3D Reconstruction of Digital Microstructures

  • Stephen D. Sintay
  • Michael A. Groeber
  • Anthony D. Rollett

The main motivation for this chapter is a decidedly practical one, in that many questions can be asked about the effect of microstructure on materials’ response. Often, the use of simple average quantities such as “grain size” is inadequate; instead one may need to consider the possibility that the full three-dimensional (3D) microstructure is important. Calculations by hand being self-evidently impracticable, computers must be used, and thus a digital microstructure is required in which all relevant microstructural features are fully described. We find sufficient complexity in materials with predominantly single-phase grain structures, perhaps containing dispersions of second phase particles. Other chapters, however, describe more complex microstructures based on, e.g., titanium alloys.


Aspect Ratio Monte Carlo Cellular Automaton Grain Shape Shape Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Brahme A, Alvi MH, Saylor D, Fridy J, Rollett AD (2006) 3D reconstruction of microstructure in a commercial purity aluminum. Scripta Mater 55:75–80CrossRefGoogle Scholar
  2. Bozzolo N, Dewobroto N, Grosdidier T, Wagner F (2005) Texture evolution during grain growth in recrystallized commercially pure titanium. Mater Sci Eng A Struct Mater 397:346CrossRefGoogle Scholar
  3. Bullard JW, Garboczi EJ, Carter WC, Fuller ER (1995) Numerical methods for computing interfacial mean curvature. Comp Mater Sci 4:103–116CrossRefGoogle Scholar
  4. Cahn JW, Fullman RL (1956) On the use of lineal analysis for obtaining particle size distribution functions in opaque samples. Trans Metall Soc AIME 206: 610–612Google Scholar
  5. Cruz-Orive LM (1976a) Correction of stereological parameters from biased samples on nucleated particle phases, part 1: nuclear volume fraction. J Microsc 107:1–18Google Scholar
  6. Cruz-Orive LM (1976b) Particle size-shape distributions: the general spheroid problem. J Microsc 107:235–253Google Scholar
  7. Dehoff RT (1962) The determination of the size distribution of ellipsoidal particles from measurements made on random plane sections. Trans Metall Soc AIME 224:474–486Google Scholar
  8. Dillard SE, Bingert JF, Thoma D, Hamann B (2007) IEEE T Vis Comput Graph 13:1528--1535Google Scholar
  9. Fernandes CP et al (1996) Multiscale geometrical reconstruction of porous structures. Phys Rev E 54:1734–1741CrossRefADSGoogle Scholar
  10. García RE et al (2004) Microstructural modeling of multifunctional material properties: the OOF project. In: Raabe D (ed) Continuum scale simulation of engineering materials. Wiley-VCH, Weinheim, Germany; Google Scholar
  11. Groeber MA (2007) Ph.D. Thesis, The Ohio State UniversityGoogle Scholar
  12. Groeber MA, Uchic MD, Dimiduk DM, Ghosh S (2008a) A framework for automated analysis and simulation of 3D polycrystalline microstructures, part 1: statistical characterization. Acta Mater 56:1257–1273CrossRefGoogle Scholar
  13. Groeber MA, Uchic MD, Dimiduk DM, Ghosh S (2008b) A framework for automated analysis and simulation of 3D polycrystalline microstructures, part 2: synthetic structure generation. Acta Mater 56:1274–1287CrossRefGoogle Scholar
  14. Hadwiger H (1957) Vorlesungen über inhalt, oberfläche und isoperimetrie. Springer, BerlinMATHGoogle Scholar
  15. Han TS, Dawson PR (2005) Representation of anisotropic phase morphology. Model Simul Mater Sci Eng 13: 203–223CrossRefADSGoogle Scholar
  16. Humphreys FJ (1999) Quantitative metallography by electron backscattered diffraction. J Microsc 195:170–185CrossRefPubMedGoogle Scholar
  17. Lewis AC, Bingert JF, Rowenhorst DJ, Gupta A, Geltmacher AB, Spanos G (2006) Two- and three-dimensional microstructural characterization of a super-austenitic stainless steel. Mater Sci Eng A 418:11–18CrossRefGoogle Scholar
  18. Li M, Ghosh S, Richmond O, Weiland H, Rouns TN (1999) Three dimensional characterization and modeling of particle reinforced metal matrix composites, part 1: quantitative description of microstructure morphology. Mater Sci Eng A A265:153–173Google Scholar
  19. MacPherson RD, Srolovitz DJ (2007) The von neumann relation generalized to coarsening of three-dimensional microstructures. Nature 446:1053CrossRefPubMedADSGoogle Scholar
  20. MacSleyne J, Simmons JP, DeGraef M (2008) On the use of moment invariants for the automated analysis of 3-D particle shapes. Model Simul Mater Sci Eng 16:045008Google Scholar
  21. Oren PE, Bakke S (2002) Process based reconstruction of sandstones and prediction of transport properties. Transport Porous Med 46:311–343CrossRefGoogle Scholar
  22. Oren PE, Bakke S (2003) Reconstruction of berea sandstone and pore-scale modeling of wetability effects. J Petrol Sci Eng 39:177–199CrossRefGoogle Scholar
  23. Przystupa MA (1997) Estimation of true size distribution of partially aligned same-shape ellipsoidal particles. Scripta Mater 37:1701–1707CrossRefGoogle Scholar
  24. Rollett AD, Manohar P (2004) The monte carlo method. In: Raabe D (ed) Continuum scale simulation of engineering materials. Wiley-VCH, Weinheim, GermanyGoogle Scholar
  25. Rowenhorst DJ, Gupta A, Feng CR, Spanos G (2006) 3D crystallographic and morphological analysis of coarse martensite: combining EBSD and serial sectioning. Scripta Mater 55:11–16CrossRefGoogle Scholar
  26. Russ JC (2006) The Image Processing Handbook. (5 ed.). CRC Press, Boca Raton, FLGoogle Scholar
  27. Saltykov SA (1958) Stereometric metallography, Metallurgizdat, MoscowGoogle Scholar
  28. Saylor DM, El-Dasher BS, Adams BL, Rohrer GS (2004a) Measuring the five-parameter grain boundary distribution from observations of planar sections. Metall Mater Trans 35A:1981–1989CrossRefGoogle Scholar
  29. Saylor DM, Fridy J, El-Dasher BS, Jung KY, Rollett AD (2004b) Statistically representative three-dimensional microstructures based on orthogonal observation sections. Metall Mater Trans A 35A:1969–1979CrossRefGoogle Scholar
  30. Sundararaghavan V, Zabaras N (2005) Classification and reconstruction of three-dimensional microstructures using support vector machines. Comp Mater Sci 32:223–239CrossRefGoogle Scholar
  31. Talukdar MS, Torsaeter O (2002) Reconstruction of chalk pore networks from 2D backscatter electron micrographs using a simulated annealing technique. J Petrol Sci Eng 33:265–282CrossRefGoogle Scholar
  32. Talukdar MS, Torsaeter O, Ioannidis MA (2002a) Stochastic reconstruction of particulate media from two-dimensional images. J Colloid Interf Sci 248:419–428CrossRefGoogle Scholar
  33. Talukdar MS, Torsaeter O, Ioannidis MA, Howard JJ (2002b) Stochastic reconstruction, 3D characterization and network modeling of chalk. J Petrol Sci Eng 35:1–21CrossRefGoogle Scholar
  34. Talukdar MS, Torsaeter O, Ioannidis MA, Howard JJ (2002c) Stochastic reconstruction of chalk from 2D images. Transport Porous Med 48:101–123CrossRefGoogle Scholar
  35. Tewari A, Spowart JE, Gokhale AM, Mishra RS, Miracle DB et al (2006) Characterization of the effects of friction stir processing on microstructural changes in DRA composites. Mater Sci Eng A 428:80–90CrossRefGoogle Scholar
  36. Torquato S (2001) Random heterogeneous materials: Microstructure and macroscopic properties. Springer-Verlag, New YorkGoogle Scholar
  37. Underwood E (1970) Quantitative Stereology, Addison-Wesley, New YorkGoogle Scholar
  38. Uyar F, Wilson S, Gruber J, Rollett AD, Srolovitz DJ (2008) Int J Mater Res (submitted)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Stephen D. Sintay
    • 1
  • Michael A. Groeber
    • 2
  • Anthony D. Rollett
    • 1
  1. 1.Department of Materials Science and EngineeringCarnegie Mellon UniversityPittsburghUSA
  2. 2.Wright Patterson Air Force BaseWPAFBUSA

Personalised recommendations