scholarly journals A Study of Strain-Driven Nucleation and Extension of Deformed Grain: Phase Field Crystal and Continuum Modeling

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 1805 ◽  
Author(s):  
Ling-yi Kong ◽  
Ying-jun Gao ◽  
Qian-qian Deng ◽  
Zhi-rong Luo ◽  
Yu-jiang Lu
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Energy Region ◽  
Strain Energy ◽  
Two Dimensions ◽  
Lower Strain ◽  
Grain Stores ◽  
Dislocation Movement ◽  
Good Agreement ◽  
Phase Field Crystal

The phase-field-crystal (PFC) method is used to investigate migration of grain boundary dislocation and dynamic of strain-driven nucleation and growth of deformed grain in two dimensions. The simulated results show that the deformed grain nucleates through forming a gap with higher strain energy between the two sub-grain boundaries (SGB) which is split from grain boundary (GB) under applied biaxial strain, and results in the formation of high-density ensembles of cooperative dislocation movement (CDM) that is capable of plastic flow localization (deformed band), which is related to the change of the crystal lattice orientation due to instability of the orientation. The deformed grain stores the strain energy through collective climbing of the dislocation, as well as changing the orientation of the original grain. The deformed grain growth (DGG) is such that the higher strain energy region extends to the lower strain energy region, and its area increase is proportional to the time square. The rule of the time square of the DGG can also be deduced by establishing the dynamic equation of the dislocation of the strain-driven SGB. The copper metal is taken as an example of the calculation, and the obtained result is a good agreement with that of the experiment.

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

2020 ◽  
Vol 85 (2) ◽  
pp. 231-262
Author(s):  
Mark Ainsworth ◽  
Zhiping Mao
Keyword(s):  
Pattern Formation ◽  
Grain Boundary ◽  
Fractional Order ◽  
Phase Field ◽  
Boundary Energy ◽  
Classical Case ◽  
Experimental Measurements ◽  
Grain Boundary Energy ◽  
Material Interface ◽  
Phase Field Crystal

Abstract We consider a fractional phase-field crystal (FPFC) model in which the classical Swift–Hohenberg equation (SHE) is replaced by a fractional order Swift–Hohenberg equation (FSHE) that reduces to the classical case when the fractional order $\beta =1$. It is found that choosing the value of $\beta $ appropriately leads to FSHE giving a markedly superior fit to experimental measurements of the structure factor than obtained using the SHE ($\beta =1$) for a number of crystalline materials. The improved fit to the data provided by the fractional partial differential equation prompts our investigation of a FPFC model based on the fractional free energy functional. It is shown that the FSHE is well-posed and exhibits the same type of pattern formation behaviour as the SHE, which is crucial for the success of the PFC model, independently of the fractional exponent $\beta $. This means that the FPFC model inherits the early successes of the FPC model such as physically realistic predictions of the phase diagram etc. and, therefore, provides a viable alternative to the classical PFC model. While the salient features of PFC and FPFC are identical, we expect more subtle features to differ. The prediction of grain boundary energy arising from a mismatch in orientation across a material interface is another notable success of the PFC model. The grain boundary energy can be evaluated numerically from the PFC model and compared with experimental measurements. The grain boundary energy is a derived quantity and is more sensitive to the nuances of the model. We compare the predictions obtained using the PFC and FPFC models with experimental observations of the grain boundary energy for several materials. It is observed that the FPFC model gives superior agreement with the experimental observation than those obtained using the classical PFC model, especially when the mismatch in orientation becomes larger.

Phase field crystal study of grain boundary structure and annihilation mechanism in low-angle grain boundary

2019 ◽  
Vol 129 ◽  
pp. 163-175 ◽  
Author(s):  
Huijun Guo ◽  
Yuhong Zhao ◽  
Yuanyang Sun ◽  
Jinzhong Tian ◽  
Hua Hou ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Boundary Structure ◽  
Grain Boundary Structure ◽  
Phase Field Crystal

Modelling of Grain Boundary Stability of Materials under Severe Plastic Deformation and Experimental Verification

2010 ◽  
Vol 638-642 ◽  
pp. 2724-2729
Author(s):  
Yoshiyuki Saito ◽  
Chitoshi Masuda
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Computer Simulations ◽  
Phase Field ◽  
Field Methods ◽  
Simulation Results ◽  
Boundary Stability ◽  
Textured Materials ◽  
Phase Field Methods ◽  
Good Agreement

Thermodynamic stability of Grain boundary in materials under severe plastic deformation was simulated by the Monte Carlo and the phase field methods. Computer simulations were performed on 3-dimensional textured materials. The Monte Carlo simulation results were qualitatively in good agreement with those by the phase field model. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. The ARB experiments were performed for pure Al and Al alloys-sheets in order to validate the computer simulation results concerning the grain boundary stability of textured materials. With use of the Monte Carlo and the phase field methods. Effect of grain boundary mobilises and interface energy given by the computer simulations.

Phase-field crystal study of segregation induced grain-boundary premelting in binary alloys

2014 ◽  
Vol 451 ◽  
pp. 128-133 ◽  
Author(s):  
Yan-Li Lu ◽  
Ting-Ting Hu ◽  
Guang-Ming Lu ◽  
Zheng Chen
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Binary Alloys ◽  
Phase Field Crystal

scholarly journals Phase field crystal simulation of grain boundary annihilation under strain strain at high temperature

2015 ◽  
Vol 64 (10) ◽  
pp. 106105
Author(s):  
Gao Ying-Jun ◽  
Qin He-Lin ◽  
Zhou Wen-Quan ◽  
Deng Qian-Qian ◽  
Luo Zhi-Rong ◽  
...  
Keyword(s):  
High Temperature ◽  
Grain Boundary ◽  
Phase Field ◽  
Phase Field Crystal
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