Based on the principle of grain refinement caused by the second-phase particles, a phase field model was built to describe the recrystallization process in the ZK60 alloy system with Y added under applied stress between temperatures 573 and 673 K for 140 min duration. The simulation of grain growth with second phase particles and applied stress during annealing process on industrial scale on the condition of real time-space was achieved. Quantitative analysis was carried out and some useful laws were revealed in ZK60 alloy system. The second phase particles had a promoting effect on the grain refinement, however the effect weakened significantly when the content exceeded 1.5%. Our simulation results reveal the existence of a critical range of second phase particle size of 0.3–0.4 μm, within which a microstructure of fine grains can be obtained. Applied stress increased the grain coarsening rate significantly when the stress was more than 135 MPa. The critical size of the second phase particles was 0.4–0.75 μm when the applied stress was 135 MPa. Finally, a microstructure with a grain size of 11.8–13.8 μm on average could be obtained when the second phase particles had a content of 1.5% and a size of 0.4–0.75 μm with an applied stress less than 135 Mpa after 30 min annealing at 573 K.

A three-dimensional (3D) multiple phase field model, which takes into account the grain boundary (GB) energy anisotropy caused by texture, is established based on real grain orientations and Read–Shockley model. The model is applied to the grain growth process of polycrystalline Mg (ZK60) alloy to investigate the evolution characteristics in different systems with varying proportions of low-angle grain boundary (LAGB) caused by different texture levels. It is found that the GB energy anisotropy can cause the grain growth kinetics to change, namely, higher texture levels (also means higher LAGB proportion) result in lower kinetics, and vice versa. The simulation results also show that the topological characteristics, such as LAGB proportion and distribution of grain size, undergo different evolution characteristics in different systems, and a more serious grain size fluctuation can be caused by a higher texture level. The mechanism is mainly the slower evolution of textured grains in their accumulation area and the faster coarsening rate of non-textured grains. Therefore, weakening the texture level is an effective way for implementing a desired homogenized microstructure in ZK60 Mg alloy. The rules revealed by the simulation results should be of great significance for revealing how the GB anisotropy affects the evolution of polycrystalline during the grain growth after recrystallization and offer the ideas for processing the alloy and optimizing the microstructure.

A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the (0001) plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter (Δd) is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the Δd increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 0001 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.

A phase-field model was revised to study the abnormal growth of Goss grains during the annealing process in Fe-3%Si steels, in which the interaction between the second-phase particles and Goss grain boundaries (GBs) was considered. The results indicate that the abnormal growth of Goss grains occurs due to the different dissolvability of the particles at Goss GBs compared with the other GBs. Moreover, the degree of abnormal growth increases first and then decreases with an increasing particle content. Meanwhile, the size advantage of Goss grain can further promote the degree of abnormal growth. Two types of island grains were found according to the simulated results, which is consistent with the experimental observations. A proper GB dissolvability of particles is the key factor for the formation of isolated island grains, and a higher local particle density at GBs is the main reason for the appearance of serial island grains. These findings can provide guidance for the desired texture control in silicon steels.

The effect of microstructure on the onset strain and rate of deformation-induced martensitic transformation (DIMT) in Q&P steel is studied by a mean-field micromechanics model, in which the residual austenite (RA) and primary martensite (M) phases are treated as elastoplastic particles embedded into the ferrite (F) matrix. The results show that when the volume fraction of the RA increases with a constant fraction of the M, the onset strain of DIMT increases and transformation rate decreases, in contrast to the case of the RA fraction effect with a fixed F fraction. Increasing the volume fraction of the M postpones the DIMT, regardless of the corresponding change from the RA or F fraction, which is similar to the effect of the RA fraction with the constant M but to a higher degree. Conversely, when increasing the fraction of the matrix F, the onset strain of DIMT increases and the rate decreases, and the effect is greater when the corresponding fraction change comes from the M rather than from the RA. Moreover, when the aspect ratio of the RA increases, the onset strain of DIMT decreases with a gradual increase in transformation rate, in agreement with the experimental observation that the equiaxial austenite is more stable in Q&P steels. However, the aspect ratio effect of the M is opposite to that of the RA, indicating that the lath-shaped primary martensite could protect the austenite from DIMT.