A New Stability Criterion for the Hot Deformation Behavior of Materials: Application to the AZ31 Magnesium Alloy
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HOT forming is a fundamental technology to obtain good properties in any material, particularly for metallic alloys used in transport and aerospace applications. This technology is based on a proper selection of the thermomechanical parameters that will ensure the production of quality products without defects. These defects could be in the form of cavities or localized deformation that may lead to failure when the material is further deformed. Therefore, it is important to determine the conditions of stress, strain rate, and temperature at which a quality part is formed, in other words, to determine the stability conditions for hot working. These three variables can be varied by means of mechanical testing, usually tension, compression, or IGNACIO RIEIRO is with the Department of Mathematics, Universidad de Castilla-La Mancha, 45071 Toledo, Spain. MANUEL CARSI´ and OSCAR RUANO are with the Department of Physical Metallurgy, CENIM-CSIC, 28040 Madrid, Spain. Contact e-mail: [email protected] Manuscript submitted November 15, 2016. Article published online May 4, 2017 METALLURGICAL AND MATERIALS TRANSACTIONS A
torsion tests, in order to simulate the forming processing of parts. The constitutive equation relating these variables is that for slip creep that can be expressed in the form of a power law or as a hyperbolic sine law, which is especially important at high strain rates, above the power-law breakdown. The constitutive equations should be integrated in a general equation, from various existing theories, that identifies instabilities. This modeling of the hot forming process is a strong tool to predict the behavior of a given material, since it allows prediction of the temperature at a given strain rate to obtain a quality part. The strain rates vary strongly depending on the equipment and the hot-working process, such as rolling, extrusion, or forging. It should be noted that the modeling was successfully applied to hundreds of materials across the entire world and constitutes now an important support in the metallurgical industry. As mentioned, the modeling is based on the material flow behavior, described by constitutive equations, and the use of efficiency and stability criteria that allow the operation of maps that are useful for determination of the optimal regions of strain rate and temperature during hot working. The zones in the map would VOLUME 48A, JULY 2017—3445
represent stable and less-stable conditions of strain rate and temperature. These maps, established by Raj,[1] are different from those of Weertman,[2] Ashby,[3] or Mohamed–Langdon[4] that are used to define the governing deformation mechanism as, for instance, Nabarro–Herring creep, grain boundary sliding, or slip creep. Our approach is to start from the dynamic material model (DMM), developed by Prasad et al.[5] in 1984, which is based on the diverse historical works of dynamic systems of thermodynamic basis, which are summarized by Wellstead.[6] Prasad and other authors apply the DMM to the hot plastic forming of metals, especially for
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