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Experimentally informed multiscale creep modelling of additive manufactured Ni-based superalloys
(2023)
Excellent creep resistance at elevated temperatures, i.e. T / T_m> 0.5, due to γ-γ’ microstructure is one of the main properties of nickel-based superalloys. Due to its great importance for industrial applications, a remarkable amount of research has been devoted to understanding the underlying deformation mechanism in a wide spectrum of temperature and loading conditions. Additive manufactured (AM) nickel-based superalloys while being governed by similar γ-γ’ microstructure, exhibit AM-process specific microstructural characteristics, such as columnar grains, strong crystallographic texture (typically <001> fiber texture parallel to build direction) and compositional inhomogeneity, which in turn leads to anisotropic creep response in both stationary and tertiary phases.
Despite the deep insights achieved recently on the correlation between process parameters and the resulting microstructure, the anisotropic creep behavior and corresponding deformation mechanism of these materials are insufficiently understood so far. One reason for this is the lack of capable material models that can link the microstructure to the mechanical behavior. To overcome this challenge, a multiscale microstructure-based approach has been applied by coupling crystal plasticity (CP) and polycrystal model which enables the inclusion of different deformation mechanisms and microstructural characteristics such as crystallographic texture and grain morphology. The method has been applied to experimental data for AM-manufactured INCONEL-738LC (IN738). The effect of different slip systems, texture, and morphology on creep anisotropy at 850°C has been investigated. Results suggest a strong correlation between superlattice extrinsic stacking fault (SESF) and microtwinning and observed creep anisotropy.
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model. By surveying the dependence of the elastic energy on the chemical composition and lattice misfit, we derive a lattice strain coefficient λ*. Studying several high-entropy alloys and superalloys, we propose that most solid solution multi-component alloys are stable when λ*<0.16, generalizing the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index δ, frequently used for describing strain in multi-component alloys, directly represents the elastic energy e with e=qδ², q being an elastic constant. Furthermore, the effects of (i) the number and (ii) the atomic-size distribution of constituting elements on the phase stability of high-entropy alloys were quantified. The present derivations and discussions open for richer considerations of elastic effects in high-entropy alloys, offering immediate support for quantitative assessments of their thermodynamic properties and studying related strengthening mechanisms.
Systematic microstructure design requires reliable thermodynamic descriptions and phase diagrams of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is greatly challenged by their individualistic aspects. In this talk, we present a density-based thermodynamic concept to describe defects based on available bulk thermodynamic data. Here dealing with grain boundaries (GBs), we apply this concept to compute GB (phase) diagram. Applications to segregation engineering of GBs in bulk and nanocrystalline alloys will be presented. We further develop this model to include the effect of elastic interactions due to atom size mismatch and obtain the corresponding GB (phase) diagram for the ternary Al-Cu-Li system.
Grain boundary (GB) chemical and structural variations can significantly influence materials performance. The former is generally ascribed to the structural gradient between the grain and GB. While GB segregation may be accompanied by chemical and structural variations, clear insights about the GB’s thermodynamic phase behaviour upon coupling between its chemistry and structure is lacking. Using the CALPHAD integrated density-based phase field model, we study the co-evolution of GB’s structure and segregation in Fe-Mn alloys. We found that the GB segregation transition is amplified if its structure can respond to chemical variation. Additionally, the coupling between GB structural and segregation evolution was found to enable co-existence of the spinodally formed low- and high-Mn phases within the GB. In the light of atomistic simulations, we expand on investigating the correlation between the parameters that characterise the GB density map with GB properties.
Phase diagrams are the roadmaps for designing bulk phases. Similar to bulk, grain boundaries can possess various phases, but their phase diagrams remain largely unknown. Using a recently introduced density-based model, here we devise a strategy for computing multi-component grain boundary phase diagrams based on available bulk (CALPHAD) thermodynamic data. Fe-Mn-Cr, Fe-Mn-Ni, Fe-Mn-Co, Fe-Cr-Ni and Fe-Cr-Co alloy systems, as important ternary bases for several trending steels and high-entropy alloys, are studied. We found that despite its solute segregation enrichment, a grain boundary can have lower solubility limit than its corresponding bulk, promoting an interfacial chemical decomposition upon solute segregation. This is revealed here for the Fe-Mn-base alloy systems. The origins of this counter-intuitive feature are traced back to two effects, i.e., the magnetic ordering effect and the low cohesive energy of Mn solute element. Different aspects of interfacial phase stability and GB co-segregation in ternary alloys are investigated as well. We show that the concentration gradient energy contributions reduce segregation level but increase grain boundary solubility limit, stabilizing the GB against a chemical decomposition. Density-based grain boundary phase diagrams offer guidelines for systematic investigation of interfacial phase changes with applications to microstructure defects engineering.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
The current lack of quantitative knowledge on processing-microstructure–property relationships is one of the major bottlenecks in today’s rapidly expanding field of additive manufacturing. This is centrally rooted in the nature of the processing, leading to complex microstructural features. Experimentally-guided modeling can offer reliable solutions for the safe application of additively manufactured materials. In this work, we combine a set of systematic experiments and modeling to address creep anisotropy and its correlation with microstructural characteristics in laser-based powder bed fusion (PBF-LB/M) additively manufactured Inconel-738LC (IN738LC). Three sample orientations (with the tensile axis parallel, perpendicular, and 45° tilted, relative to the building direction) are crept at 850 °C, accompanied by electron backscatter secondary diffraction (EBSD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations. A crystal plasticity (CP) model for Ni-base superalloys, capable of modeling different types of slip systems, is developed and combined with various polycrystalline representative volume elements (RVEs) built on the experimental measurements. Besides our experiments, we verify our modeling framework on electron beam powder bed fusion (PBF-EB/M) additively manufactured Inconel-738LC. The results of our simulations show that while the crystallographic texture alone cannot explain the observed creep anisotropy, the superlattice extrinsic stacking faults (SESF) and related microtwinning slip systems play major roles as active deformation mechanisms. We confirm this using TEM investigations, revealing evidence of SESFs in crept specimens. We also show that the elongated grain morphology can result in higher creep rates, especially in the specimens with a tilted tensile axis.
A density-based phase field model is developed where the free energy functional is explicitly linked with molecular dynamics and is referred to as the Molecular Phase Field Method (MoPF). MoPF simulations involve expressing interatomic potentials in terms of density to form a density based free energy functional. Inputs to this functional are taken from atomistics such that the phase field density profile matches the corresponding density profile from atomistic simulations. We analyze our results by comparing the MoPF calculated excess interfacial energies with excess interfacial energies calculated using molecular dynamics associated with several nickel grain boundaries. Additionally, a comparison is made between our results and the interfacial energies of a \Sigma7 boundary across a variety of FCC systems simulated using density functional theory. The MoPF method is able to successfully predict grain boundary free energy trends between grain boundary and material types offering an atomistically informed mesoscale formulation for studying grain boundary physics.
Several recent studies have revealed that the phase decomposition in medium- and high-entropy alloys is triggered by solute segregation at grain boundaries. The chemically complex nature of these alloys already clues that such segregation in materials should be something more than the interaction between solutes and grain boundary, but also affected by the solute-solute interactions during the segregation. In fact, experiments indicate the significance of such solute-solute interaction. Yet, the mechanisms of co-segregation in multi-component alloys are rather challenging to explore and rarely studied quantitatively. Recently, a CALPHAD-integrated density-based phase-field model has been proposed for studying grain boundary phenomena. Several applications of this model have shown its expansive capacity for investigating grain boundary segregation and phase behavior. In this talk, the applications of this model to studying co-segregation phenomena and grain boundary phase diagrams in multi-component alloys are presented ––the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solutes and grain boundary during the segregation. In particular, the iron-based ternary and quaternary alloys are discussed. I show how a grain boundary may have its own miscibility gap and how this immiscibility can influence the co-segregation behavior. As an alternative to grain boundary phase diagrams, rather suited for binary and ternary alloys, a new concept of co-segregation maps for screening and segregation design in multi-component alloys is presented. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation in Fe-Co-Mn-Cr is discussed.
The Gibbs free energy of a grain boundary is a complex thermodynamic function of temperature, pressure, and composition. These complexities add to the intrinsic crystallographic and chemical constraints imposed by the adjacent bulk phase. Recently we have proposed a density-based model for assessing grain boundary thermodynamics that enables a CALPHAD-informed description of the grain boundary. As such, the Gibbs free energy of the grain boundary is directly linked with available CALPHAD thermodynamic data. In this talk, new aspects of interfacial segregation and phase transformation are revealed by benchmarking the current model for various experimental cases, including several steels, high-entropy alloys and aluminum alloys. The effects of elastic interactions on the grain boundary segregation and the application of the model to a nanocrystalline Pt-Au alloy, with numerous grain boundaries of various characters, will be discussed.
Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys.
Engineering grain boundaries demands a quantitative description of both their segregation and specific phase behavior. Recently I have proposed a density-based model for grain boundary thermodynamics that enables CALPHAD integrated derivation of grain boundary phase diagrams, broadly applied now in studying various alloys. Combining this model with experimental investigations, in this talk, new aspects of interfacial segregation and phase transformation revealed in polycrystalline alloys are discussed. The effect of elastic interaction on grain boundary phase behavior is incorporated. We consider Al alloys and novel high-entropy alloys and discuss a general strategy for grain boundary engineering.
Recent advances in Deep Learning (DL) have significantly impacted the field of materials modelling. DL tools have been recently considered as promising tools to address the complex relationships among processing, microstructure and property of materials. The thermal stability of polycrystalline materials is a highly interesting and complex problem that could be addressed using DL techniques. The Multi-Phase-Field (MPF) method has emerged as a powerful tool for addressing grain growth phenomena from multiple perspectives. Unlike sharp-interface based methods, the MPF approach bypasses the need for detailed information on individual grains. In this work, we use DL to address issues related to MPF simulations of grain growth including numerical efficiency, computing speed, and resource consumption. This presents specific challenges for high-performance computing (HPC) due to the large datasets and complex computations required by both MPF and DL methods. We study various 3D microstructure settings with the goal of accelerating the simulation process while exploring different physical effects. In particular, the impact of grain boundary and triple junction energies on grain growth are to be investigated. The results will be presented in terms of the evolving size and shape distribution of the grains.
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of microstructure defects is challenging because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the homogeneous bulk and derive the grain boundary Gibbs free energy functional. The grain boundary segregation isotherm and phase diagram are computed for a regular binary solid solution, and qualitatively benchmarked for the Pt–Au system. The relationships between the grain boundary's atomic density, excess free volume, and misorientation angle are discussed. Combining the current density-based model with available bulk thermodynamic databases enables constructing databases, phase diagrams, and segregation isotherms for grain boundaries, opening possibilities for studying and designing heterogeneous microstructures.