ResearchAdditiveManufacturing—Article Data-Driven Microstructure and Microhardness Design in Additive Manufacturing Using a Self-Organizing Map

To design microstructure and microhardness in the additive manufacturing (AM) of nickel (Ni)-based superalloys, the present work develops a novel data-driven approach that combines physics-based models, experimental measurements, and a data-mining method. The simulation is based on a computational thermal-ﬂuid dynamics (CtFD) model, which can obtain thermal behavior, solidiﬁcation parameters such as cooling rate, and the dilution of solidiﬁed clad. Based on the computed thermal information, dendrite arm spacing and microhardness are estimated using well-tested mechanistic models. Experimental microstructure and microhardness are determined and compared with the simulated values for validation. To visualize process–structure–properties (PSPs) linkages, the simulation and experimental datasets are input to a data-mining model—a self-organizing map (SOM). The design windows of the process parameters under multiple objectives can be obtained from the visualized maps. The proposed approaches can be utilized in AM and other data-intensive processes. Data-driven linkages between process, structure, and properties have the potential to beneﬁt online process monitoring control in order to derive an ideal microstructure and mechanical properties. (cid:1) 2019 THE AUTHORS. Published by Elsevier LTD on behalf of Chinese Academy of Engineering and Higher Education Press Limited Company. This is an open access article under the CC BY-NC-ND license (


Introduction
Accelerating the process and materials design in additive manufacturing (AM) has been investigated in the current literature (e.g., Refs. [1][2][3]). In this respect, multiscale and multiphysics modeling and simulation are vital, because they have the potential to significantly reduce the cost and time expended in experiments [4,5]. Many efforts have been made to model and simulate AM processes in order to predict process-structure-property (PSP) relationships [6][7][8][9]. Meanwhile, it is critical for model validation and verification to employ highly controlled experimental measurements, which include online monitoring of the process, microstructure characterization, and mechanical testing [10][11][12].
However, merely combining experiments with simulations cannot achieve the desired acceleration in AM process and materials design, because it is difficult to understand and utilize the high-dimensional datasets produced by simulations and experiments. There is an essential need for supportive data science approaches that efficiently integrate the iterations between experiments and multiscale simulation. Popova et al. [13] used data science approaches to understand the process-structure linkages in AM, and used a proposed data science workflow in an attempt to understand the relationships between process conditions and synthetic grain structure. An integration of physics-based and data-mining approaches for temperature field prediction in AM has been proposed [14,15]. A surrogate model based on a functional Gaussian process was calibrated by means of three-dimensional (3D) finite-element analysis (FEA) and experimental thermal image data [14,15]. Salloum et al. [16] undertook high-dimensional dataset compression by using adaptive Alpert tree wavelets in the laser-engineered net shape (LENS) process. The self-organizing map (SOM), which was proposed by Kohonen [17,18], is an unsupervised machine learning algorithm based on neural networks that is able to map highdimensional data to two-dimensional (2D) planes while preserving topology [19,20] (ANN), which is commonly used for regression problems, the main advantage of the SOM is that it can visualize high-dimensional data in the form of a low-dimensional map, which helps researchers to visually identify underlying relations between the features. As a tool to visualize high-dimensional datasets, the SOM is beneficial for the cluster analysis of real-life design problems as well [21].
In this study, an SOM is used to visualize high-dimensional data in AM; these data are obtained from well-designed experimental measurements and multiphysics models. The SOM is introduced to find the relationships among laser power, mass flow rate, energy density, dilution, cooling rate, dendrite arm spacing, and microhardness in AM. In addition, the design windows of process parameters under multiple objectives can be obtained from the visualized SOM. A schematic diagram of this work is shown in Fig. 1 [22].

Experimental dataset
Single tracks of Inconel 718 powder were deposited on an AISI 1045 carbon steel disc using a 1020 nm high-powered continuous wave laser. The beam diameter at its focus is 3 mm. The laser power was set to be constant, while the mass flow rate was incremented from 3.35 to 27.2 gÁmin À1 in 2.65 gÁmin À1 increments. At each mass flow rate, the laser power was incremented from 1000 to 2000 W in 200 W increments, resulting in 60 single tracks. The detailed process parameters and conditions can be found in our previous paper [10]. Materials characterization in this case included CR measurements, dilution measurements, dendrite arm spacing measurements, and hardness testing. An infrared thermal camera was used to determine the cooling rate from the solidus to liquidus temperature of the steady-state melt pool, as detailed in Ref. [10]. After etching the clad cross-section, dilution and dendrite arm spacing can be identified and quantified. Vickers microhardness measurements were taken to obtain the averaged microhardness. A summary of the experimental efforts as well as a chart detailing the dilution are provided in Fig. 2. Details of experiments can be found in Ref. [22].

Physics-based simulation dataset
A computational thermal-fluid dynamics (CtFD) model was developed to simulate the directed energy deposition (DED) process [23]. The current paper does not describe the modeling equations, but rather provides a few features to offer an understanding of the CtFD model and process-structure models. The nonisothermal Navier-Stokes (N-S) equations, which include mass, momentum, and energy equations, were solved to obtain the temperature field and liquid metal flow in the melt pool [24,25]. A physics-based arbitrary Lagrangian-Eulerian (ALE) method was utilized to track the free surface of the melt pool [23]. The melt pool dimensions, dilution, and cooling rate at the liquid-solid interface can be computed based on the steady-state melt pool temperature field. Dendrite arm spacing is evaluated by the Hurt formula [26]. Vickers hardness (HV) can be determined by the Fig. 1. A schematic description of the workflow typically employed in current computational efforts (top row) and of experimental efforts (bottom row), along with a description of how this can be augmented with a data-mining approach to recover high-value PSP linkages of interest to material innovation efforts. CALC: calculated; EXP: experiment. nickel (Ni) equivalent for Ni-based superalloys [27]. Details of these models have been described in our previous work [22]. In total, 25 simulation cases with various laser power levels and mass flow rates were computed. For each case, the structures and properties observed were the melt pool geometry, dilution, cooling rate, secondary dendrite arm spacing (SDAS), and microhardness. A summary of the simulation efforts is shown in Fig. 3.

Data mining for visualizing PSPs linkages
The SOM Toolbox in MATLAB [28] was used to simultaneously visualize high-dimensional datasets and design process parameters. Using physics-based simulations and experimental measurements, seven-dimensional (7D) PSP datasets were obtained for data mining as the input vector, x m , as shown in    4. Because the simulation results agree well with the experimental results [22], 25 simulation data points and five experimental data points were used as input vectors to train a single 8 Â 8 SOM indistinctively. We compared the results from differently sized SOMs, and found that the 8 Â 8 SOM has the best performance. If the map size is too small, the map resolution is very low; however, an SOM that is too large results in overfitting. Each 7D input vector contains seven variables, including: four process variables (i.e., laser power, mass flow rate, energy density, and cooling rate), two microstructure variables (i.e., dilution and SDAS), and one property variable (i.e., microhardness). In this illustrative case, only five experimental data points were used as the input of the SOM out of the total 60 experimental points, because only five experimental data points have all seven measurements. The current version of the SOM requires data points with the same dimension of features. Therefore, the rest of the experimental data are used to validate the simulation results, rather than train the SOM. The goal of this work is to demonstrate a data-driven workflow in order to understand and design high-dimensional datasets in AM. There is potential for more experimental and simulation datasets to be involved in order to obtain better map resolution without changing the workflow.
The training procedure can be described by the pseudo code, as shown in Algorithm 1. The map neurons are hexagonal. The labels of the X and Y axes are the integers 1 i SizeX, and 1 j SizeY, respectively, as shown in Fig. 4. Initially, the weights of the neurons are set to be W i;j 0 with random number [0, 1]. The elements of each input vector are normalized linearly to [0, 1]. After initialization, the SOM is trained for a number of T epochs. For the current epoch t and each input vector x m , first, the best matching unit (BMU) is determined by calculating the distance between the input vector and each neuron weight using Eq. (1). The BMU is a map unit has the shortest distance to input vector x m . Second, the diameter of the neighborhood around the BMU can be determined by Eq. (2), where d(t) is a function that decreases monotonously with time. The initial distance coefficient is d 0 and is 8 in this study. The decrease rate is k. Third, the weights W i;j m in the BMU and its neighborhoods are updated according to Eqs.
Determine diameter of neighborhood around BMU: Update weights W i;j mþ1 in BMU and neighborhoods:

End do End do
Each map is shown in Fig. 6. The relation between the PSP variables can be understood visually. For example, as shown in Fig. 6, the mass flow rate and SDAS are positively correlated, as the component planes of the mass flow rate and SDAS have similar values at similar positions. Conversely, the mass flow rate and dilution are highly negatively correlated. Thus, according to the visualized SOM in Fig. 6, the following results are obtained in this study: The mass flow rate, more than laser power, greatly contributes to the cooling rate and SDAS. The dilution and microhardness depend on both the mass flow rate and laser power. The microhardness is dominated by the dilution, rather than by the SDAS or cooling rate. Obtained through the data-mining approach, these elations provide valuable insight into the complex underlying physical phenomena and material evolution during the AM process. In addition, it is possible to obtain the desired process parameter window with multiple objective microstructure and property ranges. In this study, the objective dilution is from 0.1 to 0.3. In this range of dilution, the solidified track can avoid both lack of fusion due to low dilution and property degradation due to high dilution [29]. The SDAS should be minimized and the microhardness should be maximized in order to maintain good mechanical properties. An iteration procedure through all the units is undertaken in order to seek units that satisfy these restrictions. An objective cluster  that includes multiple units can be selected as a white wireframe, as shown in Fig. 6. Thus, the following desired process parameters can be obtained: a laser power ranging from 1000 to 1100 W and a mass flow rate ranging from 22.4 to 24.8 gÁmin À1 . The desired energy density, which is defined as laser power divided by mass flow rate, ranges from 2.4 Â 10 6 to 2.9 Â 10 6 JÁkg À1 .
The effect of uncertainties, such as the simulation error, on the fidelity of the SOM is an interesting and important topic. In our future work, a modified SOM with uncertain inputs will be investigated by using a larger database.

Conclusion
This work presented a novel workflow to produce, visualize, and design high-dimensional PSP linkages in AM through the utilization of multiphysics modeling, experimental measurements, and advanced data science techniques. An application of this workflow to quantify and design microstructure and microhardness was demonstrated herein. High-dimensional datasets, which include laser power, mass flow rate, energy density, cooling rate, dilution, dendrite arm spacing, and microhardness, were derived by means of physics-based models and experiments. The profound relations among PSP data were visualized using an SOM, and important relationship trends were identified. Multiple objective optimization examples were proposed and solved in order to attain desired process parameters. The presented approach can be applied to a broad variety of PSP datasets for AM and other data-intensive processes. Data-driven relationships between process, structure, and property can provide online monitoring and process control to derive ideal microstructure and mechanical properties.