An Automated Fully-Computational Framework to Construct Printability Maps for Additively Manufactured Metal Alloys

In additive manufacturing, the optimal processing conditions need to be determined to fabricate porosity-free parts. For this purpose, the design space for an arbitrary alloy needs to be scoped and analyzed to identify the areas of defects for different laser power-scan speed combinations and can be visualized using a printability map. Constructing printability maps is typically a costly process due to the involvement of experiments, which restricts their application in high-throughput product design. To reduce the cost and effort of constructing printability maps, a fully computational framework is introduced in this work. The framework combines CALPHAD models and a reduced-order model to predict material properties. THen, an analytical thermal model, known as the Eagar-Tsai model, utilizes some of these materials' properties to calculate the melt pool geometry during the AM processes. In the end, printability maps are constructed using material properties, melt pool dimensions, and commonly used criteria for lack of fusion, balling, and keyholing defects. To validate the framework and its general application to laser powder-bed fusion alloys, five common additive manufacturing alloys are analyzed. Furthermore, NiTi-based alloys at three different compositions are evaluated to show the further extension of the framework to alloy systems at different compositions. The defect regions in these printability maps are validated with corresponding experimental observations to compare and benchmark the defect criteria and find the optimal criterion set with the maximum accuracy for each unique material composition. Furthermore, printability maps for NiTi that are obtained from our framework are used in conjunction with process maps resulting from a multi-model framework to guide the fabrication of defect-free additive manufactured parts with tailorable properties and performance.Comment: 18 Figures, 35 page

High-throughput Alloy and Process Design for Metal Additive Manufacturing

Designing alloys for additive manufacturing (AM) presents significant opportunities. Still, the chemical composition and processing conditions required for printability (ie., their suitability for fabrication via AM) are challenging to explore using solely experimental means. In this work, we develop a high-throughput (HTP) computational framework to guide the search for highly printable alloys and appropriate processing parameters. The framework uses material properties from state-of-the-art databases, processing parameters, and simulated melt pool profiles to predict process-induced defects, such as lack-of-fusion, keyholing, and balling. We accelerate the printability assessment using a deep learning surrogate for a thermal model, enabling a 1,000-fold acceleration in assessing the printability of a given alloy at no loss in accuracy when compared with conventional physics-based thermal models. We verify and validate the framework by constructing printability maps for the CoCrFeMnNi Cantor alloy system and comparing our predictions to an exhaustive 'in-house' database. The framework enables the systematic investigation of the printability of a wide range of alloys in the broader Co-Cr-Fe-Mn-Ni HEA system. We identified the most promising alloys that were suitable for high-temperature applications and had the narrowest solidification ranges, and that was the least susceptible to balling, hot-cracking, and the formation of macroscopic printing defects. A new metric for the global printability of an alloy is constructed and is further used for the ranking of candidate alloys. The proposed framework is expected to be integrated into ICME approaches to accelerate the discovery and optimization of novel high-performance, printable alloys.Comment: 46 pages, 20 figure

Experiment Design Frameworks for Accelerated Discovery of Targeted Materials Across Scales

Over the last decade, there has been a paradigm shift away from labor-intensive and time-consuming materials discovery methods, and materials exploration through informatics approaches is gaining traction at present. Current approaches are typically centered around the idea of achieving this exploration through high-throughput (HT) experimentation/computation. Such approaches, however, do not account for the practicalities of resource constraints which eventually result in bottlenecks at various stage of the workflow. Regardless of how many bottlenecks are eliminated, the fact that ultimately a human must make decisions about what to do with the acquired information implies that HT frameworks face hard limits that will be extremely difficult to overcome. Recently, this problem has been addressed by framing the materials discovery process as an optimal experiment design problem. In this article, we discuss the need for optimal experiment design, the challenges in it's implementation and finally discuss some successful examples of materials discovery via experiment design

Materials Design Under Bayesian Uncertainty Quantification

Uncertainty quantification and its propagation across multi-scale model/experiment chains are key elements of decision-based materials design in the framework of Integrated Computational Materials Engineering. In this context, understanding the sources of uncertainty and their quantification can provide a confidence for the applicability of models for decision making in materials design, which is generally overlooked in the field of materials science. Based on the above-mentioned motivation, different case studies are considered in this work to indicate how Bayesian inverse uncertainty quantification and forward uncertainty propagation approaches operate in various applications and procedure conditions. In this dissertation, inverse uncertainty quantification of model parameters is performed through a Markov Chain Monte Carlo approach; and all propagation of uncertainties from model parameters to model responses are accomplished through the first order second moment approach and/or the forward model analysis of parameters sampled from the posterior probability distribution after the parameter probabilistic calibrations. Moreover, different information fusion approaches are proposed here to smartly combine the probabilistic information obtained from different sources of information for more precise probabilistic predictions of physical systems behaviors. This dissertation starts with the importance of uncertainty quantification for product design and engineering. This is followed by some fundamentals about different sources of uncertainties, different statistical views and approaches for uncertainty quantification and propagation in computational modeling, and the previous work in literature for uncertainty quantification and propagation in materials science problems. Then, uncertainties are evaluated in the case of plastic flow behavior modeling of transformation induced plasticity steels using two different procedures of data training, including sequential training with each experimental data as independent evidence and simultaneous training of all data together as overall evidence. A multi-objective probabilistic calibration of an Ni-Ti precipitation model in MatCalc© are also performed against all experimental data simultaneously to quantify the uncertainties of resulting micro-structural features from the model. It should be noted that an empirical relationship for matrix/precipitate inter-facial energy in terms of aging temperature and nominal composition have also been introduced according to the values of inter-facial energy obtained from the model calibration with each given experimental data individually. However, large discrepancies and uncertainties obtained for model results are important reasons to apply co-kriging surrogate modeling for more precise prediction of precipitation behavior and its uncertainty based on the establishment of a linear correlation between the experimental responses and the fitted surrogate model over the results of the precipitation model. In addition, a constrained probabilistic calibration is carried out for a thermo-mechanical model using a distance-based comparison metric of transformation strain-temperature curves. In this case, a design of experiment followed by a variance-based sensitivity analysis are also performed to identify the most influential model parameters before the calibration. Uncertainty quantification in the calculation of Hf-Si binary phase diagram are also discussed in this dissertation. In this case, Bayesian model averaging and an error correlation-based model fusion are also applied to combine all the results obtained from randomly generated models together to make the calculation of phase diagrams more objective rather than being subjective to the expert opinions for the model selection. In the end, the major efforts for uncertainty quantification of thermodynamic properties and phase diagrams are reviewed. For future work, the probabilistic calibration of the influential parameters in expensive models (such as phase field models) can be performed through the efficient global optimization approach. In these cases, the uncertainty propagation of parameters to the model responses through an efficient method is also very important. Moreover, the proposed information fusion approaches can be applied to combine the model and experimental results for the efficient optimization cases (such as efficient global optimization or knowledge gradient) since the fused responses can be more beneficial than just physical models/simulations in solving the inverse problems in materials design under the Integrated Computational Materials Engineering framework

Materials Design Under Bayesian Uncertainty Quantification

Uncertainty quantification and its propagation across multi-scale model/experiment chains are key elements of decision-based materials design in the framework of Integrated Computational Materials Engineering. In this context, understanding the sources of uncertainty and their quantification can provide a confidence for the applicability of models for decision making in materials design, which is generally overlooked in the field of materials science. Based on the above-mentioned motivation, different case studies are considered in this work to indicate how Bayesian inverse uncertainty quantification and forward uncertainty propagation approaches operate in various applications and procedure conditions. In this dissertation, inverse uncertainty quantification of model parameters is performed through a Markov Chain Monte Carlo approach; and all propagation of uncertainties from model parameters to model responses are accomplished through the first order second moment approach and/or the forward model analysis of parameters sampled from the posterior probability distribution after the parameter probabilistic calibrations. Moreover, different information fusion approaches are proposed here to smartly combine the probabilistic information obtained from different sources of information for more precise probabilistic predictions of physical systems behaviors. This dissertation starts with the importance of uncertainty quantification for product design and engineering. This is followed by some fundamentals about different sources of uncertainties, different statistical views and approaches for uncertainty quantification and propagation in computational modeling, and the previous work in literature for uncertainty quantification and propagation in materials science problems. Then, uncertainties are evaluated in the case of plastic flow behavior modeling of transformation induced plasticity steels using two different procedures of data training, including sequential training with each experimental data as independent evidence and simultaneous training of all data together as overall evidence. A multi-objective probabilistic calibration of an Ni-Ti precipitation model in MatCalc© are also performed against all experimental data simultaneously to quantify the uncertainties of resulting micro-structural features from the model. It should be noted that an empirical relationship for matrix/precipitate inter-facial energy in terms of aging temperature and nominal composition have also been introduced according to the values of inter-facial energy obtained from the model calibration with each given experimental data individually. However, large discrepancies and uncertainties obtained for model results are important reasons to apply co-kriging surrogate modeling for more precise prediction of precipitation behavior and its uncertainty based on the establishment of a linear correlation between the experimental responses and the fitted surrogate model over the results of the precipitation model. In addition, a constrained probabilistic calibration is carried out for a thermo-mechanical model using a distance-based comparison metric of transformation strain-temperature curves. In this case, a design of experiment followed by a variance-based sensitivity analysis are also performed to identify the most influential model parameters before the calibration. Uncertainty quantification in the calculation of Hf-Si binary phase diagram are also discussed in this dissertation. In this case, Bayesian model averaging and an error correlation-based model fusion are also applied to combine all the results obtained from randomly generated models together to make the calculation of phase diagrams more objective rather than being subjective to the expert opinions for the model selection. In the end, the major efforts for uncertainty quantification of thermodynamic properties and phase diagrams are reviewed. For future work, the probabilistic calibration of the influential parameters in expensive models (such as phase field models) can be performed through the efficient global optimization approach. In these cases, the uncertainty propagation of parameters to the model responses through an efficient method is also very important. Moreover, the proposed information fusion approaches can be applied to combine the model and experimental results for the efficient optimization cases (such as efficient global optimization or knowledge gradient) since the fused responses can be more beneficial than just physical models/simulations in solving the inverse problems in materials design under the Integrated Computational Materials Engineering framework

Revisiting thermodynamics and kinetic diffusivities of uranium–niobium with Bayesian uncertainty analysis

© 2016 In this work, thermodynamic and kinetic diffusivities of uranium–niobium (U–Nb) are re-assessed by means of the CALPHAD (CALculation of PHAse Diagram) methodology. In order to improve the consistency and reliability of the assessments, first-principles calculations are coupled with CALPHAD. In particular, heats of formation of γ-U–Nb are estimated and verified using various density-functional theory (DFT) approaches. These thermochemistry data are then used as constraints to guide the thermodynamic optimization process in such a way that the mutual-consistency between first-principles calculations and CALPHAD assessment is satisfactory. In addition, long-term aging experiments are conducted in order to generate new phase equilibria data at the γ2/α+γ2 boundary. These data are meant to verify the thermodynamic model. Assessment results are generally in good agreement with experiments and previous calculations, without showing the artifacts that were observed in previous modeling. The mutual-consistent thermodynamic description is then used to evaluate atomic mobility and diffusivity of γ-U–Nb. Finally, Bayesian analysis is conducted to evaluate the uncertainty of the thermodynamic model and its impact on the system's phase stability