Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T12:30:21.178Z Has data issue: false hasContentIssue false

Dislocation dynamics modeling of precipitation strengthening in Fe–Ni–Al–Cr ferritic superalloys

Published online by Cambridge University Press:  26 September 2017

Michael J.S. Rawlings*
Affiliation:
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
David C. Dunand
Affiliation:
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

Two-dimensional dislocation dynamics (DD) simulations are performed to simulate the increase in strength of ferritic superalloys strengthened by ordered β′(B2)–NiAl precipitates. Parametric studies for three precipitate volume fractions (10, 13, and 20%) and various radii (from 1 to 75 nm) predict strengthening via a mixture of precipitate bypassing and shearing by single- and super-dislocations of edge or screw character. DD strength contributions for various precipitate radii (for a 13% volume fraction) are compared to analytical models for ordered precipitate strengthening: good agreement exists in the overaged state, but not in the peak-aged and underaged states for either dislocation configurations. DD strength contributions, converted to hardness values, are compared to experimental hardness values from previously reported literature on a ferritic superalloy [Fe–10Cr–10Ni–6.5Al–3.4Mo–0.25Zr–0.005B (wt%)] aged at various temperatures and times. DD hardness values from the single-edge dislocation simulations accurately predict the experimental peak hardness, but not the under- and over-aged hardness values or trends. By incorporating the effect of secondary NiAl nanoprecipitates formed on cooling and solid solution strengthening of Fe in the primary precipitates, reasonable agreement is achieved in the overaged condition.

Type
Articles
Copyright
Copyright © Materials Research Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Jürgen Eckert

References

REFERENCES

Bhadeshia, H.K.D.H.: Design of ferritic creep-resistant steels. ISIJ Int. 41, 626 (2001).CrossRefGoogle Scholar
Stallybrass, C. and Sauthoff, G.: Ferritic Fe-Al-Ni-Cr alloys with coherent precipitates for high-temperature applications. Mater. Sci. Eng. A 387–389, 985 (2004).CrossRefGoogle Scholar
Stallybrass, C., Schneider, A., and Sauthoff, G.: The strengthening effect of (Ni,Fe)Al precipitates on the mechanical properties at high temperatures of ferritic Fe–Al–Ni–Cr alloys. Intermetallics 13, 1263 (2005).CrossRefGoogle Scholar
Calderon, H.A., Fine, M.E., and Weertman, J.R.: Coarsening and morphology of β′ particles in Fe–Ni–AI–Mo ferritic alloys. Analysis 19, (1988).Google Scholar
Zhu, S.M., Tjong, S.C., and Lai, J.K.L.: Creep behavior of a β′(NiAl) precipitation strengthened ferritic Fe–Cr–Ni–Al alloy. Acta Mater. 46, 2969 (1998).CrossRefGoogle Scholar
Caron, P. and Khan, T.: Improvement of creep strength in a nickel-base single-crystal superalloy by heat treatment. Mater. Sci. Eng. 61, 173 (1983).CrossRefGoogle Scholar
Sugui, T., Huihua, Z., Jinghua, Z., Hongcai, Y., and Yongbo, X.: Formation and role of dislocation networks during high temperature creep of a single crystal nickel – base superalloy. Mater. Sci. Eng., A. 279, 160 (2000).CrossRefGoogle Scholar
Keller, R.R., Maier, H.J., and Mughrabi, H.: Characterization of interfacial dislocation networks in a creep-deformed nickel-based superalloy. Scr. Metall. 28, 23 (1993).CrossRefGoogle Scholar
Teng, Z.K., Ghosh, G., Miller, M.K., Huang, S., Clausen, B., Brown, D.W., and Liaw, P.K.: Neutron-diffraction study and modeling of the lattice parameters of a NiAl-precipitate-strengthened Fe-based alloy. Acta Mater. 60(13–14), 5362 (2012).CrossRefGoogle Scholar
Sauthoff, G.: Multiphase intermetallic alloys for structural applications. Intermetallics 8, 1101 (2000).CrossRefGoogle Scholar
Nembach, E.: Particle Strengthening of Metals and Alloys, 1st ed. (Wiley-VCH, New York, NY, 1996).Google Scholar
Nembach, E. and Neite, G.: Precipitation hardening of superalloys by ordered γ′-particles. Prog. Mater. Sci. 29, 177 (1985).CrossRefGoogle Scholar
Naveen Kumar, N., Tewari, R., Durgaprasad, P.V., Dutta, B.K., and Dey, G.K.: Active slip systems in bcc iron during nanoindentation: A molecular dynamics study. Comput. Mater. Sci. 77, 260 (2013).CrossRefGoogle Scholar
Ball, A. and Smallman, R.E.: The operative slip system and general plasticity of NiAl-II. Acta Metall. 14, 1517 (1966).CrossRefGoogle Scholar
Yoo, M.H., Takasugi, T., Hanada, S., and Izumi, O.: Slip modes in B2-type intermetallic alloys. Mater. Trans. 31, 435 (1990).CrossRefGoogle Scholar
Ardell, A.J.: Precipitaion hardening. Metall. Trans. A 16, 2131 (1985).CrossRefGoogle Scholar
Brown, L.M. and Ham, R.K.: Strengthening Methods in Crystals (New York, NY, Elsevier Publishing Company, 1971).Google Scholar
Mohles, V.: Simulation of dislocation glide in precipitation hardened materials. Comput. Mater. Sci. 16, 144 (1999).CrossRefGoogle Scholar
Nembach, E., Pesicka, J., Mohles, V., Baither, D., Vovk, V., and Krol, T.: The effects of a second aging treatment on the yield strength of γ′-hardened NIMONIC PE16-polycrystals having γ′-precipitate free zones. Acta Mater. 53, 2485 (2005).CrossRefGoogle Scholar
Mohles, V.: Computer simulations of particle strengthening: The effects of dislocation dissociation on lattice mismatch strengthening. Mater. Sci. Eng., A 321, 206 (2001).CrossRefGoogle Scholar
Mohles, V.: Simulations of dislocation glide in overaged precipitation-hardened crystals. Philos. Mag. A 81, 971 (2001).CrossRefGoogle Scholar
Mohles, V.: Computer simulations of the glide of dissociated dislocations in lattice mismatch strengthened materials. Mater. Sci. Eng., A 324, 190 (2002).CrossRefGoogle Scholar
Mohles, V. and Fruhstorfer, B.: Computer simulations of Orowan process controlled dislocation glide in particle arrangements of various randomness. Acta Mater. 50, 2503 (2002).CrossRefGoogle Scholar
Mohles, V.: Dislocation Dynamics Simulations of Particle Strengthening. In Contin. Scale Simul. Eng. Mater. Fundam. – Microstruct. – Process Appl., edited by Raabe, D., Roters, F., Barlat, F., and Chen, L. (Wiley-VCH, New York, NY, 2004), pp. 368388.Google Scholar
Benzerga, A.A., Bréchet, Y., Needleman, A., and Van der Giessen, E.: Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics. Modell. Simul. Mater. Sci. Eng. 12, 557 (2004).CrossRefGoogle Scholar
Ilker Topuz, A.: Enabling microstructural changes of FCC/BCC alloys in 2D dislocation dynamics. Mater. Sci. Eng., A 627, 381 (2015).CrossRefGoogle Scholar
Ahmed, N. and Hartmaier, A.: A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals. J. Mech. Phys. Solids 58, 2054 (2010).CrossRefGoogle Scholar
Liang, S., Huang, M., and Li, Z.: Discrete dislocation modeling on interaction between type-I blunt crack and cylindrical void in single crystals. Int. J. Solids Struct. 56–57, 209 (2015).CrossRefGoogle Scholar
Yang, H., Li, Z., and Huang, M.: Modeling dislocation cutting the precipitate in nickel-based single crystal superalloy via the discrete dislocation dynamics with SISF dissociation scheme. Comput. Mater. Sci. 75, 52 (2013).CrossRefGoogle Scholar
Vattré, A., Devincre, B., and Roos, A.: Dislocation dynamics simulations of precipitation hardening in Ni-based superalloys with high γ′ volume fraction. Intermetallics 17, 988 (2009).CrossRefGoogle Scholar
Vattré, A., Devincre, B., and Roos, A.: Orientation dependence of plastic deformation in nickel-based single crystal superalloys: Discrete–continuous model simulations. Acta Mater. 58, 1938 (2010).CrossRefGoogle Scholar
Yashiro, K., Kurose, F., Nakashima, Y., Kubo, K., Tomita, Y., and Zbib, H.M.: Discrete dislocation dynamics simulation of cutting of γ′ precipitate and interfacial dislocation network in Ni-based superalloys. Int. J. Plast. 22, 713 (2006).CrossRefGoogle Scholar
Hafez Haghighat, S.M., Eggeler, G., and Raabe, D.: Effect of climb on dislocation mechanisms and creep rates in γ′-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study. Acta Mater. 61, 3709 (2013).CrossRefGoogle Scholar
Liu, B., Raabe, D., Roters, F., and Arsenlis, A.: Interfacial dislocation motion and interactions in single-crystal superalloys. Acta Mater. 79, 216 (2014).CrossRefGoogle Scholar
Cai, W., Arsenlis, A., Weinberger, C., and Bulatov, V.: A non-singular continuum theory of dislocations. J. Mech. Phys. Solids 54, 561 (2006).CrossRefGoogle Scholar
Prakash, A., Guénolé, J., Wang, J., Müller, J., Spiecker, E., Mills, M.J., Povstugar, I., Choi, P., Raabe, D., and Bitzek, E.: Atom probe informed simulations of dislocation–precipitate interactions reveal the importance of local interface curvature. Acta Mater. 92, 33 (2015).CrossRefGoogle Scholar
Mohles, V.: Superposition of dispersion strengthening and size-mismatch strengthening: Computer simulations. Philos. Mag. Lett. 83, 9 (2003).CrossRefGoogle Scholar
Mohles, V.: In Contin. Scale Simul. Eng. Mater. Fundam. – Microstruct. – Process Appl., Raabe, D., Roters, F., Barlat, F., and Chen, L., eds. (Wiley-VCH, New York, NY, 2004), pp. 368388.Google Scholar
Krug, M.E., Mao, Z., Seidman, D.N., and Dunand, D.C.: Comparison between dislocation dynamics model predictions and experiments in precipitation-strengthened Al–Li–Sc alloys. Acta Mater. 79, 382 (2014).CrossRefGoogle Scholar
Bocchini, P.: Dislocation Dynamics Simulations of Precipitation- Strengthened Ni- and Co-based Superalloys. Unpublished Manuscript. (n.d.).Google Scholar
Bocchini, P.: Microstructure and Mechanical Properties in γ (f.c.c.) + γ′(L12) Precipitation-Strengthened Cobalt-Based Superalloys. PhD Thesis, Department of Materials Science and Engineering, Northwestern University, 2015.Google Scholar
Lagerpusch, U., Mohles, V., Baither, D., Anczykowski, B., and Nembach, E.: Double strengthening of copper by dissolved gold-atoms and by incoherent SiO2-particls: How do the tow strengthening contributions superimpose? Acta Mater. 48, 3647 (2000).CrossRefGoogle Scholar
Lagerpusch, U., Mohles, V., and Nembach, E.: On the additivity of solid solution and dispersion strengthening. Mater. Sci. Eng., A 319–321, 176 (2001).CrossRefGoogle Scholar
Krug, M.: Microstructural Evolution and Mechanical Properties in Al-Sc Alloys With Li and Rare Earth Additions PhD thesis, Department of Materials Science and Engineering, Northwestern University, 2011.Google Scholar
Teng, Z.K., Miller, M.K., Ghosh, G., Liu, C.T., Huang, S., Russell, K.F., Fine, M.E., and Liaw, P.K.: Characterization of nanoscale NiAl-type precipitates in a ferritic steel by electron microscopy and atom probe tomography. Scr. Mater. 63, 61 (2010).CrossRefGoogle Scholar
Teng, Z.K., Zhang, F., Miller, M.K., Liu, C.T., Huang, S., Chou, Y.T., Tien, R.H., Chang, Y.A., and Liaw, P.K.: New NiAl-strengthened ferritic steels with balanced creep resistance and ductility designed by coupling thermodynamic calculations with focused experiments. Intermetallics 29, 110 (2012).CrossRefGoogle Scholar
Sun, Z., Song, G., Ilavsky, J., Ghosh, G., and Liaw, P.K.: Nano-sized precipitate stability and its controlling factors in a NiAl-strengthened ferritic alloy. Sci. Rep. 5, 16081 (2015).CrossRefGoogle Scholar
Sun, Z., Song, G., Ilavsky, J., and Liaw, P.K.: Duplex precipitates and their effects on the room-temperature fracture behaviour of a NiAl-strengthened ferritic alloy. Mater. Res. Lett. 3, 128 (2015).CrossRefGoogle Scholar
Mohles, V. and Nembach, E.: The peak- and over-aged states of particle strengthened materials: Computer simulations. Acta Mater. 49, 2405 (2001).CrossRefGoogle Scholar
Lifshitz, I.M. and Slyozov, V.V.: The kinetics of precipitation from supersaturated solid solution. J. Phys. Chem. Solids 19, 35 (1961).CrossRefGoogle Scholar
Wagner, C.: Theorie der alterung von niederschlagen durch umlosen (Ostwald-reifung). Z. Elektrochem. 65, 581 (1961).Google Scholar
Campany, R., Loretto, M., and Smallman, R.: The determination of the 1/2〈111〉{110} antiphase boundary energy of NiAl. J. Microsc. 98, 174 (1972).CrossRefGoogle Scholar
Teng, Z.K., Liu, C.T., Ghosh, G., Liaw, P.K., and Fine, M.E.: Effects of Al on the microstructure and ductility of NiAl-strengthened ferritic steels at room temperature. Intermetallics 18(8), 1437 (2010).CrossRefGoogle Scholar
Samsonov, G.: Handbook of the Physicochemical Properties of the Elements: Mechanical Properties of the Elements (1968).CrossRefGoogle Scholar
Rosenhain, W.: The Hardness of Solid Solutions. Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character 99, 196 (1921).Google Scholar
Tabor, D.: The physical meaning of indentation and scratch hardness. Br. J. Appl. Phys. 7, 159 (1956).CrossRefGoogle Scholar
Rosenberg, J.M. and Piehler, H.R.: Calculation of the taylor factor and lattice rotations for bcc metals deforming by pencil glide. Metall. Trans. A 2, 257 (1971).CrossRefGoogle Scholar
Huther, W. and Reppich, B.: Interaction of dislocations with coherent, stree-free ordered particles. Z. Metallkd. 69, 628 (1978).Google Scholar
Raynor, D. and Silcock, J.M.: Strengthening mechanisms in γ′ precipitating alloys. Mater. Sci. Technol. 4, 121 (1970).Google Scholar
Ardell, A., Munjal, V., and Chelman, D.: Precipitation hardening of Ni–Al alloys containing large volume fractions of gamma prime. Metall. Trans. A 7, 1263 (1976).CrossRefGoogle Scholar
Vo, N.Q., Liebscher, C.H., Rawlings, M.J.S., Asta, M., and Dunand, D.C.: Creep properties and microstructure of a precipitation-strengthened ferritic Fe–Al–Ni–Cr alloy. Acta Mater. 71, 89 (2014).CrossRefGoogle Scholar
Mohles, V.: The critical resolved shear stress of single crystals with long-range ordered precipitates calculated by dislocation dynamics simulations. Mater. Sci. Eng., A 365, 144 (2004).CrossRefGoogle Scholar
Dong, Y., Nogaret, T., and Curtin, W.: Scaling of dislocation strengthening by multiple obstacle types. Metall. Mater. Trans. A 41, 1954 (2010).CrossRefGoogle Scholar
Song, G., Sun, Z., Li, L., Xu, X., Rawlings, M.J.S., and Liebscher, C.H.: Ferritic alloys with extreme creep resistance via coherent hierarchical precipitates. Sci. Rep. 5, 16327 (2015).CrossRefGoogle ScholarPubMed
Genevois, C.: Quantitative investigation of precipitation and mechanical behaviour for AA2024 friction stir welds. Acta Mater. 53, 2447 (2005).CrossRefGoogle Scholar
Khan, I., Starink, M., and Yan, J.: A model for precipitation kinetics and strengthening in Al–Cu–Mg alloys. Mater. Sci. Eng., A 472, 66 (2008).CrossRefGoogle Scholar
Gilmore, D. and Starke, E.: Trace element effects on precipitation processes and mechanical properties in an Al–Cu–Li alloy. Metall. Mater. Trans. A 28, 1399 (1997).CrossRefGoogle Scholar
Nembach, E.: Synergetic effects in the superposition of stregthening mechanisms. Acta Metall. 40, 3325 (1992).CrossRefGoogle Scholar
Schanzer, S. and Nembach, E.: The critical resolved shear stress of gamma prime-strengthened nickel-based supperalloys with volume fractions between 0.07 and 0.47. Acta Metall. 40, 803 (1992).CrossRefGoogle Scholar
Pike, L., Chang, Y., and Liu, C.T.: Solid-Solution hardening and softening by Fe addition to NiAl. Intermetallics 5, 601 (1997).CrossRefGoogle Scholar