Predicting Mesoscale Microstructural Evolution in Electron Beam Welding
JOM
Predicting Mesoscale Microstructural Evolution in Electron Beam Welding
Using the kinetic Monte Carlo simulator, Stochastic Parallel PARticle Kinetic Simulator, from Sandia National Laboratories, a user routine has been developed to simulate mesoscale predictions of a grain structure near a moving heat source. Here, we demonstrate the use of this user routine to produce voxelized, synthetic, three-dimensional microstructures for electronbeam welding by comparing them with experimentally produced microstructures. When simulation input parameters are matched to experimental process parameters, qualitative and quantitative agreement for both grain size and grain morphology are achieved. The method is capable of simulating both single- and multipass welds. The simulations provide an opportunity for not only accelerated design but also the integration of simulation and experiments in design such that simulations can receive parameter bounds from experiments and, in turn, provide predictions of a resultant microstructure.
INTRODUCTION
The Potts Monte Carlo model, a generalization of
the Ising model for magnetic systems to systems
with an arbitrary number of spins or grain
identifiers, has been used for several decades to study
grain growth in polycrystalline materials.1–4 The
simplicity of the method has led to the development
of many in-house codes for specific applications but
few widespread, general-use, publically available
ones. Stochastic Parallel PARticle Kinetic
Simulator (SPPARKS) is the result of an effort to develop a
general-use mesoscale Monte Carlo suite at Sandia
National Laboratories, much like the LAMMPS
package5 for atomic-scale simulations, thereby
providing a framework for the broad implementation of
a variety of mesoscale Monte Carlo solvers. By using
SPPARKS, the Potts model has been extended to
several novel applications, including hybrid
approaches incorporating cellular automata and
phase field models.6–9
Since the 1990s, several studies have attempted
to simulate the influence of materials processing
methods with moving heat sources on the
microstructure. Dress et al.10,11 used cellular
automata to produce an accurate grain structure within
the fusion zone (FZ) of an autogenous weld.
However, the relatively small scale and two-dimensional
(2D) nature of the method limited further
application or quantitative analysis. Significant advances
were made by Debroy et al. with a
three-dimensional (3D) weld simulation.12–15 Their studies
demonstrated good agreement with experimental
grain size distributions at various distances from
the centerline of the FZ. Debroy and co-workers
focused their analysis on the heat-affected zone
(HAZ) surrounding the FZ and excluded the FZ
from their simulation domain.
Here, we introduce a Monte Carlo Potts-based
method for the simulation of melting, solidification,
and grain growth during welding at the mesoscale.
The model simulates the widely known dependence
of solidification behavior on thermal gradient (G)
and solidification front velocity (V) in metals, rather
than on specific material system properties. As
shown in Chapter 4 of Kurz and Fisher,16 as well as
Flemings,17 there exist distinct regimes of expected
grain morphology in metals undergoing directional
solidification based on the combination of the
thermal gradient, G, and solidification velocity, V. The
model presented in this work simulates melting in
the FZ and grain growth in the FZ and HAZ to
match grain morphology predictions based on G and
V. A 3D steady-state temperature profile with a
given G is rastered with a velocity V. Since these
simulations are performed at a length scale that is
much larger than required to resolve the formation
and growth of dendrites, the authors suggest this
approach enables studying large numbers of grains
and their evolution, which in turn, provides greater
flexibility and a potentially broader range of
applicability.
THE POTTS MONTE CARLO MODEL
TO SIMULATE GRAIN GROWTH DURING
WELDING
Grain Growth
The Monte Carlo Potts model evolves spins (or
grain identifiers) on a discrete lattice to simulate
microstructural evolution. To initialize the
simulation, the starting microstructure is digitized on a 3D
lattice by assigning spins to each lattice site. Since
the driving force for curvature-driven grain growth
is the reduction in grain boundary energy, only
grain boundary energy is considered and is given by
the sum of the bond energies between neighboring
lattice sites of unlike spins:
1 XN XL
E ¼ 2
i¼1 j¼1
1
d qi; qj ;
ð1Þ
where N is the total number of lattice sites in the
simulation, qi and qj are the spins at lattices sites i
and j, and L is the number of neighbors of each
lattice site (26 for a 3D cubic lattice used here). The
1/2 prefactor eliminates double counting in the
summation. With this formulation, each pair of
unlike neighboring sites contributes one unit of
energy to the total system energy.
Grain growth is simulated by selecting a lat (...truncated)