Contribution-13

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Contents

ICME overview for Microstructure Evolution of Polycrystalline Materials.

Background

Most technologically useful materials possess polycrystalline microstructures composed of a large number of small grains separated by grain boundaries [1-2]. The orientations and arrangements of the grains and their boundary network affect significantly many properties across a wide range of scales such as fracture toughness in structures and conductivity in microprocessors [3].
Multiscale modeling diagram for the microstructure evolution of polycrystalline materials. Three different length scale studies and the main bridges needed.
The prediction of the mechanical behavior of plastically deforming polycrystalline materials, based on the directional properties and evolving microstructure of their constituent single-crystal grains is a nowadays a central problem in computational materials science [4]. The connection between most recent mesoscopic modeling approaches to microstructure evolution and macroscopic materials behavior is of crucial importance [5]. Current constitutive models are primary formulated at the macroscale without explicit consideration of the microstructure, although features such as grain size, precipitate size and spacing play a very important role in dictating the stress-strain response of polycrystalline materials like Ni-base superalloys [6].

The development of reliable computational tools that allow researchers to predict material behavior based on material’s crystalline structure, understanding structure property relations at different scales and the challenges in building synthetic polycrystalline structures that accurately represent the material's microstructure are of crucial importance. This research will be focused on the development of a multiscale model for predicting the microstructure evolution of polycrystalline materials. In this investigation we use Ni-base superalloys which are extensively used in hot section applications such as turbine engine components because of their enhanced strength, creep, fatigue, and corrosion resistance at elevated temperatures [6].

The results obtained from this investigation will provide valuable information about how the material’s microstructures influence their strength and toughness, providing insight into ways to improve the strength and toughness of other polycrystalline materials.

Electronic Scale

First- principles calculations based on density functional theory (DFT) would be used to calculate several parameters (lattice parameter, cohesive energy, bulk modulus, elastic modulus), and therefore provide the most reliable interatomic potentials for atomistic simulations. The above parameters form the bridge between electronic scale to atomic scale.

Atomistic Scale

Molecular dynamic (MD) simulations would be performed to understand the nature of the structure-property relationship and nature of materials fracture. Specifically, it would be determined the parameters defining the force-displacement behavior of elements within the system and correct contact properties. Due to differences in simulation timescales strain will be the quantity linking the atomistic scale and the mesoscopic scale.

Mesoscopic Scale

Discrete element (DEM) simulations would be performed to study the microstructure's mechanical behavior. First, the microstructures would be digitally build by using DREAM.3D, an open and modular software package that allows user to re-construct, instatiate, quantify and vizualize microstructure digitally [7]. Grain size distribution (mean, standard deviation), crystallographic orientation distribution, misorientation would be the input information to generate polycrystalline geometries. Second, the microstructures would be pass as an input to DEM. Center of mass, vertices, facet connectivity for each polygonal grain or grain slab coming from DREAM.3D would be required to perform DEM simulations. Parameters defining the force-displacement behavior of elements within the system coming from MD would be required. And Force-displacement curve would require attractive and repulsive terms to allow for both compression and tension of the system.


References

[1] K. Barmak, M. Emelianenko, D. Golovaty, D. Kinderlehrer, and S. Ta’asan, Towards A Statistical Theory of Texture Evolution in Polycrystals.

[2] K. Barmak, D. Kinderlehrer, I. Livshits, and S. Ta’asan, Remarks on a multiscale approach to grain growth in polycrystals, in Variational Problems in Materials Science, Progr. Nonlinear Differential Equations Appl. 68, Birkh¨auser, Basel, 2006, pp. 1–11

[3] S. Ta’asan, P. Yu, D. Kinderlehrer, I. Livshits and J. Lee, Multiscale modeling and simulation of grain boundary evolution, AIAA-2003-1611, 44th AIAA/ ASME/ ASCE/ AHS Structures, Structural Dynamics, and Materials Conference, Norfolk , VA, 2003.

[4] R. Lebensohn, et al. Orientation image-based micromechanical modeling of subgrain texture in polycrystalline cooper. Acta Materialia 56 . 2008. 3914–3926.

[5] Maria Emelianenko. Multiscale computational modeling of complex materials systems. . Mathematics and the Genome Initiative Workshop. Institute for Mathematics and Its Applications. September 12-15, 2012. [6] M. Shenoy et al. Microstructure-sensitivity modeling of Polycrystalline IN 100. International Journal of plasticity 24, 2008, 1694-1730.

[6] M. Shenoy et al. Microstructure-sensitivity modeling of Polycrystalline IN 100. International Journal of plasticity 24, 2008, 1694-1730.

[7] DREAM.3D Repository, \textit{http://dream3d.bluequartz.net}. Accessed November 14, 2012.

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