Phase-field analysis of volume-diffusion controlled shape-instabilities in metallic systems-II: Finite 3-dimensional rods

2018 ◽  
Vol 144 ◽  
pp. 374-385 ◽  
Author(s):  
P.G. Kubendran Amos ◽  
L.T. Mushongera ◽  
Tobias Mittnacht ◽  
Britta Nestler
Keyword(s):  
Phase Field ◽  
Volume Diffusion ◽  
Field Analysis ◽  
3 Dimensional ◽  
Diffusion Controlled ◽  
Metallic Systems

A TEM investigation of a hyper-eutectic lead-tin alloy

1988 ◽  
Vol 46 ◽  
pp. 562-563
Author(s):  
John A. Sutliff
Keyword(s):  
Volume Diffusion ◽  
Eutectic Mixture ◽  
Precipitation Reaction ◽  
Directionally Solidified ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Diffusion Controlled ◽  
Discontinuous Precipitation Reaction ◽  
Controlled Precipitation

Near-eutectic Pb-Sn alloys are important solders used by the electronics industry. In these solders, the eutectic mixture, which solidifies last, is the important microstructural consituent. The orientation relation (OR) between the eutectic phases has previously been determined for directionally solidified (DS) eutectic alloys using x-ray diffraction or electron chanelling techniques. In the present investigation the microstructure of a conventionally cast, hyper-eutectic Pb-Sn alloy was examined by transmission electron microscopy (TEM) and the OR between the eutectic phases was determined by electron diffraction. Precipitates of Sn in Pb were also observed and the OR determined. The same OR was found in both the eutectic and precipitation reacted materials. While the precipitation of Sn in Pb was previously shown to occur by a discontinuous precipitation reaction,3 the present work confirms a recent finding that volume diffusion controlled precipitation can also occur.Samples that are representative of the solder's cast microstructure are difficult to prepare for TEM because the alloy is multiphase and the phases are soft.

Fourth-order hybrid phase field analysis with non-equal order elements and dual meshes for simulating crack propagation

2022 ◽  
Vol 142 ◽  
pp. 104587
Author(s):  
Feng Zhu ◽  
Hongxiang Tang ◽  
Xue Zhang ◽  
George Papazafeiropoulos
Keyword(s):  
Crack Propagation ◽  
Fourth Order ◽  
Phase Field ◽  
Field Analysis

scholarly journals 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 1049-1054 ◽  
Author(s):  
Anna Firych-Nowacka ◽  
Krzysztof Smółka ◽  
Sławomir Wiak ◽  
Eulalia Gliścińska ◽  
Izabella Krucińska ◽  
...  
Keyword(s):  
Experimental Method ◽  
Computer Model ◽  
Electrostatic Field ◽  
Field Analysis ◽  
Technological Parameters ◽  
3 Dimensional

AbstractElectrospinning is an experimental method of the polymer super thin fibres formation using the electrostatic field. The distribution of electrostatic field affects the effectiveness of the electrospinning. In order to analyse the electrostatic field for given technological parameters the 3-D computer model of an electrospinning device must be applied.

scholarly journals Kinetic transition in the order–disorder transformation at a solid/liquid interface

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170207 ◽  
Author(s):  
P. K. Galenko ◽  
I. G. Nizovtseva ◽  
K. Reuther ◽  
M. Rettenmayr
Keyword(s):  
Long Range ◽  
Phase Field ◽  
Order Parameter ◽  
Numerical Solutions ◽  
Liquid Interface ◽  
Range Order ◽  
Field Analysis ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Kinetic Transition

Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A 50 B 50 crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined. For rapidly growing crystals, analogies and qualitative differences are found in comparison with known non-equilibrium effects, particularly solute trapping and disorder trapping. The results and model predictions are compared qualitatively with results of the theory of kinetic phase transitions (Chernov 1968 Sov. Phys. JETP 26 , 1182–1190) and with experimental data obtained for rapid dendritic solidification of congruently melting alloy with order–disorder transition (Hartmann et al. 2009 Europhys. Lett. 87 , 40007 ( doi:10.1209/0295-5075/87/40007 )). This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals Morphological stability of three-dimensional cementite rods in polycrystalline system: A phase-field analysis

2021 ◽  
Vol 77 ◽  
pp. 252-268
Author(s):  
Tobias Mittnacht ◽  
P.G. Kubendran Amos ◽  
Daniel Schneider ◽  
Britta Nestler
Keyword(s):  
Phase Field ◽  
Three Dimensional ◽  
Field Analysis ◽  
Morphological Stability ◽  
System A

scholarly journals Towards a 3-Dimensional Phase-Field Model of Non-Isothermal Alloy Solidification

2014 ◽  
Vol 783-786 ◽  
pp. 2166-2171 ◽  
Author(s):  
Andrew M. Mullis ◽  
Peter C. Bollada ◽  
Peter K. Jimack
Keyword(s):  
Phase Field ◽  
Adaptive Mesh Refinement ◽  
Phase Field Model ◽  
Lewis Number ◽  
Adaptive Mesh ◽  
Implicit Time ◽  
Dimensional Problem ◽  
Alloy Solidification ◽  
Field Problem ◽  
3 Dimensional

We review the application of advanced numerical techniques such as adaptive mesh refinement, implicit time-stepping, multigrid solvers and massively parallel implementations as a route to obtaining solutions to the 3-dimensional phase field problem for coupled heat and solute transport during non-isothermal alloy solidification. Using such techniques it is shown that such models are tractable for modest values of the Lewis number (ratio of thermal to solutal diffusivities). Solutions to the 3-dimensional problem are compared with existing solutions to the equivalent 2-dimensional problem.

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