scholarly journals Discussion of hardening effects on phase field models for fracture

2021 ◽  
Vol 349 ◽  
pp. 02001
Author(s):  
Aris Tsakmakis ◽  
Michael Vormwald
Keyword(s):  
Fracture Mechanics ◽  
Phase Field ◽  
Fatigue Cracks ◽  
Brittle Materials ◽  
Additional Term ◽  
Field Method ◽  
Systematic Investigation ◽  
Phase Field Method ◽  
Isotropic Hardening ◽  
Phase Field Models

Phase field models have been successfully applied in recent years to a variety of fracture mechanics problems, such as quasi-brittle materials, dynamic fracture mechanics, fatigue cracks in brittle materials, as well as ductile materials. The basic idea of the method is to introduce an additional term in the energy functional describing the state of material bodies. A new state variable is included in this term, the so-called phase field, and enables to determine the surface energy of the crack. This approach allows to model phenomena such as crack initiation, crack branching and buckling of cracks, as well as the modelling of the crack front in three-dimensional geometries, without further assumptions. There is yet no systematic investigation of the influence of strain hardening on crack development within the phase field method. Thus, the aim of the paper is to provide an analysis of the effect of kinematic and isotropic hardening on the evolution of the phase field variable.

Phase Field Simulation of the Pure Material Dendrite Growth in a Forced Flow

2012 ◽  
Vol 571 ◽  
pp. 3-7
Author(s):  
Jing Liu ◽  
Ying Shuo Wang
Keyword(s):  
Phase Field ◽  
Vertical Direction ◽  
Field Method ◽  
Dendritic Morphology ◽  
Forced Flow ◽  
Phase Field Method ◽  
Pure Material ◽  
Phase Field Models ◽  
Field Simulation ◽  
Control Equation

The phase field method is effective in simulating the formation of solidification microstructure. Based on the phase field models of coupling flow field and noise field proposed by Tong and Beckermann, using finite difference method to solve control equation, apartly simulating the dendritic morphology under the condition of convection or none convection, and drawing the following conclusions after comparing the results: in the side, the dendrite will no longer be symmetrical under the condition of countercurrent and downstream, the dendrite tip grows faster with countercurrent than that of the latter, while the dendrite grows almost naturally in the vertical direction of convection.

Machine learning aided phase field method for fracture mechanics

2021 ◽  
Vol 169 ◽  
pp. 103587
Author(s):  
Yuan Feng ◽  
Qihan Wang ◽  
Di Wu ◽  
Zhen Luo ◽  
Xiaojun Chen ◽  
...  
Keyword(s):  
Machine Learning ◽  
Fracture Mechanics ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method

One-Dimensional Phase Field Models With Adaptive Grids

1998 ◽  
Vol 120 (4) ◽  
pp. 956-964 ◽  
Author(s):  
J. F. McCarthy
Keyword(s):  
Phase Field ◽  
Solid Sphere ◽  
Field Method ◽  
Adaptive Grid ◽  
Phase Field Method ◽  
Adaptive Grids ◽  
One Dimensional ◽  
Macroscopic Models ◽  
Phase Field Models ◽  
Grid Technique

The phase field method has been demonstrated to hold promise for enabling the physics at the microscale to be incorporated in macroscopic models of solidification. However, for quantitatively accurate simulations to be performed, it will be necessary to develop algorithms which enable the interface width to be made very small. Adaptive grid techniques offer a means of achieving this within practical computational limits. This paper investigates the solution of one-dimensional phase field models using an adaptive grid technique. Three problems are considered: (1) the classical Stefan model, (2) the case of a solid sphere in equilibrium with its melt, and (3) a modified Stefan model with a generalized kinetic undercooling term. The numerical results are compared with those obtained using a fixed grid algorithm. In general, the adaptive grid technique is shown to be far more efficient, but it requires some care in its implementation.

Phase-Field Simulation of Binary Alloy Crystal Growth Prepared by a Fluid Flow

2015 ◽  
Vol 833 ◽  
pp. 11-14
Author(s):  
Ming Chen ◽  
Xiao Dong Hu ◽  
Dong Ying Ju
Keyword(s):  
Fluid Flow ◽  
Crystal Growth ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Al Alloy ◽  
Structural Pattern ◽  
Fluid Field ◽  
Phase Field Models

Phase field method (PFM) was employed to investigate the crystal growth of Mg-Al alloy, on the basis of binary alloy model, the fluid field equation was coupled into the phase-field models, and the marker and cell (MAC) method was used in the numerical calculation of micro structural pattern. In the cast process, quantitative comparison of different anisotropy values that predicted the dendrite evolution were discussed in detail, and when the fluid flow rate reaches a high value, we can see the remelting of dendrite arms.

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