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Modeling Microstructure Evolution during Phase Transformation and Plastic Deformation

The key to predicting and therefore optimizing properties of materials is the knowledge of the state of microstructure and its evolution. To properly attack such a complex problem which involve phenomena occurring at different length and time scales, the Center for Accelerated Maturation of Materials (CAMM) has adopted an approach that integrates multi-scale modeling with critical experiment. The synergy of coupling computer simulation to experimental characterization at CAMM has allowed for the development of (a) fundamental understanding of the mechanisms that govern microstructural evolution during phase transformations and plastic deformation and (b) microstructure- and mechanism-based modeling tools to assist in alloy design and optimization.

Detailed experimental characterization of deformation mechanisms in Ni-base superalloys and a/b Ti-alloys at CAMM has show clearly that without capturing the spatial non-uniformity, correlation and anisotropy of precipitate microstructures and detailed insights into how the microstructures interact with dislocations, any modeling attempt to describe microstructure-property relationship in these alloys will remain phenomenological and of limited predictive power. Therefore, one of the principal modeling activities within the CAMM is Phase Field Modeling. This approach is based on fundamental thermodynamic and kinetic principles [1,2] and can simultaneously accommodate different thermodynamic driving forces (including stress and capillarity force) and kinetic pathways [3-6]. Using gradient thermodynamics of nonuniform systems [7] and microelasticity theory [8], the method describes spatio-temporal evolution of arbitrary microstructures consisting of various types of extended defects including homo- and hetero-phase interfaces, antiphase domain boundaries, dislocations, and microcracks. With model inputs linked directly to ab initio calculations and CALPHAD thermodynamic/mobility databases, the method has received much attention lately as a quantitative technique at multi-scales to model complex morphological patterns formed during many materials processes including phase transformation, grain growth, sintering, interdiffusion, and plastic deformation. Typical examples of microstructures simulated by the phase field method at mesoscale for dislocation network, g/g' microstructure in Ni-base superalloys and a/b microstructure in Ti-alloys are shown in the figures and animations on the right. It is readily seen that the models self-consistently account for arbitrary morphology and highly non-random spatial distribution of dislocations and precipitates, long-range elastic interactions, growth anisotropy and topological changes such as dislocation reactions and coalescence between neighboring precipitates.

At CAMM, quantitative 3D phase field models of microstructure evolution [9-12] are being developed and integrated with phase field model of dislocations [13-15] to study dislocation-microstructure interactions [16,17] (see also animation on the right). Simulations have been carried out using a representative volume that is large enough to capture the morphological and spatial variation of precipitates and dislocations. Using parallel algorithms and supercomputers at OSU and HPCC at WPAFB, the microstructure development in the volume element under different processing and service conditions are documented and the constitutive deformation behavior of the volume element are determined. These results are then passed to other modeling schemes (e.g., Crystal Plasticity/FEM and Neural Networks). Similarly, these models can receive as inputs the microstructures characterized by SEM/TEM and the micromechanisms informed by the experimental studies, as well as the key materials parameters and activation pathways of individual deformation processes characterized by the ab initio and atomistic simulations.

Recent investigations of creep deformation of Ni-base superalloys and a/b Ti-alloys at CAMM have demonstrated clearly the importance of detailed microstructural features in determining dislocation-precipitate interactions and the corresponding kinetic pathways of the deformation process. Many new dislocation processes beyond the conventional bypass and cutting mechanisms have been observed. To properly address these problems we have been developing microscopic phase field (MPF) models to describe dislocation core structures and complicated dislocation-microstructure interactions without any a priori assumptions about dislocation geometry, dissociation and reaction. In combination with ab initio calculations of generalized stacking fault (GSF) energy and the free-end nudged elastic band (NEB) method, the MPF methods have been shown to be a powerful tool in quantitative characterization of the minimum energy path, activation energy and critical nucleus configuration during phase transformations and plastic deformation. Some of the examples can be found in the figures on the right.

References:

  1. Hohenberg, P. C. & Halperin, B. I. Theory of Dynamic Critical Phenomena. Reviews of Modern Physics 49, 435-479 (1977).
  2. Gunton, J. D., Miguel, M. S. & Sahni, P. S. in Phase Transitions and Critical Phenomena (eds. Domb, C. & Lebowitz, J. L.) 267-466 (Academic Press, New York, 1983).
  3. Wang, Y. Z., Chen, L. Q. & Khachaturyan, A. G. in Computer simulation in Materials Science -Nano/Meso/Macroscopic Space and Time Scales (eds. Kirchner, H. O., Kubin, K. P. & Pontikis, V.) 325-371 (Kluwer Academic Publishers, 1996).
  4. Wang, Y. Z. & Chen, L. Q. in Methods in Materials Research (ed. Kaufmann, E. N.) 2a.3.1-2a.3.23 (Wiley, New York, 2000).
  5. A. Karma, "Phase Field Methods", in Encyclopedia of materials: science and technology, K. H. Buschow, Ed., Volume 7 of the series: Elsevier, Oxford, 2001, p. 6873-86.
  6. Chen, L. Q. Phase-field models for microstructure evolution. Annual Review of Materials Research 32, 113-140 (2002).
  7. Cahn-Hilliard: Cahn, J.W. and J.E. Hilliard, Free Energy of a Nonuniform System .1. Interfacial Free Energy. Journal of Chemical Physics, 1958. 28(2): p. 258-267.
  8. Khachaturyan, A.G., Theory of Structural Transformations in Solids. 1983, New York, John Wiley.
  9. Wu, K., Chang, Y. A. & Wang, Y. Simulating interdiffusion microstructures in Ni-Al-Cr diffusion couples: a phase field approach coupled with CALPHAD database. Scripta Materialia 50, 1145-1150 (2004).
  10. Chen, Q., Ma, N., Wu, K. S. & Wang, Y. Z. Quantitative phase field modeling of diffusion-controlled precipitate growth and dissolution in Ti-Al-V. Scripta Materialia 50, 471-476 (2004).
  11. Y. Wang, N. Ma, Q. Chen, F. Zhang, S.-L. Chen, Y. A. Chang, “Predicting of Phase Equilibrium, Phase Transformation, and Microstructure Evolution in Advanced Titanium Alloys,” JOM, pp32-39, Sept. 2005.
  12. Y.H. Wen, B. Wang, J.P. Simmons and Y. Wang, “A Phase-Field Model for Heat Treatment Applications in Ni-base Alloys, Acta Mater. 54 (2006) 2087-2099.
  13. Wang, Y. U., Jin, Y. M., Cuitino, A. M. & Khachaturyan, A. G. Nanoscale phase field microelasticity theory of dislocations: Model and 3D simulations. Acta Materialia 49, 1847-1857 (2001).
  14. Shen, C. & Wang, Y. Phase field model of dislocation networks. Acta Materialia 51, 2595-2610 (2003).
  15. Shen, C. & Wang, Y. Incorporation of gamma-surface to phase field model of dislocations: simulating dislocation dissociation in fcc crystals. Acta Materialia 52, 683-691 (2004).
  16. C. Chen, M. J. Mills and Y. Wang, “Modeling Dislocation Dissociation and Cutting of ’ Precipitates in Ni-based Superalloys by Phase Field Method,” pp309-314 in Defect Properties and Related Phenomena in Intermetallic Alloys, edited by E. P. George, H. Inui, M. J. Mills and G. Eggeler, MRS Sym. Proc. Vol. 753 (2003).
  17. C. Shen, J. Li, M.J. Mills and Y. Wang, “Modeling Shearing of ’ in Ni-Base Superalloys,” Proceedings on Integral Materials Modelling, Aachen, Germany, Dec. 1-2, 2005.