Introduction. Aluminum alloys, nickel-base alloys, 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 (by 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 computed solidification cracking susceptibility. The end goals are to optimize existing alloy chemistries and to formulate 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 during solidification (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 susceptibility. Open source thermodynamic databases available at online repositories are demonstrated (van de Walle, 2018). 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 further 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 computed solidification cracking susceptibility provided by 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 one-size-fits-all specified composition limits in the current standards. Furthermore, the results have use in determining processing steps such 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 crack susceptibility was calculated for those alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency that each alloying element had. 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, a numerical approach has been developed using Python code and open source CALPHAD software 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.
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