A Finite Element-Phase Field Study of Solid State Phase Transformation: Coarsening of Coherent Precipitates and Instability of Multilayer Thin Films

2011 ◽  
pp. 341-348
Author(s):  
Mohsen Asle Zaeem ◽  
Haitham El Kadiri ◽  
Sinisa Dj. Mesarovic ◽  
Paul T. Wang ◽  
Mark F. Horstemeyer
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Phase Transformation ◽  
Solid State ◽  
Field Study ◽  
Phase Field ◽  
Multilayer Thin Films ◽  
Solid State Phase Transformation

A Phase-Field – Finite Element Model for Instabilities in Multilayer Thin Films

2011 ◽  
Vol 1297 ◽  
Author(s):  
Mohsen Asle Zaeem ◽  
Sinisa Dj. Mesarovic ◽  
Haitham El Kadiri ◽  
Paul T. Wang
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Phase Transformation ◽  
Phase Field ◽  
Intermediate Phase ◽  
Fe Model ◽  
Multilayer Thin Films ◽  
Mixed Order ◽  
Compositional Strain ◽  
Interpolation Functions

ABSTRACTCahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C0 interpolation functions for the displacement, and C1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model.Using the PF – FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface.Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and metastable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.

Simple Benchmark Problems for Finite Element Weld Residual Stress Simulation

2013 ◽  
Author(s):  
Mike C. Smith ◽  
Steve Bate ◽  
P. John Bouchard
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Phase Transformation ◽  
Solid State ◽  
Residual Stresses ◽  
Benchmark Problems ◽  
Transient Temperature ◽  
Beam Specimen ◽  
Weld Residual Stress ◽  
Solid State Phase Transformation

Finite element methods are used increasingly to predict weld residual stresses. This is a relatively complex use of the finite element method, and it is important that its practitioners are able to demonstrate their ability to produce accurate predictions. Extensively characterised benchmark problems are a vital tool in achieving this. However, existing benchmarks are relatively complex and not suitable for analysis by novice weld modellers. This paper describes two benchmarks based upon a simple beam specimen with a single autogenous weld bead laid along its top edge. This geometry may be analysed using either 3D or 2D FE models and employing either block-dumped or moving heat source techniques. The first, simpler, benchmark is manufactured from AISI 316 steel, which does not undergo solid state phase transformation, while the second, more complex, benchmark is manufactured from SA508 Cl 3 steel, which undergoes solid state phase transformation during welding. A number of such beams were manufactured using an automated TIG process, and instrumented with thermocouples and strain gauges to record the transient temperature and strain response during welding. The resulting residual stresses were measured using diverse techniques, and showed markedly different distributions in the austenitic and ferritic beams. The paper presents the information necessary to perform and validate finite element weld residual stress simulations in both the simple austenitic beam and the more complex ferritic beam, and provides performance measures for the austenitic beam problem.

A phase field study of morphological instabilities in multilayer thin films

2009 ◽  
Vol 57 (4) ◽  
pp. 1060-1067 ◽  
Author(s):  
B.G. Chirranjeevi ◽  
T.A. Abinandanan ◽  
M.P. Gururajan
Keyword(s):  
Thin Films ◽  
Field Study ◽  
Phase Field ◽  
Multilayer Thin Films ◽  
Morphological Instabilities

Grain growth stagnation in solid state thin films: A phase-field study

2021 ◽  
Vol 130 (2) ◽  
pp. 025305
Author(s):  
M. Verma ◽  
R. Mukherjee
Keyword(s):  
Thin Films ◽  
Solid State ◽  
Field Study ◽  
Grain Growth ◽  
Phase Field

TEM studies of solid-state reactions in sputter-deposited Nb/Al multilayer thin films

1996 ◽  
Vol 54 ◽  
pp. 1020-1021
Author(s):  
F. Ma ◽  
S. Vivekanand ◽  
K. Barmak ◽  
C. Michaelsen
Keyword(s):  
Thin Films ◽  
Solid State ◽  
Stoichiometric Composition ◽  
Analytical Electron Microscopy ◽  
Grain Structure ◽  
Solid State Reactions ◽  
Multilayer Thin Films ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sputter Deposited

Solid state reactions in sputter-deposited Nb/Al multilayer thin films have been studied by transmission and analytical electron microscopy (TEM/AEM), differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The Nb/Al multilayer thin films for TEM studies were sputter-deposited on (1102)sapphire substrates. The periodicity of the films is in the range 10-500 nm. The overall composition of the films are 1/3, 2/1, and 3/1 Nb/Al, corresponding to the stoichiometric composition of the three intermetallic phases in this system.Figure 1 is a TEM micrograph of an as-deposited film with periodicity A = dA1 + dNb = 72 nm, where d's are layer thicknesses. The polycrystalline nature of the Al and Nb layers with their columnar grain structure is evident in the figure. Both Nb and Al layers exhibit crystallographic texture, with the electron diffraction pattern for this film showing stronger diffraction spots in the direction normal to the multilayer. The X-ray diffraction patterns of all films are dominated by the Al(l 11) and Nb(l 10) peaks and show a merging of these two peaks with decreasing periodicity.

scholarly journals Solid state phase transformation kinetics in Zr-base alloys

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
A. R. Massih ◽  
Lars O. Jernkvist
Keyword(s):  
Phase Transformation ◽  
Solid State ◽  
Zirconium Alloys ◽  
Excess Oxygen ◽  
Transformation Kinetics ◽  
Fuel Cladding ◽  
Reactor Accident ◽  
Phase Transformation Kinetics ◽  
Solid State Phase Transformation ◽  
Water Reactors

AbstractWe present a kinetic model for solid state phase transformation ($$\alpha \rightleftharpoons \beta$$ α ⇌ β ) of common zirconium alloys used as fuel cladding material in light water reactors. The model computes the relative amounts of $$\beta$$ β or $$\alpha$$ α phase fraction as a function of time or temperature in the alloys. The model accounts for the influence of excess oxygen (due to oxidation) and hydrogen concentration (due to hydrogen pickup) on phase transformation kinetics. Two variants of the model denoted by A and B are presented. Model A is suitable for simulation of laboratory experiments in which the heating/cooling rate is constant and is prescribed. Model B is more generic. We compare the results of our model computations, for both A and B variants, with accessible experimental data reported in the literature covering heating/cooling rates of up to 100 K/s. The results of our comparison are satisfactory, especially for model A. Our model B is intended for implementation in fuel rod behavior computer programs, applicable to a reactor accident situation, in which the Zr-based fuel cladding may go through $$\alpha \rightleftharpoons \beta$$ α ⇌ β phase transformation.

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