Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242
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INTRODUCTION
K = large positive constant which penalizes the dilational strain kkk = strain-rate component or = effective stress = flow stress e = effective strain rate
THE mechanical behavior of materials under processing is generally characterized by constitutive equations which relate the flow stress to the strain, strain rate, and temperature. The constitutive relations are experimentally evaluated using mechanical testing techniques I and represented either in the form of empirical rate equations 2 which aid in identification of the specific atomistic rate-controlling mechanisms or in the form of simple algebraic equations 3 which can be used in process modeling. In recent years, hotforming processes have been successfully modeled using a rigid viscoplastic finite-element method 4'5 which predicts deformation behavior at selected points (nodes) in each element by application of a variational principle. The variational-principle functional t~ for a rigid viscoplastic material is written as 5
where
fE(k*)dv = work function = f ~ . de f F 9 V* 9 ds
boundary function which takes into account the frictional force (F) and admissible velocity V*
Y. V. R. K. PRASAD, Associate Professor, Department of Metallurgy, Indian Institute of Science, Bangalore 560012, India, is now NRC-AFSC Senior Research Associate in Air Force Wright Aeronautical Laboratories (AFWAL/MLLM), Wright-Patterson Air Force Base, OH 45433. H.L. GEGEL is Senior Scientist, AFWAL/MLLM, Wright-Patterson Air Force Base, OH 45433. J.C. MALAS, J.T. MORGAN, and K.A. LARK are Materials Research Engineers, AFWAL/MLLM, Wright-Patterson Air Force Base, OH 45433. S.M. DORAIVELU and D.R. BARKER are Visiting Scientists, Universal Energy Systems, Inc., Dayton, OH 45432. Manuscript submitted October 24, 1983. METALLURGICALTRANSACTIONS A
The work function takes into account in an implicit fashion the metallurgical phenomena which occur during hot working. For a given set of constitutive equations used in the work function, the numerical method offers an admissible solution to a given plasticity problem. It is often desirable to arrive at a unique or optimum solution, and this is possible only if the dynamic material behavior is incorporated explicitly into the finite-element method. The interconnective material constraints, however, are too complicated to be written directly in algebraic form. The development of a processing map 6'7 delineating the "safe" temperature-strain rate regimes for processing represents a major step toward acceptable solutions. Often, the "safe" regime defined by these maps is still a wide area 7 which provides several combinations of temperature and strain rate at which processing can be carried out. In this paper a method of modeling the dynamic material behavior in terms of a parameter which defines unique T-k combination(s) for hot forming is presented and applied to the hot upsetting of Ti-6A1-2Sn-4Zr-2Mo-0.1Si (Ti-6242) a l l o y - - a material of interest in the dual-property disk application. 8 The hotdeformation characteri
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