Phase Field Modeling of Brittle Fracture Based on the Cell-Based Smooth FEM by Considering Spectral Decomposition

2020 ◽  
pp. 2050016 ◽  
Author(s):  
Fan Peng ◽  
Wei Huang ◽  
Y. E. Ma ◽  
Z. Q. Zhang ◽  
Yao Zhang
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Spectral Decomposition ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Constitutive Response ◽  
Order Stress ◽  
Effective Phase

The spectral decomposition of the strain tensor is an essential technique to deal with the fracture problems via phase field method, and some incorrect results may be obtained without it. A novel phase field model for brittle fracture is developed based on cell-based smooth finite element (CS-FEM) and the spectral decomposition is taken into account. In order to describe the nonlinearity behaviors which contain the varied stress and elastic constitutive response caused by spectral decomposition. A second-order stress tensor and a fourth-order constitutive tensor based on decomposition of strain tensor are derived. A fundamental framework of CS-FEM is established to solve the phase field fracture problems, implemented by user-defined element (UEL) subroutine of ABAQUS software. The proposed model is validated by a typical Mode II crack, and the results show that the derived tensors are effective. Phase field parameter, CS-FEM parameter and mesh inhomogeneity are investigated to provide some useful suggestion for further development. Some classical numerical examples are solved by using the present model. The studies demonstrate that the proposed method can successfully overcome mesh distortion; the number of smooth cell does not show influences on the accuracy. Moreover, some results show that this method has the advantage over the standard FEM in convergence and computing efficiency.

Phase Field Model for Influence of Edge Dislocation on Precipitation

2011 ◽  
Vol 415-417 ◽  
pp. 1482-1485
Author(s):  
Chuang Gao Huang ◽  
Ying Jun Gao ◽  
Li Lin Huang ◽  
Jun Long Tian
Keyword(s):  
Edge Dislocation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Second Phase ◽  
Free Energy Function ◽  
Phase Nucleation ◽  
Good Agreement

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

scholarly journals Application of phase-field method in rechargeable batteries

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Qiao Wang ◽  
Geng Zhang ◽  
Yajie Li ◽  
Zijian Hong ◽  
Da Wang ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Rechargeable Batteries ◽  
Computational Approach ◽  
Phase Field Method ◽  
Electrochemical Systems ◽  
Material Systems ◽  
Physical And Chemical

AbstractRechargeable batteries have a profound impact on our daily life so that it is urgent to capture the physical and chemical fundamentals affecting the operation and lifetime. The phase-field method is a powerful computational approach to describe and predict the evolution of mesoscale microstructures, which can help to understand the dynamic behavior of the material systems. In this review, we briefly introduce the theoretical framework of the phase-field model and its application in electrochemical systems, summarize the existing phase-field simulations in rechargeable batteries, and provide improvement, development, and problems to be considered of the future phase-field simulation in rechargeable batteries.

Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

2013 ◽  
Vol 470 ◽  
pp. 100-103
Author(s):  
Dong Sheng Chen ◽  
Ming Chen ◽  
Rui Chang Wang
Keyword(s):  
Crystal Growth ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Pure Substance ◽  
Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

Impact on Solidification Dendrite Growth by Interfacial Atomic Motion Time with Phase Field Method

2013 ◽  
Vol 749 ◽  
pp. 660-667
Author(s):  
Yu Hong Zhao ◽  
Wei Jin Liu ◽  
Hua Hou ◽  
Yu Hui Zhao
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Dendrite Growth ◽  
Atomic Motion ◽  
Phase Field Method ◽  
Dendrite Morphology ◽  
Motion Time ◽  
Solidification Processes

The Phase Field model of solidification processes was carried out coupled with temperature field model. The influence of interface atomic time on dendrite growth morphology in undercooled melt was simulated with pure nickel. The experimental results show that when the interface atomic motion time parameter is minor, the liquid-solid interfaces were unstable, disturbance can be amplified easily so the complicated side branches will grow, and the disturbance speed up the dendrite growth. With the increase of , the liquid-solid interfaces become more stable and finally the smooth dendrite morphology can be obtained.

Modeling Dislocation Dissociation and Cutting of γ′ Precipitates in Ni-Based Superalloys by the Phase Field Method

2002 ◽  
Vol 753 ◽  
Author(s):  
Chen Shen ◽  
Michael J. Mills ◽  
Yunzhi Wang
Keyword(s):  
Ab Initio ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Planar Defects ◽  
The Core ◽  
Surface Data ◽  
Dislocation Dissociation

ABSTRACTWe incorporate γ-surface data of both γ and γ′ phases from ab initio calculations into the phase field model to study dislocation dissociation and interaction with γ′ particles in Ni-based superalloys. Through three examples we demonstrate the unique capabilities of the model in characterizing the core structure of a dissociated superdislocation in γ′ phase, the creation and annihilation of planar defects such as CSF and APB caused by dislocation cutting through the γ′ phase and the interplay between the cutting and looping mechanisms.

Effect of Grain Boundary Energy in Recrystallization Simulation by Phase Field Method

2020 ◽  
Vol 993 ◽  
pp. 953-958
Author(s):  
Yan Wu ◽  
Ren Chuang Yan ◽  
Er Wei Qin ◽  
Wei Dong Chen
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Grain Boundary Energy ◽  
Average Grain Size

In this paper, the effect of grain boundary energy in AZ31 Mg alloy with multi-order parameters phenomenological phase field model has been discussed during the progress of recrystallization. The average grain size of the recrystallization grain at a certain temperature and a certain restored energy but various grain boundary energies have been studied, and the simulated results show that the larger the grain boundary energy is, the larger the average grain size will be, and the speed of grain growth will increase with the increase of grain boundary energy. Additionally, temperature will also increase the grain growth rate.

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