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Defining heat treatments for compositionally functionally graded materials (FGMs) is challenging due to varying processing conditions in terminal alloys and gradient regions. In the present work, we studied the impact of heat treatments on phase transformations and the resulting mechanical properties along an FGM grading from stainless steel 304L (SS304L) to Inconel 625 (IN625) FGM fabricated using directed energy deposition (DED) additive manufacturing (AM). We applied heat treatments at 700 °C, 900 °C, and 1150 °C and the microstructure and hardness, as a function of layer-wise composition and applied heat treatment, were characterized. The applicability of computational methods previously developed by the team to predict experimentally observed phases by the hybrid Scheil-equilibrium approach was evaluated. This approach improves the accuracy of predicting phases formed after heat treatment compared to equilibrium thermodynamic calculations using the overall layer compositions and provides a simple pathway to assist in designing heat treatment for FGMs. 

A database for the Cr-Ni-V system was constructed by modeling the binary Cr-V and ternary Cr-Ni-V systems using the CALPHAD approach aided by density functional theory (DFT)-based first-principles calculations and ab initio molecular dynamics (AIMD) simulations. To validate this new database, a functionally graded material (FGM) using Ni-20Cr and V was fabricated using directed energy deposition additive manufacturing (DED AM) and experimentally characterized. The deposited Ni-20Cr was pure fcc phase, while increasing V content across the gradient resulted in sigma phase formation, followed by bcc phase formation. The experimentally measured phases were compared with CALPHAD computations made using a Cr-Ni-V thermodynamic database from the literature and the database developed in the present work. The newly developed database was shown to better predict the experimentally observed phases due to its accurate modeling of binary systems within the database and the ternary liquid phase, which is critical for accurate Scheil calculations. 

The Fe-Nb and Fe-Nb-Ni systems are remodeled using updated sublattice models for the topologically close packed (TCP) phases of Laves_C14, δ and μ with new experimental data and first-principles and phonon calculations based on density functional theory (DFT). Experimental techniques are used to determine phase compositions and tie-lines in the Fe-Nb-Ni system. The three-, three-, and five- sublattice models are used for Laves_C14, δ, and μ phases, respectively. DFT calculations are employed to predict thermochemical data as a function of temperature for Laves_C14, δ, and μ phases. The new thermodynamic description of the Fe-Nb-Ni system includes a new hexagonal phase named - hP24 - and the updates for the Fe-Nb system and reproduces better the experimental and computational thermochemical and phase equilibrium data from the present study and the literature. The new results will improve thermodynamic predictions of TCP and other phases in both Fe-based and Ni-based alloy systems. 

Density functional theory (DFT) prescribes the existence of a ground-state configuration at 0 K for a given system. However, the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above 0 K. Our multiscale entropy approach, Zentropy, postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground-state and symmetry-breaking non-ground-state configurations represents the building blocks of materials and can be used to quantitatively predict free energy of individual phases with the free energy of each configuration predicted from DFT as well as all properties derived from free energy of individual phases. 

In functionally graded materials (FGMs) fabricated using directed energy deposition (DED) additive manufacturing (AM), cracks may form due to interdendritic stress during solidification, the formation of deleterious phases, or the buildup of residual stresses. This study builds on our previously proposed concept of FGM feasibility diagrams to identify gradient pathways that avoid deleterious phases in FGMs by also considering hot cracking. Here, five hot cracking criteria were integrated into the feasibility diagrams, and equilibrium simulations were carried out based on Scheil results (termed hybrid Scheil-equilibrium simulation) to predict phase formation below the solidus temperature considering solidification micro-segregation. The new feasibility diagrams were applied to four previously studied FGMs, and the newly proposed approach predicted high crack susceptibility, detrimental phase formation, or interdendritic BCC phase formation in the experimentally observed cracking region. This demonstrates the utility of the proposed framework for crack prediction in the design of future FGMs gradient pathways.