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Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗
DOE OSTI2023

EXPERIMENTAL AND COMPUTATIONAL STUDY OF DIRECT CONTACT MEMBRANE DISTILLATION

Experimental and computational studies of direct contact membrane distillation (DCMD) are conducted. The permeate flux is measured in a module containing a flat sheet membrane. Polytetrafluoroethylene (PTFE) hydrophobic membrane (Membrane Solutions, FPB045A16) with a nominal pore size of 0.45 μm, the thickness of 179~239 μm, the porosity of 80% is used in the experiments. The feed solution is a binary mixture of water and NaCl. The inlet feed temperature is fixed at 70°C, and the feed Reynolds number is varied between 500 and 2000. Two inlet feed concentrations, 0 and 35g/L, are considered. The permeate flow rate was kept constant at Re of 1300 and temperature of 20°C. Three-dimensional steady-state computational fluid dynamics (CFD) simulations are performed using the laminar model. The Navier’s Stokes, energy, and mass transport equations in each channel coupled with flux boundary conditions imposed at the membrane surface are solved. The predicted module-averaged flux is compared to measured data for all operating conditions. Measured and predicted flux agrees well; validating both experiments and model, Temperature polarization in the feed and permeate channel and concentration polarization in the feed channel are characterized by validated CFD simulations.

Oztekin, Alparslan↗
DOE OSTI2024

Method of tuning physical properties of thermosets

Polymerization-induced phase separation enables fine control over thermoset network morphologies, yielding heterogeneous structures with domain sizes tunable over 1-100 nm. However, the controlled chain-growth polymerization techniques exclusively employed to regulate morphology at these length scales are unsuitable for most thermoset materials typically formed through step-growth mechanisms. By employing binary mixtures in place of the classic constituents of phase-separating thermosets—resin, curing agent, and secondary polymer—facile tunability over morphology can be achieved through a single compositional parameter. Indeed, this method yields morphologies spanning nano-scale to macro-scale, controlled by the relative reactivities and thermodynamic compatibility of the network components. Due to the connection between chain dynamics and microstructure in these materials, the tunable morphology enables exquisite control over glass transition and other physical and mechanical properties.

Jones, Brad Howard↗
NASA NTRS1990

Calculating Masses, Densities, And Compositions Of Alloys

Metallurgical Programs include three simple programs calculating solutions to problems common to metallurgical engineers and persons making metal castings. First program calculates mass of binary ideal mixture (alloy). Second, calculates densities of binary ideal mixture. Third, converts atomic percentages of binary mixture to weight percentages. Uses simple equations to assist with routine calculations. Written in Microsoft QuickBASIC.

De Groh, H.↗
DOE OSTI2020

Nonlinear Logistic Regression Mixture Experiment Modeling for Binary Data Using Dimensionally Reduced Components

This article presents and illustrates an approach using nonlinear logistic regression for modeling binary response data from a mixture experiment when the components can be partitioned into groups used to form dimensionally-reduced pseudocomponents (DRPs). A DRP is a linear combination of the components in a group, where the linear combinations over all groups are normalized so that the DRP proportions sum to unity. Nonlinear logistic regression is required because, after normalization of the linear combinations, the model expressed in terms of the DRPs is nonlinear in the parameters that specify the linear combinations. A method for obtaining nonparametric tolerance limits on the probability of a “success” for the binary response variable using a bootstrap approach is also presented. Having three DRPs enables viewing data and modeling results on a ternary plot even though there may be many more than three mixture components. A real database, involving whether or not nepheline crystals form in simulated nuclear waste glass after cooling, is used to illustrate the nonlinear logistic regression modeling and nonparametric tolerance limit approaches when there are three DRPs.

Waste glass, Nepheline, Mixture experiment, Logist↗
DOE OSTI2023

Phase diagram to demarcate supercritical, transcritical, and continuous phase regimes for binary fluid equilibrium mixing relevant to combustion applications

Here, a robust methodology to develop phase diagrams of binary fluid mixtures at fixed thermo dynamic conditions (pressure, temperature, and mole fraction) as well as of two initially separated fluids undergoing mixing near critical conditions are presented for fluids and con ditions relevant to rockets, gas turbines, and diesel engine applications. Phase equilibria of mixtures is first examined to provide insight into the continuous-phase mixing behavior (including but not limited to supercritical behavior), and to develop a broadly applicable phase-diagram for binary fluid mixtures at fixed conditions. Next, adiabatic mixing theory and reduced Helmholtz equations of state are used to predict the thermodynamic conditions required to attain continuous-phase binary fluid mixing near critical conditions. Then, a 3D surface diagram (P,T fuel ,T amb ) separating single and two-phase regions is constructed by varying the ambient pressure and the initial temperatures of the two fluids. Polynomial fits of the 3D surfaces for 10 different binary mixtures are tabulated for nitrogen-alkane and methane-oxygen blends relevant to air-breathing and propellant based engines, respectively.

42 ENGINEERING↗
NASA NTRS1979

Process feasibility study in support of silicon material, task 1

Analyses of process system properties were continued for materials involved in the alternate processes under consideration for semiconductor silicon. Primary efforts centered on physical and thermodynamic property data for dichlorosilane. The following property data are reported for dichlorosilane which is involved in processing operations for solar cell grade silicon: critical temperature, critical pressure, critical volume, critical density, acentric factor, vapor pressure, heat of vaporization, gas heat capacity, liquid heat capacity and density. Work was initiated on the assembly of a system to prepare binary gas mixtures of known proportions and to measure the thermal conductivity of these mixtures between 30 and 350 C. The binary gas mixtures include silicon source material such as silanes and halogenated silanes which are used in the production of semiconductor silicon.

Li, K. Y.↗
DOE OSTI2022

Effects of non-thermal termolecular reactions on detonation development in hydrogen (H 2 )/methane (CH 4 ) - air mixtures

The binary fuel blend of H 2 /CH 4 is one of the most promising hydrogen-enriched hydrocarbon fuels in spark-ignition (SI) engines. Yet, the undesirable phenomenon of super-knock, which can severely and in-stantaneously damage an SI engine, limits its widespread adoption. Moreover, there is still a lack of con-sensus on the precise mechanism by which this phenomenon occurs i.e. via flame acceleration or spon-taneous ignition, despite numerous previous investigations. At the same time, recent studies [M. P. Burke, S. J. Klippenstein, Nat. Chem. 9 (2017) 1078 -1082, Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522] have demonstrated a high probability of occurrence of non-thermal reactions in premixed flames of such H 2 /CH 4 fuel blends with air due to the presence of non-trivial amounts of highly reactive radicals including H, O and OH apart from O 2 . The present study focuses on the evolution of an initial deflagration front to a detonation wave in H 2 /CH 4 - air mixtures under SI engine relevant conditions through fully resolved, constant volume 1D simulations with and without non-thermal reactivity. Non-thermal reactions were included in the macroscopic kinetics model as chemically termolecular reactions facilitated by the H + CH 3 and H + OH radical-radical recombination and the H + O 2 radical-molecule association reactions. Further, the nonthermal reactions result in a corresponding decrease in the reaction fluxes of the incipient recombination/association reactions. Therefore, an additional set of simulations were performed by applying corrections to the respective incipient recombination/association rate constants using the methodology demonstrated by Tao et al. [Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522]. Compared to the baseline case, the onset of spontaneous ignition in the end-gas region was observed to be delayed in the presence of non-thermal termolecular reactions. Concurrently, the developing detonation was observed to be significantly stronger. In contrast, applying corrections to the recombi-nation/association rate constants resulted in a completely different behavior. Specifically, detonation was observed to occur due to self acceleration of the primary flame in the absence of spontaneous ignition in the end-gas region. Sensitivity analysis was performed to quantify the effects of non-thermal reactions on the duration of heat release rate and thereby the mechanism of detonation formation. In addition, chemical explosive mode analysis (CEMA) was performed to identify the dominant species/reactions re-sponsible for the observed results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote—and, in some cases, may be necessary for—the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Heat Capacity Anomaly Near the Lower Critical Consolute Point of Triethylamine-Water

The heat capacity of the binary liquid mixture triethylamine-water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent a was determined to be 0.107 +/- 0.006, consistent with theoretical predictions. When alpha was fixed at 0.11 to determine various amplitudes consistently, our values of A(+) and A(-) agreed with a previous heat capacity measurement, but the value of A(-) was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A(+)/ A(-) = 0.56 +/- 0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid-vapor systems. The correction to scaling amplitude ratio D(+)/D(-) = 0.5 +/- 0.1 was half of that predicted. As a result of several more precise theoretical calculations and experimental determinations, the two-scale-factor universality ratio X, which we found to be 0.019 +/- 0.003, now is consistent among experiments and theories. A new 'universal' amplitude ratio R(sup +/-)(sub Bcr) involving the amplitudes for the specific heat was tested. Our determination of R(sup +/-)(sub Bcr) = -0.5 +/- 0.1 and R(sup -)(sub Bcr) = 1.1 +/- 0.1 is smaller in magnitude than predicted and is the first such determination in a binary fluid mixture.

Flewelling, Anne C.↗
DOE OSTI2020

Mechanochemical Synthesis of High-Purity Anhydrous Binary Alkali and Alkaline Earth Chloride Mixtures

A direct synthesis route for high-purity, anhydrous binary salt mixtures has been developed. This atom efficient, solvent-free process is easily scalable, with the potential to produce salt mixtures that meet the purity standards required for industrial heat transfer and nuclear applications. The essence of the methodology lies in mechanochemical synthesis of carnallite precursors that can mitigate the hydrolysis of MgCl 2 ·6H 2 O under direct heating. Each dehydrated salt carnallite was then analyzed for purity and oxide content through subsequent powder X-ray diffraction, and strong acid titration. In conclusion, this process presents a more effective alternative route compared to previous methods for obtaining low-oxide, high-purity chloride salt mixtures.

Alkali↗
DOE OSTI2021

Comprehensive Assessment of the Accuracy of the Ideal Adsorbed Solution Theory for Predicting Binary Adsorption of Gas Mixtures in Porous Materials

Quantifying the adsorption of chemical mixtures in porous adsorbents is critical to developing these materials for useful separation applications. The ideal adsorbed solution theory (IAST) is the most widely applied mixing theory for predicting mixture adsorption using single-component adsorption data, but a perceived lack of experimental data has limited previous efforts to explore the accuracy of IAST in a systematic way. In this paper, we take advantage of a large collection of binary experimental data for gas adsorption that became available recently to tackle this issue. Specifically, we identify more than 400 examples in which binary adsorption data and single-component data are available in the same publication and apply IAST to all these examples. This analysis includes experimental data from 63 gas mixtures of 37 different molecular species and 174 different adsorbents. In addition to being the most systematic evaluation to date of the accuracy of IAST for gas adsorption, these data will be valuable for future efforts to test or develop mixing theories that improve upon IAST.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗