PHASE-FIELD SIMULATION DURING RECRYSTALLIZATIONPROCESS COUPLED WITH CRYSTAL PLASTICITY THEORYTomohiro Takaki*, Akinori Yamanaka**, Yoshikazu Higa***, Yoshihiro Tomita*****Faculty of Maritime Sciences, Kobe University
Fukaeminami, Higashinada, Kobe 658-0022, Japan,
takaki@maritime.kobe-u.ac.jp**, ****
Graduate School of Science and Technology, Kobe University
Rokkodai, Nada, Kobe 657-8501, Japan,**
yamanaka@solid.mech.kobe-u.ac.jp, ****tomita@mech.kobe-u.ac.jp***
Department of Mechanical System Engineering, Okinawa National College ofTechnology,Henoko, Nago 905-2192, Japan,y.higa@okinawa-ct.ac.jp
ABSTRACT A phase-field model and computational procedure for primary static
recrystallization are developed to study the recrystallization kinetics. The deformation
microstructures and plastic deformation behaviors of polycrystalline metal are simulated
by finite element method using strain gradient crystal plasticity theory. Based on theresults of crystallographic orientation and dislocation density, recrystallization phasefield simulation is performed. The effects of nucleation model of recrystallized grain on
the recrystallization kinetics are also evaluated.
INTRODUCTION: It is well known that the key to controlling properties of metallic
material is to control microstructure. It is, therefore, very important to understand therelationships between processing parameters and microstructural evolution. Monte CarloPotts models [Srolovitz et al. 1986] and cellular automata models [Hesselbarth et al.
1991, Raabe 2002] are widely used as numerical models for static recrystallization. The
both models are very similar each other and describe the state in terms of discrete values.
The MC Potts model requires an introduction of spatial and kinetic scaling, because timeand space in MC simulation is not real. On the other hand, although cellular automata
model is more efficient and easier to extend to 3D problem than MC model, it does notallow for curvature as a driving force for migration.
Phase-field models have attracted considerable interest in the last decade as a means ofsimulating complicated microstructures. It does not require any scaling because oftreating real time and space, and the curvature effect is included in the model explicitly.
We, therefore, believe that the phase-field model is promising approach to simulate
recrystallization. In this study, we develop a phase-field model and computational
procedure of primary static recrystallization. We adopt an adaptive mesh technique toperform the phase-field simulation efficiently [Takaki et al. 2005]. The crystallographic
orientation and dislocation density of plastically deformed material, which are required as
driving force of recrystallized grain and information of nucleation site, are calculated bystrain gradient crystal plasticity finite element method [Higa et al. 2003]. Some
recrystallization simulations are conducted to compare nucleation models, because thenucleation condition is considered to be dominant factor that decide the recrystallization
microstructures.
PROCEDURES, RESTULTS AND DISCUSSION: The procedure for primary static
recrystallization developed here consists of three steps. First, the deformation behavior isevaluated by finite element method using strain gradient crystal plasticity theory. Second,
the results, such as the crystallographic orientation, accumulated dislocation density andstored energy, are transferred into phase-field method. Finally, phase-field simulation isperformed during isothermal annealing to simulate the nucleation and evolution ofrecrystallized grains.
Figure 1 shows the results of crystal plasticity finite element simulation, wherepolycrystalline aluminum with regular hexagonal grains is compressed 45%. The blacklines are original grain boundaries. The distribution of dislocation density ρ (ρmin = 0.30,
ρmax = 1.47 [ × 1015 1/m2]) and high angle grain boundaries in which misorientation islarger than 15o are illustrated in Fig.1. These data are transferred into phase-field
simulation and used for calculating a stored energy and used as information of nucleation.
In recrystallization phase-field simulation, we solve following TDGL equations for phasefield φ and crystallographic orientation θ :1∇θ ∂θ∂φ∂f (φ )= M φ α 2 ∇ 2φ −(1),(2)− 2φs ∇θ = M θ 2 ∇ ⋅  φ 2 s∂tθ∇∂φ∂tφ
where phase field φ equals zero in the deformed matrix and unity in recrystallized grain,
and have 0<φ <1 inside recrystallized grain boundary. f (φ ) is a free energy density andexpressed by double well type function: f (φ ) = (1 − p (φ ))E store + Wq(φ ) where~2p(φ ) = φ 3 10 − 15φ + 6φ 2 , q(φ ) = φ 2 (1 − φ ) , E store = 0.5 ρµb 2 stored energy, and()W = 6σ δ energy wall height related to interface energy σ and interface thickness δ.
Furthermore, α = 3δσ gradient coefficient and s = α 2W π . M φ = m 2W 6α andM θ = (1 − p(φ ))M φ + p (φ ) M φ 1000 are mobilities for φ and θ, respectively, where m is a

mobility of grain boundary migration. Here we consider three types of nucleation model,i.e. site saturated nucleation (nuclei are placed at t = 0 on area satisfying ∆θ >15 o and ρ >aρmax where a = 0.5, 0.6 and 0.7), constant nucleation rate (one nucleus is placed every
10, 100, 500 and 1000 time steps) and decreasing nucleation rate (constant nucleation
rate for unrecrystallized area). Figure 2 shows time evolutions of recrystallized grains andadaptive mesh, and final recrystallized microstructures for decreasing nucleation rate
model (100 steps). Comparing with Fig.1, we can see from Fig.2 that the nuclei occur athigh dislocation density area and on the high angle boundaries. Figure 3 indicates therecrystallized area fraction X versus time for three nucleation models.

Fig. 1 Distributions of dislocation density and high angle grain boundary
at 45% compression of polycrystalline aluminum(a) t = 280 s(b) t = 560 s(c) t = 840 s(d) t = 1820 s
Fig. 2 Time evolutions of recrystallized grain (blue region) and adaptive mesh, and final
recrystallized microstructure (color indicates crystallographic orientation).
(a)

(b)

(c)

Fig.3 Recrystallized area fraction vs time for (a) site saturated nucleation, (b) constantnucleation rate and (c) decreasing nucleation rate.
REFERENCES:
Srolovitz D. J., Grest G. S. and Anderson M. P., 1986, “Computer Simulation ofRecrystallization – I. Homogeneous Nucleation and Growth”, Acta metal. 34, 18331845.
Hasselbarth H. W. and Göbel I. R., 1991, “Simulation of Recrystallization by CellularAutomata”, Acta metal. mater. 39, 2135-2143.
Raabe D., 2002, “Cellular Automata in Materials Science with Particular Reference toRecrystallization Simulation”, Annu. Rev. Mater. Res. 32, 53-76.
Takaki T., Fukuoka T. and Tomita Y., 2005, “Phase-field simulation during directional
solidification of a binary alloy using adaptive finite element method”, J. Crystal Growth283, 263-278.
Higa Y., Sawada Y. and Tomita Y., 2003, “Computational Simulation of Characteristic
Length Dependent Deformation Behavior of Polycrystalline Metals”, Tran. JSME 69,
523-529.