Katsuyo Thornton

L.H. and F.E. Van Vlack Professor

kthorn@umich.edu

2022 HH Dow

T: (734) 615-1498

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Microstructural Evolution in Elastically Stressed Solids

Collaborators: Norio Akaiwa, Peter Voorhees, Xiaofan Li, Qing Nie
Sponsor: NSF
Microstructures play a crucial role in material properties. Microstructural evolution in high temperature alloy during operation is governed by the minimization of the combination of elastic and interfacial energy, mediated by diffusion. Our group (in collaboration with Northwestern University, Illinois Institute of Technology. and University of California, Irvine) utilizes a sharp interface model of phase transition to simulate evolution of precipitate morphologies and arrangements. The governing equations are solved by using the boundary integral method in 2D or the boundary element collocation method in 3D, which only requires meshing on the interfaces (not the bulk) to achieve a very high resolution and accuracy. We adopt state-of-the-art numerical methods such as the fast multipole methods and adaptive mesh to increase the computational efficiency of simulations. Furthermore, we are also examining sharp interface models on simulating vicinal step dynamics. Steps exist and induce elastic fields on crystal surface. The interstep elastic interaction will affect adatom diffusions and step motions.
Highlights (Click an image for more information)
  • Three-Dimensional Equilibrium Precipitate Shape

    The boundary integral method is employed to calculate the equilibrium shapes of precipitates with lattice misfit. Due to the stress engendered by the misfit (lattice parameter difference), the equilibrium shape can range from rounded cuboidal to plate-like to rod-like. The equilibrium shape of precipitate is depends on the ratio between the elastic strain energy and interfacial energy. The picture shows different equilibrium particle shapes with different elastic-interfacial energy ratio, with (a) having the smallest and (d) having the largest.

  • Large Scale Simulation of Microstructure Coarsening

    Many alloys are strengthened by precipitate particles that restrict dislocation motion. At high temperatures occurring in jet engines and electric generator turbines, the average size of precipitates grows with time. The microstructural evolution is complex due to the presence of elastic stress that stems from the misfit between the matrix and precipitates. The animation shows a result of two-dimensional simulation for a Ni-Al model alloy, showing elongation and alignment of precipitates due to elastic stress, as observed in many experiments.