Precipitate effects on the mechanical behavior of aluminum copper alloys: Part II. Modeling
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I. INTRODUCTION
IN the first part of this series of articles, the deformation behavior of pure aluminum and an aluminum-4 wt. pct copper alloy as a function of crystal orientation and precipitate morphology was described. Since there are three different precipitates that can form, the yield strength and the work hardening coefficients change depending on the aging treatment. To develop a physically based model that has better capabilities than conventional plasticity models, it is necessary to understand how the microstructural picture changes with the deformation. Incorporating microstructural theory into the model provides a sound basis for predicting the mechanical response of a material. Visco-plastic continuum models[1] for aluminum copper alloys have been investigated in a previous study with some success. These models do not explicitly incorporate texture effects and precipitate effects in polycrystalline and single crystalline materials.[2] The crystal plasticity models[3,4,5] have the versatility to account for the role of crystal orientation, or preferred texture, and can incorporate the dislocation evolution terms directly into the constitutive description. For example, as the mean free path of dislocation motion is governed by precipitate spacing, the crystal plasticity models take into account this lengthscale effect. Previous work on aluminum alloys has focused on single aging treatments. The current effort has focused on several aging treatments to create all possible precipitate types in aluminum-copper alloys.[6–9] The current motivation is to develop a comprehensive hardening law for different aging treatments. This work attempts to develop a physically sound and comprehensive hardening law and uses a modified viscoplastic self-consistent (VPSC) polycrystal model that can H. SEHITOGLU, C.J. Ganthier Professor and Interim Head, is with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801. Contact e-mail: [email protected] T. FOGLESONG formerly with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801, is Research Engineer, with Exxon Mobile Upstream Research Company, Houston, TX 77046. H.J. MAIER, Professor, is with the Department of Materials Science, University of Paderborn, D-33905 Paderborn, Gemany. Manuscript submitted October 6, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS A
be applied to precipitation-hardened alloys.[10] The materials to be studied in this work are pure aluminum and an aluminum-copper alloy in both single and polycrystalline forms. The pure aluminum represents a baseline for comparison. The choice of single-crystal specimens eliminates the complicating effects of grain boundaries and constraints imposed on one grain by neighboring grains. Single crystals have no contribution from grain boundary effects, and thus, work hardening only has components due to dislocationdislocation interactions in the solutionized case; and in the aged samples, there are additional dislocation-precipitatio
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