Abstract
This chapter discusses fundamental aspects of the development of statistically equivalent virtual microstructures (SEVMs) and microstructure and property-based statistically equivalent representative volume elements (M-SERVE and P-SERVE) of the Ni-based superalloy at multiple scales. The two specific scales considered for this development are the subgrain scale of intragranular γ − γ′ microstructures and the polycrystalline scale of grain ensembles with annealing twins. A comprehensive suite of computational methods that can translate microstructural data in experimental methods to optimally defined representative volumes for effective micromechanical modeling is the objective of this study. The framework involves a sequence of tasks, viz., serial sectioning, image processing, feature extraction, and statistical characterization, followed by micromechanical analysis and convergence tests for statistical functions. A principal motivation behind this paper is to translate high-fidelity microstructural image data into statistics of parametric descriptors in constitutive laws governing material performance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. McLean, R.W. Cahn, Nickel-Base Superalloys: Current Status and Potential (Chapman and Hall, London, 1996)
D. Furrer, H. Fecht, Ni-based superalloys for turbine discs. J. Miner. Met. Mater. Soc. 51, 14–17 (1999)
T.M. Pollock, S. Tin, Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties. J. Prop. Power 22(2), 361–374 (2006)
A. Epishin, T. Link, U. Bruckner, P.D. Portella, Kinetics of the topological inversion of the γ∕γ′-microstructure during creep of a nickel-based superalloy. Acta Mater. 49, 4017–4023 (2001)
M. Ignat, J.Y. Buffiere, J.M. Chaix, Microstructures induced by a stress gradient in a nickel-based superalloy. Acta Mater. 41, 855–862 (1993)
G.B. Viswanathan, P.M. Sarosi, D.H. Whitis, M.J. Mills, Deformation mechanisms at intermediate creep temperatures in the Ni-base superalloy Rene 88 DT. Mater. Sci. Eng. A 400, 489–495 (2005)
J.S. Van Sluytman, T.M. Pollock, Optimal precipitate shapes in nickel-base γ −γ′ alloys. Acta Mater. 60, 1771–1783 (2012)
L. Kovarik, R.R. Unocic, J. Li, P. Sarosi, C. Shen, Y. Wang, M.J. Mills, Microtwinning and other shearing mechanisms at intermediate temperatures in Ni-based superalloys. Progr. Mater. Sci. 54, 839–873 (2009)
R.R. Unocic, N. Zhou, L. Kovarik, C. Shen, Y. Wang, M.J. Mills, Dislocation decorrelation and relationship to deformation microtwins during creep of a γ′ precipitate strengthened Ni-based superalloy. Acta Mater. 54, 7325–7339 (2011)
J. Cormier, X. Milhet, J. Mendez, Non-isothermal creep at very high temperature of the nickel-based single crystal superalloy. Acta Mater. 55, 6250–6259 (2007)
H.U. Hong, I.S. Kim, B.G. Choi, M.Y. Kim, C.Y. Jo, The effect of grain boundary serration on creep resistance in a wrought nickel-based superalloy. Mat. Sci. Eng. A 517, 125–131 (2009)
Y.S. Choi, T.A. Parthasarathy, D.M. Dimiduk, M.D. Uchic, Microstructural effects in modeling the flow behavior of single-crystal superalloys. Met. Mat. Trans. A 37(3), 545–550 (2006)
C. Allan, Plasticity of Nickel Base Single Crystal Superalloys. Ph.D. thesis, Massachusetts Institute of Technology (1995)
A. Ma, F. Roters, A constitutive model for FCC single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals. Acta Mater. 52(12), 3603–3612 (2004)
A.M. Cuitino, M. Ortiz, Constitutive modeling of L12 intermetallic crystals. Mater. Sci. Eng. A 170(1), 111–123 (1993)
T. Tinga, W.A.M. Brekelmans, M.G.D. Geers, Cube slip and non-Schmid effects in single crystal Ni-base superalloys. Model. Simul. Mater. Sci. Eng. 18(1), 015005 (2010)
E.P. Busso, K.S. Cheong, Length scale effects on the macroscopic behaviour of single and polycrystalline FCC crystals. Le J. Phys. IV 11(PR5), 161–170 (2001)
J. Zhang, M. Shenoy, D.L. McDowell, Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach. Fatigue Fract. Eng. Mater. Struct. 30, 889–904 (2007)
S. Keshavarz, S. Ghosh, Multi-scale crystal plasticity finite element model approach to modeling nickel-based superalloys. Acta Mater. 61(17), 6549–6561 (2013)
S. Keshavarz, S. Ghosh, Hierarchical crystal plasticity FE model for nickel-based superalloys: sub-grain microstructures to polycrystalline aggregates. Int. J. Sol. Struct. 55, 17–31 (2015)
S. Ghosh, G. Weber, S. Keshavarz, Multiscale modeling of polycrystalline nickel-based superalloys accounting for subgrain microstructures. Mech. Res. Commun. 78, 34–46 (2016)
S. Keshavarz, S. Ghosh, A crystal plasticity finite element model for flow stress anomalies in Ni3Al single crystals. Philos. Mag. 95(24), 2639–2660 (2015)
S. Keshavarz, S. Ghosh, A. Reid, S. Langer, A non-Schmid crystal plasticity finite element approach to multi-scale modeling of nickel-based superalloys. Acta Mat. 114, 106–115 (2016)
R. Hill, Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11(5), 357–372 (1963)
I.M. Gitman, H. Askes, L.J. Sluys, Representative volume: existence and size determination. Eng. Fract. Mech. 74(16), 2518–2534 (2007)
S. Swaminathan, S. Ghosh, N.J. Pagano, Statistically equivalent representative volume elements for composite microstructures, Part I: without damage. J. Comput. Mater. 40(7), 583–604 (2006)
S. Swaminathan, S. Ghosh, Statistically equivalent representative volume elements for composite microstructures, Part II: with interfacial debonding. J. Comput. Mater. 40(7), 605–621 (2006)
D. McDowell, S. Ghosh, S. Kalidindi, Representation and computational structure-property relations of random media. JOM J. Miner. Met. Mater. Soc. 63(3), 45–51 (2011)
A. Bagri, G. Weber, J.C. Stinville, W. Lenthe, T. Pollock, C. Woodward, S. Ghosh, Microstructure and property-based statistically equivalent representative volume elements for polycrystalline Ni-based superalloys containing annealing twins. Metall. Mater. Trans. A 49(11), 5727–5744 (2018)
M. Pinz, G. Weber, W.C. Lenthe, M.D. Uchic, T.M. Pollock, S. Ghosh, Microstructure and property based statistically equivalent RVEs for intragranular γ −γ’ microstructures of Ni-based superalloys. Acta Mat. 157, 245–258 (2018)
X. Tu, A. Shahba, J. Shen, S. Ghosh, Microstructure and property based statistically equivalent RVEs for polycrystalline-polyphase aluminum alloys. Int. J. Plast. 115, 268–292 (2019)
M. Echlin, W. Lenthe, T. Pollock, Three-dimensional sampling of material structure for property modeling and design. Int. Mater. Manuf. Innov. 3(1), 21–34 (2014)
M.A. Groeber, M. Jackson, DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr. Mater. Manuf. Innov. 3, 5 (2014)
M.A. Groeber, S. Ghosh, M.D. Uchic, D.M. Dimiduk, A framework for automated analysis and representation of 3D polycrystalline microstructures, Part 1: statistical characterization. Acta Mat. 56(6), 1257–1273 (2008)
M.A. Groeber, S. Ghosh, M.D. Uchic, D.M. Dimiduk, A framework for automated analysis and representation of 3D polycrystalline microstructures, Part 2: synthetic structure generation. Acta Mat. 56(6), 1274–1287 (2008)
Y. Bhandari, S. Sarkar, M.A. Groeber, M.D. Uchic, D. Dimiduk, S. Ghosh, 3D polycrystalline microstructure reconstruction from FIB generated serial sections for FE analysis. Comput. Mater. Sci. 41, 222–235 (2007)
S. Niezgoda, D. Turner, D. Fullwood, S. Kalidindi, Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics. Acta Mat. 58, 4432–4445 (2010)
D.M. Saylor, J. Fridy, B.S. El-Dasher, K.-Y. Jung, A.D. Rollett, Statistically representative 3D microstructures based on orthogonal observation sections. Met. Mat. Trans. A 35, 1969–1979 (2004)
Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76(3), 031110 (2007)
Y. Jiao, E. Padilla, N. Chawla, Modeling and predicting microstructure evolution in lead/tin alloy via correlation functions and stochastic material reconstruction. Acta Mat. 61(9), 3370–3377 (2013)
G. Saheli, H. Garmestani, B.L. Adams, Microstructure design of a two phase composite using two-point correlation functions. J. Comput.-Aided Mater. Des. 11(2), 103–115 (2004)
S. Torquato, G. Stell, Microstructure of two-phase random media. I. the n-point probability functions. J. Chem. Phys. 77(4), 2071–2077 (1982)
J. MacSleyne, M.D. Uchic, J.P. Simmons, M. De Graef, Three-dimensional analysis of secondary γ’ precipitates in René-88 dt and UMF-20 superalloys. Acta Mat. 57(20), 6251–6267 (2009)
M. Kühbach, G. Gottstein, L.A. Barrales-Mora, A statistical ensemble cellular automaton microstructure model for primary recrystallization. Acta Mater. 107, 366–376 (2016)
C. Schwarze, R.D. Kamachali, M. Kühbach, C. Mießen, M. Tegeler, L. Barrales-Mora, I. Steinbach, G. Gottstein, Computationally efficient phase-field simulation studies using RVE sampling and statistical analysis. Comp. Mater. Sci. 147, 204–216 (2018)
W. Lenthe, Twin Related Domains in Polycrystalline Nickel-Base Superalloys: 3D Structure and Fatigue. Ph.D. thesis, University of California- Santa Barbara (2017)
M. Pinz, G. Weber, S. Ghosh, Generating 3D virtual microstructures and statistically equivalent representative volume elements for intragranular nickel-based superalloy microstructures. Submitted 2019.
M.P. Echlin, A. Mottura, C.J. Torbet, T.M. Pollock, A new TriBeam system for three-dimensional multimodal materials analysis. Rev. Sci. Instrum. 83(2), 023701 (2012)
F. Meyer. Topographic distance and watershed lines. Signal Process. 38(1), 113–125 (1994)
S.J. Ahn, W. Rauh, H.-J. Warnecke, Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recogn. 34(12), 2283–2303 (2001)
D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, 1989)
W.W. Daniel, Kolmogorov-Smirnov One-Sample Test (PWS-Kent, Boston, 1990)
Simulation Modeling Suite (Simmetrix Inc., 2015). http://www.simmetrix.com/
G. Casella, C.P. Robert, M.T. Wells, Generalized Accept-Reject Sampling Schemes Lecture Notes: Monograph Series 45(Institute of Mathematical Statistics. Wiley StatsRef: Statistics Reference Online, John Wiley & Sons Ltd.), 342–347 (2004)
J.K. Mackenzie, 2nd Paper on statistics associated with the random disorientation of cubes. Biometrika 45, 229–240 (1958)
Z. Alam, D. Eastman, M. Jo, K. Hemker, Development of a high-temperature tensile tester for micromechanical characterization of materials supporting meso-scale ICME models. JOM 68(11), 2754–2760 (2016)
J.C. Stinville, N. Vanderesse, F. Bridier, P. Bocher, T.M. Pollock, High resolution mapping of strain localization near twin boundaries in a nickel-based superalloy. Acta Mat. 98(1), 29–42 (2015)
Acknowledgements
This work has been supported through a grant No. FA9550-12-1-0445 to the Center of Excellence on Integrated Materials Modeling (CEIMM) at Johns Hopkins University awarded by the AFOSR/RSL Computational Mathematics Program (Manager Dr. A. Sayir) and AFRL/RX (Monitors Drs. C. Woodward and C. Przybyla). These sponsorships are gratefully acknowledged. 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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ghosh, S. et al. (2020). Multi-scale Microstructure and Property-Based Statistically Equivalent RVEs for Modeling Nickel-Based Superalloys. In: Ghosh, S., Woodward, C., Przybyla, C. (eds) Integrated Computational Materials Engineering (ICME). Springer, Cham. https://doi.org/10.1007/978-3-030-40562-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-40562-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-40561-8
Online ISBN: 978-3-030-40562-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)