Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential

Computational methods are increasingly being incorporated into the exploitation of microstructure–property relationships for microstructure-sensitive design of materials. In the present work, we propose non-intrusive materials informatics methods for the high-throughput exploration and analysis of a synthetic microstructure space using a machine learning-reinforced multi-phase-field modeling scheme. We specifically study the interface energy space as one of the most uncertain inputs in phase-field modeling and its impact on the shape and contact angle of a growing phase during heterogeneous solidification of secondary phase between solid and liquid phases. We evaluate and discuss methods for the study of sensitivity and propagation of uncertainty in these input parameters as reflected on the shape of the Cu6Sn5 intermetallic during growth over the Cu substrate inside the liquid Sn solder due to uncertain interface energies. The sensitivity results rank σSI,σIL, and σIL, respectively, as the most influential parameters on the shape of the intermetallic. Furthermore, we use variational autoencoder, a deep generative neural network method, and label spreading, a semi-supervised machine learning method for establishing correlations between inputs of outputs of the computational model. We clustered the microstructures into three categories (“wetting”, “dewetting”, and “invariant”) using the label spreading method and compared it with the trend observed in the Young-Laplace equation. On the other hand, a structure map in the interface energy space is developed that shows σSI and σSL alter the shape of the intermetallic synchronously where an increase in the latter and decrease in the former changes the shape from dewetting structures to wetting structures. The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME.

Phase-field modeling of nonequilibrium solidification processes in additive manufacturing

This project models dendrite growth during nonequilibrium solidification of binary alloys using the phase-field method (PFM). Understanding the dendrite formation processes is important because the microstructural features directly influence mechanical properties of the produced parts. An improved understanding of dendrite formation may inform design protocols to achieve optimized process parameters for controlled microstructures and enhanced properties of materials. To this end, this work implements a phase-field model to simulate directional solidification of binary alloys. For applications involving strong nonequilibrium effects, a modified antitrapping current model is incorporated to help eject solute into the liquid phase based on experimentally calibrated, velocity-dependent partitioning coefficient. Investigated allow systems include SCN, Si-As, and Ni-Nb. The SCN alloy is chosen to verify the computational method, and the other two are selected for a parametric study due to their different diffusion properties. The modified antitrapping current model is compared with the classical model in terms of predicted dendrite profiles, tip undercooling, and tip velocity. Solidification parameters—the cooling rate and the strength of anisotropy—are studied to reveal their influences on dendrite growth. Computational results demonstrate effectiveness of the PFM and the modified antitrapping current model in simulating rapid solidification with strong nonequilibrium at the interface.

Phase Field Modeling of Anisotropic Tension Failure of Rock-Like Materials

The tensile fracture is a widespread feature in rock excavation engineering, such as spalling around an opened tunnel. The phase field method (PFD) is a non-local theory to effectively simulate the quasi-brittle fracture of materials, especially for the propagation of a tensile crack. This work is dedicated to study the tensile failure characteristics of rock-like materials by the PFD simulation of the Brazilian test of the intact and fissure disk samples. The numerical results indicate that the tensile strength of the disk sample is anisotropic due to the influence of pre-existing cracks. The peak load decreases at first and then increases with the increase of the inclination angle, following the U-shaped trend. The simulation results also indicate that the wing crack growth is the main failure characteristic. Moreover, the crack propagation path initiates at the tip of the pre-existing crack when the inclination angle is less than 60°. Crack propagation initiates near the tip of the pre-existing crack when the angle is 75°, and it initiates at the middle of the pre-existing crack when the angle is 90°. Finally, all cracks extend to the loading position and approximately parallel to the loading direction. This process is in agreement with the Brazilian test of pre-existing cracks in the laboratory, which can validate the effectiveness of the PFD in simulating the tensile fracture of rock-like materials. This study can provide a reference for the fracture mechanism of the surrounding rock in the underground excavation.

Microstructure-dependent rate theory model of defect segregation and phase stability in irradiated polycrystalline LiAlO2

Gamma lithium aluminate (LiAlO2) is a breeder material for tritium and is one of key components in a tritium-producing burnable absorber rod (TPBAR). Dissolution and precipitation of second phases such as LiAl5O8 and voids are observed in irradiated LiAlO2. Such microstructure changes cause the degradation of thermomechanical properties of LiAlO2 and affect tritium retention and release kinetics, and hence, the TPBAR performance. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed for investigating the accumulation of species and phase stability in polycrystalline LiAlO2 structures under irradiation. Three sublattices (i.e., [Li, Al, V]I [O, Vo]II [Lii, Ali, Oi, Vi]III), and concentrations of six diffusive species (i.e., Li; vacancy of Li or Al at [Li, Al, V]I sublattice, O vacancy at [O, Vo]II sublattice, and Li, Al and O interstitials at [Lii, Ali, Oi, Vi]III interstitial sublattices; are used to describe spatial and temporal distributions of defects and chemistry. Microstructure-dependent thermodynamic and kinetic properties including the generation, reaction, and chemical potentials of defects and defect mobility are taken into account in the model. The parametric studies demonstrated the capability of the developed RIS model to assess the effect of thermodynamic and kinetic properties of defects on the segregation and depletion of species in polycrystalline structures and to explain the phase stability observed in irradiated LiAlO2 samples. The developed RIS model will be extended to study the precipitation of LiAl5O8 and voids and tritium retention by integrating the phase-field method.