Predicting Mesoscale Microstructural Evolution in Electron Beam Welding

JOM, Mar 2016

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 electron-beam 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.

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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)


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T. M. Rodgers, J. D. Madison, V. Tikare, M. C. Maguire. Predicting Mesoscale Microstructural Evolution in Electron Beam Welding, JOM, 2016, pp. 1419-1426, Volume 68, Issue 5, DOI: 10.1007/s11837-016-1863-8