Precipitate shape transitions during coarsening under uniaxial stress

Coarsening of Ni3Ge precipitates in Ni–Ge alloys aged under uniaxial compression

“…Using data on the lattice mismatches at 625 • C [35] (0.00614 and 0.00432 for the Ni-Ge and Ni-Al systems, respectively), C 44 at 625 • C for Ni 3 Ge [36] and Ni 3 Al [37] (88.8 and 105.7 GPa, respectively) and the values of σ i for the Ni-Ge and Ni-Al alloys systems [38] (16.1 and 8.3 mJ/m 2 , respectively), we obtain values of l 0 = 4.81 and 4.21 nm for the Ni-Ge and Ni-Al alloys, respectively. Theoretically, microstructures observed at the same value of L should be indistinguishable, and since l 0 for Ni-Ge alloys is only about 15% bigger than for Ni-Al alloys, the values of r at which Ni 3 Ge and Ni 3 Al microstructures at which this should happen are almost the same. As noted above, this is clearly not the case.…”

“…The theoretically predicted preference for plates or rods in a rafted microstructure depends on the state of strain in the alloy. When the deformation is purely elastic the predicted preference depends on the sign of the applied stress, the lattice mismatch between the matrix (␥) and ␥ phases, and on the differences between the elastic constants C 11 and C 12 of the ␥ and ␥ phases via the parameter [3][4][5]. The earliest observations of rafting were made on Ni-base superalloys subjected to considerable plastic deformation under creep conditions [6].…”

A hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities

“…Most theoretical considerations are based on the assumption that the equilibrium morphology of such particles is governed by minimizing the total system energy. For example, Kaganova and Roitburd [45], Johnson and coworkers [46,47] analyzed the shape transitions of precipitate particles in an infinite elastic matrix. The equilibrium shape and morphological development of misfit particles were also formulated based on boundary integral methods, in which a set of marker particles are placed on the phase interface to track the moving boundaries [48][49][50].…”

Diffusional evolution of precipitates in elastic media using the extended finite element and the level set methods

“…The different approaches for simulating microstructure evolution can be broadly classified on the basis of how the interface is resolved (sharp vs diffused interface) and how it is represented (Lagrangian vs Eulerian). Previous work on simulating the evolution of two phase microstructures can be classified as: sharp interface methods in Lagrangian framework [2][3][4][6][7][8][9][10][11]; diffused (or smooth) interface methods in Eulerian framework [12][13][14][15][16][17][18]; sharp interface methods in Eulerian framework [19][20][21][22].…”