over a wide range of temperatures and strain rates. Hence, it is not surprising that considerable effort has been expended on theoretical analyses of the tension test. For situations involving no cavitation, several finite difference approaches involving direct application of the load equilibrium equation have been utilized. For example, Ghosh,t11 Semiatin et al.,[21 and Lombard et al. [3] have used such direct equilibrium techniques to predict successfully the kinetics of flow localization and overall tensile ductility as a function of material properties and initial sample geometry. In addition, Lombard et al. compared the results of a number of direct equilibrium calculations to more detailed finite-element method predictions and obtained reasonably good agreement. Several theoretical analyses have also been conducted for the case when cavitation occurs simultaneously with tensile deformation. Jonas and Baudelet141 investigated the influence of initial geometric defects and the generation and growth of cavities on flow stability. They concluded that cavitation reduces the apparent magnitude of the strain-rate sensitivity and strain-hardening coefficients, thus increasing the tendency for flow instability. In a more detailed (numerical) approach, Lian and SuerytSJ modeled necking in P D. NICOLAOU, formerly Visiting Scientist, Metals and Ceramics Division, Materials Directorate, Wright Laboratory, WL/MLLN, is Research Scientist, Materials and Processes Division, UES Inc., Dayton, OH 45432-1894. S.L. SEMIATIN, Senior Scientist, and C.M. LOMBARD, Materials Research Engineer, are with the Metals and Ceramics Division, Materials Directorate, Wright Laboratory, WL/MLLN, Wright-Patterson Air Force Base, OH 45433-7817. Manuscript submitted November 9, 1995. 3112--VOLUME 27A, OCTOBER 1996
the presence of cavitation. In their long-wavelength approach,t6.71 they examined the effect of strain-rate sensitivity and cavity growth rate on the competition between necking and cavitation (fracture) in controlling tensile ductility. The objective of the present work was to develop a direct equilibrium analysis of the hot-tension test from which the detailed effect of cavity growth parameters, strain-rate hardening, and specimen geometry on flow behavior (e.g., elongation, strain profiles, failure mode) could be determined. The direct equilibrium approach was chosen because it enables, in a relatively simple manner, the incorporation of cavitation into the description of deformation as well as stress triaxiality effects on flow stability. II.
MODEL FORMULATION
In this section, the analysis of the sheet-tension test based on the direct-equilibrium approach is described. In the absence of cavitation, the approach is identical to the onedimensional one formulated by Semiatin et al.121 and, thus, will be summarized only
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