Phase-field modeling of nonequilibrium solidification processes in additive manufacturing

This project models dendrite growth during nonequilibrium solidification of binary alloys using the phase-field method (PFM). Understanding the dendrite formation processes is important because the microstructural features directly influence mechanical properties of the produced parts. An improved understanding of dendrite formation may inform design protocols to achieve optimized process parameters for controlled microstructures and enhanced properties of materials. To this end, this work implements a phase-field model to simulate directional solidification of binary alloys. For applications involving strong nonequilibrium effects, a modified antitrapping current model is incorporated to help eject solute into the liquid phase based on experimentally calibrated, velocity-dependent partitioning coefficient. Investigated allow systems include SCN, Si-As, and Ni-Nb. The SCN alloy is chosen to verify the computational method, and the other two are selected for a parametric study due to their different diffusion properties. The modified antitrapping current model is compared with the classical model in terms of predicted dendrite profiles, tip undercooling, and tip velocity. Solidification parameters—the cooling rate and the strength of anisotropy—are studied to reveal their influences on dendrite growth. Computational results demonstrate effectiveness of the PFM and the modified antitrapping current model in simulating rapid solidification with strong nonequilibrium at the interface.

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

Materials Science Forum ◽

10.4028/www.scientific.net/msf.749.660 ◽

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.

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A Phase-Field Model for the Formation of Martensite and Bainite

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.922.31 ◽

2014 ◽

Vol 922 ◽

pp. 31-36 ◽

Cited By ~ 4

Author(s):

Tansel T. Arif ◽

Rong Shan Qin

Keyword(s):

Free Energy ◽

Phase Field ◽

Materials Science ◽

Current Model ◽

Phase Field Model ◽

Field Method ◽

Field Variable ◽

Phase Field Method ◽

Cubic Symmetry ◽

Chemical Free Energy

The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.

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Numerical Simulation of Dendrite Growth of Binary Alloy Using Phase-Field Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.716-717.133 ◽

2014 ◽

Vol 716-717 ◽

pp. 133-136

Author(s):

Fang Hui Liu ◽

Ming Gao

Keyword(s):

Temperature Gradient ◽

Binary Alloy ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Field Method ◽

Dendrite Growth ◽

Phase Field Method ◽

Dendrite Morphology ◽

Anisotropic Strength

In order to study the growth process and morphology of dendrite directly, a phase field model of binary alloy was established. In this model the order parameter equation was coupled with the temperature field and the solute field. The growing processes and morphology of dendrite were simulated by using this phase field model. Through analyzing the results, we discussed the effects of anisotropic strength and temperature gradient on dendrite morphology. The results shows that with the increasing of anisotropic strength, the dendrite growth rate of the dendrite will increase and the secondary branches appear more clearly. Besides, the temperature gradient has influence on the appearance of secondary arms during the dendrite growing. With the increase of temperature gradient, the size of secondary dendrite arms increase.

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Numerical Simulation of Binary Alloy Crystal Growth of Multiple Dendrites and Direcitonal Solidification Using Phase-Field Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.774-776.703 ◽

2013 ◽

Vol 774-776 ◽

pp. 703-706

Author(s):

Ming Chen ◽

Yu Jiang ◽

Wen Long Sun ◽

Xiao Dong Hu ◽

Chun Li Liu

Keyword(s):

Directional Solidification ◽

Binary Alloy ◽

Phase Field ◽

Phase Field Model ◽

Solidification Process ◽

Solute Concentration ◽

Field Method ◽

Dendrite Growth ◽

Phase Field Method ◽

Competitive Growth

Phase field method (PFM) offers the prospect of carrying out realistic numerical calculation on dendrite growth in metallic systems. The dendritic growth process of multiple dendrites and direcitonal solidification during isothermal solidifications in a Fe-0.5mole%C binary alloy were simulated using phase field model. Competitive growth of multiple equiaxed dendrites were simulated, and the effect of anisotropy on the solute segregation and microstructural dedritic growth pattern in directional solidification process was studied in the paper. The simulation results showed the impingement of arbitrarily oriented grains, and the grains began to impinge and coalesce the adjacent grains with time going on, which made the dendrite growth inhibited obviously. In the directional solidification, the maximum concentration gradient showed in the dendrite tip, and highest solute concentration existed at the bottom of the dendrites. With the increasing of the anisotropy, dendrite tip radius became smaller, and the crystal structure is more uniform and dense.

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Phase Field Model for Influence of Edge Dislocation on Precipitation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.415-417.1482 ◽

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.

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