3D Minimum Channel Width Distribution in a Ni-Base Superalloy
Tóm tắt
The strength of a Ni-base superalloy depends strongly on its microstructure consisting of cuboidal
$${\gamma }^{^{\prime}}$$
precipitates surrounded by narrow channels of
$$\gamma $$
matrix. According to the theory of Orowan, a moving dislocation has to crimp through the minimal inter-precipitate spacing to admit the plastic deformation. We present a novel approach to evaluate the matrix channel width distribution of a matrix/
$${\gamma }^{^{\prime}}$$
microstructure in binary representation. Our method relies on precise determination of the matrix/precipitate interfaces and requires no additional user input. For each matrix channel between two neighboring precipitates, we identify the minimal interface to interface distance vector with its length being the channel width. The performance of this method is demonstrated on the example of the commercial alloy CSMX-4. We show that, in contrast to conventional line sectioning approaches, the approach consistently handles experimental 2D micrographs and 3D phase-field simulation data. The identified distance vectors correlate to the underlying crystal symmetry independent of the image orientation. The obtained channel width distributions compare well between the 2D and 3D data. This is in terms of similar median and
$$\sigma $$
of a log-normal distribution. The presented method overcomes limitations of the conventional line slicing approaches and provides a versatile tool for automated microstructure characterization.
Tài liệu tham khảo
Suzuki A, Inui H, Pollock TM (2015) L1 2 -Strengthened cobalt-base superalloys. Annu Rev Mater Res 45:345–368
Haas S, Manzoni AM, Holzinger M et al (2021) Influence of high melting elements on microstructure, tensile strength and creep resistance of the compositionally complex alloy Al10Co25Cr8Fe15Ni36Ti6. Mater Chem Phys 274:125163
Liebscher CH, Glatzel U (2014) Configuration of superdislocations in the γ′-Pt3Al phase of a Pt-based superalloy. Intermetallics 48:71–78
Galindo-Nava EI, Connor LD, Rae CMF (2015) On the prediction of the yield stress of unimodal and multimodal γ ′ Nickel-base superalloys. Acta Mater 98:377–390
Goodfellow AJ, Galindo-Nava EI, Christofidou KA et al (2018) The effect of phase chemistry on the extent of strengthening mechanisms in model Ni-Cr-Al-Ti-Mo based superalloys. Acta Mater 153:290–302
Kozar RW, Suzuki A, Milligan WW et al (2009) Strengthening mechanisms in polycrystalline multimodal nickel-base superalloys. Metall Mater Trans A 40:1588–1603
Ahmadi MR, Povoden-Karadeniz E, Whitmore L et al (2014) Yield strength prediction in Ni-base alloy 718Plus based on thermo-kinetic precipitation simulation. Mater Sci Eng, A 608:114–122
Li W, Ma J, Kou H et al (2019) Modeling the effect of temperature on the yield strength of precipitation strengthening Ni-base superalloys. Int J Plast 116:143–158
Glatzel U, Schleifer F, Gadelmeier C et al (2021) Quantification of solid solution strengthening and internal stresses through creep testing of Ni-containing single crystals at 980 °C. Metals 11:1130
Preußner J, Rudnik Y, Völkl R et al (2005) Finite-element modelling of anisotropic single-crystal superalloy creep deformation based on dislocation densities of individual slip systems. Zeitschrift für Metallkunde 96 Heft 96:595–601
Reed RC (2006) The superalloys–Fundamentals and applications. Cambridge University Press, Cambridge, UK
Rae C, Reed RC (2007) Primary creep in single crystal superalloys: origins, mechanisms and effects. Acta Mater 55:1067–1081
Kirchmayer A, Lyu H, Pröbstle M et al (2020) Combining experiments and atom probe tomography-informed simulations on γ′ precipitation strengthening in the polycrystalline Ni-base superalloy A718Plus. Adv Eng Mater 22:2000149
Hays C (2008) Size and shape effects for gamma prime in alloy 738. J Mater Eng Perform 17:254–259
Nathal MV (1987) Effect of initial gamma prime size on the elevated temperature creep properties of single crystal nickel base superalloys. Metall Mater Trans A 18:1961–1970
Kim HN, Iskakov A, Liu X et al (2022) Digital protocols for statistical quantification of microstructures from microscopy images of polycrystalline nickel based superalloys. Integr Mater Manuf Innov, 11(3): 313-326
Tiley JS, Viswanathan GB, Shiveley A et al (1993) Measurement of gamma’ precipitates in a nickel-based superalloy using energy-filtered transmission electron microscopy coupled with automated segmenting techniques. Micron Oxford England 41(2010):641–647
Mao J, Chang K-M, Yang W et al (2001) Cooling precipitation and strengthening study in powder metallurgy superalloy U720LI. Metall Mater Trans A 32:2441–2452
Wusatowska-Sarnek AM, Ghosh G, Olson GB et al (2003) Characterization of the microstructure and phase equilibria calculations for the powder metallurgy superalloy IN100. J Mater Res 18:2653–2663
Payton EJ, Phillips PJ, Mills MJ (2010) Semi-automated characterization of the phase in Ni-based superalloys via high-resolution backscatter imaging. Mater Sci Eng, A 527:2684–2692
Chen YQ, Slater TJA, Lewis EA et al (2014) Measurement of size-dependent composition variations for gamma prime (γ’) precipitates in an advanced nickel-based superalloy. Ultramicroscopy 144:1–8
Tang S, Zheng Z, Ning LK (2014) Gamma prime coarsening in a nickel base single crystal superalloy. Mater Lett 128:388–391
Mallikarjuna HT, Caley WF, Richards NL (2019) The dependence of oxidation resistance on gamma prime intermetallic size for superalloy IN738LC. Corros Sci 147:394–405
Katsari C-M, Katnagallu S, Yue S (2020) Microstructural characterization of three different size of gamma prime precipitates in Rene 65. Mater Charact 169:110542
MacSleyne JP, Simmons JP, Graef M, de, (2008) On the use of 2-D moment invariants for the automated classification of particle shapes. Acta Mater 56:427–437
Holzinger M, Schleifer F, Glatzel U et al (2019) Phase-field modeling of γ′-precipitate shapes in nickel-base superalloys and their classification by moment invariants. European Phys J, B, 92: 1–9
Schleifer F, Müller M, Lin Y-Y et al (2022) Consistent quantification of precipitate shapes and sizes in two and three dimensions using central moments. Integr Mater Manuf Innov 11:159–171
Guo Z., Song Z., Huang D. et al. 2022 Matrix channel width evolution of single crystal superalloy under creep and thermal mechanical fatigue: experimental and modeling investigations. Metals Mater Int
Ahmed M, Horst OM, Obaied A et al (2021) Automated image analysis for quantification of materials microstructure evolution. Modell Simul Mater Sci Eng 29:55012
Yao Z, Degnan CC, Jepson MAE et al (2013) Effect of rejuvenation heat treatments on gamma prime distributions in a Ni based superalloy for power plant applications. Mater Sci Technol 29:775–780
Horst OM, Ruttert B, Bürger D et al (2019) On the rejuvenation of crept Ni-Base single crystal superalloys (SX) by hot isostatic pressing (HIP). Mater Sci Eng, A 758:202–214
Tonks MR, Aagesen LK (2019) The phase field method: mesoscale simulation aiding material discovery. Annu Rev Mater Res 49:79–102
Mikula J, Ahluwalia R, Laskowski R et al (2021) Modelling the influence of process parameters on precipitate formation in powder-bed fusion additive manufacturing of IN718. Mater Des 207:109851
Böttger B, Apel M, Jokisch T et al (2020) Phase-field study on microstructure formation in Mar-M247 during electron beam welding and correlation to hot cracking susceptibility. IOP Conf Series Mater Sci Eng 861:12072
Fleck M, Querfurth F, Glatzel U (2017) Phase field modeling of solidification in multi-component alloys with a case study on the Inconel 718 alloy. J Mater Res 32:4605–4615
Fleck M, Schleifer F, Holzinger M et al. (2021) Phase-field modeling of precipitation microstructure evolution in multicomponent alloys during industrial heat treatments. In: U Reisgen, D Drummer, H Marschall (Hrsg.), Enhanced material, parts optimization and process intensification, lecture notes in mechanical engineering. Springer International Publishing, Cham, 70–78.
Fleck M, Schleifer F, Holzinger M et al (2018) Phase-field modeling of precipitation growth and ripening during industrial heat treatments in Ni-base superalloys. Metall Mater Trans A 49:4146–4157
Böttger B, Altenfeld R, Laschet G et al (2018) An ICME process chain for diffusion brazing of alloy 247. Integr Mater Manuf Innov 7:70–85
Eiken J (2012) Numerical solution of the phase-field equation with minimized discretization error. IOP Conf Series Mater Sci Eng 33:12105
Finel A, Le Bouar Y, Dabas B et al (2018) Sharp phase field method. Phys Rev Lett 121:25501
Fleck M, Schleifer F (2022) Sharp phase-field modeling of isotropic solidification with a super efficient spatial resolution. Eng Comput
Pollock TM, Tin S (2006) Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties. J Propul Power 22:361–374
Fleischmann E, Konrad C, Preußner J et al (2015) Influence of solid solution hardening on creep properties of single-crystal nickel-based superalloys. Metall Mater Trans A 46:1125–1130
Fleischmann E, Miller MK, Affeldt E et al (2015) Quantitative experimental determination of the solid solution hardening potential of rhenium, tungsten and molybdenum in single-crystal nickel-based superalloys. Acta Mater 87:350–356
Matan N, Cox DC, Rae C et al (1999) On the kinetics of rafting in CMSX-4 superalloy single crystals. Acta Mater 47:2031–2045
Sass V, Glatzel U, Feller-Kniepmeier M (1996) Anisotropic creep properties of the nickel-base superalloy CMSX-4. Acta Mater 44:1967–1977
Harris K, Erickson GL, Sikkenga SL et al (1993) Development of two rhenium- containing superalloys for single-crystal blade and directionally solidified vane applications in advanced turbine engines. J Mater Eng Perform 2:481–487
Schleifer F, Fleck M, Holzinger M et al. (2020) Phase-field modeling of γ′ and γ″ precipitate size evolution during heat treatment of Ni-based superalloys. In: S Tin, MC Hardy, J Clews, et al. (eds), Superalloys 2020. Springer International Publishing, Cham, 500–508
Pollock TM, Argon AS (1988) Intermediate temperature creep deformation in cmsx-3 single crystals. In: Superalloys 1988 (sixth international symposium). TMS, 285–294.
Caron P, Khan T (1983) Improvement of Creep strength in a nickel-base single-crystal superalloy by heat treatment. Mater Sci Eng 61:173–184
Konrad CH, Brunner M, Kyrgyzbaev K et al (2011) Determination of heat transfer coefficient and ceramic mold material parameters for alloy IN738LC investment castings. J Mater Process Technol 211:181–186
Andersson J-O, Helander T, Höglund L et al (2002) Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26:273–312
Fleischmann E (2013) Einfluss der Mischkristallhärtung der Matrix auf die Kriechbeständigkeit einkristalliner Nickelbasis-Superlegierungen, Berichte aus der Materialwissenschaft. Shaker, Aachen
Badrinarayanan V, Kendall A, Cipolla R (2017) SegNet: a deep convolutional encoder-decoder architecture for image segmentation. IEEE Trans Pattern Anal Mach Intell 39:2481–2495
Stan T, Thompson ZT, Voorhees PW (2020) Optimizing convolutional neural networks to perform semantic segmentation on large materials imaging datasets: X-ray tomography and serial sectioning. Mater Charact 160:110119
ACCESS e.V.; MICRESS©; accessible at: micress.rwth-aachen.de/; Accessed: 01.01.2022.
Böttger B, Apel M, Budnitzki M et al (2020) Calphad coupled phase-field model with mechano-chemical contributions and its application to rafting of γ’ in CMSX-4. Comput Mater Sci 184:109909
Eiken J, Böttger B, Steinbach I (2006) Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys Rev E Statistical Nonlinear Soft Matter Physics 73:66122
Böttger B, Eiken J, Apel M (2015) Multi-ternary extrapolation scheme for efficient coupling of thermodynamic data to a multi-phase-field model. Comput Mater Sci 108:283–292
Fleck M, Schleifer F, Holzinger M et al. 2019 Improving the numerical solution of the phase-field equation by the systematic integration of analytic properties of the phase-field profile function. In: 8th GACM colloquium. Kassel University Press, (2019) 445–450.
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. ACM SIGGRAPH Comput Graphics 21:163–169
Li B (1993) The moment calculation of polyhedra. Pattern Recogn 26:1229–1233
Sheynin SA, Tuzikov AV 2001 Formulae for polytope volume and surface moments. In: Proceedings 2001 international conference on image processing (Cat. No.01CH37205). IEEE, Thessaloniki, Greece, 720–723.
Sheynin SA, Tuzikov AV (2001) Explicit formulae for polyhedra moments. Pattern Recogn Lett 22:1103–1109
van Rossum G, Drake Jr FL, Python tutorial; The Netherlands: Centrum voor Wiskunde en Informatica, Heft 620, Amsterdam, (1995).
Virtanen P, Gommers R, Oliphant TE et al (2020) SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods 17:261–272
Harris CR, Millman KJ, van der Walt SJ et al (2020) Array programming with NumPy. Nature 585:357–362
Pedregosa F, Varoquaux G, Gramfort A et al (2011) Scikit-learn: machine learning in python. J Mach Learn Res 12:2825–2830
Reback J., jbrockmendel, McKinney W. et al.; pandas-dev/pandas: Pandas 1.4.3. Zenodo. 2022.
McKinney W (2010) Data structures for statistical computing in python. In: Proceedings of the 9th python in science conference. SciPy, Austin, Texas, 56–61.
Sullivan C, Kaszynski A (2019) PyVista: 3D plotting and mesh analysis through a streamlined interface for the visualization toolkit (VTK). J Open Source Softw 4:1450