Crack propagation under tensile strain in samples with pre-deformation is simulated using phase field crystal(PFC) method. It shows that crack of sample without pre-deformation, under tensile strain, begins to crack due to strain concentration as strain reaches a critical value. For pre-deformed samples, crack starts to propagate at a less critical strain value, and the larger the pre-deformation, the faster and more obvious the crack growth. For samples with pre-deformation during early process of crack propagation, growth characteristics of expansion-turning direction-expansion are presented. The essence is that crack growth is extended by atomic bond alternative fracture in directions[√3,1] and[√3,-1] of primary and secondary atomic arrangement direction, which leads to zigzag edge of the crack. For samples with pre-deformation at later stage crack propagation present longer cleavage crack extension in directions along[√3,1] and[√3,-1]. And the larger the pre-deformation of sample, the quicker the expansion of cleavage crack.

In a moving hot zone model with uniform temperature and an infinite temperature gradient under directional annealing, effect of second-phase particles (SPPs) on growth of columnar grain microstructure in polycrystalline materials was studied with phase field method. It shows that SPPs inhibit formation of columnar grain structure and inhibitory effect increases with increasing volume fraction of SPPs and decreasing size of SPPs. Effect of SPPs on final grain radius follows Zener relation under condition of directional annealing. Volume fraction of SPPs and their dispersive distribution at grain boundaries in materials should be reduced as far as possible to obtain better columnar grain structures during directional annealing.

Morphology of microcrack propagation and crack branching of single crystal ductile materials under tensile are simulated with phase-field-crystal method. It shows that shape of notch has a strong effect on crack propagation. With uniaxial tension crack propagation appears if only strain reaches a critical value. With biaxial tension a crack branches if only strain reaches a critical value. Temperature parameter takes significant effects on crack propagation. The smaller the temperature parameter is (the temperature is higher), the faster the cracks propagate and the more the crack branches are. It is observed that free energy of system decreases with time and decreases faster after crack starts to branch. During crack propagation, disconnectedly isolated cavities around the main cracks can be found and these defects become new cracks. They grow up along a line and become a branching crack. Simulated results are in agreement with other simulations and experimental results.

Two-mode phase-field-crystal (PFC) method is used to simulate coherent boundary of nano-twins.It shows that atomic arrangement in coherent twin-grain boundary is not in good order as sphere grains grow and run into each other to form dislocations.Atomic arrangement in coherent twin-grain boundary as band-shape grains colliding each other is more tidy.For designing and controlling numbers of atomic layer in nano-twins,PFC model can be used to realize manipulation for coherent nano-twins structure.It is significant for guiding experiment and revealing nano-twins structure and properties.