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Modeling Texture Evolution in Polycrystalline Materials Using Spherical Harmonics

For decades the prime role of metallurgists has been to optimize material microstructure for performance by designing and applying appropriate thermo-mechanical processing steps. Until recently the study of the relationships between processing and microstructure has largely remained within the purview of experimental metallurgists because the mechanisms that contribute to the microstructural changes are very complex, and the changes occur either simultaneously or successively to varying degrees, depending on location within the material. The development of computational models for predicting the overall response of materials to such a complex microstructural changes is extremely difficult. However, recent advances in high-performance computing have led to considerable progress in addressing this challenge. This study addresses this question by focusing on the textural point of view which in this work is represented by the crystallographic texture (also called Orientation Distribution Function or ODF). The textural representation of the material is expanded in terms of spherical harmonics. Developing such approach is a crucial to advances in material-by-design. This model is based on a conservation principle in the orientation space. It links any desired final microstructure of a polycrystalline material to a given initial state. To investigate a typical processing example of deformation in tension, compression and rolling for isotropic copper, an FCC material, a microstructure is numerically simulated using a Taylor type model. Taylor models are known to correctly fit the deformation of cubic microstructures. A first goal is to determine the number of texture coefficients and their values for different expansions of the Fourier series. The second to use the texture coefficients in a processing path model to predict the microstructure evolution. The difference between the experimental and the predicted texture coefficients will be evaluated using the root mean square deviation for various expansions of the Fourier series. Also it is necessary to know how small a step size one needs to use in the numerical discretization of the deformation process. To increase accuracy we introduce Richardson extrapolation. This method allows us to increase the size of the discretization step and result in a small error. For hexagonal close-packed materials, the Taylor model is not applicable. Therefore to verify the processing path model for the example of commercially pure titanium, the texture evolution matrix is modeled using experimental data obtained for cold and warm rolling. The model appears to be of good accuracy. To examine how much of the possible microstructural material properties are achievable using typical deformation processes, the microstructural evolution is visualized within the microstructure hull. The results suggest that vast amounts of possible microstructural configurations are unexplored by those classical deformation methods. / A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2006. / June 19, 2006. / Processing Path, Texture Evolution, Spherical Harmonics, Material by Design / Includes bibliographical references. / Hamid Garmestani, Professor Co-Directing Dissertation; Justin Schwartz, Professor Co-Directing Dissertation; Young Park, Outside Committee Member; Leon Van Dommelen, Committee Member.
ContributorsBouhattate, Jamaa (authoraut), Garmestani, Hamid (professor co-directing dissertation), Schwartz, Justin (professor co-directing dissertation), Park, Young (outside committee member), Van Dommelen, Leon (committee member), Department of Mechanical Engineering (degree granting department), Florida State University (degree granting institution)
PublisherFlorida State University, Florida State University
Source SetsFlorida State University
LanguageEnglish, English
Detected LanguageEnglish
TypeText, text
Format1 online resource, computer, application/pdf
RightsThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.

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