Physics-Based porosity prediction in powder bed fusion – laser beam using a thermal simulation algorithm

Additive Manufacturing (AM) is a technique that enables the production of complex parts that are difficult or impossible to fabricate using conventional methods by building them layer by layer [1]. It also offers greater design flexibility, minimizes raw material consumption, and eliminates the need for additional tooling compared to traditional manufacturing approaches [2]. Owing to these advantages, it has found widespread application in aerospace, automotive, biomedical, and energy sectors. However, defects such as porosity, cracking, and anisotropic material properties inherent to layer-based fabrication can significantly impair the mechanical performance and reliability of the final parts [3]. Because of their high strength-to-weight ratio, resistance to corrosion, and biocompatibility, alloys like Ti6Al4V are used extensively in the aerospace and biomedical industries, making internal structure prediction crucial in additive manufacturing.

Powder Bed Fusion–Laser Beam PBF-LB is one of the most widely used powder bed fusion technologies. This method allows the selective melting of metal powder with a high-energy laser beam, layer by layer, and the production of complex geometry parts with high precision in a directly usable form. However, accurate calibration and optimization of process parameters such as laser power, scanning speed, layer thickness, and powder density are essential to ensure part quality and process stability. Any error or mismatch in these parameters directly affects the energy density transferred to the material [4]. As a result of the changing Volumetric Energy Density (VED), defects can occur in the produced part, which directly affect the final product quality. While VED provides a simplified framework to describe the amount of energy delivered to the material, recent studies have shown that it does not fully capture the complexity of melt pool dynamics or defect formation mechanisms [5, 6]. In particular, VED fails to account for temporal laser-material interaction effects, scan path strategies, and thermal accumulation across layers [7]. Although VED is used in this study to provide a baseline comparison among process conditions, its predictive capability is limited. Therefore, it is complemented by a physics-based thermal simulation that models transient heat flow and temperature-dependent material behavior at the voxel level for a more accurate prediction of porosity formation.

Lack of fusion, keyhole instability, and gas porosity are recognized as the primary mechanisms of pore formation in PBF‑LB processes [8, 9]. Under high energy densities, keyhole-induced voids may form as a result of an unstable vapor depression that collapses and traps vapor pockets inside the solidifying melt pool contrary to earlier assumptions. This phenomenon is not caused directly by evaporation but by the dynamic instability of the vapor cavity itself [10]. Lack of fusion, on the other hand, occurs due to insufficient overlap between adjacent melt pools or successive layers, often due to suboptimal combinations of laser power, scan speed, hatch spacing, or layer thickness [11]. Although lack of fusion may manifest as internal pores within the part, it is characterized by irregularly shaped, elongated voids typically located along layer boundaries or scan track interfaces, reflecting inadequate melting or bonding rather than trapped gas [12]. Both defect types directly compromise the density, strength, and fatigue resistance of the final component [13]. Therefore, eliminating such defects prior to production through predictive modeling is critical to improving the quality and reliability of parts manufactured using PBF-LB. To promote wider industrial adoption of PBF-LB technology, time and cost-efficient process optimization strategies must be developed to prevent internal defects before fabrication begins. The literature presents various approaches for defect detection and mitigation. Among these, Non-Destructive Testing (NDT) methods such as X-ray micro-Computed Tomography (µ-CT) and ultrasonic inspection are widely used for post-process defect detection, whereas defect prevention relies on process parameter optimization, in-situ monitoring, and predictive modeling techniques [14, 15].

Machine Learning (ML) has emerged as a powerful tool for predicting defect formation and optimizing process parameters in layered manufacturing processes. Models such as Support Vector Machines (SVM) and decision trees have been applied to porosity prediction using various feature sets derived from process parameters [16‐18]. For instance, Pi et al. developed four different porosity prediction models by applying the DBSCAN algorithm on Archimedes density measurements of 49 Inconel 718 specimens fabricated with PBF-LB [19]. However, their findings indicate that even after outlier removal and data cleaning, the models exhibited considerable variability in prediction accuracy. Similarly, Faizan Mohamed et al. proposed a reinforcement learning approach supported by the Eagar-Tsai thermal model, trained on laser power, scan speed, and inter-scan distance as inputs [20]. They experimentally validated their results using 12 different process parameter combinations with A205 aluminum alloy powder. Despite incorporating a physics-based model, their study also required extensive data cleaning and exhibited inconsistencies between predicted and actual porosity values. In another study, Staszewska et al. combined machine learning classification techniques with regression analysis to identify porosity types in PBF-LB-fabricated AlSi10Mg specimens [16]. As with most ML-based frameworks, their pipeline involved manual labeling, geometric feature extraction, data filtering, and training, which are time-consuming and labor-intensive. A review of the existing literature reveals that ML models for porosity prediction typically require large volumes of high-quality, labeled data to perform effectively [21]. Despite their potential, these models are typically not generalizable. They tend to match closely to certain datasets or process windows, which makes them less useful in other situations [22, 23]. Furthermore, in real-time quality control applications, the primary source of latency is not the inference speed of the trained model. Instead, the delays arise from data acquisition, preprocessing, and integration with machine control algorithms [24, 25]. These system-level bottlenecks can impair timely decision-making and compromise the responsiveness of feedback control systems in PBF-LB. To promote wider adoption of PBF-LB technology, both detection and prevention strategies must be employed to reduce internal structural defects before and during production. These strategies can be broadly categorized into three groups: non-destructive methods, destructive analysis, and in-situ process monitoring. Non-destructive techniques such as µ-CT [26, 27], ultrasonic inspection [28, 29], and infrared thermography [30] are widely used to detect internal porosity post-fabrication. Destructive methods, including cross-sectional microscopy and density measurements via the Archimedes principle, are commonly used for validation and calibration purposes [31]. In contrast, in-situ monitoring approaches focus on detecting and correcting defects in real time during the build process, using optical sensors, pyrometers, or thermal cameras integrated into the machine [32].

In recent years, ML has been applied across all three categories, particularly in in-situ monitoring and defect classification tasks. However, ML itself is not a standalone category, but rather a computational tool used to enhance decision-making based on sensor data or experimental results [33]. Models such as Support Vector Machines (SVM) and decision trees have been proposed to predict porosity and optimize process parameters based on labeled datasets [34]. For instance, Pi et al. and Faizan Mohamed et al. utilized SVM and reinforcement learning, respectively, to identify defect-prone parameter regions. Yet, recent work has shown that lack of fusion regions in process maps do not follow hard classification boundaries but rather exhibit gradual transitions depending on thermal history and melt pool morphology [35]. This suggests that traditional classification models may have limited accuracy in capturing such complex and continuous boundaries without additional physical context or hybrid modeling approaches. Therefore, ML models must be carefully validated and possibly combined with physics-based models to improve robustness and generalizability in porosity prediction tasks [36, 37]. When the literature is examined, the size and change of the melt pool can be predicted before production starts, as an approach different from machine learning with the use of artificial intelligence. It is clearly seen that internal structure analysis can be performed based on process parameters in various melt pool models developed for this purpose. In the PBF-LB method, modeling the melt pool dynamics correctly and optimizing the process parameters requires computer-based simulation approaches as an alternative to the experimental trial-and-error method [38]. In this context, numerical models including physical processes such as thermal conduction, mass transfer, and laser absorption are widely used to predict melt pool dimensions and surface morphology. Numerical models based on the direct finite element method, such as in the study by Slama et al., are also widely available in the literature aiming at porosity prediction [39]. In particular, models developed based on volumetric heat sources provide a critical tool in understanding the effects of parameters such as laser power, scanning speed, and powder layer properties on energy distribution within the material. However, such models included partial error rates in the past because they considered parameters such as laser absorptivity and heat conduction coefficient that change with temperature as fixed values. As a result of studies conducted in recent years, the changes of these material-dependent properties with temperature have been better understood and explained. Thanks to these developments, the compatibility with experimental results in melt pool modeling has increased and porosity estimation from melt pool geometry has become more possible. Adapting the temperature-dependent changes of parameters such as the heat conduction coefficient or laser absorptivity, which directly affect the melt pool geometry, to mathematical models is challenging. This process also leads to an increase in processing load and calculation times. To reduce the calculation time, simulation models that include certain approaches and assumptions to estimate melt pool dimensions are available in the literature [40].

Although various CFD-based models have been proposed in the literature to simulate melt pool dynamics, often calibrated using single-track laser scan experiments [41], these models generally suffer from high computational cost and limited scalability. Most focus on microscale or short-time simulations and are not feasible for full-layer or volumetric porosity prediction in practical build domains. Furthermore, many rely on constant thermophysical properties and neglect inter-layer thermal interactions and cumulative heat effects, which are essential for capturing defect formation mechanisms in multi-layer PBF-LB processes. To address these limitations, the present study proposes a voxel-based, finite volume simulation framework that models transient heat conduction across a three-dimensional build domain using temperature-dependent material properties. The build space is discretized into thermal voxels, and the heat equation is solved layer by layer using OpenMP-based parallelization to ensure computational efficiency. The algorithm predicts porosity by directly analyzing key process parameters such as laser power, scanning speed, layer thickness, and initial temperatures without requiring large datasets or extensive training, as required in ML approaches. Its flexible structure allows adaptation to different materials and process settings. Experimental validation was performed using Ti6Al4V specimens produced under multiple parameter combinations, with porosity quantified via Archimedes density measurements. The results demonstrate that the proposed method offers a fast, scalable, and physically grounded tool for porosity prediction and process optimization in PBF-LB, contributing to enhanced quality control and broader industrial applicability of the technology.

A schematic representation of the PBF-LB process is provided in Fig. 1. The illustration emphasizes the principal components of the system, including the laser source, galvanometer-driven beam steering unit, and powder bed, along with the underlying physical phenomena such as steep thermal gradients, vaporization, and lack-of-fusion defects. This schematic serves as a conceptual framework for understanding the role of localized heat input in governing melting and solidification within the powder bed, which in turn dictates defect formation mechanisms. To facilitate a clearer understanding of the study, the subsequent sections are organized under specific subheadings, wherein the materials, experimental setup, process parameters, and numerical framework are presented in detail.

This study presents the development and implementation of a physics-informed porosity prediction algorithm tailored for Ti6Al4V components fabricated by the PBF-LB process. Built upon a finite volume-based thermal simulation framework, the model computes voxel-wise transient temperature distributions with a fixed spatial resolution of 1 μm and constant time step, thereby ensuring high spatial and temporal fidelity. Unlike data-driven approaches or empirically tuned models, the algorithm relies exclusively on first-principles thermal behavior, incorporating temperature thresholds associated with melt instability to identify and quantify pore-prone regions across the build volume.

The predictive accuracy of the model was rigorously validated against experimental data obtained from Archimedes density measurements and µ-CT. The algorithm successfully reproduced the relative ordering and severity of porosity across six specimens fabricated under distinct process parameter sets, without requiring parameter-specific calibration or additional experimental input beyond the initial processing conditions. This alignment demonstrates the model’s capability to capture the thermodynamically driven nature of defect formation and its sensitivity to process variations such as laser power, scan speed, and scan strategy.

Despite these strengths, the model shows limitations in spatial accuracy when predicting the precise localization of pores. Although predicted porosity levels align quantitatively with experimental findings, discrepancies were observed in the spatial distribution of pores, particularly when compared with µ-CT reconstructions. An additional source of deviation arises from differences in temporal sequencing between the experimental and simulated conditions. In actual fabrication, all six specimens were produced simultaneously on the same build plate, introducing natural delays between successive layer depositions due to scanning sequence and hatch spacing. This inter-part thermal interaction leads to cumulative heat retention and layer-wise thermal coupling across specimens. By contrast, the simulation models each part independently, assuming uniform interlayer time intervals and neglecting cross-part heat accumulation. As a result, the transient thermal histories in the model do not fully capture the complex interdependencies present in real builds, which may contribute to variations in predicted porosity magnitudes. Addressing this limitation will require either synchronized multi-part simulations or the integration of real build sequencing data into the thermal solver.

Future extensions of the algorithm will therefore focus on incorporating these additional physical and temporal effects, potentially through multi-physics coupling, synchronized multi-part simulations, and real-time data assimilation from in-situ monitoring systems. Such advancements will be critical for enabling spatially resolved, high-fidelity porosity predictions in practical additive manufacturing environments.

Key findings of this study can be summarized as follows: