High-temperature deformation of commercial-purity aluminum
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INTRODUCTION
ONE of the most relevant aspects of microstructural control during thermomechanical processing is the precise characterization of the flow behavior of the material under the corresponding processing conditions. Knowledge of the adequate relationships that govern the flow stress dependence on the strain applied, rate of straining, deformation temperature, and microstructure is of utmost importance in determining the material response to the requirements of the particular processing operation. In the past few years, there has been an important development aimed at understanding the mechanical behavior of materials under manufacturing conditions based on the concepts of dynamic material modeling (DMM), which have been advanced by Gegel and co-workers[1,2,3] and applied extensively by Prasad and co-workers for different materials.[4–9] The fundamental basis of DMM has also been reviewed by Alexander in relation to the hot deformation of steels.[10] Dynamic material modeling, as presented by the previously referenced authors, deals mainly with the mechanisms of dissipation of the instantaneous power applied to the material during manufacturing and the concurrent changes in the rate of entropy production that is set up by the material system. According to Gegel et al.,[3] DMM is capable of providing information consistent with important aspects of finite-element models employed in determining optimal solutions concerning different materials processing operations. The basic assumption of DMM is that the rate of work applied to the material per unit volume (P) is dissipated coherently by partitioning it into a so-called ‘‘dissipator content’’ (G), related basically to the temperature rise that takes place during the processing operation and other E.S. PUCHI and M.H. STAIA, Professors, are with the School of Metallurgical Engineering and Materials Science, Central University of Venezuela, Caracas 1045, Venezuela. Manuscript submitted February 17, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
continuum effects, including plastic instability and fracture processes, and a so-called ‘‘dissipator co-content’’ (J), related to the microstructural changes that occur in the material during manufacturing. This can be simply expressed as P5
s
z ε
0
0
* εz d s 1 * s dεz 5 sεz
[1]
where J5
s
z ε
0
0
* εz d s and G 5 * s dεz
[2]
Since both J and G are complementary functions, they are related by means of a Legendre transformation, and therefore, the partitioning of power between J and G at a given temperature and strain is given by ]J ~]G !
T,ε
5
~]] lnln εsz !
[3]
T,ε
The critical assumption made at this point by Gegel and co-workers[1,2] is that this ratio is equivalent to the strain rate sensitivity exponent of the material and that, therefore, the dynamic constitutive equation is the power-law relationship advanced by Tegart and co-workers[11,12,13] to describe the temperature and strain rate dependence of steadystate flow stress data under conditions of ‘‘low stress’’ (s , 18 MPa for aluminum appr
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