Incorporation of Solid Solution Alloying Effects into Polycrystal Modeling of Mg Alloys
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THE plastic deformation of Mg and its alloys is accommodated primarily by the glide of hai-type dislo cations on (0001) basal and 1010 prismatic (and other nonbasal) planes, the glide of hc + ai-type dislocations pyramidal planes, and 1012 extension and on 1122 1011 contraction twinning.[1] This multiplicity of deformation modes makes it difficult to predict the deformation behavior of these metals. To overcome this problem, conventional characterization methods are commonly supplemented by continuum mechanics-based polycrystal deformation models. These models allow one to probe the micromechanical phenomena indirectly that take place within a polycrystal. Examples of studies that exploit such a methodology, to understanding the deformation behavior of Mg alloy AZ31 (containing 2.7 at. pct Al and 0.4 at. pct Zn), are listed in Table I. Among the different modeling approaches that could be used to study the deformation behavior of Mg, BABAK RAEISINIA, formerly Postdoctoral Fellow, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904-4745, is now Research Fellow, Department of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. Contact e-mail: [email protected] SEAN R. AGNEW, Associate Professor, is with the Department of Materials Science and Engineering, University of Virginia. AINUL AKHTAR, Adjunct Professor, is with the Department of Materials Engineering, the University of British Columbia, Vancouver, BC V6T 1Z4, Canada. Manuscript submitted: February 1, 2010 Article published online November 19, 2010 1418—VOLUME 42A, MAY 2011
models based on the self-consistent homogenization[15] scheme have become a popular choice. These models provide an attractive balance between the microstructural detail that may be incorporated and the computational load of the problem. As with any polycrystal plasticity model, the crux of the problem is the partitioning of the macroscopic stresses and strains among the grains at the mesoscopic level or the inverse problem of projecting the local behavior of the grains to the macroscopic level of the polycrystal. On the other hand, numerous studies have been performed on Mg single-crystals to shed light on their deformation behavior; examples are noted in Table II. However, linking the results of these experiments with the aforementioned polycrystal models has, in general, been a challenge. The main issue is that the ratio of the CRSSs required to activate the glide of hai-type dislocations on nonbasal vs basal planes, as determined from single-crystal studies, are not comparable with those necessary for polycrystal simulations. This suggests that single-crystal CRSS values may not be used directly within the polycrystal plasticity modeling framework. A comparison of the CRSS values presented in Tables I and II shows that the results of the two methods can differ by a factor as high as ~50. An implication of this discrepancy is that the material constants in the models may be considered as not
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