Thursday 8:00 AM

May 25, 2017

Room: Salon II, III

Location: Ann Arbor Marriott Ypsilanti at Eagle Crest

Grain boundary (GB) migration and grain rotation are important mechanisms for grain growth in nanocrystalline materials. In order to deeply understand these mechanisms, molecular dynamics (MD) simulations of grain coarsening and shrinkage driven by GB curvature have been often performed. Although MD simulations enable us to quantitatively investigate atomic motions in the vicinity of GBs, the timescale of MD simulations is too short to study the GB migration and the grain rotation in real timescales. On the other hand, the phase-field crystal (PFC) model has attracted much attention as a powerful methodology for simulating atomistic scale motion of GBs that occurs on diffusive timescales. In this presentation, we will report on three-dimensional (3D) PFC simulations of the shrinkage of a spherical grain embedded in a single crystal. The results clarify the structure and evolution of the dislocation network formed in the GB. We find that the evolution of the dislocation network strongly affects morphology and rotation of the embedded grain. Furthermore, the grain translation of a columnar grain in a tricrystal simulated by 3D PFC simulations will be presented.

The structural phase field crystal (XPFC) model is used to study material phenomena at atomic length-scales and diffusive time-scales, bridging the gap between atomistic and mesoscale models. As a result of these properties, the XPFC model can be used to simulate the dynamic behavior of grain boundary structures. However, the XPFC model needs to be parameterized using experimental data or other computational results in order to simulate the properties of a specific material. One method by which the XPFC model can be parameterized is through changes to the two-body density correlation function (DCF), which is a term in the XPFC model’s free energy functional. In the XPFC model, the DCF is approximated using one or more Gaussian functions. Previous work has shown that changing the height and width of the Gaussian function(s) in the XPFC correlation function can predictably alter the grain boundary energy (GBE) and structure in two-dimensional hexagonal systems. Building on these results, three-dimensional hexagonal close packed grain boundaries are created using the XPFC model, and the DCF is parameterized so that the GBEs agree with molecular dynamics simulations of magnesium grain boundaries (Mg) performed by Ni et al. [1]. This parameterized XPFC model will be used to study equilibrium and non-equilibrium phenomena associated with Mg grain boundaries. These results will be used as input for larger scale continuum models, e.g., phase field simulations, within an integrated computational materials engineering framework.[1] C. Ni, H. Ding, M. Asta, X. Jin, Scripta Materialia, 109 (2015), 94-99

In order to reproduce the microstructure evolution by a numerical simulation, the phase-field method is attracting much attention. While it has been applied for simulating various phenomena that occur in various materials, there are unknown parameters that strongly influence the simulation result. Moreover, phenomena such as phase transformation and grain growth etc. occur inside materials, consequently making it difficult to measure and determine such unknown parameters. Therefore, identification of suitable parameter is one of the critical issue for phase-field method to reproduce actual phenomena. Recently, we have developed a method to estimate such unknown parameters in the phase-field model from experimental measurements. In this study, the ensemble Kalman filter (EnKF), which is one of the sequential Bayesian filters commonly used in data assimilation, is applied to the phase-field simulation of austenite-to-ferrite transformation in Fe-C-Mn alloy. We have already validated its effectiveness in one dimensional simulation by performing the twin experiments, where synthetic experimental data created by the simulation model is used instead of the real measurements. Next, in order to apply for two dimensional simulation we have employed parallel computation using GPU since EnKF requires running a large number of simulation at the same time resulting in large computational cost. In this presentation, we are showing the result of parameter estimation for two dimensional phase-field simulation with different conditions.

Materials frequently exhibit interfacial energy anisotropy. When the anisotropy is sufficiently large, flat facets and sharp corners (edges) form in the equilibrium shape of a second-phase particle, and interfaces with unstable orientations undergo thermal faceting, the decomposition of thermodynamically unstable orientations into stable ones. Strong anisotropy poses two numerical challenges: flat facets and sharp corners are difficult to resolve, and thermal faceting is associated with mathematical ill-posedness. We have implemented and verified a phase field model with bulk diffusion and strong interfacial anisotropy that can generate nearly flat facets and that results in the expected corner (edge) and thermal-faceting behavior. The model retains well-posedness via the incorporation of a higher-order regularization term, which affects equilibrium shapes in a predictable way, and we omit the gradient penalty in concentration in order to reduce the order of the regularized equations. This model has been implemented in the phase field (PF) code developed within the Center for PRedictive Integrated Structural Materials Science (PRISMS), which is an open source phase field code that employs the deal.II finite element library. PRISMS-PF employs matrix-free elements, explicit time-stepping, and state of the art numerical and parallelization libraries to deliver high performance and scalability. The features and performance of the anisotropic PRISMS-PF applications will be discussed, including methods to easily implement anisotropy for different crystalline symmetries.

A three-dimensional (3D) computational framework has been developed to model recrystallization and grain growth phenomena in Ti-Al alloys by using the phase-field approach with inputs from a crystal plasticity model. In this framework, the evolution of the dislocation density during the deformation process of polycrystalline Ti and Ti-Al alloys is predicted using a 3D multiscale crystal plasticity finite element (CPFE) code. The grain structure from a phase-field simulation and experimental texture data from electron backscatter diffraction are used as the initial condition for a CPFE simulation. The CPFE simulation then provides the crystal orientation and dislocation density of each grain during the deformation of polycrystalline metals. The results are then used as the initial condition for a phase-field simulation of recrystallization. The kinetics of the microstructural evolution is analyzed by examining the recrystallized volume fraction as well as grain size distribution and grain morphology. The simulation results are compared with the experimental data for range of temperatures and alloy compositions to determine how those factors influence the microstructural evolution.

Mechanical properties of interest such as yield strength, UTS, ductility etc.,are affected by the hierarchical features of the microstructure. This necessitates the use of multiscale approaches in a physics based simulation framework to obtain desired properties of the representative microstructure. However, a change in the process conditions results in a different microstructure of the material. This requires a rerun of the compute intensive multiscale simulations to obtain desired properties and may not be of utility when quick decisions have to be taken. Instead, a data-driven approach is more feasible to obtain properties corresponding to a changed morphology and composition of the microstructure. In the present work, representative microstructures and corresponding mechanical properties are generated for a low carbon steel (0.08 - 0.14 %C) during annealing for different processing conditions, initial composition and morphology. Phase field method is used to obtain the representative microstructures which are then used as input to micromechanics simulation to compute the properties. The obtained microstructures are digitally represented using two point statistics. To make the computations tractable the dimensions of the digitized microstructure are reduced using the principal component analysis (PCA) technique. Further to this, utilizing the PyMKS framework, polynomial regression is deployed on a sample set to obtain the structure-property relations which are cross validated using data derived from the sample set. The structure-property relations so obtained could be useful in the solution of the inverse problem of arriving at a process route for a desired material property.