Mechanical properties of materials and associated engineered components are controlled by the material structure at various lengths and time scales. As materials are being further utilised to the maximum extent of their capabilities, tails on property distributions become significant. These tails are often driven by the extremities of microstructural feature distributions, suggesting the need for a statistically relevant description of the microstructure and a reciprocity relationship with the range of property measurement capabilities and the models that represent this information.
Representative volume elements (RVE) and statistically equivalent representative volume elements (SERVE) have emerged as frameworks for such microstructural characterisation and quantification.
This review covers the evolution of quantitative microstructure description for use in material behaviour predictions from homogenised representations, large volume statistical representation, to the determination of the minimum spatial size to statistically represent a microstructure based on features of interest and properties of interest.
Get full access to this article
View all access options for this article.
References
1.
FurrerDNoraasRBroughD.Industrial applications of microstructural characterization – current and potential future issues and applications, statistical methods for materials science. 1st ed. Boca Raton: CRC Press; 2019.
2.
DallairMFurrerD.Quantitative metallography of titanium alloys. Adv Mater Processes. 2004;162(12):25–28.
3.
TileyJSearlesTLeeE, et al.Quantification of microstructural features in α/β titanium alloys. Mater Sci Eng A. 2004;372(1–2):191–198. doi:10.1016/j.msea.2003.12.008
4.
OlsonGB.Computational design of hierarchically structured materials. Science. 1997;277:1237–1242. doi:10.1126/science.277.5330.1237
5.
MondiereADéneuxVBinotN, et al.Controlling the MC and M2C carbide precipitation in Ferrium® M54® steel to achieve optimum ultimate tensile strength/fracture toughness balance. Mater Charact. 2018;140:103–112. doi:10.1016/j.matchar.2018.03.041
PinzMWeberGStinvilleJC, et al.Data-driven Bayesian model for predicting fatigue crack nucleation in polycrystalline Ni-based superalloys. npj Comp Mater. 2022;8:39. doi:10.1038/s41524-022-00727-5
8.
SangidMDSehitogluHMaierHJ, et al.Role of microstructure in predicting fatigue performance, 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, 23 - 26 April 2012, 2012; Honolulu, Hawaii.
9.
StinvilleJCLentheWCMiaoJ, et al.A combined grain scale elastic–plastic criterion for identification of fatigue crack initiation sites in a twin containing polycrystalline nickel-base superalloy. Acta Mater. 2016;103:461–473. doi:10.1016/j.actamat.2015.09.050
10.
DeCostBLFrancisTHolmEA.Exploring the microstructure manifold: image texture representations applied to ultrahigh carbon steel microstructures. Acta Mater. 2017;133:30–40. doi:10.1016/j.actamat.2017.05.014
11.
GeMSuFZhaoZ, et al.Deep learning analysis on microscopic imaging in materials science. Mater Today Nano. 2020;11:100087, doi:10.1016/j.mtnano.2020.100087
12.
NoraasRVenkateshVRettbergL, et al.Recognition and quantification of dual phase titanium alloy microstructures using convolutional neural networks. The 14th World Conference on Titanium, MATEC Web of Conferences. 2020;321:11084. doi:10.1051/matecconf/202032111084
13.
NoraasRSomanathNGieringM, et al. Structural material property tailoring of dual phase titanium alloy microstructures using deep neural networks, AIAA Scitech 2020 Forum, 6-10 January 2020, 2020 Orlando, FL https://doi.org/10.2514/6.2020-1151.
14.
LarmuseauMSluydtsMTheuwissenK, et al.Compact representations of microstructure images using triplet networks. NPJ Comp Mater. 2020;6:156, doi:10.1038/s41524-020-00423-2
15.
FeriLEAhnJLutfillohonovS, et al.A three-dimensional microstructure recognition framework for permeable pavement analysis based on a 3D-IWGAN with enhanced gradient penalty. Sensors. 2021;21:3603, doi:10.3390/s21113603
16.
FuJCuiSCenS, et al.Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network. Comp Meth Appl Mech Engr. 2021;373:113516, doi:10.1016/j.cma.2020.113516
17.
JangidDKBrodnikNRKhanA, et al.3D grain shape generation in polycrystal using generative adversarial networks. Integr Mater Manuf Innov. 2022;11:71–84. doi:10.1007/s40192-021-00244-1
18.
BeckerRRichmondO.Incorporation of microstructural geometry in material modelling. Modell Simul. Mater. Sci. Engr. 1994;2:439–454. doi:10.1088/0965-0393/2/3A/002
19.
SpearADHochhalterJDCerroneAR, et al.A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue crack propagation. Fat Frac. Engr. Mater Struct. 2016;39:737–751. doi:10.1111/ffe.12449
20.
ChengJTuXGhoshS.Wavelet-enriched adaptive hierarchical FE model for coupled crystal plasticity-phase field modeling of crack propagation in polycrystalline microstructures. Comp Meth Appl Mech Eng. 2020;361:112757. doi:10.1016/j.cma.2019.112757
21.
TuXRayAGhoshS.A coupled crystal plasticity FEM and phase-field model for crack evolution in microstructures of 7000 series aluminum alloys. Eng Fract Mech. 2020a;230:106970. doi:10.1016/j.engfracmech.2020.106970
22.
MalothTGhoshS.Coupled crystal plasticity phase-field model for ductile fracture in polycrystalline microstructures. Int J Multiscale Comp Eng. 2023;21(2):1–19. doi:10.1615/IntJMultCompEng.2022042164
23.
ShenJKothaSNoraasR, et al.Developing parametrically upscaled constitutive and crack nucleation models for the α/β Ti64 alloy. Int. Jour. Plast. 2022;151:103182. doi:10.1016/j.ijplas.2021.103182
24.
KothaSOzturkDSmarslokB, et al.Uncertainty quantified parametrically homogenized constitutive models for microstructure-integrated structural simulations. Integ Mater Manuf Innov IMMI. 2020a;9:322–338. doi:10.1007/s40192-020-00187-z
LiuXFurrerDUKostersJ, et al. Vision 2040: A roadmap for integrated, multiscale modeling and simulation of materials and systems. 2018 NASA/CR-2018-219771, E-19477, GRC-E-DAA-TN52454.
27.
DimidukDMParthasarathyTARaoSIet alPredicting the microstructure-dependent mechanical performance of materials for early-stage design. In: GhoshS.CastroJM., and LeeJK, editors, Materials processing and design: modeling, simulation, and applications, NUMIFORM 2004, AIP CP712, American institute of physic. New York: Springer-Verlag: 2004. p. 1705–1710.
28.
AllisonJBackmanDChristodoulouL.Integrated computational materials engineering: a new paradigm for the global materials profession. JOM. 2006a;58(11):25–30. doi:10.1007/s11837-006-0223-5
29.
BackmanDGWeiDYWhitisDD, et al.ICME at GE: accelerating the insertion of New materials and processes. JOM. 2006;58(11):36–41. doi:10.1007/s11837-006-0225-3
GhoshSGroeberMA.Developing virtual microstructures and statistically equivalent representative volume elements for polycrystalline materials. crystal plasticity: atomistics to macroscale (section editors W. Cai and S. ghosh) In: YipS. and AndreoniW.Handbook of materials modeling, 2nd ed, methods: theory and modeling. Springer International Publishing AG; 2020.
ShenGRollinsJFurrerD. Microstructure modeling of forged Waspaloy discs. Superalloys 1996, eds. R. D. Kissinger, et. al., TMS, 1996. p. 613–620.
35.
GaydaJFurrerD.Dual-microstructure heat treatment. Adv Mater Processes. 2003;July:36–39.
36.
GlavicicMGVenkateshV.Integrating computational materials engineering of titanium: current capabilities being developed under the metals affordability initiative. JOM. 2014;66(7):1310–1320. doi:10.1007/s11837-014-1013-0
37.
HillR.Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Sol. 1963;11(5):357–372. doi:10.1016/0022-5096(63)90036-X
38.
HashinZShtrikmanS.A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Sol. 1963;11(2):127–140. doi:10.1016/0022-5096(63)90060-7
39.
KrönerE.Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids. 1977;25:137–155. doi:10.1016/0022-5096(77)90009-6
40.
SwaminathanSGhoshS.Statistically equivalent representative volume elements for composite microstructures. Part I: With interfacial debonding. J Comp Mater. 2006a;40(7):605–621. doi:10.1177/0021998305055274
41.
SwaminathanSGhoshSPaganoNJ.Statistically equivalent representative volume elements for composite microstructures. Part I: Without damage. J Comp Mater. 2006b;40(7):583–604. doi:10.1177/0021998305055273
42.
PinzMWeberGLentheW, et al.Microstructure-based statistically equivalent RVEs for sub-grain γ − γ′ microstructures of Nickel-base superalloys. Acta Mater. 2018;157(15):245–258. doi:10.1016/j.actamat.2018.07.034
43.
TuXShahbaAShenJ, et al.Microstructure and property based statistically equivalent RVEs for polycrystalline-polyphase aluminum alloys. Int Jour Plast. 2019;115:268–292. doi:10.1016/j.ijplas.2018.12.002
44.
TuX.Developing image-based crystal plasticity models for deformation and crack propagation in polycrystalline 7000-series aluminum alloys. [PhD thesis]. Johns Hopkins University; 2020b.
45.
UchicMDGroeberMWheelerR, et al.Augmenting the 3D characterization capability of the dual beam FIB SEM. Micros. Microanal. 2004;10(Supp 2):1136–1137. doi:10.1017/S1431927604886859
46.
UchicMDGroeberMADimidukDM, et al.3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-sem. Scripta Mat. 2006;55(1):23–28. doi:10.1016/j.scriptamat.2006.02.039
47.
GroeberMAHaleyBKUchicMD, et al.3D reconstruction and characterization of polycrystalline microstructures using a FIB-SEM system. Mat Char. 2006;57(4-5):259–273. doi:10.1016/j.matchar.2006.01.019
48.
EchlinMPHusseiniNSNeesJA, et al.A New femtosecond laser-based tomography technique for multiphase materials. Adv Mater. 2011;23:2339–2342. doi:10.1002/adma.201003600
49.
EchlinMPPolonskyATLambJ, et al.Recent developments in femtosecond laser-enabled Tribeam systems. JOM. 2021;73(12):4258–4269. doi:10.1007/s11837-021-04919-0
50.
Juul JensenDLauridsenEMMarguliesL, et al.X-ray microscopy in four dimensions. Mater.Tod. 2006;9:18–25. doi:10.1016/S1369-7021(05)71334-1
51.
ThorntonKPoulsenHF.Three-dimensional materials science: an intersection of three-dimensional reconstructions and simulations. MRS Bull. 2008;33:587–595. doi:10.1557/mrs2008.123
52.
LudwigWReischigPKingA, et al.Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis. Rev Sci Instrum. 2009;80:033905. doi:10.1063/1.3100200
53.
LienertULiSFHefferanCM, et al.High-Energy diffraction microscopy at the advanced photon source. JOM. 2011;63(7):70–77. doi:10.1007/s11837-011-0116-0
54.
SchurenJCShadePABernierJV, et al.New opportunities for quantitative tracking of polycrystal responses in three dimensions. Curr. Opin. Solid State Mater. Sci. 2015;19:235–244. doi:10.1016/j.cossms.2014.11.003
55.
Ostoja-StarzewskiM.Material spatial randomness: from statistical to representative volume element. Prob Eng Mech. 2006;21(2):112–132. doi:10.1016/j.probengmech.2005.07.007
56.
Ostoja-StarzewskiM.Microstructural randomness and scaling in mechanics of materials. New York: Chapman and Hall/CRC; 2007.
57.
McDowellDGhoshSKalidindiS.Representation and computational structure-property relations of random media. JOM. 2011;63(3):45–51. doi:10.1007/s11837-011-0045-y
58.
MadejL.Digital/virtual microstructures in application to metals engineering – A review. Arch. Civil Mech. Engr. 2017;17:839–854. doi:10.1016/j.acme.2017.03.002
59.
BargmannSKlusemannBMarkmannJ, et al.Generation of 3D representative volume elements for heterogeneous materials: a review. Prog Mater Sci. 2018;96:322–384. doi:10.1016/j.pmatsci.2018.02.003
60.
BostanabadRZhangYLiX, et al.Computational microstructure characterization and reconstruction: review of the state-of-the-art techniques. Prog Mater Sci. 2018;95:1–41. doi:10.1016/j.pmatsci.2018.01.005
61.
JonesRM.Mechanics of composite materials. New York: Hemisphere Publishing Corporation; 1975.
62.
DruganWJWillisJR.A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J Mech Phys Sol. 1996;44:1497–1524. doi:10.1016/0022-5096(96)00007-5
63.
TorquatoS.Random heterogeneous materials. New York: Springer-Verlag; 2002.
64.
PyrzR.Quantitative description of the microstructure of composites. Part I: morphology of unidirectional composite systems. Comp Sci Tech. 2006;50(2):197–208. doi:10.1016/0266-3538(94)90141-4
65.
BöhmJHRammerstorferFGWeissenbekE.Some simple models for micromechanical investigations of fiber arrangement effects in MMCs. comp. Mater. Sci. 1993;1:177–194.
66.
SunCTVaidyaRS.Prediction of composite properties from a representative volume element. compos. Sci. Tech. 1996;56:171–179.
67.
ZemanJSejnohaM.From random microstructures to representative volume elements. Modell. Simul. Mat. Sci. Engin. 2007;15(4):S325–S335. doi:10.1088/0965-0393/15/4/S01
68.
WeissenbekEBoehmHJRammerstofferFG.Micromechanical investigations of arrangement effects in particle reinforced metal matrix composites. Comput Mater Sci. 1994;3(2):263–278. doi:10.1016/0927-0256(94)90141-4
69.
YinXToAMcVeighC, et al.Statistical volume element method for predicting microstructure–constitutive property relations. Comp. Meth. Appl. Mech. Engrg. 2008;197:3516–3529. doi:10.1016/j.cma.2008.01.008
70.
FullwoodDTNiezgodaSRAdamsBL, et al.Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 2010;55:477–562. doi:10.1016/j.pmatsci.2009.08.002
71.
QidwaiSMTurnerDMNiezgodaSR, et al.Estimating the response of polycrystalline materials using sets of weighted statistical volume elements. Acta Mater. 2012;60:5284–5299. doi:10.1016/j.actamat.2012.06.026
72.
GhoshSKubairDV.Exterior statistics-based boundary conditions for optimal representative volume elements in elastic composites. Jour Mech Phys Sol. 2016;95:1–24. doi:10.1016/j.jmps.2016.05.022
73.
KubairDVGhoshS.Exterior statistics based boundary conditions for establishing statistically equivalent representative volume elements of statistically nonhomogeneous elastic microstructures. Int Jour Sol Struct. 2017;112:106–121. doi:10.1016/j.ijsolstr.2017.02.015
74.
KubairDVPinzMKollinsK, et al.Role of exterior statistics-based boundary conditions for property-based statistically equivalent RVEs of polydispersed elastic composites. Jour Comp Mater. 2018;52(21):2919–2928. doi:10.1177/0021998318758498
75.
WeberGPinzMGhoshS.Machine learning-enabled self-consistent parametrically-upscaled crystal plasticity model for Ni-based superalloys. Comp Meth Appl Mech Engng. 2022;402:115384. doi:10.1016/j.cma.2022.115384
76.
WillisJRElasticity theory of composites, mechanics of solids, The R. hill 60th anniversary volume: 1982, Oxford; Pergamon Press; 1982. p. 653–686
77.
KanitTForestSGallietI, et al.Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct. 2003;40(13-14):3647–3679. doi:10.1016/S0020-7683(03)00143-4
78.
JiaoYStillingerFTorquatoS.Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys Rev E. 2007;76(3):031110. doi:10.1103/PhysRevE.76.031110
79.
EchlinMPLentheWCPollockTM.Three-dimensional sampling of material structure for property modeling and design. Integ Mater Manuf Innov. 2014a;3(1):21.
80.
BagriAWeberGStinvilleJC, et al.Microstructure and property-based statistically equivalent RVEs for polycrystalline Ni-based superalloys with twins. Metall Mater Trans A. 2018;49(11):5727–5744. doi:10.1007/s11661-018-4858-y
81.
DehoffRT.Quantitative serial sectioning analysis: preview. J Micros. 1983;131:259–263. doi:10.1111/j.1365-2818.1983.tb04254.x
82.
KralMSpanosG.Three-dimensional analysis of proeutectoid cementite precipitates. Acta Mater. 1999;47:711–724. doi:10.1016/S1359-6454(98)00321-8
83.
KralMVManganMASpanosG, et al.Three-dimensional analysis of microstructure. Mater. Char. 2000;45:17–23. doi:10.1016/S1044-5803(00)00046-2
84.
AlkemperJVoorheesP.Quantitative serial sectioning analysis. J Micros. 2001;201:388–394. doi:10.1046/j.1365-2818.2001.00832.x
85.
SpowartJEMullensHMPuchalaBT.Collecting and analyzing microstructures in three dimensions: a fully automated approach. JOM. 2003;55:35–37. doi:10.1007/s11837-003-0173-0
86.
UchicMD.Serial sectioning methods for generating 3D characterization data of grain- and precipitate-scale microstructures. In: GhoshSDimidukD, editors. Comp. meth. microstructure-property relationships. New York: Springer; 2011. p. 53–98.
87.
LevinsonAJRowenhorstDJSharpKW, et al.Automated methods for the quantification of 3D woven architectures. Mater Char. 2017;124:241–249. doi:10.1016/j.matchar.2017.01.005
88.
InksonBJMulvihillMMöbusG.3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography. Scripta Mater. 2001;45:753–758. doi:10.1016/S1359-6462(01)01090-9
89.
GroeberMA.Digital representation of materials grain structure. In: GhoshSDimidukD, editors. Comp. meth. microstructure-property relationships. New York: Springer; 2006. p. 53–98.
90.
LewisACBingertJFRowenhorstDJ, et al.Two- and three-dimensional microstructural characterization of a super-austenitic stainless steel. Mater Sci Engr A. 2006;418:11–18. doi:10.1016/j.msea.2005.09.088
91.
EchlinMPStrawMRandolfS, et al.The TriBeam system: femtosecond laser ablation in situ SEM. Mater Char. 2015;100:1–15. doi:10.1016/j.matchar.2014.10.023
92.
LiMGhoshSRichmondO, et al.Three-dimensional characterization and modeling of particle reinforced metal matrix composites: Part I: quantitative description of microstructural morphology. Mater Sci Engin A. 1999a;265:153–173. doi:10.1016/S0921-5093(98)01132-0
93.
LiMGhoshSRichmondO, et al.Three-dimensional characterization and modeling of particle reinforced metal matrix composites: Part II: damage characterization. Mater Sci Engin A. 1999b;265:221–240. doi:10.1016/S0921-5093(98)01133-2
94.
BossiRHGeorgesonGE.The application of X-ray computed tomography to materials development. JOM. 1991;43(9):8–15. doi:10.1007/BF03222228
95.
LarsonBCYangWIceGE, et al.Three-dimensional X-ray structural microscopy with submicrometre resolution. Nature. 2002;415:887–890. doi:10.1038/415887a
96.
IceGEPangJWLBarabashRI, et al.Characterization of three-dimensional crystallographic distributions using polychromatic X-ray microdiffraction. Scripta Mater. 2006;55:57–62. doi:10.1016/j.scriptamat.2006.02.046
97.
BhandariYSarkarSGroeberMA, et al.3D polycrystalline microstructure reconstruction from FIB generated serial sections for FE analysis. Comp Mater Sci. 2007;41:222–235. doi:10.1016/j.commatsci.2007.04.007
98.
PlimptonSBattaileCChandrossM, et al. Crossing the Mesoscale No-Man's Land via Parallel Kinetic Monte Carlo. Sandia report SAND2009-6226, October 2009.
99.
ChenLQ.Phase-field models for microstructure evolution. Ann. Rev. Mater. Res. 2002;32(1):113–140. doi:10.1146/annurev.matsci.32.112001.132041
100.
WangYChenLQ and ZhouN.Simulation of microstructural evolution using the phase field method. In: KaufmannEN editor. Characterization of materials, volume 1, John Wiley & Sons. Inc; 2012. p. 216– 248
101.
XuTSarkarSLiM, et al.Quantifying microstructures in isotropic grain growth from phase field modeling: methods. Acta Mater. 2012;60:4787–4799. doi:10.1016/j.actamat.2012.05.040
102.
KühbachMGottsteinGBarrales-MoraL.A statistical ensemble cellular automaton microstructure model for primary recrystallization. Acta Mater. 2016;107:366–376. doi:10.1016/j.actamat.2016.01.068
103.
SchwarzeCKamachaliRDKühbachM, et al.Computationally efficient phase-field simulation studies using RVE sampling and statistical analysis. Comput Mater Sci. 2018;147:204–216. doi:10.1016/j.commatsci.2018.02.005
104.
QueyRDawsonPRBarbeF.Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. Comp. Meth Appl. Mech. Engrg. 2011;200:1729–1745. doi:10.1016/j.cma.2011.01.002
105.
GroeberMAGhoshSUchicMD, et al.A framework for automated analysis and representation of 3D polycrystalline microstructures, part 1: statistical characterization. Acta Mat. 2008a;56(6):1257–1273. doi:10.1016/j.actamat.2007.11.041
106.
GroeberMAGhoshSUchicMD, et al.A framework for automated analysis and representation of 3D polycrystalline microstructures, part 2: synthetic structure generation. Acta Mat. 2008b;56(6):1274–1287. doi:10.1016/j.actamat.2007.11.040
107.
GroeberMAJacksonM.DREAM.3d: A digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov. 2014;3:56–72. doi:10.1186/2193-9772-3-5
108.
JacksonMGroeberMDoneganS, et al.Advancements to the digital representation environment for analysis of materials in 3-dimensions—DREAM.3D. Micros. Microanal. 2019;25(Supp 2):176–177. doi:10.1017/S1431927619001612
109.
RichterH.Mote3D: an open-source toolbox for modelling periodic random particulate microstructures. Modell. Simul. Mater. Sci. Engr. 2017;25:035011, doi:10.1088/1361-651X/aa629a
110.
LatypovMIKhanALangCA, et al.Bisque for 3D materials science in the cloud: microstructure–property linkages. Integr Mater Manuf Innov. 2019;8:52–65. doi:10.1007/s40192-019-00128-5
111.
HartKARimoliJJ.Generation of statistically representative microstructures with direct grain geometry control. Comput. Methods Appl. Mech. Engrg. 2020;370:113242, doi:10.1016/j.cma.2020.113242
112.
Henry SerraoPSandfeldSPrakashA.Optimic: A tool to generate optimized polycrystalline microstructures for materials simulations. Software X. 2021;15:100708.
113.
Usseglio-VirettaFLEPatelPBernhardtE, et al.MATBOX: An open-source microstructure analysis toolbox for microstructure generation, segmentation, characterization, visualization, correlation and meshing. Software X. 2022;17:100915.
114.
SaylorDMFridyJEl-DasherBS, et al.Statistically representative 3D microstructures based on orthogonal observation sections. Met Mater Trans A. 2004;35:1969–1979. doi:10.1007/s11661-004-0146-0
115.
SaheliGGarmestaniHAdamsB.Microstructure design of a two phase composite using two-point correlation functions. J. Comp Aided Mat Des. 2004;11(2):103–115. doi:10.1007/s10820-005-3164-3
116.
SundararaghavanVZabarasN.Classification and reconstruction of three-dimensional microstructures using support vector machines. Comp Mater Sci. 2005;32(2):223–239. doi:10.1016/j.commatsci.2004.07.004
117.
RollettADRobertCSaylorD.Three dimensional microstructures: statistical analysis of second phase particles in AA7075-T651. Mater Sci Forum. 2006;519-521:1–10. doi:10.4028/www.scientific.net/MSF.519-521.1
118.
RollettADLeeSBCampmanR, et al.Three-dimensional characterization of microstructure by electron back-scatter diffraction. Annu Rev Mater Res. 2007;37:627–658. doi:10.1146/annurev.matsci.37.052506.084401
119.
JiaoYPadillaEChawlaN.Modeling and predicting microstructure evolution in lead/tin alloy via correlation functions and stochastic material reconstruction. Acta Mater. 2013;61:3370–3377. doi:10.1016/j.actamat.2013.02.026
120.
MacSleyneJUchicMSimmonsJ, et al.Three-dimensional analysis of secondary gamma precipitates in René-88 DT and UMF-20 superalloys. Acta Math. 2009;57(20):6251–6267. doi:10.1016/j.actamat.2009.08.053
121.
NiezgodaSRTurnerDMFullwoodDT, et al.Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics. Acta Mater. 2010;58:4432–4445. doi:10.1016/j.actamat.2010.04.041
122.
BaniassadiMGarmestaniHLiDS, et al.3-phase solid oxide fuel cell anode microstructure realization using 2-point correlation functions. Acta Mat. 2011;59(1):30–43. doi:10.1016/j.actamat.2010.08.012
123.
GuoEYChawlaNJingT, et al.Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method. Mater Charac. 2014;89:33–42. doi:10.1016/j.matchar.2013.12.011
124.
HasanabadiABaniassadiMAbriniaK, et al.Optimization of solid oxide fuel cell cathodes using two-point correlation functions. comp. Mater. Sci. 2016;111:107–115.
125.
KumarANguyenLDeGraefM, et al.A Markov random field approach for microstructure synthesis. Mod Simul Mater Sci Eng. 2016;24(3):1–13. doi:10.1088/0965-0393/24/3/035015
126.
AcarPSundararaghavanV.A Markov random field approach for modeling spatio-temporal evolution of microstructures. Modell. Simul. Mater. Sci. Engr. 2016;24:075005). doi:10.1088/0965-0393/24/7/075005
127.
TewariAGokhaleAMSpowartJE, et al.Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions. Acta Mater. 2004;52(2):307–319. doi:10.1016/j.actamat.2003.09.016
128.
BostanabadRBuiAXieW, et al.Stochastic microstructure characterization and reconstruction via supervised learning. Acta Mater. 2016;103:89–102. doi:10.1016/j.actamat.2015.09.044
129.
JungJYoonJIParkHK, et al.Microstructure design using machine learning generated low dimensional and continuous design space. Materialia. 2020;11:100690. doi:10.1016/j.mtla.2020.100690
130.
HsuTEptingWKKimH, et al.Microstructure generation via generative adversarial network for heterogeneous, topologically complex 3D materials. JOM. 2021;73:90–102. doi:10.1007/s11837-020-04484-y
131.
UnocicRRZhouNKovarikL, et al.Dislocation decorrelation and relationship to deformation microtwins during creep of a γ′precipitate strengthened Ni-based superalloy. Acta Mater. 2011;59:7325–7339. doi:10.1016/j.actamat.2011.07.069
132.
PollockTMArgonA.Creep resistance of CMSX-3 Nickel-base superalloy single crystals. Acta Mat. 1992;40:1–30. doi:10.1016/0956-7151(92)90195-K
133.
NouailhasDCailletaudG.Multiaxial behaviour of Ni-base single crystals. Scrip Mater. 1996;34:565–571. doi:10.1016/1359-6462(95)00547-1
134.
BussoEMeissonierFODowdN.Gradient-dependent deformation of two-phase single crystals. Jour Mech Phys Sol. 2000;48:2333–2361. doi:10.1016/S0022-5096(00)00006-5
135.
FrommBSChangKMcDowellDL, et al.Linking phase-field and finite-element modeling for process-structure-property relations of a Ni-base superalloy. Acta Mater. 2012;60:5984–5999. doi:10.1016/j.actamat.2012.06.058
136.
ParthasarathyTARaoSIDimidukDM.A fast spreadsheet model for the yield strength of superalloys. Superalloys. 2004;2004:887–896. doi:10.7449/2004/Superalloys_2004_887_896
137.
KeshavarzSGhoshS.Hierarchical crystal plasticity FE model for nickel-based superalloys: Sub-grain microstructures to polycrystalline aggregates. Int Jour Sol Struc. 2015;55:17–31. doi:10.1016/j.ijsolstr.2014.03.037
138.
LentheW.Twin related domains in polycrystalline nickel-base superalloys: 3D structure and fatigue [PhD thesis, University of California- Santa Barbara; 2017
139.
EchlinMPMotturaAWangM, et al.Three-dimensional characterization of the permeability of W-Cu composites using a new “TriBeam” technique. Acta Mater. 2014b;64:307–315. doi:10.1016/j.actamat.2013.10.043
MeyerF.Topographic distance and watershed lines. Sign Proc. 1994;38(1):113–125. doi:10.1016/0165-1684(94)90060-4
142.
GoldbergDE.Genetic algorithms in search, optimization, and machine learning. MA: Addison- Wesley, Reading; 1989.
143.
MasseyFJ.The Kolmogorov-Smirnov test for goodness of Fit. J Amer Stat Assoc. 1951;46(253):68–78. doi:10.1080/01621459.1951.10500769
144.
GhoshS.Micromechanical analysis and multi-scale modeling using the voronoi cell finite element method. Boca Raton: CRC Press/Taylor & Francis; 2011.
145.
KeshavarzSGhoshS.Multi-scale crystal plasticity finite element model approach to modeling nickel-based superalloys. Acta Mater. 2013;61:6549–6561. doi:10.1016/j.actamat.2013.07.038
146.
Nemat-NasserSHoriM.Micromechanics: overall properties of heterogeneous materials. Amsterdam: North-Holland; 1993.
147.
KovacˇMSimonovICizeljL.The effect of grain structure on the elastic-plastic response of a polycrystalline aggregate. Jol Mech. Engr. 2002;48:580–590.
148.
ZohdiTIWriggersP.An introduction to computational micromechanics. Berlin, Heidelberg: Springer; 2004.
149.
WeberGPinzMGhoshS.Machine learning-aided parametrically-homogenized crystal plasticity model (PHCPM) for single crystal Ni-based superalloys. JOM. 2020;72(12):4404–4419. doi:10.1007/s11837-020-04344-9
150.
LeveraniktGRMcClungRCWuY-T, et al. Turbine rotor material design. US Dept of Transportation, Federal Aviation Administration report DOT/FAA/AR-00/64 2000.
LeverantGRMcClungRCMillwaterHR, et al. A new tool for design and certification of aircraft turbine rotors. Proceedings of ASME TURBO EXPO 2002 Jun 3–6 2002; Amsterdam, The Netherlands, GT-2002-30303.
153.
EnrightMPMcClungRCChanKS, et al. Micromechanics-based fracture risk assessment using integrated probabilistic damage tolerance analysis and manufacturing process models. Proceedings of ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, GT; 2016, Jun 13–17, Seoul, South Korea, GT2016-58089.
154.
McClungRCEnrightMPLiangW, et al. Integration of manufacturing process simulation with probabilistic damage tolerance analysis of aircraft engine components. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference; 2012 Apr 23 - 26; Honolulu, Hawaii, AIAA 2012-1528.
155.
MillwaterHPFitchSHKWuY-T, et al. A probabilistically based damage tolerance analysis computer program for hard alpha anomalies in titanium rotors. IGTI 2000, ASME TURBO EXPO 2000: LAND, SEA, AND AIR, May 8-11, 2000 – Munich Germany, 2000-GT-0421.
156.
OzturkDKothaSPilchakAL, et al.Two-way multi-scaling for predicting fatigue crack nucleation in titanium alloys using parametrically homogenized constitutive models. JMPS. 2019;128:181–207.
157.
VenkateshVNoraasRPilchakRA, et al.Data driven tools and methods for microtexture classification and dwell fatigue life prediction in dual phase titanium alloys. The 14th world conference on titanium, MATEC Web of conferences 321; 2020. 11091. doi:10.1051/matecconf/202032111091
158.
XuYJosephSKaramchedP, et al.Predicting dwell fatigue life in titanium alloys using modelling and experiment. Nature Comm. 2020;11(5868 (2020)). doi:10.1038/s41467-020-19470-w.
159.
LiuYDunneFPE.The mechanistic link between macrozones and dwell fatigue in titanium alloys. Int J Fatigue. 2021;142:105971. doi:10.1016/j.ijfatigue.2020.105971
160.
ShenJVenkateshVNoraasR, et al. Parametrically upscaled crack nucleation model (PUCNM) for fatigue nucleation in titanium alloys containing micro-texture regions (MTR). 2023. (in review).
161.
OzturkDPilchakALGhoshS.Experimentally validated dwell and cyclic fatigue crack nucleation model for (-titanium alloys. Scripta Mater. 2017;127:15–18. doi:10.1016/j.scriptamat.2016.08.031
162.
AllisonJLiMWolvertonC, et al.Virtual aluminum castings: An industrial application of ICME. JOM. 2006b;58:28–35. doi:10.1007/s11837-006-0224-4
163.
SemiatinSLFurrerDU. Modeling of microstructure evolution during THE THERMOMECHANICAL PROCESSING of titanium alloys, fundamentals of modeling for metals processing, ASM-International Metals Handbook Volume 22A, ASM-International, 2009, pp. 522-533.
164.
FurrerDChatterjeeAShenG, et al.Development and application of microstructure and mechanical property models for titanium alloys. In: MinomiM.AkiyamaS.IkedaM.etal, editors. Ti-2007 Science and Technology. Sendai, Japan: The Japan Institute of Metals; 2007. pp. 781–788.
165.
FurrerDGoetzRShenG. Modeling and simulation of alloy 718 microstructure and mechanical properties, Proceedings of the 7th International Symposium on Superalloy 718 & Derivatives, 2010 Oct 10–13, 2010. Pittsburgh, Pennsylvania: TMS.
166.
ShenG.Microstructure modeling of forged components of ingot metallurgy nickel base superalloys, In: ChangK.-M.SrivastavaS. K.FurrerK. R.etal, editors. Advanced technologies for superalloy affordability; The minerals, metals and materials society; 2000, p 223–231.
167.
FurrerDGroppiG, and BungeG.Current and future trends in the manufacture of turbine engine disks; 2004ASM materials solutions conference. 2004 Oct. 18-21; Columbus, OH.
168.
BurlatskySFFurrerDUVenkateshVet al. Probabilistic model, system, and application for component design optimization, to be published 2022.
169.
DoneganSGroeberM.Data structures and work- flows for ICME. In: GhoshS.WoodwardC.PrzybylaC. editors. Integrated computational materials engineering (ICME). Cham: Springer; 2020. doi:10.1007/978-3-030-40562-5_2
170.
KaufmanLRousseeuwPJ.Clustering by means of medoids. In: DodgeY., editor. Statistical data analysis based on the L_1 norm and related methods ; North-Holland; 1987 p. 405–416.
171.
RousseeuwPJ.Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Jol. Comput. Appl. Mathem. 1987;20:53–65. doi:10.1016/0377-0427(87)90125-7
172.
SpowartJEMayuramaBMiracleDB.Multiscale characterization of spatially heterogeneous systems: implications for discontinuously reinforced metal-matrix composite microstructures. Mater Sci Eng A. 2001;307:51–66. doi:10.1016/S0921-5093(00)01962-6
173.
ValivetiDMGhoshS.Morphology based domain partitioning of multi-phase materials: A preprocessor for multi-scale modelling. Int Jol. Numer. Meth. Engr. 2007;69:1717–1754. doi:10.1002/nme.1834
174.
PilchakA.Fatigue crack growth rates in alpha titanium: faceted vs. striation growth. Scrip Mater. 2013;68(5):277–280. doi:10.1016/j.scriptamat.2012.10.041
175.
ChisholmSACastroJFChapmanBDet al. Smarter testing through simulation for efficient design and attainment of regulatory compliance. 30th ICAF Symposium – Kraków, 5–7 June 2019.
176.
ChengJHuXLancasterDet al. Modeling deformation and failure in AlSi-polyester abradable sealcoating material using microstructure-based finite element simulation. Available from SSRN: https://ssrn.com/abstract = 4046348 or 2022 Posted: 1 Mar 2022.
177.
AlamAEastmanDJoMet al.Development of a high-temperature tensile tester for micromechanical characterization of materials supporting meso-scale ICME models. JOM. 2016;11(68):2754–2760. doi:10.1007/s11837-016-2100-1
