Phase Field Modeling of Recrystallization Grain Growth during Re-Aging Process in Cu-Ni-Si Alloy

2007 ◽  
Vol 561-565 ◽  
pp. 1805-1808
Author(s):  
Yong Qiang Long ◽  
Ping Liu ◽  
Wei Min Zhang
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Aging Process ◽  
Structural Evolution ◽  
Diffuse Interface ◽  
Gradual Transition ◽  
Ginzburg Landau ◽  
Pinning Effect ◽  
Structural Variables ◽  
Strong Pinning

The micro structural evolution and the mechanism of recrystallization grain growth were studied during re-aging process in Cu-Ni-Si alloy containing finely pre-aging δ-Ni2Si precipitates using computer simulations based on a diffuse-interface phase-field kinetic model. In this model, the temporal evolution of the spatially dependent field variables is determined by numerically solving the time-dependent Ginzburg-Landau (TDGL) equations for the structural variables. The simulation results quantify the effects of the precipitation on recrystallization. It is shown that the finely dispersed pre-aging δ-Ni2Si precipitates exert a strong pinning effect on the recrystallization grain boundaries. The recrystallization grain growth for r = 3 fa = 0.015 can be described as R =1.04∗t 0.33 at the beginning, followed by a gradual transition to growth stagnation. The final grain size follows a Zener type relation lim 0.49 1.41 a R r f =     for 0.01 ≤ fa ≤ 0.21 and r = 2.5 or 3.

Phase Field Modeling of Ferroelectric Domain Wall Interactions With Charge Defects

2006 ◽  
Author(s):  
Chad M. Landis
Keyword(s):  
Phase Field ◽  
Domain Walls ◽  
Virtual Work ◽  
Landau Equation ◽  
Second Law Of Thermodynamics ◽  
Ferroelectric Material ◽  
Diffuse Interface ◽  
Element Formulation ◽  
Ginzburg Landau ◽  
Domain Structures

The overall objective of this work is to develop a theoretical model that can track the evolution of the domain structures in ferroelectric crystals, which are responsible for the non-linear electromechanical behavior of these materials. To this end, a continuum thermodynamics framework is devised, and the theory falls into the class of phase-field or diffuse-interface modeling approaches. Here a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships. The approach is shown to yield the commonly accepted Ginzburg-Landau equation for the evolution of the polarization order parameter. Within the theory a form for the free energy is postulated that can be applied to fit the general elastic, piezoelectric and dielectric properties of a ferroelectric material near its spontaneously polarized state. Thereafter, a principle of virtual work is specified for the theory and is implemented to devise a finite element formulation. The theory and numerical methods are used to investigate the interactions of 180° and 90° domain walls with an array of charge defects and to determine the electromechanical pinning strength of the array on the walls.

Grain Growth of Polycrystalline AZ31 Mg Alloy Containing Second Phase Particles by Phase Field Simulation

2016 ◽  
Vol 850 ◽  
pp. 307-313
Author(s):  
Yan Wu ◽  
Si Xia ◽  
Bernie Ya Ping Zong
Keyword(s):  
Particle Size ◽  
Grain Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Free Energy Density ◽  
Critical Value ◽  
Spherical Particles ◽  
Second Phase ◽  
Pinning Effect ◽  
Second Phase Particles

A phase field model has been established to simulate the grain growth of AZ31 magnesium alloy containing spherical particles with different sizes and contents under realistic spatial-temporal scales. The expression term of second phase particles are added into the local free energy density equation, and the simulated results show that the pinning effect of particles on the grain growth is increased when the contents of particles is increasing, which is consistent with the law of Zener pinning. There is a critical particle size to affect the grain growth in the microstructure. If the size of particles is higher than the critical value, the pinning effect of particles for grain growth will be increased with further decreasing the particle size; however the effect goes opposite if the particle size is lower than the critical value.

Dual Scale Simulation of Grain Growth Using a Multi Phase Field Model

2001 ◽  
Vol 677 ◽  
Author(s):  
Ingo Steinbach ◽  
Markus Apel
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Individual Characteristics ◽  
Interfacial Stress ◽  
Pinning Force ◽  
Pinning Effect ◽  
Multi Phase

ABSTRACTThe kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and interfacial stress balance at the vertices of the grain boundaries. A comprehensive way to treat both effects in one model is given by the time dependent Ginzburg Landau model or phase field model. The paper presents the application of a multi phase field model, recently developed for solidification processes to grain growth of a multicrystalline structure. The specific feature of this multi phase field model is its ability to treat each grain boundary with its individual characteristics dependent on the type of the grain boundary, its orientation or the local pinning at precipitates. The pinning effect is simulated on the nanometer scale resolving the interaction of an individual precipitate with a curved grain boundary. From these simulations an effective pinning force is deduced and a model of driving force dependent grain boundary mobility is formulated accounting for the pinning effect on the mesoscopic scale of the grain growth simulation. 2-D grain growth simulations are presented.

Phase Field Simulation of Grain Growth with Particle Pinning

2016 ◽  
Vol 724 ◽  
pp. 8-11
Author(s):  
Chun Yu Teng ◽  
Yun Fu ◽  
Zhan Yong Ren ◽  
Yong Hong Li ◽  
Yun Wang ◽  
...  
Keyword(s):  
Particle Size ◽  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Particle Number ◽  
Boundary Energy ◽  
Service Condition ◽  
Second Phase ◽  
Pinning Effect

The properties of alloys depend on its microstructure, such as the size of grains. In general, the balanced mechanical properties of alloys can be obtained with small grain size. While the grain size of alloys may increases under heat treatment, thermal mechanical processing and service condition of high temperature, i.e., the grain growth is inevitable. The effort of most research is to control the rate of grain growth and avoid abnormal grain growth. For example, pinning the grain boundary and reduce its mobility with the second phase particles in order to prevent grain growth. Therefore, the properties of the alloys will not decreases dramatically and the structure retains a high degree of integrity. The details of grain growth with particle pinning were investigated by phase field simulations in the present paper. It is found that, with the same size of pinning particles, the pinning effect increases with the increases of the pinning particle number. With the same pinning particle number, the pinning effect increases with the increases of pinning particle size. Under the same total volume of pinning particles while different particle size and number, the pinning effect is complicated and it will be discussed in details. The pinning effect decreases with the increases of grain boundary energy. These findings could shed light on the understanding of the grain growth kinetics with particle pinning.

Phase-Field Simulation of Interface Effect during Grain Nucleation

2012 ◽  
Vol 490-495 ◽  
pp. 3339-3343
Author(s):  
Fei Huo ◽  
Ji Wei Zhao
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Landau Theory ◽  
Phase Field Model ◽  
Ginzburg Landau ◽  
Euler Formula ◽  
Topological Theory ◽  
Field Simulation ◽  
Simulation Results

In this paper, a phase field model based on Ginzburg-Landau theory is used to analyze the topological phenomena during grain growth. The simulation results show that two topological transformations exist during the grain growth—Neighbor Switching and Grain Annihilation; and we have found different kinds of topological events during the disappearance of a grain: direct vanishing of trilateral grain and pentagonal grain, as well as neighbor switching，which are right with classical topological theory and Euler formula. The simulation results are similar with experiments.

3D Phase Field Simulation of Austenite Grain Growth in Microalloyed Linepipe Steel

2012 ◽  
Vol 715-716 ◽  
pp. 800-805
Author(s):  
Morteza Toloui ◽  
Matthias Militzer
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Rapid Heating ◽  
Three Dimensional ◽  
Heating And Cooling ◽  
Austenite Grain ◽  
Cooling Conditions ◽  
Strong Pinning ◽  
Austenite Grain Growth ◽  
Linepipe Steel

Three dimensional (3D) phase field modelling is used to simulate austenite grain growth in X80 linepipe steel for thermal paths that are typical in the heat affected zone (HAZ). In the HAZ austenite grain growth is affected by pinning due to precipitates and their potential dissolution. Effective grain boundary mobilities are introduced that are consistent with strong pinning at lower temperatures and weak pinning at higher temperatures separated by the estimated dissolution temperature range of fine NbC precipitates. These mobility relationships are then used to describe austenite grain growth in bulk samples subjected to rapid heating and cooling conditions to replicate thermal cycles at various positions in the HAZ.

Simulation of recrystallization grain growth during re-aging process in the Cu–Ni–Si alloy based on phase field model

2008 ◽  
Vol 62 (17-18) ◽  
pp. 3039-3042 ◽  
Author(s):  
Yong-qiang Long ◽  
Ping Liu ◽  
Yong Liu ◽  
Wei-min Zhang ◽  
Jian-sheng Pan
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Aging Process ◽  
Field Model ◽  
Phase Field Model
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