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A Spectral Iterative Method for the Computation of Effective Properties Of Elastically Inhomogeneous Polycrystals

Published online by Cambridge University Press:  20 August 2015

Saswata Bhattacharyya ,
Tae Wook Heo ,
Kunok Chang  and
Long-Qing Chen
Saswata Bhattacharyya*
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Tae Wook Heo*
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Kunok Chang*
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Long-Qing Chen*
Affiliation:
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

We report an efficient phase field formalism to compute the stress distribution in polycrystalline materials with arbitrary elastic inhomogeneity and anisotropy The dependence of elastic stiffness tensor on grain orientation is taken into account, and the elastic equilibrium equation is solved using a spectral iterative perturbation method. We discuss its applications to computing residual stress distribution in systems containing arbitrarily shaped cavities and cracks (with zero elastic modulus) and to determining the effective elastic properties of polycrystals and multilayered composites.

Keywords

74B1074S25Elasticityspectral methoditerative method
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 3 , March 2012 , pp. 726 - 738
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Doi, M., Elasticity effects on the microstructure of alloys containing coherent precipitates, Prog. Mater. Sci., 40 (1996), 79.Google Scholar
[2]Fratzl, P., Penrose, O. and Lebowitz, J., Modeling of phase separation in alloys with coherent elastic misfit, J. Stat. Phys., 95 (1999), 1429.Google Scholar
[3]Chen, L.-Q., Phase-field models for microstructural evolution, Ann. Rev. Mater. Res., 32 (2002), 113.Google Scholar
[4]Leo, P. H., Lowengrub, J. S. and Jou, H. J., A diffuse interface model for microstructural evolution in elastically stressed solids, Acta Mater., 46 (1998), 2113.CrossRefGoogle Scholar
[5]Zhu, J., Chen, L.-Q. and Shen, J., Morphological evolution during phase separation and coarsening with strong inhomogeneous elasticity, Modell. Simul. Mater. Sci. Eng., 9 (2001), 499.CrossRefGoogle Scholar
[6]Hu, S. Y. and Chen, L.-Q., A phase-field model for evolving microstructures with strong elastic inhomogeneity, Acta Mater., 49 (2001), 1879.Google Scholar
[7]Yu, P., Hu, S. Y., Chen, L.-Q. and Du, Q., An iterative-perturbation scheme for treating inho-mogeneous elasticity in phase-field models, J. Comput. Phys., 208 (2005), 34.CrossRefGoogle Scholar
[8]Wang, Y. U., Jin, Y. M. and Khachaturyan, A. G., Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid, J. Appl. Phys., 92 (2002), 1351.Google Scholar
[9]Jin, Y. M., Wang, Y. U. and Khachaturyan, A. G., Three-dimensional phase field microelasticity theory and modeling of multiple cracks and voids, Appl. Phys. Lett., 79 (2001), 3071.Google Scholar
[10]Fan, D. and Chen, L.-Q., Computer simulation of grain growth using a continuum field model, Acta Mater., 45 (1997), 611.Google Scholar
[11]Fan, D., Geng, C. and Chen, L.-Q., Computer simulation of topological evolution in 2-D grain growth using a continuum diffuse-interface field model, Acta Mater., 45 (1997), 1115.Google Scholar
[12]Khachaturyan, A. G., Theory of Structural Phase Transformations in Solids, John Wiley and Sons, New York, 1983.Google Scholar
[13]Li, D. Y. and Chen, L.-Q., Shape evolution and splitting of coherent particles under applied stresses, Acta Mater., 47 (1998), 247.Google Scholar
[14]Mura, T., Micromechanics of Defects in Solids, Springer, 1987.CrossRefGoogle Scholar
[15]Torquato, S., Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer, 2002.CrossRefGoogle Scholar
[16]Toonder, J.M.J. den, Dommelen, J. A. W. van and Baaijens, F. P. T., The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: Theory, measurement and computation, Modell. Simul. Mater. Sci. Eng., 7 (1999), 909.Google Scholar
[17]Vedantam, S. and Patnaik, B. S. V., Efficient numerical algorithm for multiphase field simulations, Phys. Rev. E, 73 (2006), 016703.Google Scholar
[18]Ni, Y. and Chiang, M., Prediction of elastic properties of heterogeneous materials with complex microstructures, J. Mech. Phys. Solids, 55 (2007), 517.CrossRefGoogle Scholar