Machine-learning-assisted microstructure–property linkages of carbon nanotube-reinforced aluminum matrix nanocomposites produced by laser powder bed fusion

2.1 Material and the LPBF process

Commercial gas atomized AlSi10Mg powder (a particle size ranges from 25 to 112 μm) and multiwalled carbon nanotubes (MWCNTs with an outer diameter of 3–15 nm, a length of 15–30 μm) without any surface treatment were used as raw materials for carbon nanotube (CNT)-reinforced aluminum matrix nanocomposites (MWCNTs with a mass fraction of 0.5 wt%). An XQM-4 planetary ball milling machine (Changsha Tianchuang Powder Tech Co., China) was used to homogenously deposit MWCNTs on the surfaces of AlSi10Mg powders. The powder mixture was sealed in stainless steel bowls with a steel ball-to-powder ratio of 1:1. The rotation speed was set at 200 rpm with a total milling time of 4 h. After each 15 min of milling, a 5 min rest was set to avoid overheating of the powder mixture. The milled powder was dried in a vacuum chamber for 4 h at a temperature of 80°C and sealed in an aluminum bottle.

The LPBF process was conducted on a commercial SLM system (FS271, Farsoon Tech, Changsha, China) with a 275 mm × 275 mm × 340 mm build volume, consisting of an MFSC-500W ytterbium fiber laser with a maximum power of ∼500 W, a spot size of ∼90 μm and a continuous wavelength of 1,080 nm. A total of 16 samples fabricated using different scan speeds (1.8–2.4 m/s) and laser powers (350–450 W) were analyzed in this study as shown in Table 1. The detailed material characterization and mechanical testing results of the CNTs/AlSi10Mg nanocomposites were reported elsewhere [20]. Our previous study found that the addition of CNTs can enhance the mechanical properties (e.g., more than 10% yield strength increase) of the nanocomposites compared with AlSi10Mg without the CNT reinforce.

This article aims to build a high fidelity experimental-computational framework for subgrain cellular structure characterization of the CNTs/AlSi10Mg nanocomposites, relating the subgrain microstructure with their mechanical properties in a feature dimension of sub-micrometer to several micrometers.

The relative density of the CNTs/AlSi10Mg nanocomposites is measured using the Archimedes density principle. In addition, the areal density and void identification of micropores were measured using optical images and processed using the algorithm in ImageJ. These two density methods have similar measured values for different samples. Hardness tests were conducted using a Vickers hardness tester (HVS-30, Shanghai Testermachine Co., China) operated at a load of 10 kg and a duration of 5 s. The scanning electron microscopes (SEMs) used in this study are the Zeiss Evo 25 and Phenom ProX (Eindhoven, Netherlands). The SEM images of the subgrain cellular microstructure were taken in 13,000× and 26,000× magnitude. The sample microstructures and melt pool morphology were characterized by optical microscopy (Keyence VH-1000).

2.2 Cellular structure image processing scheme

Different melt pool microstructures of about several hundred micrometers size of the as-built CNTs/AlSi10Mg nanocomposites are shown in Figure 1. Figure 1(a) shows the melt pool morphology of the sample top surface with a nearly 45° texture along with the laser scan pattern. Figure 1(b) shows the melt pool morphology of the sample cross-section, showing melt layers formed along the build direction with no apparent micropores or defects. For the top surface melt pool morphology, the melt pool overlaps with each other, making it difficult to quantitively distinguish the melt pool morphology of different laser parameters (e.g., laser power and scanning speed). The nonuniformity of the macro-scale melt pool microstructure may consist of micro-pores as well observed from our previous study, making it further impossible for relating the melt pool morphology to their mechanical properties such as hardness and relative density.

Figure 1

Microscopy of CNTs/AlSi10Mg nanocomposites (the highly dense sample no. 3 with a relative density of 99.3%) showing melt pool morphology: (a) dark field microscopy of the top surface and (b) the cross-section showing melt layers along the build direction with no apparent micropores or defects.

To address the issue of correlating the microstructure to mechanical properties, SEM images of the CNTs/AlSi10Mg nanocomposite specimens were processed and characterized to expose their subgrain cellular eutectic structure as shown in Figure 2. The subgrain structure of CNTs/AlSi10Mg nanocomposites exhibits a eutectic and subcellular Al–Si microstructure in a plane perpendicular to the build direction. It can be seen that for sample no.s 1 and 15, laser parameters have a significant effect on the geometry and size of the subgrain cellular microstructure. Most subcells in the fine region have a size range within 0.5–1 μm, while the cell size in the coarse region is about 1–2 μm. α-Al matrix (dark color) is surrounded by a network of Si precipitates (white color) for the fine subgrain region. Discontinuous Si precipitates can be seen in the heat-affected zone (HAZ). The majority phase is fine subgrain instead of the HAZ/coarse subgrain region. Thus, this study is focused on investigating the effect of fine subgrain texture features on the hardness and relative density of CNTs/AlSi10Mg nanocomposites. A total of 96 SEM images of the fine cellular structure were used in this study with six images of each sample. More than 2,000 cells can be detected for each image, so in this study, six images for each sample are assumed adequate to represent the geometry characteristics in the fine cellular zone.

Figure 2

The subgrain textures of CNTs/AlSi10Mg nanocomposites exhibit a eutectic and subcellular Al–Si microstructure in a plane perpendicular to the build direction for (a) sample no. 1 with a laser power of 450 W and a laser scan speed of 2.4 m/s showing fine and coarse cellular microstructure, and (b) sample no. 15 with a laser power of 350 W and a laser scan speed of 2.0 m/s showing a nonuniform fine cell distribution.

The mechanical properties of the nanocomposites such as surface hardness are related to both bulk properties such as porosity, as well as their unique Al–Si eutectic microstructure. To separate each cell and get their geometric features in an SEM image, cell segmentation software CellProfiler 4.1.3 [21] was used. Several image processing steps were taken to get high-quality cell segmentation features as shown in Figure 3(d):

1. the original SEM image has been black/white-inversed into a gray image to have a better color contrast;

2. the cell nuclei size is set to a range of 0.15–0.4 μm and then Otsu thresholds [22,23] were used to detect the nuclei of each cellular structure in an SEM image. The Otsu approach is used to calculate and establish optimum threshold separating two classes of pixels (foreground and background) by minimizing the variance within each class by Eq. (1),

   (1) T opt = arg max P ( T ) [ 1 − P ( T ) ] [ m f ( T ) − m b ( T ) ] 2 P ( T ) σ f 2 ( T ) + [ 1 − P ( T ) ] σ b 2 ( T ) ,

   where P ( T ) is a probability function, σ f 2 ( T ) and σ b 2 ( T ) are variances of foreground and background class, and m f ( T ) and m b ( T ) are foreground and background class means. This method gives high-quality results when the numbers of pixels in each cell are close to each other (Figure 3(c)).

3. Based on the nuclei information generated for each cellular structure, the cell geometry and coordination were calculated and are shown in Figure 3(d). The propagation method is used to delineate the boundary between neighboring cells. The minimum cross-entropy is calculated between the foreground and background distributions (Eq. (2)) and the lowest cross-entropy value is chosen as the final threshold:

   (2) T opt = arg min ∑ g = 0 T g p ( g ) log g m f ( T ) + ∑ g = T + 1 G g p ( g ) log g m b ( T ) ,

   where ∑ g ≤ T g = ∑ g ≤ T m f ( T ) and ∑ g ≥ T g = ∑ g ≥ T m b ( T ) .

4. For example, 2,466 cells were detected in Figure 3(a). The cell geometry characteristics were calculated for each cell. A total of 83 coordinate-independent features were extracted and calculated for each cell. Among all features used in this study, several key features are described as follows:

Figure 3

Fine cellular zone cell detection of sample no. 13 of CNTs/AlSi10Mg nanocomposites: (a) the original SEM image of the fine cellular zone in CNTs/AlSi10Mg nanocomposites, (b) the inversed gray image, (c) a cell nuclei map generated from the inversed gray image, and (d) a cell segmentation map showing high fidelity representation of the cell shape and size of the fine cellular zone.

Perimeter is the length around the boundary of each cell. Eccentricity is the ratio of the distance between the focus points of the ellipse and its major axis length. The value is between 0 and 1 (a circle’s eccentricity is 0, while an ellipse with an eccentricity of 1 is a line segment). FormFactor is defined as 4 * π * area/perimeter² and the FormFactor of a perfectly circular object is equal to 1. Extent is the proportion of the area in the bounding box that is also in the cell. Solidity is the proportion of the area in the convex hull that is also in the cell. Compactness is the mean squared distance of the cell’s pixels from the centroid divided by the area. A filled circle has a compactness of 1. The cells with holes or irregular shapes have a value greater than 1. MeanRadius is the mean distance of any pixel in the object to the closest pixel outside of the cell. Several moments were used to accurately describe the shape and geometry of a cell. For Zernike moments [24], the center of mass for each cell was firstly calculated and a circle is defined. The Zernike moments Z _nl for a cell was calculated using

where x 2 + y 2 ≤ 1 , 0 ≤ l ≤ n , n − l is even, and V n l ⁎ ( x , y ) is the complex conjugate of a nth degree of Zernike polynomial and angular dependence l, and V n l ( x , y ) is defined as

where 0 ≤ l ≤ n , n − l is even, θ = tan − 1 ( y / x ) , and i = − 1 .

In this study, Zernike polynomials from order 0 to order 9 were calculated and a total of 30 features were calculated. The other moment features are briefly introduced here. Spatial moment features represent a series of weighted averages of shape, size, rotation and location of cells. Central moment features are normalized to the cell’s centroid and therefore not influenced by a cell’s location within an image. Normalized moment features are further normalized to be scale-invariant and therefore not influenced by a cell’s size within an image. Hu moment features are a set of cell moment features that are not altered by the cell’s location, size or rotation. Different moments primarily describe the shape of a cell.

The schematic of the proposed cell segmentation and machine-learning assisted microstructure–property linkage framework pipeline for LBPF produced CNTs/AlSi10Mg nanocomposites are shown in Figure 4. The scope of the SEM image processing and cell segmentation is to assess the microstructure cellular distribution of the Si-rich phase and α-Al phase. For the images in which the Si-rich phase is discontinuous, dash dots were connected to form complete cells. The pixels inside a cell can be considered as the α-Al phase and the perimeter can be considered as the Si-rich phase. Then, morphological features for each cellular cell were extracted and calculated, presenting the information of both the Si-rich phase and α-Al phase. As shown in the training phase, 76 randomly selected SEM images were used as the training set. The rest 20 samples were used as the test set. Machine learning algorithms AdaBoost, gradient tree boosting, K-nearest neighbors, decision tree, and extra trees regressors were used to relate the subgrain cellular structure to the mechanical properties of CNTs/AlSi10Mg nanocomposites.

Figure 4

Schematic of the proposed processing framework pipeline for LBPF produced AlSi10Mg nanocomposites microstructure–properties linkages.

2.3 Machine learning methods

To measure the performance of a machine learning regressor, the root-mean-square error (RMSE) shown in Eq. (5) was used as the performance metric. The RMSE is more sensitive to outliers than the square root of the mean-squared error (MSE) since the effect of each error on RMSE is proportional to the size of the squared error [25]. Relative errors are also calculated:

where y ˆ t is the predicted value of a regression dependent variable y t and N is the number of data points.

The feature value was mean normalized by using

where average(X) is the average value of X, and stdev(X) is the standard deviation of X.

Different machine learning regressors were used in this study. AdaBoost is a meta-estimator that fits a regressor on the input dataset and then fits additional copies of the regressor on the same dataset but adjusted the weights of instances according to the error of prediction [26]. Gradient Tree Boosting builds an additive model in a forward stage-wise way [27]. It allows the optimization of arbitrary differentiable loss functions. In each stage, a regression tree is fit on the negative gradient of A given the loss function. KNN is an instance-based method, which uses the input consisting of the k closest training examples in the data set and the output is the property value for the object. The prediction value is the average of the values of k nearest neighbors [28]. Given the input data x and a number of K, the prediction value can be calculated as y ˆ t = ( 1 / K ) ∑ x i ∈ N k ( x ) y i , where N _k (x) are the K nearest neighbor points to the input x, and y _i represents the output value for each x _i in N _k (x). In KNN regression, the Euclidean or Mahalanobis distance from the query example was calculated to the labeled examples. Then, the labeled examples with increased distance find a heuristically optimal number K of nearest neighbors, based on RMSE through cross-validation. Decision trees are to create a model that predicts the value of a target by learning simple decision rules inferred from the data features. Each tree can be seen as a piecewise constant approximation with each internal node represents a test on an attribute, each branch represents the outcome of the test, and each leaf node represents a class label. It breaks down a dataset into increasingly smaller subsets while an associated decision tree is incrementally developed [29]. Extra Trees, as a tree-based machine learning algorithm, grow a series of unpruned trees with a top-down approach [30]. The Extra Trees uses all training data to build the trees. During the splitting process, a total number of m features are selected randomly as split candidates at each node. The cutting points of each selected feature are also decided randomly. The extreme randomization introduced by feature and cutting point selection will help to further reduce the variance. Three important hyperparameters that need to be tuned are the number of trees, the number of randomly selected features and the minimum number of samples on the leaf nodes. Extra Trees or extremely randomized trees provide another layer of randomness to decision forests algorithms [30]. It implements a meta estimator that fits a number of randomized decision trees on various subsamples of the dataset and averaging algorithm to improve the predictive accuracy and control overfitting. The prediction of this ensemble learning is given as the averaged prediction of the individual classifiers.

A typical form of approximation by Extra Trees is shown as [30]:

where N is the sample size, I(i ₁,…, i _n )(x) is the characteristic function of the hyper-interval, and the real-valued parameters λ ( i 1 , … , i n ) X depend on input x _j and output y _j of the algorithm.

In addition to the original features, principal component analysis [31] is also used in this study for dimensionality reduction by projecting each feature onto several principal components to obtain lower-dimensional features while preserving as much of the data’s variation as possible. It is mainly used to explore the internal relationships between large amounts of data. The main principle of the PCA method is to select K (where K is 3 in this study and indicates that data dimensions have been selected) units of orthogonal basis. After the original data is transformed to these three sets of bases, the covariance between each pair of features is set to zero, and the variance between features is as large as possible. In this new space, the information represented by the dimensionality reduction data (three new features) can be used to replace the message of a large amount of data (83 features) in the original space.

3.1 Nanocomposites and cellular structure characterization

After ball milling, CNTs are deposited onto the surface of AlSi10Mg powders. Figure 5 shows the elemental distribution mapping of the ball-milled nanocomposites powder surface with 67.8 wt% aluminum, 25.3 wt% carbon, 6.6 wt% silicon and 0.34 wt% magnesium. The carbon element map reveals a uniform and homogeneous distribution of CNTs on the AlSi10Mg powder surfaces after ball milling, which is a prerequisite for SLM of homogeneous and densification of CNTs/AlSi10Mg nanocomposites.

Figure 5

(a) SEM image of the ball-milled CNTs/AlSi10Mg nanocomposite powders with 0.5 wt% CNTs. EDS mapping showing the elemental distribution and concentration of (b) Al, (c) Si, (d) Mg and (e) C on the particle surface.

Three LPBF-produced tensile samples of CNTs/AlSi10Mg nanocomposites are shown in Figure 6(b). A typical yield strength of 380 ± 14 was achieved. A detailed tensile tests analysis is out of the scope of this study and will be reported elsewhere. In order to reveal the melt pool morphology, the fractured nanocomposites samples were etched. A Keller solution containing 2.5 mL of HNO₃, 1.5 mL of HCl, 1.0 mL of HF and 95 mL of deionized water was used as an etching agent. Figure 7 shows the crack fronts with respect to the melt pool structure. The melt pool was stretched, showing the structure with a high aspect ratio near the crack front. The CNT phase in the nanocomposites can be also observed. Figure 7(a) and (b) shows the crack propagation path deviations triggered by melt pool boundaries and elongated melt pool structure. Liu et al. [12] found that when a crack is confined to the melt pool core regions, the cellular structure provides the main resistance to crack growth. It again suggests the correlation between the subgrain size cellular structure to the mechanical properties of the AlSi10Mg-based composites. Figure 8 shows the tensile specimen fractographs of CNTs/AlSi10Mg nanocomposites; ductile fracture with dimple rupture features was observed. The size of the microdimples is about 0.5–2 μm (shown in Figure 8(c)), which is consistent with the fine cellular size in the core melt pool area.

Figure 6

(a) CAD showing tensile bar’s dimension; (b) LPBF-produced CNTs/AlSi10Mg nanocomposites tensile samples after machining.

Figure 7

Crack front melt pool morphology of the tensile test specimen showing (a) the crack propagation path deviations triggered by melt pool boundaries and (b) an elongated melt pool structure.

Figure 8

Tensile specimen fractographs of CNTs/AlSi10Mg nanocomposites indicating typical ductile fracture with dimples (a) 200X, (b) 1000X, (c) 3000X.

The unique Al–Si eutectic microstructures of LPBF-produced CNTs/AlSi10Mg nanocomposites exhibited a cellular microstructure as shown in Figure 9(a). Cells in fine and coarse grain/HAZ regions have different shapes and size factors, resulting in a large difference in mechanical properties including hardness and relative mass density of the nanocomposites. The cell segmentation framework was tested on an SEM image of the HAZ coarse cellular zone as shown in Figure 9(b). The HAZ zone, showing a coarse cellular structure, was successfully processed with a high cell segmentation accuracy as shown in Figure 9(d). It can be observed that the cell in the coarse cellular zone has a higher eccentricity value of 0.77 representing elongated cellular grain, a larger cell area value of 16.21 μm², a longer perimeter of 2.279 μm and major axis length of 0.628 μm, about 30% higher than those of fine cellular zones. The results showed that the framework proposed in this study is robust and could represent the precise shape and size information for both the fine and HAZ coarse cellular zone of CNTs/AlSi10Mg nanocomposites. The corresponding mean feature values are listed in Table 2. However, the majority phase of the CNTs/AlSi10Mg nanocomposites is the fine cellular structure. Thus, in this study, only fine cellular zones are analyzed and related to their mechanical properties such as hardness and relative mass density.

Figure 9

Heat affected zone cellular structure cell detection: (a) subgrain cellular structure of CNTs/AlSi10Mg nanocomposites, (b) the HAZ coarse cellular zone, (c) inversed gray image of the HAZ coarse cellular zone and (d) the HAZ coarse cellular zone cell segmentation shows high fidelity representation of the cell shape and size.

3.2 Machine learning-based microstructure–property linkages prediction

AdaBoost, GradientBoost, KNN, decision trees, and Extra Trees were used to predict hardness and relative mass density of the CNTs/AlSi10Mg nanocomposites using 83 features generated from the subgrain cellular cell segmentation framework. The features were normalized to avoid any feature bias. Randomly selected 76 SEM images were used as a training set. The rest 20 SEM images were used as a test set for model performance evaluation.

Feature importance was calculated using AdaBoost, decision tree and Extra Trees regressor (Figure 10). It can be seen that the five most important features for AdaBoost to determine the hardness of the CNTs/AlSi10Mg nanocomposites are Zernike moment 2_0 (9.92%), perimeter (8.48%), eccentricity (7.52%), compactness (6.77%), and maximum radius (5.14%). For decision tree regressor, the five most important features are eccentricity (33.52%), mean radius (28.19%), extent (17.74%), orientation (8.86%) and formfactor (6.34%). For Extra Trees, the 5 most important features are Zernike moment 5_3 (9.92%), Zernike moment 2_0 (9.92%), eccentricity (9.03%), formfactor (7.18%), and compactness (6.42%), showing the aspect ratio of the subgrain cell shape and size are crucial to the mechanical properties of the CNTs/AlSi10Mg nanocomposites. In all cases, eccentricity is one of the key features for the prediction of mechanical properties.

Figure 10

Feature importance rank to predict hardness of CNTs/AlSi10Mg nanocomposites for different ML methods: (a) AdaBoost, (b) decision tree, and (c) Extra Trees.

The model predictive results were plotted against the original data for hardness and relative mass density of CNTs/AlSi10Mg nanocomposites. It can be seen from Figure 11 that high accuracy was achieved for the predicted hardness values. Table 3 lists the performance metrics for different machine learning algorithms. AdaBoost has the best prediction performance with an RMSE of 5.936 HV, an MSE of 35.239 HV² and a RE of 2.47%. Extra Trees have the prediction performance of the largest error with an RMSE of 8.402 HV, an MSE of 70.596 HV² and a RE of 5.30%. Even the worst machine learning algorithm in this study can render a RE of 5.30%, showing the strong correlation between subgrain cellular structure and the mechanical properties of CNTs/AlSi10Mg nanocomposites. For relative mass density prediction, the decision tree method has the highest prediction accuracy with an RMSE of 2.36%, an MSE of 0.0558% and a RE of 1.59%. It provides better predictive performance over the other base learners (Table 4).

Figure 11

(a) Surface hardness and (b) relative mass density prediction of CNTs/AlSi10Mg nanocomposites using different ML methods with subgrain cellular structure features as input.

Figure 12 shows the SEM image and cell segmentation maps for low hardness (99.52 HV) and high hardness (124.29 HV) samples with good machine learning model prediction accuracy. The key feature values for low hardness samples are eccentricity, 0.75; mean radius, 3.69 pixels; compactness, 7.18; perimeter, 3.47 μm; extent, 0.46; and zernike_2_0–0.15. The key feature values for high hardness sample are eccentricity, 0.76; mean radius, 3.56; compactness, 5.47; perimeter, 2.65 μm; extent, 0.46; and zernike_2_0–0.16. With a similar mean radius value, the smaller compactness and perimeter can render a higher surface hardness. These results show that the proposed model can predict mechanical properties very well with subgrain cellular features as input. The cause for outliers such as sample no. 14 in Figure 11 may be due to the limited SEM images used in this study but it again suggests the model developed in this study can produce relatively accurate results with even limited data for the training set.

Figure 12

Low hardness (99.52 HV) and high hardness (124.29 HV) samples with good prediction accuracy: (a) and (b) low hardness sample (sample no. 5 in Figure 11) SEM image and cell segmentation map; (c) and (d) high hardness sample (sample no. 8 in Figure 11) SEM image and cell segmentation map.

3.3 Principal component analysis of prediction of microstructure–property linkages

PCA normalizes the high dimension feature dataset (83 features in this study) with correlated variables and converts it into a set of linearly uncorrelated vectors that can describe the variances of the features. Three principal components PC₁, PC₂ and PC₃ are used in this study for reducing the dimensionality of the feature datasets, evaluating the primary variances of the observations.

The PCA model predictive results are plotted against the original data for hardness and relative mass density of CNTs/AlSi10Mg nanocomposites. The hardness prediction performance after PCA decomposition is shown in Figure 13 and Table 5. The best performance machine learning algorithm compared with before PCA decomposition changes to Extra Tress from AdaBoost. The original RMSE of 5.936 HV, an MSE of 35.239 HV² and a RE of 2.47% were changed to 6.313 HV, 39.858 HV² and 3.61%, respectively. The predictive accuracy becomes a little worse but with PCA dimensional reduction, the number of features became much less, making it easier for SEM image data registration, especially for a large amount of data handling.

Figure 13

Surface hardness prediction of CNTs/AlSi10Mg nanocomposites using different ML methods with PCA decomposition reduced features.

The relative mass density prediction performance after PCA decomposition is shown in Figure 14 and Table 6. The best performance algorithm compared to before PCA decomposition changes to AdaBoost from decision trees. The original RMSE of 2.36%, an MSE of 0.0558% and a RE of 1.59% were improved to 1.71, 0.0294 and 1.42%, respectively. The predictive accuracy for relative mass density becomes better with PCA dimensional reduction, demonstrating the PCA decomposition contains the main shape and geometry information of the major features.

Figure 14

Relative mass density prediction of CNTs/AlSi10Mg nanocomposites using different ML methods with PCA decomposition reduced features.