Skip to main content
SpringerLink
Log in

Developing Virtual Microstructures and Statistically Equivalent Representative Volume Elements for Polycrystalline Materials

  • Living reference work entry
  • First Online:
Book cover Handbook of Materials Modeling

Abstract

This chapter introduces computational methods for generating virtual material microstructures of engineering materials with heterogeneities. Microstructures of polycrystalline materials containing localized features such as annealing twins, particulates or precipitates, and subgrain phases are the focus of this discussion. The methods use data from characterization methods to provide 3D statistical distribution and correlation functions that serve as inputs to the virtual microstructure generation process. Computational methods infer 3D statistical descriptors from 2D surface data and use stereology or other optimization-based projection techniques for 2D to 3D development. The chapter reviews the DREAM.3D software package and discusses newly developed methods to incorporate twins, particles, and subgrain-scale phases. Finally, the microstructure-based SERVE is introduced in the realm of establishing microstructure-property relations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Alam A, Eastman D, Jo M, Hemker KJ (2016) Development of a high-temperature tensile tester for micromechanical characterization of materials supporting meso-scale ICME models. JOM 11(68):2754–2760

    Article  Google Scholar 

  • Bagri A, G W, Stinville JC, Lenthe W, Pollock T, Woodward C, Ghosh S (2018, in press) Microstructure and property-based statistically equivalent representative volume elements for polycrystalline Ni-based superalloys containing annealing twins. Met Mat Trans A

    Google Scholar 

  • Baniassadi M, Garmestani H, Li DS, Ahzi S, Khaleel M, Sun X (2011) 3-phase solid oxide fuel cell anode microstructure realization using 2-point correlation functions. Acta Mat 59(1):30–43

    Article  Google Scholar 

  • Bhandari Y, Sarkar S, Groeber MA, Uchic MD, Dimiduk D, Ghosh S (2007) 3D polycrystalline microstructure reconstruction from FIB generated serial sections for FE Analysis. Comput Mat Sci 41:222–235

    Article  Google Scholar 

  • Busso E, Meissonier F, O’Dowd N (2000) Gradient-dependent deformation of two-phase single crystals. J Mech Phys Sol 48:2333–2361

    Article  ADS  Google Scholar 

  • Cai B, Adams B, Nelson T (2007) Relation between precipitate-free zone width and grain boundary type in 7075-T7 Al alloy. Acta Mat 55(5):1543–1553

    Article  Google Scholar 

  • Donegan SP, Tucker JC, Rollett A, Barmak K, Groeber MA (2013) Extreme value analysis of tail departure from log-normality in experimental and simulated grain size distributions. Acta Mat 61(15):5595–5604

    Article  Google Scholar 

  • Echlin MP, Lenthe WC, Pollock TM (2014) Three-dimensional sampling of material structure for property modeling and design. Integ Mat Manuf Innov 3(1):21

    Article  Google Scholar 

  • Fromm BS, Chang K, McDowell DL, Chen L, Garmestani H (2012) Linking phase-field and finite-element modeling for process-structure-property relations of a Ni-base superalloy. Acta Mat 60:5984–5999

    Article  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Groeber MA, Jackson M (2014) DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mat Manuf Innov 3:5

    Google Scholar 

  • Groeber MA, Haley BK, Uchic MD, Dimiduk D, Ghosh S (2006) 3D reconstruction and characterization of polycrystalline microstructures using a FIB-SEM system. Mat Char 57(4–5):259–273

    Article  Google Scholar 

  • Groeber MA, Ghosh S, Uchic MD, Dimiduk D (2008a) A framework for automated analysis and representation of 3D polycrystalline microstructures, part 1: statistical characterization. Acta Mat 56(6):1257–1273

    Article  Google Scholar 

  • Groeber MA, Ghosh S, Uchic MD, Dimiduk D (2008b) A framework for automated analysis and representation of 3D polycrystalline microstructures, part 2: synthetic structure generation. Acta Mat 56(6):1274–1287

    Article  Google Scholar 

  • Guo EY, Chawla N, Jing T, Torquato S, Jiao Y (2014) Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method. Mat Charac 89:33–42

    Article  Google Scholar 

  • Hasanabadi A, Baniassadi M, Abrinia K, Safdari M, Garmestani H (2016) 3D microstructural reconstruction of heterogeneous materials from 2D cross sections: a modified phase-recovery algorithm. Comput Mat Sci 111:107–115

    Article  Google Scholar 

  • Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Sol 11(5):357–372

    Article  ADS  Google Scholar 

  • Jackson M (2018) DREAM.3D 6.4 Release. http://dream3d.bluequartz.net/?page_id=32

  • Jiao Y, Stillinger FH, Torquato S (2007) Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys Rev E 76(3):031110

    Article  MathSciNet  ADS  Google Scholar 

  • Jiao Y, Padilla E, Chawla N (2013) Modeling and predicting microstructure evolution in lead/tin alloy via correlation functions and stochastic material reconstruction. Acta Mat 61(9): 3370–3377

    Article  Google Scholar 

  • Keshavarz S, Ghosh S (2015) Hierarchical crystal plasticity fe model for nickel-based superalloys: sub-grain microstructures to polycrystalline aggregates. Int J Solids Struct 55:17–31

    Article  Google Scholar 

  • Kumar A, Nguyen L, DeGraef M, Sundararaghavan V (2016) A Markov random field approach for microstructure synthesis. Model Simul Mater Sci Eng 24(3):035015

    Article  ADS  Google Scholar 

  • Lenthe W (2017) Twin related domains in polycrystalline nickel-base superalloys: 3d structure and fatigue. PhD thesis, University of California- Santa Barbara

    Google Scholar 

  • Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recogn 26(4):617–625

    Article  Google Scholar 

  • MacSleyne J, Uchic MD, Simmons JP, De Graef M (2009) Three-dimensional analysis of secondary γ’ precipitates in rené-88 DT and UMF-20 superalloys. Acta Mat 57(20):6251–6267

    Article  Google Scholar 

  • Massey FJ (1951) The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 46(253): 68–78

    Article  Google Scholar 

  • McDowell D, Ghosh S, Kalidindi S (2011) Representation and computational structure-property relations of random media. JOM J Miner Met Mater Soc 63(3):45–51

    Article  Google Scholar 

  • Meyer F (1994) Topographic distance and watershed lines. Signal Process 38(1):113–125

    Article  Google Scholar 

  • Niezgoda S, Turner D, Fullwood D, Kalidindi S (2010) Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics. Acta Mat 58:4432–4445

    Article  Google Scholar 

  • Nouailhas D, Cailletaud G (1996) Multiaxial behaviour of Ni-base single crystals. Scrip Mat 34:565–571

    Article  Google Scholar 

  • Ostoja-Starzewski M (2006) Material spatial randomness: from statistical to representative volume element. Prob Eng Mech 21(2):112–132

    Article  MathSciNet  Google Scholar 

  • Parthasarathy TA, Rao SI, Dimiduk D (2004) A fast spreadsheet model for the yield strength of superalloys. In: Green KA, Pollock TM, Harada H, Howson TE, Reed RC, Schirra JJ, Walston S (eds) TMS (The Minerals, Metals & Materials Society), Superalloys, pp 887–896

    Google Scholar 

  • Pilchak A (2013) Fatigue crack growth rates in alpha titanium: faceted vs. striation growth. Scrip Mat 68(5):277–280

    Article  Google Scholar 

  • Pinz M, Weber G, Lenthe W, Uchic M, Pollock T, Woodward C, Ghosh S (2018, in press) Microstructure and property based statistically equivalent representative volume elements for modeling subgrain γ − γ′ microstructures in Ni-based superalloys. Acta Mater

    Google Scholar 

  • Pollock TM, Argon A (1992) Creep resistance of CMSX-3 Nickel-base superalloy single crystals. Acta Mat 40:1–30

    Article  Google Scholar 

  • Pollock TM, Tin S (2006) Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties. J Propuls Power 22(2):361–374

    Article  Google Scholar 

  • Pyrz R (2006) Quantitative description of the microstructure of composites. part I: morphology of unidirectional composite systems. Comput Sci Technol 50(2):197–208

    Article  Google Scholar 

  • Rollett AD, Robert C, Saylor D (2006) Three dimensional microstructures: statistical analysis of second phase particles in AA7075-T651. Mater Sci Forum 519–521:1–10

    Article  Google Scholar 

  • Rollett AD, Lee SB, Campman R, Rohrer GS (2007) Three-dimensional characterization of microstructure by electron back-scatter diffraction. Annu Rev Mater Res 37:627–658

    Article  ADS  Google Scholar 

  • Saylor DM, Fridy J, El-Dasher BS, Jung KY, Rollett AD (2004) Statistically representative 3D microstructures based on orthogonal observation sections. Metall Mater Trans A 35:1969–1979

    Article  Google Scholar 

  • Sundararaghavan V, Zabaras N (2005) Classification and reconstruction of three-dimensional microstructures using support vector machines. Comput Mater Sci 32(2):223–239

    Article  Google Scholar 

  • Swaminathan S, Ghosh S (2006) Statistically equivalent representative volume elements for composite microstructures, part I: with interfacial debonding. J Compos Mater 40(7):605–621

    Article  Google Scholar 

  • Swaminathan S, Ghosh S, Pagano NJ (2006) Statistically equivalent representative volume elements for composite microstructures, part I: without damage. J Compos Mater 40(7): 583–604

    Article  Google Scholar 

  • Tewari A, Gokhale AM, Spowart JE, Miracle DB (2004) Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions. Acta Mater 52(2):307–319

    Article  Google Scholar 

  • Torquato S (2002) Random heterogeneous materials. Springer, New York

    Book  Google Scholar 

  • Tu X, Shahba A, Ghosh S (2018, in review) Microstructure and response-based statistically equivalent RVEs for 7000-series Aluminum alloys

    Google Scholar 

  • Turner TJ, Shade PA, Bernier JV, Li SF, Schuren JC, Kenesei P, Suter RM, Almer J (2017) Crystal plasticity model validation using combined high-energy diffraction microscopy data for a Ti-7Al specimen. Metall Mater Trans A 48:627–647

    Article  Google Scholar 

  • Uchic MD, Groeber MA, Dimiduk DM, Simmons JP (2006) 3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-SEM. Scripta Mat 55(1):23–28

    Article  Google Scholar 

  • Underwood E (1972) The mathematical foundations of quantitative stereology. In: Stereology and quantitative metallography. American Society for Testing and Materials, Philadelphia, pp 3–38

    Chapter  Google Scholar 

  • Unocic RR, Zhou N, Kovarik L, Shen C, Wang Y, Mills MJ (2011) Dislocation decorrelation and relationship to deformation microtwins during creep of a γ′ precipitate strengthened Ni-based superalloy. Acta Mater 59:7325–7339

    Article  Google Scholar 

  • Wang Q, Zhang H, Cai H, Fan Q, Zhang X (2016) Statistical three-dimensional reconstruction of co-continuous ceramic composites. Finite Elem Anal Des 114:85–91

    Article  Google Scholar 

  • Zhang C, Enomoto M, Suzuki A, Ishimaru T (2004) Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metall Mater Trans A 35(7):1927–1933

    Article  Google Scholar 

Download references

Acknowledgements

S. Ghosh acknowledges the contributions of his graduate students, M. Pinz, G. Weber, and X. Tu, and postdoctoral researcher, Dr. A. Bagri, for their contributions to various aspects presented in this chapter. He also acknowledges the sponsorship of the Air Force Office of Scientific Research, Air Force Research Laboratories (Program Manager A. Sayir), and Office of Naval Research (Program Manager W. Nickerson). Computing support by the Homewood High Performance Compute Cluster (HHPC) and Maryland Advanced Research Computing Center (MARCC) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Departments of Civil, Mechanical and Materials Science & Engineering, Johns Hopkins University, Baltimore, MD, USA

    Somnath Ghosh

  2. Wright Patterson Air Force Base, Air Force Research Laboratory, Dayton, OH, USA

    Michael A. Groeber

Authors
  1. Somnath Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael A. Groeber
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Somnath Ghosh .

Editor information

Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering , Massachusetts Institute of Technology , Cambridge, Massachusetts, USA

    Sidney Yip

Section Editor information

  1. Department of Mechanical Engineering, Stanford University, 450 Serra Mall, 94305, Stanford, CA, USA

    Wei Cai

  2. Dept. of Mechanical Engineering, Johns Hopkins Univeristy, 21218, Baltimore, MD, USA

    Somnath Ghosh

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Ghosh, S., Groeber, M.A. (2018). Developing Virtual Microstructures and Statistically Equivalent Representative Volume Elements for Polycrystalline Materials. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_13-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42913-7_13-1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42913-7

  • Online ISBN: 978-3-319-42913-7

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics

Search

Navigation