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# Determination of Representative Volume Element (RVE) based on Microstructure

Estimating the response of polycrystalline materials using sets of weighted statistical volume elements

Siddiq M. Qidwai, David M. Turner, Stephen R. Niezgoda, Alexis C. Lewis, Andrew B. Geltmacher, David J. Rowenhorst, Surya R. Kalidindi

Acta Materialia, 60, 5284–5299, 2012; http://dx.doi.org/10.1016/j.actamat.2012.06.026

In the last 10 years or so, advancements in the capabilities of microstructural characterization techniques and tools, such as EBSD, XRD, XCMT, SEM and TEM, have made it possible for the computational mechanics researchers to consider direct or statistical utilization of the microstructure in their computational models. This desire brings to focus the ever recurring question on the accurate definition of the representative volume element (RVE) for the microstructure under condiseration. The common understanding is that the RVE should be large enough to reflect all of the "salient features" in the microstructure in a statistically accurate manner. In practice, this is achieved by iteratively increasing the RVE size until convergence is achieved in the calculated values of selected effective properties. It is generally assumed then that the chosen RVE provides an accurate statistical description of the microstructure. However, it is quite establised that the microstructure–property mapping is many-to-one. That is, different microstructures could exhibit the same behavior for a given effective property.

Recently, researchers at the Naval Research Laboratory and Drexel University have publised a paper on the concept of building RVEs of polycrystalline materials as weighted sets of statistical volume elements (SVEs) based on microstructure, in the sense of most dominant statistical features, to ensure that a wide range of material phenomena and their associated variations can be predicted. This is in contrast with the above-mentioned traditional material property convergence-based methods. An added advantage of this technique is that smaller, computationally manageable models (SVEs) are obtained instead of large and sometimes intractable RVEs.

All credit for the development of the SVE method used in this research goes to the Drexel Univesrity group headed by Dr. Surya Kalidindi.

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