Y Wang, A.G. Khachaturyan/ Materials Science and Engineering A 438-440 (2006)55-63 T 5 IT 自=最自 Fig. 2. Formation of herringbone structure through autocatalytic growth during a cubic- tetragonal martensitic transformation. The nine small squires in each micrograph are the consecutive 2D cross sections of a 3D cube along the [0 1 0] axis. t is reduced time. applied to the SftS derived for each grain within each grain but differs from one grain to another. Fig. 4 shows the microstructural evolution obtained under external uni- ey (r)=Rik()rj(r)eu(r). (7) axial stresses in a system of 1283 mesh points and a mesh size where Ri (r) is a 3 x 3 matrix that defines the orientation of the of 0.5 pm. The strength parameter of the MT, s, is chosen to grain in the global coordinate system. It has a constant value be 5.0, which corresponds to a small undercooling. The four orientation variants are represented by four different shades of gray in the figure(color online). The multivariant microstru tures observed in the polycrystalline system is found to be quite different from the one observed in a single crystal. Because of the elastic coupling between neighboring randomly oriented par tially transformed grains, the MT in the polycrystalline system did not go to completion and the multi-domain structure is sta- ble against further growth, which is contrary to the simulation results obtained in a single crystal where the mt went to com- pletion under exactly the same conditions. This difference is caused by the geometrical constraints imposed on the mt in a polycrystalline system. The stress-strain hysteresis correspond ing to the microstructures under different uniaxial stresses also shown in Fig. 4. The nucleation of new variants and the domain boundary movement is clearly reproduced in the simu- lation. This example demonstrates well the potential of the phase field method in predicting very complex strain accommodating assemblages of multiple orientation domains produced by mts in polycrystalline materials under applied stresses. 3. Microscopic phase field model of dislocation core structures and its applications to martensitic transformations Polycrystal structure of the parent phase with eight randomly oriented While the mesoscopic phase field model of MT has achieved remarkable success in predicting stain-accommodating packingY. Wang, A.G. Khachaturyan / Materials Science and Engineering A 438–440 (2006) 55–63 59 Fig. 2. Formation of herringbone structure through autocatalytic growth during a cubic→tetragonal martensitic transformation. The nine small squires in each micrograph are the consecutive 2D cross sections of a 3D cube along the [0 1 0] axis. τ is reduced time. applied to the SFTS derived for each grain, ε 0,g ij (r) = Rik(r)Rjl(r)ε0 ij(r), (7) where Rij(r) is a 3 × 3 matrix that defines the orientation of the grain in the global coordinate system. It has a constant value Fig. 3. Polycrystal structure of the parent phase with eight randomly oriented grains in the computational volume. within each grain but differs from one grain to another. Fig. 4 shows the microstructural evolution obtained under external uni￾axial stresses in a system of 1283 mesh points and a mesh size of 0.5m. The strength parameter of the MT, ζ, is chosen to be 5.0, which corresponds to a small undercooling. The four orientation variants are represented by four different shades of gray in the figure (color online). The multivariant microstruc￾tures observed in the polycrystalline system is found to be quite different from the one observed in a single crystal. Because of the elastic coupling between neighboring randomly oriented par￾tially transformed grains, the MT in the polycrystalline system did not go to completion and the multi-domain structure is sta￾ble against further growth, which is contrary to the simulation results obtained in a single crystal where the MT went to com￾pletion under exactly the same conditions. This difference is caused by the geometrical constraints imposed on the MT in a polycrystalline system. The stress–strain hysteresis correspond￾ing to the microstructures under different uniaxial stresses is also shown in Fig. 4. The nucleation of new variants and the domain boundary movement is clearly reproduced in the simu￾lation. This example demonstrates well the potential of the phase field method in predicting very complex strain accommodating assemblages of multiple orientation domains produced by MTs in polycrystalline materials under applied stresses. 3. Microscopic phase field model of dislocation core structures and its applications to martensitic transformations While the mesoscopic phase field model of MT has achieved remarkable success in predicting stain-accommodating packing