1 Introduction

Additive manufacturing (AM) refers to the process of creating objects from 3D model data by progressively joining materials, typically layer by layer [1]. AM is also known as rapid manufacturing or rapid prototyping [2]. Unlike conventional manufacturing methods that involves material removal from a larger stock to fabricate products, AM constructs the final shape by adding materials [3,4,5]. This approach optimizes raw material utilization, minimizes waste production, and achieves precise geometric accuracy [6, 7]. Utilizing AM, a computerized 3D solid model can be directly transformed into a finished product, eliminating the need for tooling and fixtures, opening the potential for crafting parts with intricate geometries that are challenging to attain through traditional manufacturing processes [8]. Consequently, the considerations for design in terms of manufacturing and assembly can be minimized, fostering design innovation. AM also promotes environmentally conscious product design [6]. In contrast to traditional manufacturing techniques that impose restrictions on design, the flexibility of AM empowers manufacturers to refine design for efficient production, inherently reducing waste [9]. Additionally, AM’s capacity to fabricate intricate geometries allows for the consolidation of multiple separate parts into a single object [10]. Furthermore, the topologically optimized designs achievable through AM have the potential to enhance a product’s functionality, consequently diminishing the energy, fuel, or natural resources required for operation [11]. To sum up, AM offers personalized components, diminished consumption of raw materials and energy, on-demand manufacturing, and a resilient supply chain network [12].

The generation of imperfections within AM components is a significant concern for critical operational uses [13]. If these imperfections are not eliminated, they can adversely affect the performance of AM components during their operational lifespan [14]. Consequently, comprehending the mechanisms underlying the creation of defects in fusion-based processes becomes crucial in determining the appropriate process parameters tailored to the specific alloy system and the chosen processing method [15, 16]. Laser-based metal AM methods are primarily divided into two (a) laser powder bed fusion (LPBF) and (b) laser-directed energy deposition (LDED) [17, 18]. In LPBF, a thin layer of powder is uniformly spread over a building platform [19,20,21]. A focused laser energy source then selectively melts the powder onto a metal substrate, resulting in intricately shaped components with high geometric intricacy [22,23,24]. On the other hand, LDED employs controlled powder flow propelled by an inert gas through a set of nozzles, combined with a focused laser beam to construct relatively complete structures [25,26,27]. The processing conditions for AM can markedly differ not only between LPBF and LDED but also among different AM processing chambers [28,29,30]. The rapid cycles of heating, cooling, and solidification inherent in the fabrication of AM metal components lead to intricate microstructures and properties that can substantially diverge from those typically found in conventional wrought or cast components [31]. The intricate transitional conditions intrinsic to metal AM processing exert an influence on the resultant metallurgical integrity, microstructures, residual stresses, and distortions within the components [32]. The occurrence of instabilities during processing frequently contributes to the emergence of internal defects, diminishing the mechanical characteristics of the component and substantially compromise its overall performance [33]. Table 1 has been compiled for a comprehensive overview of defects and their diverse sources in laser-based metal AM process.

Table 1 Various defects in laser-based metal additive manufacturing processes
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The most recent developments in machine learning (ML) and artificial intelligence (AI) can have a significant positive impact on AM [45]. Since every step of the AM process is completed digitally, data organization and collection are made easier [46,47,48]. However, AM is a highly automated process when it comes to design, process setup, and printing [49,50,51]. Numerous system data are generated as a result, which are challenging for humans to visualize and understand [52]. It becomes more difficult due to the enclosed setup, which makes it difficult to observe and keep track of the process [53,54,55]. Cracks, delamination, distortion, rough surfaces, lack of fusion, porosity, foreign inclusions, keyholes, and balling are just a few of the processing-related flaws that still plague the AM process today [56,57,58]. These flaws are typically caused by the layer-by-layer material deposition process. Some could cause the entire build to fail if they spread from one layer to the next. Researchers have worked very hard to keep track of printing defects before, during, and after. In this regard, ML offers a novel approach for overcoming the difficulties, as listed in Table 2. The ML is essential to improving defect identification in metal AM processes, according to all the studies [45, 59]. ML models can accurately classify defects in the printed parts by extracting meaningful features and patterns from the data collected during these processes [52, 60]. By identifying anomalies and deviations from regular patterns, these models make real-time monitoring, predictive maintenance, and process optimization possible [61, 62]. Additionally, ML is essential for developing practical solutions that boost metal AM product quality and dependability while streamlining quality control with automated and data-driven defect detection techniques [63].

Table 2 Various machine learning algorithms for defects identification in metal additive manufacturing
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Mostly, AM techniques include iterative testing to optimize the process, with the goal of producing defect-less components while conserving resources. Due to the resource-intensive nature, however, AM has found limited uses in specialized fields. On the other hand, the development of AM process maps will increase the acceptance of AM in industrial applications. The fundamental goal of this research is to acquire a systematic approach that can be easily applied for process optimization. In particular, the LPBF technique for metal AM necessitates a consistent framework to determine process maps for specific materials or alloys. These process maps delineate zones with no macroscopic component defects. For this purpose, a novel framework that combines an experimentally validated finite element method (FEM) model with a backpropagation-based artificial neural network (BPANN) model has been presented. To fine tune the weights, BPANN uses the error rate of a forward propagation, with the goal of reducing error in comparison to other artificial neural network techniques [79]. The laser scan speed, laser power, powder bed thickness, pre-heating temperature of the powder bed, and temperature-dependent material parameters were all changed to develop a set of 81 simulations. The resulting dataset was used to train and test the BPANN. Following that, process maps were generated using the trained and tested BPANN model by varying the process parameters. Here, a process map commonly uses melt pool dimensions to determine inadequacies such as lack of fusion, balling, and keyhole flaws. After removing the indicated areas, any remaining zone was determined as a region where defect-free components can be obtained.

2 Proposed methodology

The method used to develop process maps is shown in Fig. 1. The groundwork was developed using a FEM model that included thermally dependent material parameters, laser power and scan speed, powder bed thickness, and pre-heating temperature of the powder bed. Experimental investigations were used to validate the proposed FEM model. The modification of the process parameters and data generation was then conducted by the experimentally validated simulation model. The data gathered from the validated simulation model was used to build, train, and assess backpropagation-based artificial neural network (ANN) model. Notably, the laser power and scan speed, powder bed thickness, and pre-heating temperature of the powder bed served as the ANN model’s inputs, and the outputs were the melt pool’s dimensional ratios. In compliance with the guidelines outlined in the following section, processing maps were developed using the trained and tested ANN model.

Fig. 1
figure 1

Proposed methodology for current research

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2.1 Modelling and simulation

Several assumptions were applied when establishing the heat distribution model for Inconel 718 (IN-718) process maps. To begin, a Gaussian-shaped moving heat source was used. The powder particles within the powder bed were spherical, allowing for the development of a highly dense powder bed. The dilution rate between the substrate and the printed layer was ignored throughout the printing process [80]. Increasing the dilution rate causes the substrate to have a higher impact on the composition dilution of the deposited layer, resulting in poor performance [80]. Furthermore, the printing process frequently introduces cracks and other defects. The ideal dilution between the deposited layer and the substrate during the printing process is between 2 and 10%, and can be ignored for modeling purposes [80]. During modeling, temperature-dependent thermo-physical parameters were incorporated in the simulations, ensuring precise and accurate simulation results. The transient heat equation in 3D can be written as [81, 82]:

$$\rho {C}_p\frac{\partial T}{\partial t}=\nabla \left(k\nabla T\right)+Q$$
(1)

In Eq. 1, T, Cp, ρ, and k are the thermal distribution, specific heat, density, and thermal conductivity. The temperature-dependent characteristics can be introduced as [81, 82]:

$$\frac{\partial T}{\partial t}=\frac{\partial T}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial T}{\partial y}\frac{\partial y}{\partial t}+\frac{\partial T}{\partial z}\frac{\partial x}{\partial t}=\nabla T\overrightarrow{v}$$
(2)

Here, x, y, and z are the universal coordinates. Besides, the laser beam speed is expressed as \(\overrightarrow{v}\). During printing process, heat losses have been considered as [81,82,83]:

$$Q={q}_{\textrm{rad}}+{q}_{\textrm{conv}}+{q}_{\textrm{laser}\ \textrm{beam}}$$
(3)
$${q}_{\textrm{rad}}=\varepsilon {\sigma}_B\left({T}_{\textrm{amb}}^4-{T}^4\right)$$
(4)
$${q}_{\textrm{cov}}=h\left({T}_{\textrm{amb}}-T\right)$$
(5)
$${q}_{\textrm{laser}\ \textrm{beam}}=\frac{2 AP}{\pi {\sigma}^2}{e}^{-\frac{2{r}^2}{\sigma^2}}$$
(6)

It worthy to mention here that Eqs. 4 and 5 are from ref. [83], Eq. 6 has been adopted from ref. [81] while Eq. 3 has been cited from ref. [82]. Here, σB, Tamb, ε, P, A, σ, h, and r are the Stefan-Boltzmann constant, room temperature, emissivity, laser power, laser beam absorptivity, beam radius, convection coefficient, and radial distance between the beam and point of material heat [81, 82]. For 7-mm layer deposition on a 10 mm × 7 mm × 5 mm substrate, ANSYS simulation software was used. The FE simulation domain by ANSYS software is compiled in Fig. 2. During solution, a mesh size of 0.0192 mm was applied based on the aspect ratio (= 0.9) and skewness (= 0.08), defining a good quality mesh. Here, aspect ratio defines the compression or tension in an element while skewness identifies the distortion or misalignment on an element’s internal angle, having ideal values equal to 1 and 0, respectively. Temperature-dependent IN-718 properties were used during stimulation, as provided in Table 3. All the simulations were carried out on intel(R) Core (TM) i7-7700 CPU at 3.60 GHz, and 16 GB RAM. With the mentioned conditions, the results for one simulation were obtained in 1.5 h. To validate the FEM simulation model, the laser power was kept equivalent to 180 W; laser scanning speed equal to 400 mm/s, 600 mm/s, and 800 mm/s; and powder layer thickness equal to 40 μm. Following the model validation, a design of experiment (DoE) was developed and carried out using validated FEM model. The DoE included changing the laser power from 50 to 250 W with an interval of 50 W; laser scanning speed from 500 to 2500 mm/s with an interval of 500 mm/s; powder layer thickness was kept equal to 30, 50, and 70 μm; and powder bed pre-heating was equivalent to 60, 90, and 120 °C. For thermal distribution, all the calculations have been carried out in degree Celsius (°C).

Fig. 2
figure 2

Simulation model for process maps

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Table 3 Inconel-718 properties [84, 85]
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The other parameters used in the simulation are compiled in Table 4.

Table 4 Operating conditions used in simulation model
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2.2 Experimental validation

A comparison between the current simulation model and experiment described in ref. [90] was conducted to determine the reliability of the proposed simulation model. The authors used a Nd:YAG laser with a 54-μm laser spot on a Tongtai AM250, Taiwan, system for LPBF investigations. The specifications of Tongtai AM250 are provided in Table 5.

Table 5 Specifications of Tongtai AM250 [91]
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A laser power = 180 W and laser scanning speed = 400, 600, and 800 mm/s were used to prepare single layer specimens. For each sample, the powder layer thickness was 40 μm. The dimensions of the melt pool were measured using a Nikon AF-S high-speed CMOS camera. The camera was positioned 40° away from the build chamber at 35 cm. The camera was carefully calibrated before the experimentation. Additionally, an optical filter with a spectral range of 788–828 nm was installed on the camera to eliminate the high-frequency signal and enhance the image quality. More information can be read in ref. [90].

2.3 Process sensitivity analyses using validated FEM model

Table 6 compiles the design of experiment carried out using experimentally validated FEM model. These simulations included changing the laser power from 50 to 250 W with an interval of 50 W; laser scanning speed from 500 to 2500 mm/s with an interval of 500 mm/s; powder layer thickness was kept equal to 30, 50, and 70 μm; and powder bed pre-heating was equivalent to 60, 90, and 120 °C. The artificial neural network model was trained and tested using the outcome of these simulations.

Table 6 Design of experiment for simulation analysis
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2.4 Backpropagation-based artificial neural network development

The artificial neural network (ANN) is made up of interconnected processing elements with configurable connectivity weights that are fine-tuned during the learning phase. Each input in the ANN framework is assigned a weight that represents the strength of the connection between units. Individual nodes combine these weighted inputs and use an activation function to translate them into outputs. A backpropagation training approach is used to construct the architecture and optimize the network weights, which has proven superior capability in computing various Boolean functions when compared to networks with a single layer of calculating units. The backpropagation algorithm is divided into two phases: (a) forward and (b) backward propagations. The key operational factors in our ANN model were laser power and scan speed, powder bed thickness, and pre-heating temperature of the powder bed. These parameters were fed into the ANN model as inputs. Among the several architectures tested, the 4-15-3 ANN model performed exceptionally well [92, 93]. The number of nodes in the input, hidden, and output layers is represented by the notation 4-15-3. The employed learning rate coefficient was set to 0.01.

2.5 Processing window criteria

Lack of fusion is utilized to recognize inter-layer joining for a given material, and defined by using melt pool dimensions [94]. To successfully bond a deposited layer to a prior layer, melt pool depth (D) should surpass powder bed thickness (t) and adequately remelt the previously deposited layer. The smallest value of lack of fusion for confirming link between two subsequent deposition is equal to 1, implying that D should equal t, which is, however, insufficient for proper bonding. One recent study [95] found 99.9% dense AM portions of Ti6Al4V, showing proper inter-layer bonding. The lack-of-fusion value was calculated to be 1.15. As a result, a penetration of 15% of t into the prior layer indicates strong inter-layer joining. Hence, for lack of fusion to appear in IN-718, the criterion was referenced as D/t ≤ 1.15. In keyhole, the energy density is adequate to foster metal evaporation causing cavity formation [96]. The plasma formation due to metal evaporation results in an increased laser absorption. According to Roehling et al. [97], keyhole usually occurs at an aspect ratio of W/D < 1.5, where W indicates width of the melt pool. This value, however, is insignificant to display within the processing window [12, 98]. As a result, the keyhole requirement for IN-718 was chosen as W/D = 2.0. Balling is a defect caused by the inadequate wetting between the solidified deposited layer and the substrate, leading to uneven tracks [82, 99]. Balling can be linked with the melt pool dimensions calculated as L/W > 2.1. This threshold value can be linked to the Plateau-Rayleigh uncertainty in molten material. Figure 3 presents a schematic approach to select hatch distance after selecting operating conditions based on melt pool dimensions.

Fig. 3
figure 3

Schematic approach to print near-dense components after selecting operating conditions based on melt-pool dimensions

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3 Results and discussion

Figures 4a and b depict the sequential evolution of the melt pool during LPBF of IN-718, illustrating the powder layer’s early, middle, and final stages. The dynamic changes in the thermal distribution profiles along the laser scanning path (from left to right) can also be observed in the Fig. 4. The LPBF was carried out via laser with a power of 180 W and scan speed of 400 mm/s. During simulation, the powder bed thickness was 40 μm. It is important to mention here that the properties used in the FEM model are temperature dependent. Hence, phase change can be identified in Fig. 4 using different codes, including red color code for melt pool, green color for mushy zone, and light blue color for the solidified region. The isotherm curves show the temperature at which IN-718 melts. The material reaches its melting point at the highest temperature indicated by the isotherm, creating an asymmetrical melt pool marked by a series of ellipses. The laser beam’s energy is transported through the material, resulting in an unequal distribution of isotherms, with more significant generation noted towards the front compared to the rearward region. When the laser is positioned at the start, the temperature within the powder layer exceeds the melting temperature of IN-718, reaching up to 1700 °C in Fig. 4a. It is due to the material’s lower heat conductivity within the laser-material regime, which causes localized melting. However, as the beam advances, the peak thermal distribution drops to 1335 °C at the center and 1340 °C at the end of the powder bed. Heat transfer from the powder bed to the base plate causes this decrease, which stabilizes the temperature distribution. Figure 4d depicts the temperature evolution across the powder bed.

Fig. 4
figure 4

Single-layer LPBF simulation of Inconel-718 at a start, b intermediate, c end of the scan, and d melt pool depth at the end of the laser scan

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The developed simulation model was validated with the experimental and simulation analyses from ref. [90]. The authors in ref. [90] used in situ CMOS camera to measure melt pool width and length. Figures 5a and b show a comparison for melt pool’s length and width. For samples 1, 2 and 3, laser power was kept equal to 180 W while laser scanning speed was selected as 400 mm/s, 600 mm/s, and 800 mm/s, respectively. From the results, it can be identified that the FEM model presented a reliable solution for melt pool length and width compared to the experimental analyses. It is worthy to mention here that the accuracy of FEM simulation model depends on the modelling details, mesh quality, boundary and initial conditions, material properties, and software module. As explained above, the authors have used temperature-dependent properties along with the well-structured and appropriately refined mesh size in current simulation. To replicate the LPBF printing process in simulation environment, the non-linear transient heat transfer analysis with well-defined initial and boundary conditions has been applied in the ANSYS software. Hence, it can be observed that the accuracy of current simulation model is close to the experimental results compared to those provided in ref. [90] utilizing linear simulation framework.

Fig. 5
figure 5

Inconel-718 laser powder bed fusion current FEM model validation with published experimental [90] and simulation [90] data for melt pool a length and b width

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After FEM model had been experimentally validated, the simulations were conducted using the design of experiment presented in Table 6. Figure 6 shows a correlation chart that was generated using the collected data. The relationship between inputs (laser power, powder layer thickness, powder bed pre-heating temperatures) and outputs (average melt pool depth, length and width) has been produced on a correlation chart. A perfect positive correlation between the two items is shown by green, whereas a perfect negative correlation is shown by red in the correlation chart. Due to an increased energy transfer from the laser beam to the material with a surge in the laser power, a positive correlation among laser power, average melt pool depth, length, and width has been identified. On the other hand, due to the shortened laser-material contact period caused by an increased laser scanning speed, average melt pool depth, length, and width were negatively correlated with laser scanning speed. Additionally, a negative association between layer thickness and average melt pool depth has been found; however, no correlation between layer thickness and average melt pool length or width has been found. Additionally, it has been shown that the powder bed pre-heating temperature and average melt pool depth have a significant positive correlation that is on the verge of being strongly inversely correlated with the average width of the melt pool. Based on the results, it is evident that an excessive powder bed pre-heating temperature causes the melt pool to grow deeper and narrower, which encourages defects during printing. To reduce thermal stresses in the powder bed while preventing defects during LPBF, it is crucial to establish the ideal temperature for pre-heating the powder bed.

Fig. 6
figure 6

Correlation between process inputs and outputs

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A correlation chart was developed in Fig. 7 using the data from the FEM simulations to examine the correlations between the input parameters of laser power and scan speed, powder bed thickness, and pre-heating temperature of the powder bed, and the output parameters having ratios of average melt pool depth to powder layer thickness (D/t), average melt pool length to melt pool width (L/W), and average melt pool width to melt pool depth (W/D). As these ratios are critical for determining printability, it is important to note that the selection and computation of D/t, L/W, and W/D values were exclusively based on the melt pool’s dimensions. A color-coding scheme was used in the correlation chart, with blue denoting a high positive correlation, red denoting a strong negative correlation, and white denoting no significant connection between the two quantities. After investigation, it was shown that laser scanning speed showed only weak associations with L/W and W/D and a strong negative connection with D/t. In the case of D/t, L/W, and W/D, respectively, laser power showed positive, strongly positive, and no relationships. The analysis also exhibited the correlations among the powder layer thickness, D/t, L/W, and W/D. It showed a weakly negative association with D/t as well as W/D while a weak correlation with L/W ratio. The powder bed pre-heating temperature presented a very weak connection with D/t, L/W, and W/D ratios.

Fig. 7
figure 7

Correlation between process inputs ((laser power, layer thickness, and powder bed pre-heating temperature) and melt pool dimensional ratios (D/t, L/W, and W/D; D = average depth, L = average length, W = average width, and t = powder layer thickness)

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The design of experiment provided in Table 6 was used to run simulations via the experimentally validated model. For training and testing, the simulation data was fed into an artificial neural network (ANN) via backpropagation. The ANN model was developed using MATLAB software. Inputs to the ANN model were laser scanning speed, laser power, powder layer thickness, and powder bed pre-heating temperatures, while outputs included D/t, L/W, and W/D ratios, which provided useful insights on process maps. To ensure robust model development, the complete dataset was divided into 70% (for training) and 30% (for testing). A total of 400 epochs were carefully chosen for the iterative training of the ANN model. Following that, the model achieved a low mean squared error (MSE) of 0.001 and a gradient of 0.014 at epoch 400, as shown in Fig. 8a and b, respectively. Following the completion of the training procedure, the trained ANN model was applied to a parametric investigation by systematically altering the operating conditions.

Fig. 8
figure 8

Artificial neural network training based on the simulation analysis a mean squared error and b gradient plot

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After the training and testing of ANN, a parametric sensitivity analysis was conducted employing the ANN model to investigate the impact of varying operational parameters on the LPBF process. These parameters encompassed laser power and scan speed, powder bed thickness, and pre-heating temperature of the powder bed. Figures 9a–d exhibit the effect of powder bed pre-heating temperature on the processing region defined as the region obtained after excluding lack-of-fusion, balling, and keyhole defect areas, at temperatures of 120 °C, 90 °C, 60 °C, and 30 °C, respectively. In literature, researchers have developed processing regions using energy density for 7075 aluminum and TiC, tungsten, and tungsten-based alloys [100,101,102]. However, in this study, processing windows have been developed between laser power and scan speed. By developing a process map, using laser power and scan speed provides several benefits. These parameters streamline printing process setup and fine tuning, promoting improved process insight. The impact of process characteristics such as laser power and scan speed on the printing process can be observed individually, assisting in process optimization. This technique allows for adaptable processing conditions, simplifying experimental design and understanding of the LPBF system. While energy density has significant applications, focusing on laser power and scan speed increases process control, flexibility, and insight into the LPBF process. At a temperature of 120 °C for powder bed pre-heating, the predominant defect observed is lack of fusion with the availability of printability region, which can be further categorized as either lack-of-fusion root or lack-of-fusion sidewall [103]. In the lack-of-fusion root defect, the deposited layer fails to adequately fuse with the base plate, while in the lack-of-fusion sidewall defect, the deposited layer in immediate proximity to the base plate fails to adhere properly [103]. The utilization of a powder bed pre-heating temperature can alleviate thermal stresses, minimize distortion in the printed components, and reduce thermal gradients generated during the printing process [104]. Nevertheless, excessively high powder bed pre-heating temperatures can give rise to excessive thermal gradients, causing the printed layer to immediately adhere to the base plate, resulting in lack-of-fusion sidewall defects [105]. As the powder bed pre-heating temperature decreases from 120 to 90 °C, the lack-of-fusion region notably diminishes in comparison to the region observed at 120 °C. However, the printability and keyhole-based defect regions increase significantly compared to 120 °C. As the temperature further decreases from 90 to 60 °C, it becomes evident that keyhole-based defects dominate over lack-of-fusion and balling defects. The predominance of keyhole-based defects can be explained by the correlation between sub-atmospheric pressure and thermal gradients. A linear relationship was identified between sub-atmospheric pressure and thermal gradients, where a decline in sub-atmospheric pressure leads to a rise in the depth of the molten pool, transforming conduction melt flow from to depression mode [106]. A very low sub-atmospheric pressure stabilizes the keyhole during the laser printing process. Conversely, at a powder bed pre-heating temperature of 30 °C, no defect-free region was achieved, and lack-of-fusion defects prevailed over balling and keyhole defects. In this case, the lack-of-fusion root defect was identified due to insufficient powder bed pre-heating temperature as well as the operating conditions that did not permit thorough melting of the powder layer.

Fig. 9
figure 9

Printability maps of Inconel-718 with layer thickness = 30 μm when powder bed pre-heating temperatures are a 120 °C, b 90 °C, c 60 °C, and d 30 °C

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The printability maps produced by the trained ANN model for 50-μm powder layer thickness with different pre-heating temperatures of the powder bed (120 °C, 90 °C, 60 °C, and 30 °C) are shown in Fig. 10a, b. It can be observed that after increasing the powder layer thickness from 30 to 50 μm, powder bed pre-heating temperature = 120 °C provided printable region besides having lack-of-fusion, balling, and keyhole defects. When the powder bed pre-heating temperature is lowered to 90 °C, the printability region vanishes, and lack-of-fusion defects become more common. This issue can be ascribed to the 90 °C temperature in combination with other operating conditions not being enough to completely melt the powder layer. Similar outcomes can be seen at 60 °C and 30 °C powder bed pre-heating temperatures, where lack-of-fusion defects predominate because of the insufficient energy density offered, preventing full melting of the powder layer.

Fig. 10
figure 10

Printability maps of Inconel-718 with layer thickness = 50 μm when powder bed pre-heating temperatures are a 120 °C, b 90 °C, c 60 °C, and d 30 °C

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The impact of different powder bed pre-heating temperatures, specifically 120 °C, 90 °C, 60 °C, and 30 °C, on the printability maps for a powder layer thickness of 70 μm has been illustrated in Fig. 11a–d utilizing the trained ANN model. At 120 °C, a higher proportion of defects related to keyhole formation and balling are observed compared to lack-of-fusion defects. This observation can be attributed to the direct relationship between powder bed pre-heating temperatures and the depth of the molten pool, which influences the flow of molten material, resulting in non-uniformity of the molten pool and promoting the occurrence of balling and keyhole-based defects. As the powder bed pre-heating temperature is decreased from 120 to 90, 60, and 30 °C, a larger region is dominated by lack-of-fusion defects rather than balling and keyhole defects. This outcome arises due to the combination of a thicker powder layer and lower powder bed pre-heating temperature, which hinders the propagation of thermal intensity across the powder bed, consequently leading to the absence of defect-free regions. Lack of fusion usually occurs when the provided energy density is not adequate to melt the given powder layer. In Fig. 11d, the combination of process parameters such as laser power = 50–150 W, laser scanning speed = 540–1080 mm/s, and powder layer thickness = 70 μm, the provided energy is not enough to melt down the given material. However, while moving from laser power = 150 W to onwards, laser scanning speed = 540–1080 mm/s, and powder layer thickness = 70 μm, the operating conditions moved the LPBF printing process from conduction mode to keyhole mode.

Fig. 11
figure 11

Printability maps of Inconel-718 with layer thickness = 70 μm when powder bed pre-heating temperatures are a 120 °C, b 90 °C, c 60 °C, and d 30 °C

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Figures 12a–d depict the printability maps obtained for a powder layer thickness of 100 μm at various powder bed pre-heating temperatures, including 120 °C, 90 °C, 60 °C, and 30 °C, utilizing the trained ANN model. The analyses reveal the predominance of lack-of-fusion and balling defects under all operating conditions, with no region exhibiting successful prints. It is crucial to note that, in the case of a 100-μm powder layer thickness, the powder bed pre-heating temperatures fail to establish a molten pool with a stabilized and deep thermal gradient required for complete melting of the powder layer. Consequently, lack-of-fusion and balling defects arise. Keyhole-based defects are not observed under the given conditions since the molten pool does not attain sufficient depth to achieve complete melting throughout the powder layer. Therefore, selecting a 100-μm powder layer thickness is not logical for defect-free component printing.

Fig. 12
figure 12

Printability maps of Inconel-718 with layer thickness = 100 μm when powder bed pre-heating temperatures are a 120 °C, b 90 °C, c 60 °C, and d 30 °C

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LPBF experimental investigations were carried out to validate the outcomes provided by the ANN model, as provided in ref. [107]. The results are compiled in Fig. 13a–c. Figure 13a shows the processing map developed using ANN, Fig. 13b compiles the experimental results from ref. [107], and Fig. 13c exhibits the keyhole from Fig. 13b. According to the processing maps, the operating conditions highlighted as “1 and 2” have been identified as the conditions providing keyhole and lack-of-fusion defects, respectively. The output of the conditions 1 and 2 can be counter-verified from Fig. 13b as well. In Fig. 13a, distinct regions were defined using the given criteria. The lack-of-fusion defects have been highlighted using light purple hue. Meanwhile, keyhole defects are represented by the light red color code. Furthermore, the dominating defect, known as balling, caused by capillary instabilities inside the molten pool, has been highlighted using the color bright pink. The absence of a defect-free zone was identified under the stipulated operational parameters of room temperature at 30 °C and powder layer thickness of 50 μm. When the process maps obtained from the trained and tested ANN model are compared to experimental analyses, the ANN has showed exceptional reliability. One of the primary benefits of the trained ANN model is its capacity to efficiently monitor the impact of operational variables on outcomes, outperforming simulations, and experimental studies, resulting in significant time and cost savings.

Fig. 13
figure 13

Verification of a Inconel-718 processing maps using laser powder bed fusion, b experimental analyses with laser scanning speed = 600 mm/s and powder layer thickness = 50 μm [107], and c keyhole for laser power = 400 W, laser scanning speed = 600 mm/s, and powder layer thickness = 50 μm [107]; b and c with permission from publisher

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4 Conclusions and outlook

In this study, the FEM simulation model was integrated with the backpropagation ANN machine learning model. Initially, the FEM model was validated experimentally and, later, used to develop a dataset for ANN training. This combination aided in the development of processing maps for Inconel-718 using LPBF while considering crucial parameters such as laser power, scan speed, powder layer thickness, and powder bed pre-heating temperature. Melt pool characteristics, including depth, length, and width, were used to designate zones prone to defects such as lack-of-fusion, balling, and keyhole.

  • It has been identified that, in addition to operating conditions, the powder bed thickness and pre-heating temperatures played important roles in defect formation. Excessive pre-heating and thick powder layers were found to increase these undesired defects. As for laser power and laser scanning speed, their effects on the molten pool dimensions have been well established; higher laser power or reduced scanning speed leads to an enlarged molten pool. Moreover, elevated powder bed pre-heating temperatures were observed to increase the melt pool depth, transforming its mode from conduction to keyhole. Comprehensive processing maps were generated using the trained and validated ANN model, which revealed that regions with zero defects could be achieved under specific conditions: (a) a powder bed thickness of 30 μm at 120 and 90 °C pre-heating temperatures and (b) a powder bed thickness of 50 μm at a 120 °C pre-heating temperature. However, no healthy prints were achieved for powder layer thicknesses of 70 and 100 μm.

  • LPBF processing maps provide vital insights by allowing for precise predictions of printed part quality and reliability. These maps essentially function as a set of recommendations for improving prints by fine-tuning operating conditions. A dense part is built utilizing the LPBF technique by selectively melting and fusing successive layers of powder. However, this technique frequently entails trial and error, which may risk the final part’s strength, precision, and surface polish. To reduce such hazards, processing maps can be used to systematically optimize process parameters. In conjunction with processing maps, the suggested method helps the determination of optimal parameters for generating defect-free components. Using processing maps as a starting point, it is possible to successfully turn a single-layer design into a multi-layer structure by selecting appropriate parameters, such as hatch distance.

  • The developed model and technique can be used to develop processing maps for other material systems as well, including Al [100] and refractory materials [100] in the case of the LPBF process. To achieve reliable results, it is extremely important to determine the thermo-physical properties of the given material system. Currently, the developed model cannot predict hot cracking issues in the LPBF process. However, the FEM model can be extended to calculate the distance between liquidus and solidus temperatures (DLST) [108]. The cracking susceptibility will be lower if the DLST value is small. For process automation, the ML model can be developed by providing operating conditions as an input while the outcomes, including DLST, as an output. This approach will result in the hot cracking identification framework [109,110,111]. Another domain that can be explored in the near future is to link the subtractive manufacturing with AM to identify the effect of machining on features’ shape and size in the AM components [112].