Recent Developments in Simulating Grain Growth with Monte Carlo Algorithms
- PDF / 409,241 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 81 Downloads / 239 Views
Recent Developments in Simulating Grain Growth with Monte Carlo Algorithms Qiang Yu and Sven K. Esche Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 ABSTRACT Both isotropic and anisotropic single-phase grain growth processes modeled using a modified Monte Carlo method exhibit parabolic growth kinetics, and the anisotropy degree affects only the rate of change of the mean grain area. In some cases, with significantly anisotropic grain boundary energies, the normalized grain size distributions are not timeinvariant during the lattice evolution. INTRODUCTION The grain growth kinetics of normal single-phase materials obey a power law of the form m
− R
(a )
R
( b)
R = Kt n
m 0
= Bt
if
R
0
0.46 indicates that 0 is approximately equal to 3, while the commonly assumed value of 0 is 1 [5,7,13]. Therefore, Eq. 1a is preferable for the calculation of n unless only grain sizes much larger than 3 are used in the regression analysis.
(a)
(b)
Figure 3: (a) Distribution of values for grain growth exponent n using conventional MC algorithm with the fitting function 〈R 〉 m − 〈R 0 〉 m = Bt . (b) Typical grain growth kinetics with Q = 80 resulting in n ≈ 0.5 and 0 ≈ 3 In most of the cases where n < 0.46, the vs. t data were observed to fluctuate significantly around a fitted parabolic curve throughout the entire time domain, and these local fluctuations are large enough to cause the small values of n obtained in the regression analyses. Grain growth of single-phase materials with anisotropic grain boundary energies The following anisotropic grain boundary energy potentials were investigated using Q ≈ 10,000 initially randomly distributed grains θ′ θ′ * J * 1 − ln * θ′ < θ V1 (θ) = θ θ θ′ ≥ θ* J θ′ θ′ < θ* J V2 (θ) = θ* θ′ ≥ θ* J θ θ′ = 2π − θ
(4)
0≤ θ ≤π π ≤ θ ≤ 2π
where θ* is the anisotropy parameter varying from 0 to π. V1 is the well-known Read-Shockley potential [9], V2 is called linear-isotropic potential [8], and J is the energy scale. For these two potentials, it was observed that for varying degrees of anisotropy, the grain boundary configurations (i.e., grain morphologies) appear to be time-invariant. Figure 4 shows typical microstructures at = 15 for the following three cases: isotropic, (V1, θ* = π), and (V2, θ* = π). Furthermore, the topological features (i.e., time-invariant grain shape distribution and mean number of grain edges per grain equal to 6) in all anisotropic cases remain unaltered W6.14 Downloaded from https:/www.cambridge.org/core. University of Arizona, on 16 Apr 2017 at 11:11:24, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1557/PROC-731-W6.11
compared with the isotropic case. While the normalized grain size distributions for varying degrees of anisotropy for V1 are time-invariant, the normalized grain size distributions for significant degrees of anisotropy for V2 change during the lattice evolution as shown in Figure 5.
(a)
(c ) (c)
Data Loading...
