Texture mediated grain boundary network design in two dimensions
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Christopher A. Schuh Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Received 8 January 2016; accepted 15 March 2016)
While materials design in the context of texture dependent properties is well developed, theoretical tools for microstructure design in the context of grain boundary sensitive properties have not yet been established. In the present work, we present an invertible relationship between texture and grain boundary network structure for the case of spatially uncorrelated twodimensional textures. By exploiting this connection, we develop mathematical tools that permit the rigorous optimization of grain boundary network structure. Using a specific multi-objective materials design case study involving elastic, plastic and kinetic properties, we illustrate the utility of this texture mediated approach to grain boundary network design. We obtain a microstructure that minimizes grain boundary network diffusivity while simultaneously improving yield strength by an amount equal to half of the theoretically possible range. The theoretical tools developed here could complement experimental grain boundary engineering efforts to help accelerate the discovery of materials with improved performance.
I. INTRODUCTION
Much of microstructure science is focused on two intimately related tasks: (i) predicting the properties of a given microstructure and (ii) designing a microstructure to achieve a desired property. Both of these endeavors are fundamentally rooted in the notion that material structure determines material performance. Mathematically this idea has been canonized in various structure-property relations (see, e.g., Refs. 1, 2 and references therein). However, within the meso-scale microstructure community, rigorous theoretical developments have been largely restricted to the forward problem of property prediction. Various predictive models of material performance have been formulated and have proven successful.3–5 However, the inverse problem of microstructure design has often consisted of an empirical trial-and-error approach. Over the last decade, theoretical tools have been developed that allow materials designers to explore the complete universe of physically realizable microstructures for a given material and identify those that meet various performance objectives/design constraints.6,7 This design formalism is referred to as microstructure sensitive design for performance optimization (MSDPO). Whereas the materials designer formerly had a finite (and rather incomplete) catalogue of observed microstructures Contributing Editor: Susan B. Sinnot a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2016.138 J. Mater. Res., Vol. 31, No. 9, May 14, 2016
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and forward models at his/her disposal, the advent of these new microstructure design tools has allowed for the consideration of material structure as a continuous design variable and the rigorous solution
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