Application of a self-consistent model to study the flow behavior of CuZn39Pb3 at elevated temperatures
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Hot compression tests were carried out on the duplex a 1 b leaded brass CuZn39Pb3 in temperature range of 600–800 °C and at strain rates of 0.001–1 s1. A self-consistent model was used to analyze the flow behavior of the constituents and the material. A linear viscoplastic model was used to relate the flow stress of b and a 1 b composite to strain rate and the corresponding viscosity parameters were calculated at various deformation conditions. Using the viscosity parameters of b and a 1 b and the volume fractions of the constituents, the viscosity parameter of a was calculated. The values of the viscosity-like parameters and strain rate sensitivity for b and a 1 b composite were calculated using the nonlinear powerlaw viscoplastic equation. The results showed that the flow stress of a calculated using the self-consistent model was considerably higher than that of b. The difference could be attributed to the lower Zn content in a. The flow stress of a 1 b composite was calculated using the law of mixture rule. The law of mixture modeling of a 1 b composite for the iso-strain condition resulted to the overestimation of flow stress. The difference between the experimental and predicted results was attribute to the strain partitioning between a and b.
I. INTRODUCTION
Leaded brasses are characterized by a duplex structure of a, with face-centered cubic (FCC) and b with bodycentered cubic (BCC) microstructures. They have a wide range of applications, especially for brass forging and machining parts. The hot deformation behavior of brasses with different microstructures of single-phase a or b and duplex a 1 b has been investigated and documented in the literature.1–6 Despite our insight into the flow behaviors of individual a or b, our knowledge about their coexistence is still lacking. This is attributed to the different flow behaviors of a and b and their interactions during straining at elevated temperatures. Similar investigations into duplex stainless steels7,8 and Ti alloys9,10 have shown that different deformation mechanisms of the constituents complicate the modeling of flow curves at elevated temperatures. The situation is more complicated when we deal with leaded duplex brass comparing to those which are free of lead. Due to the limited solubility of lead in Cu alloys, it is often observed as the undissolved particles in a. This means that the present models for the flow behavior of a at hot working temperatures cannot be simply used to describe the flow behavior of lead-bearing a in leaded duplex brass alloys.
Contributing Editor: Yang-T. Cheng a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.337 J. Mater. Res., Vol. 30, No. 22, Nov 27, 2015
Modeling the flow behavior of alloys has been always interesting and has drawn scholars’ considerable attention.11,12 For multi-phase alloys, modeling on the basis of the constituents individual responses has been always interesting. The constitutive equations13,14 as well as the self-consistent models15–17 have been tried for differen
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