A Combined Precipitation, Yield Stress, and Work Hardening Model for Al-Mg-Si Alloys Incorporating the Effects of Strain
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DUCTION
AGE-HARDENING Al-Mg-Si aluminum alloys are widely used by the industry since they offer a good combination of properties like strength, ductility, corrosion resistance, formability, and weldability. Precipitation hardening from different types of metastable phases and clusters is the main strengthening contribution in these alloys,[1–5] but for many of the properties mentioned above, due consideration must also be given to elements in solid solution as well as OLE RUNAR MYHR is with Hydro Aluminium, Research and Technology Development, N-6601, Sunndalsøra, Norway and also with the SIMLab, Centre for Advanced Structural Analysis (CASA), Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway. Contact e-mail: [email protected] ODD STURE HOPPERSTAD and TORE BØRVIK are with the SIMLab, Centre for Advanced Structural Analysis (CASA), Norwegian University of Science and Technology (NTNU). Manuscript submitted December 3, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
dislocation structures that may develop due to different types of forming operations. During thermal processing, the alloys undergo complex structural changes that bring about corresponding changes in the mechanical properties. It is therefore obvious that any model, which intends to capture the effect of the thermomechanical processing on the resulting tensile properties without the use of a vast amount of experimental data, needs an advanced precipitation model as a cornerstone. During the last decades, several precipitation models have been developed based on the principles outlined in the pioneer works by Langer and Schwarts[6] and Kampmann and Wagner.[7,8] These so-called Kampmann–Wagner (KW) type of models have become increasingly sophisticated and they can incorporate several particle size distributions representing individual phases with various stoichiometry and interface energies as well as different particle shapes.[9–13] Lately they have been integrated with multi-component thermodynamic databases to predict the effect of several alloying elements on the precipitation kinetics.[14–18] These precipitation models are particularly useful when they are
coupled with mechanical models based on dislocation mechanics, which allows for predictions of the yield strength and work hardening behavior resulting from a corresponding evolution of the precipitate structure.[19,20] The models by Cheng et al.[21] and Poole and Lloyd[22] are well suited for coupling with precipitation models for predictions of the work hardening behavior of age-hardening aluminum alloys. They are based on the classical work hardening models by Kocks,[23] Mecking and Kocks[24] and Estrin,[25,26] but are recast to account for various metallurgical parameters like solute content and number density and size of shearable and non-shearable particles. Even though the models presented by Cheng et al.[21] and Poole and Lloyd[22] are useful for work hardening predictions, they are mainly restricted to room temperature deformation where strain rate effects ar
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