Temperature-Dependent Misfit Stress in Gamma Double Prime Strengthened Ni-Base Superalloys
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lloys derive strengthening from a coherent precipitate phase embedded in a matrix phase.[1] The precipitate phase would normally possess lattice parameter(s) different from that of the matrix phase which leads to a lattice misfit between the two phases.[2] The lattice misfit generates misfit stresses in both the precipitates and the matrix. Misfit stresses will influence microstructure evolution including precipitate shape required to accommodate the misfit stresses, precipitate coarsening kinetic and rafting phenomenon at elevated temperatures during processing or servicing of the alloys.[2] Such misfit stresses will also interact with dislocations during plastic deformation and influence the strength of the alloys.[3] Misfit stresses are determined by the misfit strains and elastic moduli which are both temperature dependent. Therefore, misfit stresses
R.Y. ZHANG, J. LI, S. PAUL, and H.B. DONG are with the School of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK. Contact e-mail: [email protected]. H.L. QIN, Z.N. BI, and J. ZHANG are with the High Temperature Materials Research Division, Central Iron and Steel Research Institute, No. 76 Xueyuannanlu, Haidian, Beijing, 100081, China. T.L. LEE is with ISIS Neutron Source, Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Chilton, Oxfordshire, OX11 0QX, UK. S.Y. ZHANG is with the Centre of Excellence for Advanced Materials, No.1 Libin Road, Songshan Lake, Dongguan, 523808, China. Manuscript submitted September 19, 2019. Article published online January 21, 2020 1860—VOLUME 51A, APRIL 2020
are temperature dependent and their influence on the alloys will vary with temperature. Quantitative analysis of misfit stresses in the system would thus help deepen the understanding of the materials in different aspects. Inconel 718 (IN718) is a widely used Ni-base superalloys in turbine engines. IN718 derives its strengthening mainly from the c¢¢ precipitates which is body-centered tetragonal.[3] The c¢¢ precipitates are coherently embedded in the c matrix with different misfit strains along a and c-axes of the c¢¢ precipitates. Due to the anisotropic misfit strains that lead to anisotropic misfit stresses, the c¢¢ precipitates grow into oblate ellipsoids.[4] Lattice misfit between the two phases can be up to 3 pct along the c-axis,[5] which is much larger than the misfits in c¢-strengthened Ni-base superalloys where the misfits between c and c¢ phases are normally less than 1 pct.[6] The large lattice misfits lead to large misfit stresses. Phase field simulations have shown the misfit stresses in the c¢¢ precipitates at the level of 1 GPa in compression at 790 C.[7] Misfit stresses can vary significantly at different temperatures due to the different thermal expansion of the strengthening and matrix phases and the temperature-dependent elastic moduli. The misfit stresses arising from the lattice misfit between the strengthening phase and matrix phase can be calculated using the Eshelby inclusion method.[8] The dilute dispersion of ellipsoidal c¢¢ precipitates in
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