Computer Simulations of the Martensitic Transformation
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Computer Simulations of the Martensitic Transformation Y.M. Jin, A. Artemev, and A.G. Khachaturyan
The following is a Web Extra expanding upon the introductory article, “Science and Technology of Shape-Memory Alloys: New Developments,” by Kazuhiro Otsuka and Tomoyuki Kakeshita, Guest Editors, published in MRS Bulletin 27 (2002) pp. 91–100. A three-dimensional phase-field microelasticity model has been employed to simulate the time evolution of the martensitic transformation—that is, the development of the transformation through the nucleation, growth, and coarsening of orientation variants for both single-crystal and polycrystalline materials. Figures 1–3 show the simulation results of the cubic l trigonal martensitic transformation in AuCd alloys, producing 2 martensite. For the cubic l trigonal transformation, there are four lattice-correspondence variants. Four types of martensite orientation variants, with trigonal axes along the [111], [ 111], [ 1 11], and [111] directions of the parent phase, are numbered 1, 2, 3, and 4 and are shown by shades of gray in Figures 1–2 and by four different colors in Figure 3. The symbol indicates reduced time, and represents the ratio of the typical trans-
MRS BULLETIN/FEBRUARY 2002—Web Extra
formation strain energy to the “chemical” driving force. Figure 1 shows cross sections of the simulated microstructure obtained with the parameter 1 at 9. The microstructure presented in the different cross sections is complicated. The “herringbone” and banded structures are typical. The domain boundaries between the orientation variants correspond to twinning planes. Figure 2a shows the corresponding three-dimensional picture of the microstructure shown in Figure 1. The microstructure obtained at 30 is presented in Figure 2b, where the coarsening of domains is revealed. To investigate the effect of the contribution of elastic-strain energy to the total free energy, we simulated another case with a high value of 5 for a single crystal. The result obtained at 30 is shown in Figure 2c. The microstructure
is a herringbone structure with coarsened domains. The schematic illustration of the arrangement of the domains in Figure 2c is shown in Figure 2e, which coincides with that observed in experiment. A typical optical micrograph of the herringbone structure is shown in Figure 2d for comparison. Since the system with a higher value of coarsens faster, Figures 2a–2c actually illustrate the coarsening process of the domain structures with time. Figure 3a shows the 2 martensite transformed from a polycrystalline AuCd alloy with eight randomly oriented grains. The microstructure is obtained with 5 at 30. Our simulation shows that this structure is stable and does not undergo coarsening, due to the elastic coupling between transformed grains that results in the elastic interaction of microstructures in different grains. To see the microstructure evolution under external load, we applied an external uniaxial stress to the martensitic structure shown in Figure
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