An Internal State Variable Constitutive Description for the Deformation of Metals at Elevated Temperatures
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PLASTIC deformation of metals and alloys under hot-working conditions (mean deformation temperatures above ~0.6 TM and strain rates above ~0.1 s)1, where TM represents the absolute temperature of the material) usually leads to the development of highly heterogeneous microstructures and mechanical properties of the workpiece as a consequence of the wide distribution of strains, strain rates, and temperatures imposed on the material being processed. In some forming operations such as hot rolling and forging, the strain is applied sequentially at decreasing mean temperatures and increasing mean strain rates, which gives rise to the static recovery and recrystallization of the material in between passes. In other deformation processes such as hot extrusion, the material is deformed in a single pass at a given mean temperature and strain rate, and therefore, the microstructural changes during deformation take place by means of dynamic restoration mechanisms. Regardless of the nature of these manufacturing processes, it is widely acknowledged that numerical modeling can provide a better understanding of the complex phenomena involved, which have led to the extensive use of such analytical methods. However, as pointed out by Abbod et al.,[1] the availability of a E.S. PUCHI-CABRERA, Professor, is with the School of Metallurgical Engineering and Materials Science, Faculty of Engineering, Universidad Central de Venezuela, Caracas 1041, Venezuela. Contact e-mail: [email protected] Manuscript submitted August 7, 2006. Article published online May 24, 2007. 990—VOLUME 38A, MAY 2007
reliable constitutive description of the material together with the accurate estimation of the parameters involved in such models represents essential features for the successful application of the computational codes employed in the analysis of metalworking processes. Such a constitutive description is expected to provide accurate flow stress values of the material, as a function of deformation temperature, rate of straining, and given internal state variables, which represent its current microstructure, over a wide range of loading conditions. In a recent article,[2] the author has proposed a simple constitutive description of a commercial aluminum-5.5 wt pct magnesium alloy. The analysis was conducted on the basis of a zero-internal state variable approach known as the Sellars–Tegart–Garofalo (STG) model, employing for this purpose a number of stress-strain curves obtained from tests conducted at nominally constant deformation temperature and strain rate. This work showed that such a model provided a satisfactory description of the flow stress data of the material as a function of the deformation conditions and that its formulation required the determination of a relatively small number of material constants from the experimental data. Also, it demonstrated that the constitutive analysis could be conducted from the actual stressstrain-temperature-strain rate data, without the need for performing any previous temperature or strain rate correction
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