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A focused review on numerical computation in wire arc additive manufacturing for high strength low alloy steels: past insights and potential opportunities
Dieser Artikel bietet einen konzentrierten Überblick über die Anwendung numerischer Berechnung in der Wire Arc Additive Manufacturing (WAAM) für hochfeste, niedrig legierte Stähle (HSLA). Es untersucht die bisherigen Erkenntnisse und potenziellen Chancen in diesem sich rasch entwickelnden Bereich. Der Bericht beginnt mit der Einführung in die Grundlagen von WAAM und betont seine Vorteile und Herausforderungen, insbesondere bei der Erreichung hoher Präzision und Qualitätskontrolle. Es geht auf die multiskalige Natur numerischer Berechnungen ein und diskutiert makro-, meso- und mikroskalige Analysen und ihre Bedeutung für das Verständnis des WAAM-Prozesses. Der Artikel unterstreicht die Bedeutung präzisen Wärmemanagements, Schichtverbindungen und Phasentransformationen bei der Bestimmung der endgültigen mechanischen Eigenschaften von HSLA-Stählen. Er überprüft auch aktuelle Forschungstrends und identifiziert kritische Lücken in der bestehenden Literatur, insbesondere das Fehlen umfassender TTT- und CCT-Diagramme, die auf WAAM zugeschnitten sind. Der Bericht schließt mit einer Beschreibung zukünftiger Forschungsrichtungen und betont die Notwendigkeit integrierter rechnerischer Rahmenwerke, die experimentelle Daten, fortschrittliche Simulationswerkzeuge und KI-Techniken kombinieren, um den WAAM-Prozess für HSLA-Stähle zu optimieren. Dieser Artikel ist eine wertvolle Ressource für Fachleute, die die Komplexität und Möglichkeiten der numerischen Berechnung für WAAM verstehen wollen, und bietet Einblicke, wie diese Fortschritte Innovationen in der Fertigung vorantreiben können.
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Abstract
Wire Arc Additive Manufacturing (WAAM) has emerged as a transformative technology in Metal Additive Manufacturing (MAM), offering significant advantages for fabricating large, complex metal structures that are often difficult or economically unfeasible to produce using traditional methods. Despite its cost-effectiveness and design flexibility, WAAM continues to rely heavily on trial-and-error attempts to achieve high-quality results, leading to significant time, effort and financial costs, particularly when producing large-scale parts. High Strength Low Alloy (HSLA) steels, known for their superior strength-to-weight ratios, mechanical properties and corrosion resistance, have become essential in industries where high performance is critical, such as aerospace, automotive and construction. The integration of HSLA steels into WAAM presents unique challenges that require precise predictions of material behavior and process dynamics. Recent advancements in numerical computation have significantly enhanced the understanding and optimization of WAAM process and have been disseminated in various publications. However, existing research on dedicated topics is often fragmented and lacks sufficient integration, which limits the potential for comprehensive insights. This review synthesizes the state of the art in research from 2020 to mid-2025, with a particular focus on integrating numerical computation, HSLA and WAAM. Through the application of staggered scaling methods, significant strides have been made in predicting critical outputs such as temperature distribution, residual stresses, part distortion and microstructural evolution at the grain level. Building on past insights, emerging research trends are focusing on more advanced methods to further optimize the WAAM process. One exciting direction is the use of Hybrid Physics-Informed Neural Networks (PINNs), which integrate neural networks, governing physical laws, analytical models and data-driven methods to offer more accurate and efficient process control. Although still in its early stages, this methodology provides an opportunity to address existing gaps in material performance and process optimization. By leveraging past insights and emerging computational methods, future research holds the potential to significantly advance the industrial adoption of HSLA-WAAM, enabling the production of parts with unprecedented design flexibility, customized material performance and enhanced reliability. This could reshape the manufacturing landscape and position manufacturing modelling and MAM as cornerstones of next-generation manufacturing technology.
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1 Introduction
Additive Manufacturing (AM), which evolved from the technology of 3D printing, has become an integral technology in modern manufacturing. AM is distinguished by using a layer-by-layer method to build objects [1‐3]. This technology represents a marked departure from traditional manufacturing, offering a more efficient and flexible production process that can significantly reduce cost and time [4‐6].
Within the broader field of AM, Metal Additive Manufacturing (MAM) focuses on the layer-by-layer deposition of metals from a computer-aided design (CAD) model [7]. This technology provides the fabrication of metallic parts with tailored mechanical properties [8, 9]. The nature of layer bonding process is critical, as it heavily influences the interlayer strength and overall characteristics of the final component [10, 11]. MAM has become an appealing solution for various industrial applications including aerospace, automotive, military and biomedical industries [12, 13]. Over the past decade, categories of MAM as illustrated in Fig. 1, have been the subject of important research. These methods are valued for their ability to rapidly produce intricate designs that are difficult to manufacture using conventional process [14].
Among these MAM technologies, Wire Arc Additive Manufacturing (WAAM) is recognised as one of the most effective and proficient methods in additive manufacturing, which is classified as a Directed Energy Deposition (DED) [15]. WAAM uses metal wire as the material for the component and an electric arc as the heat source to melt the feedstock. It is ideal for producing large metal components and imposes fewer geometric constraints compared to traditional manufacturing process such as machining or casting [16]. This process constructs a part layer-by-layer using basic robotic welding system as illustrated in Fig. 2.
The WAAM process can use standard, readily available and relatively inexpensive welding equipment compared to other additive manufacturing methods. As a result, it is a cost-effective option for producing large metal parts, especially those that require strength and durability of the welded structure [17]. The capability to manufacture components with intricate shapes makes WAAM a promising technology for future manufacturing [18]. Furthermore, it has also been applied for new part fabrication as well as the repair and remanufacturing of component [19, 20].
Despite its advantages, the industrial implementation of WAAM is hindered by several challenges, mostly related to manufacturing accuracy, quality assurance and the level of automation [21]. To address these issues, researchers have explored various process monitoring and control strategies adapted from conventional welding. These strategies include thermal monitoring and the development of digital twins for closed-loop process control [22‐24]. Effective process control must therefore focus on the precise management of several critical and interrelated process parameters. Heat accumulation is the main concern, as the deposited layer creates thermal gradients across the component during heating and cooling which can induce excessive residual stresses and geometric distortion [25‐27]. Similarly, the interpass temperature must be carefully managed to promote better metallurgical bonding of WAAM-ed components, thereby enhances structural strength and reduce the formation of cracks [28‐30]. Finally, the layer deposition strategy where precise control over the toolpath and bead geometry is required to achieve the desired dimensional accuracy. The inconsistent layer deposition can cause defects such as gaps, overlaps or misalignments [31‐33].
The interplay of thermal, metallurgical and geometric factors highlights the complexity of WAAM. Therefore, controlling these process parameters is crucial in maximising the potential and enabling its broader application [34, 35]. Continuous study and progress in this area are necessary to gain a deeper insight into how these factors influence the mechanical characteristics of additively manufactured components. As illustrated in Fig. 3, data from the Scopus database reveals a significant and continuous increase in WAAM-related publications between 2020 and 2024. Up to mid-2025, a total of 864 were recorded and has already exceeded the number of publications from mid-2024. The number of publications is estimated to continue increasing to reach the number of more than 1200 articles.
Figure 4 summarises the most frequently used keywords in paper titles. Keywords in research papers can offer significant insights into the current and future trends. Through synthesising keywords, it is possible to identify evolving areas of interest and potential new directions in research. This approach helps to understand scientific inquiries and fosters interdisciplinary collaborations that can lead to innovative breakthroughs. From 2020 to mid-2025, the top words used in publications for WAAM were "Tensile Strength" (868), followed by "Mechanical Properties” (734) and “Texture” (470). It has been observed that the terms "High Strength Steel" with a frequency of 76 and "Numerical Computation" appear in publications with a frequency of 7. This shows a relatively low frequency of these keywords in publications.
Fig. 4
Keywords used in WAAM publications from 2020 to mid-2025
This article aims to review the application of numerical computation in WAAM with a dedicated focus on High Strength Low Alloy (HSLA) steels. This first section serves as an introduction, while the second discusses the fundamental objectives by establishing a framework for understanding the numerical computation across macro-, meso- and micro-scaled. The third section narrows this focus to HSLA-WAAM by providing a comprehensive overview of existing research, material-specific modelling challenges and a critical examination of the significant knowledge gaps that currently hinder process optimization. Finally, the last section concludes by synthesizing these insights into a coherent outlook on future research trajectories, highlighting the transformative potential of integrated modelling, artificial intelligence and advanced material science for the next generation of numerical computation.
2 Numerical computation applied in WAAM
Numerical computation is a powerful tool used by scientists and engineers to analyse and identify the behaviour of complex systems. The core of simulation is the mathematical modelling, which uses governing equations that represent the physical behaviour of a real-world system [36]. Numerical computation excels at tackling problems where traditional analytical solutions are difficult or impossible to obtain [37]. Real-world systems involve non-linear relationships and intricate interactions which make them challenging to solve with just experimentation.
This computational method facilitates a shift from traditional, trial-and-error experimentation to a simulation-driven design, as illustrated in Fig. 5. Generally, process development relied on physical experimentation and testing, a costly and time-consuming process. In contrast, numerical computation allows for the simulation investigation and optimization of process parameters before the actual fabrication begins. For this reason, researchers can predict and mitigate issues, thereby reducing the need for expensive experiments and accelerating the development manufacturing process [38, 39].
A typical numerical computation workflow for the WAAM process, as illustrated in Fig. 6, starts with model inputs that is the component geometry, heat source, material data and mechanical boundary conditions. Advanced Finite Element Method (FEM) software discretizes the governing equations of heat transfer, metallurgical transformations and mechanical response into computer instructions [40‐42]. The computer program executes the instructions, iteratively calculating the system behaviour over time or across different conditions [43]. Upon completion, the results are post-processed and visualised to provide insight into the inherent mechanism [44, 45]. The model then predicts outputs such as temperature distribution, phase transformation, residual stress and distortion [46, 47].
Applying numerical computation serves as a strategic approach to enhance process efficiency and reliability. By integrating simulation-based methods, researchers and engineers can address key challenges related to quality, performance and resource utilization. Simulations allow the detection of potential issues and make necessary adjustments before fabrication, leading to a more efficient and cost-effective production process.
One of the main objectives of simulation is to determine the optimal set of process parameters and planning the most effective deposition strategy before physical fabrication. Models are used to simulate the thermal and mechanical part, allowing for investigation on process parameters. This simulation experiment is often coupled with Design of Experiments (DOE) to identify process windows for higher quality final component [48‐51]. A second objective is the mitigating and forecasting defects in WAAM components where numerical computation is used to identify areas prone to high thermal stresses that could reduce mechanical performance. For example, Fig. 7 shows how simulation can be used to identify the residual stress distribution highlighting potential best-case and worst-case scenarios. Through varying parameters such as voltage, current and travel speed, model defines process that reduce defects to improve mechanical performance [52‐54].
Fig. 7
Numerical Computation for Predicting Best and Worst Case for Residual Stress [55]
Another objective of numerical computation is to predict the final mechanical properties of the component. This is achieved through modelling method where the simulated thermal cycle serves as input for metallurgical models. It becomes possible to estimate mechanical properties such as hardness, yield strength and toughness. This predictive capability allows engineers to modify the material properties by adjusting process parameters to meet specific performance requirements [56‐58]. Finally, the economic capability and sustainability of the WAAM process are equally critical for industrial implementation. Replacing expensive physical experiments with numerical models can significantly reduce the costs of trial-and-error process. The importance of this objective is highlighted by the typical cost distribution in WAAM workflow, as shown in Fig. 8. Although material deposition is the largest single expense (37%), a substantial portion such as post-processing (21%), substrate preparation/removal (24%) and machining (10%) creates another major portion of the total cost. In using simulation, the use on these expensive secondary operations can be minimized leading to significant savings in time, cost and energy consumption [59‐63].
To fully understand the material behaviour and structural performance of WAAM components, numerical computation is often applied across different length macro-, meso- and micro-scaled, as illustrated in Fig. 9. This scaled approach is necessary because the situation occurring at a meso-scale directly influence the outcomes at macro-scale. For instance, insufficient heat input can affect metallurgical bonding at the meso-scale, which results in low mechanical properties such as distortion or cracking at the macro-scale [64].
Fig. 9
Illustration and Description of a Macro-, b Meso- and c Micro-scale
At macro-scale analysis measured in millimeters to centimeters, focus is on structural performance and geometric accuracy of the final part. Simulation at this scaled compute the temperature distributions and predict part distortion resulting from the thermo-mechanical during deposition process [65, 66]. Analysis at this scaled is on mechanical effects, component properties and size. In which the deposited material meets the design specifications within acceptable tolerances [67, 68].
The meso-scale ranges between macro- and micro-scaled connecting between component behaviour and microstructural physics. Simulations typically use detailed thermo-mechanical models to investigate the interaction between process parameters, thermal cycles and evolution of material characteristics [69, 70]. Research at this scaled analyses heat transfer between layers, phase transformations and evaluating interlayer bonding that directly affect properties which can cause for component failure [71‐74].
The micro-scale, which ranges from nanometers to micrometers focuses on the grains and phases present within the microstructure. The main goal is to understand the microstructure formation and material behaviour. Advanced simulations are used to model grain solidification orientation and phase transformation in response to mechanical performance [75‐78]. Study on the scaled are important for predicting how cooling rates and thermal cycles influence final grain size and phase distribution, for example α and β phases in high strength steel that can affect final material properties [79, 80]. This research is crucial for developing the material models used in simulations and for the computational design for WAAM process [81‐84].
In summary, the macro-, meso- and micro-scaled analysis provides a comprehensive approach on the WAAM process. Through connecting macro-scale component performance with meso-scale localized process dynamics and micro-scale material behaviour, researchers can establish the critical process-structure–property relationships that govern final component quality, researchers can develop a deeper comprehension of the factors that govern the final component quality. The characteristics, applications and computational demands of each scaled are summarized in Table 1. Selecting the appropriate scaled is important to improve the process and create high-quality WAAM components.
Table 1
Characteristics on Numerical Scales
Characteristic
Macro-scale
Meso-scale
Micro-scale
Computational Time
Short
Short—Moderate
Long
Level of Detail
Low
Low—Moderate
High
Quality of Result
Adequate
Good
Very Good
Required Material Data
Basic
Detail
More Detail
Required Process Parameter
Low
High
Very High
User
Industry
R&D/Industry
R&D
Research Analysis
Mechanical analysis on dimensional accuracy
Mechanical and thermal analysis on thermal cycles and effects on properties
Advanced simulation methods, investigation
of microstructure evolution and morphology evolution
2.2 Governing equations for Macro-, Meso- and Micro-scaled simulation
The numerical simulation of WAAM across different scales is founded on distinct sets of governing physical equations that represent the dominant situation at each level. At the macro-scaled simulation, distortion can be predicted efficiently by Inherent Strain Methods (ISM). These methods replace explicit transient thermo-mechanics with prescribed inherent strains localized to the weld and derived from calibration or analytical relations. Macro-scale is rooted in the classic inherent-strain framework developed for welding by Ueda et al., widely documented and adapted to AM [85‐87]. ISM partitions the structure into parent regions and applies longitudinal or transverse shrinkage per unit length over an effective area to recover final deformation and stress as in Eq. (1‐4). Current WAAM studies show ISM delivers comparable distortion accuracy with major wall-time reductions [88].
where δx ∗,δy ∗ are the longitudinal/transverse shrinkage per unit length, these are the membrane-type inherent deformations applied along the weld, εx ∗ ,εy ∗ is the longitudinal and transverse components of inherent strain, A is cross-sectional area normal to weld line (m2) and h is section thickness (m).
While κx ∗,κy ∗ is the inherent curvatures (1/m) causing bending about x or y due to non-uniform through-thickness inherent strain, z is the through-thickness coordinate measured from the mid-plane (m).
In meso-scaled simulations, the primary objective is to predict the component-level thermo-mechanical response. Typically simplify the physics by treating the deposition as a solid-state problem, neglecting the complex fluid dynamics of the melt pool. The analysis is governed by two coupled partial differential equations as in Eq. (5), the transient heat conduction equation, which calculates the temperature field and the quasi-static equilibrium equation, which solves for stress and strain [89]. In its matrix form for Finite Element Analysis (FEA), the transient heat transfer is expressed as:
$$[C]\{\dot{T}\} + [K]\{T\}=\{q\}$$
(5)
where [C] is the heat capacity matrix, [K] is the conductivity matrix, {T} is the nodal temperature vector, \(\{\dot{T}\}\) is its time derivative and {q} is the thermal load vector from the heat source.
This thermal analysis is coupled with the mechanical equilibrium equations, which relate forces, stiffness and displacements to determine the stress and strain fields. To accurately model the thermal input for this analysis, a double-ellipsoid heat source model, developed by Goldak et al., is commonly used in WAAM. This model effectively captures the asymmetric heat deposition ahead of and behind the moving arc, providing the necessary thermal load for the coupled mechanical equilibrium equations that determine the final stress and strain fields [90‐92]. Meso-scale simulations aim to capture the complex, multi-physics interactions within the melt pool and electric arc, which are omitted at the macro-scale. At micro-scale, the models switch to conservation of mass, momentum and energy for an incompressible and free-surface liquid domain. These models are governed by the fundamental conservation laws of fluid dynamics as shown in Fig. 10.
Fig. 10
Illustration of multiple physics related to the thermo-fluid dynamics of the melt pool in WAAM [93]
The core equations are the Navier–Stokes equations, which describe the conservation of mass continuity and momentum for the fluid flow in the melt pool [94]. The terms \({\mathrm{S}}_{\mathrm{M}}\), \({\overrightarrow{\mathrm{S}}}_{\mathrm{U}}\), \({\mathrm{S}}_{\mathrm{T}}\) and \({\mathrm{S}}_{{\alpha }}\) of Eq. (6–9) relate with mass source because of droplet, momentum source, energy source and volume fraction respectively.
where \({\partial }_{\mathrm{t}}\) is the partial derivative operator with respect to time, \(\uprho\) is the density, \(\overrightarrow{\mathrm{U}}\) is for velocity vector and \(\uprho\) for pressure. Additionally, \(\upmu\) for dynamic viscosity, \({\mathrm{c}}_{\mathrm{p}}\mathrm{ is}\) the specific heat capacity, \(\mathrm{T}\) for temperature, \(\mathrm{k}\) for thermal conductivity and \({\alpha }\) as volume fraction.
The momentum equation includes source terms for various driving forces, such as the electromagnetic Lorentz force, surface tension including the Marangoni effect, buoyancy and arc pressure. This is coupled with the energy conservation equation, which governs heat transfer and phase changes melting and solidification within the domain. For models that include the arc plasma, Maxwell’s equations for electromagnetism are also solved to calculate the current density and magnetic fields that give rise to the Lorentz force and resistive heating [95].
Another approach of micro-scale models shifts the focus from mechanics to the evolution of the material’s internal structure, such as grains and phases, within a representative volume element (RVE). Instead of solving for temperature and stress directly, these simulations use the thermal history predicted by macro- or meso-scale models as an input to predict microstructural development. The governing equations at this scale belong to specialized computational materials science methods, such as the Phase-Field (PF), Cellular Automata or Monte Carlo approaches [96].
The PF method is a density-based computational method applied for modelling and predicting the temporal microstructure and property evolution during materials processes. This method has been proven to be extremely powerful in the visualization of the development of microstructures without having to track the evolution of individual interfaces. This method also allows many physical phenomena to be treated simultaneously [97‐99]. In the model, there are two types of variable fields used, firstly is the conserved variables that define the physically measurable quantities and provide information about the number and types of atoms at the given point as described in Eq. (10) and defined as the Cahn–Hilliard equation. The second type is the non-conserved variables which identify the distinct regions such as phases or grains related to the structure of atoms present at the material point as defined in Eq. (11) known as Allen–Cahn equation.
where in both equations, \({\mathrm{c}}_{\mathrm{i}}\), as conserved variable, \({\mathrm{M}}_{\mathrm{i}}\) is the concentration mobility tensor, \(\mathrm{t}\) for time, F for free energy system, \({\uppsi }_{\mathrm{j}}\) is non-conserved variable and \({\mathrm{L}}_{\mathrm{j}}\mathrm{ as}\) order parameter scalar mobility.
The repeated thermal cycles in WAAM produce complex microstructural features, primarily columnar and equiaxed dendritic grains. The solidification morphology is governed by two key metrics derived from the thermal history which are the temperature gradient (G) and the solidification rate (R) at the solid–liquid interface. A low G/R ratio promotes equiaxed nucleation near the bead crown, whereas a higher ratio stabilizes epitaxial columnar growth along the melt-pool wall [100]. The layer-by-layer nature of the process introduces further complexity through the partial remelting of previous layers and competitive grain growth between layers. These mechanisms lead to a characteristic columnar-to-equiaxed transition (CET) band near the top of each deposit and explain why deposition speed, interlayer cooling time and path strategy are primary controls over the final grain size and morphology [101]. To model this evolution, a multi-scale computational framework spanning macro-, meso- and micro- scales is typically employed. First, a thermal simulation calculates the local thermal history, providing the transient temperature field, T(t), from which the critical G and R fields are derived. This thermal history then serves as the input for a PF model, which predicts the resulting grain evolution and phase patterns. The micro-scale outputs, such as detailed grain maps or homogenized properties, can subsequently be passed back to inform meso- or macro-scale models to createa fully integrated simulation framework [102, 103].
Compared to PF, cellular automata (CA) provide a coarser, grain-scale description of cellular/dendritic microstructure as shown in Fig. 11. CA typically track only the convex envelope of a dendrite and do not resolve intra-dendritic segregation. Tip growth kinetics are prescribed as functions of local undercooling, with parameters often informed by phase-field predictions of the undercooling–velocity relationship [104]. Due to the lower computational cost and broad experimental validation, CA models have recently been used to simulate the formation of grain structure during solidification under various thermal conditions, namely under the conditions of casting, welding and additive manufacturing [105‐110].
Fig. 11
Illustration of three different modelling approaches: a Phase-field method, b Cellular automaton and c Monte Carlo Potts model [111]
The Monte Carlo Potts model is an on-lattice method for simulating curvature-driven grain growth [112]. To simulate additive manufacturing, the standard Potts model is modified so that grain evolution is computed only within the melt pool. The effect of the moving heat source is described by defining a molten zone surrounded by a high-temperature heat-affected zone (HAZ) with a steep thermal gradient. These regions supply the kinetics required for microstructural change. Research utilizes 3D Monte Carlo simulations of grain-structure evolution in metal AM [113]. Their low computational cost allows prediction of 3D microstructures over hundreds of heat-source passes. However, most implementations capture grain morphology only and do not explicitly evolve crystallographic texture, which limits orientation-dependent property predictions.
2.3 Aims of numerical computation in WAAM
Application macro-scale simulation in WAAM is the prediction and validation of part distortion, a critical factor for geometric accuracy in large components. For example, several studies developed a model to predict the final distortion of a multi-layer wall [114, 115]. The accuracy of the simulation was verified through an experiment, as shown in Fig. 12. The simulation predicts the y-axis distortion of the substrate and the results showed discrepancy of approximately 10% with the experimental data.
Fig. 12
Simulation and Experimental Results of Substrate deformation [116]
Another example of macro-scale application is the use of the inherent strain method, which serves as a computationally efficient technique for predicting part distortion as in Fig. 13. This procedure involves estimate of inherent strains and the residual plastic strains that remain after a thermal cycle from a detailed meso-scale model of the deposition process. To achieve efficiency, the inherent strains which are directly influenced by process parameters such as heat input and travel speed are applied as an initial condition [117]. A computational elastic analysis is then performed on the model to predict the final part distortion. The distribution of inherent strains are the main cause of distortion in large components [118]. Therefore, achieving high accuracy requires careful calibration of the inherent strain model, typically either detailed simulations or experimental data.
Fig. 13
Prediction of distortion using Inherent strain in the upper layer [119]
The meso-scale research is to understand and predict interlayer bonding, solidification, phase transformations, grain growth and residual stresses on component [120, 121]. These detailed models have proven effective, with studies proving that the predicted residual stress show correlation with experimental data [122]. One example of meso-scale as illustrated in Fig. 14, simulated final residual stress distribution in a multi-layer deposit. The results revealed a high stress concentration near the start and end heat points.
Fig. 14
Residual stress with heat source distribution in a WAAM [123]
Another research related to transient heat-transfer FE model for layer thermal history with convection and a Goldak double-ellipsoid source that is characteristics of meso-scale thermal modelling for WAAM. It then uses the computed thermal cycles as shown in Fig. 15 to interpret hardness bands and heat affected sub-regions.
Fig. 15
Thermal history of layer deposition with result to hardness [124]
Furthermore, finer scales simulations are used to investigate the physics of metal transfer, the process molten metal travels from the wire to the weld pool [125]. The specific transfer mode illustrated in Fig. 16, has a profound impact on the stability of the melt pool, the final bead geometry and the overall quality of the deposited layer.
Fig. 16
Types of molten metal transfer in the WAAM: a droplet, b liquid bridge and c wire stubbing [126]
Applications at the micro-scale focus on interaction between the local thermal history and the resulting microstructure. These include modelling grain growth morphology such as dendritic solidification, predicting the formation of phases and final crystallographic texture that related to mechanical anisotropy [127‐129]. While computational studies at this scaled are still evolving, they are often validated against detailed experimental characterization, as illustrated in Fig. 17. This study investigates microstructural change at different build heights of a WAAM component in which bainitic ferrite grains were significantly coarser in the top zone compared to the bottom. This effect comes from the lower cooling rates derives from by the upper layers due to the overall heat accumulation in the part [130].
Fig. 17
Microstructural Evolution of the corresponding areas [131]
These scaled simulation approaches are particularly valuable for modifying the properties of high-performance materials. For example, a study on S690 steel combined thermal simulations with experiments to locally control the heat input by adjusting travel speed and interpass temperature. This research showed that process control can manipulate the final microstructure and mechanical properties. The resulting microstructures, which can be engineered to a specific phase such as ferrite and bainite as shown in Fig. 18, determine the component performance.
Fig. 18
Phases Transformation on Different Build Layers, a bottom region and b top region [132]
The main application of micro-scale simulation is to predict the final microstructure resulting from the rapid and complex thermal cycles inherent to WAAM [133]. The cooling rate is a critical parameter that governs phase transformations in steels [134]. For example, high cooling rates tend to promote the formation of hard martensite, whereas lower rates favour the development of tougher microstructures containing bainite or ferrite [135, 136]. Therefore, micro-scale computational models are developed to simulate these transformations. The goal is to establish a clear connection between cooling rates and final mechanical properties, such as hardness and toughness. The simulation results are typically validated against experimental characterization such as electron microscopy [137, 138].
In the future, using scaled simulation along with new technologies such as Artificial Intelligence (AI) and Digital Twin (DT) is expected to bring even more benefits. For instance, RAMLAB automated WAAM facility highlights the potential of AI-enhanced process management [139]. Thales Alenia Space combines its expertise and knowledge with WAAM3D applying meso-scale analysis to determine the distortion effect using FEM [140]. A scientific research applied macro-, meso- and micro-scaled analysis for nickel and cobalt in WAAM which led to reduction in development time and increase in its performance [141]. Ongoing research in scaled analysis on WAAM shows potential for future improvements in process control, material properties and manufacturing efficiency.
3 Past insights on HSLA and HSLA-WAAM: experiment vs numerical simulation
HSLA steels have gained widespread acceptance across multiple industries due to their excellent strength-to-weight ratio, weldability and toughness [142, 143]. This type of steel uses low-carbon structural grades that consist of small additions of niobium, vanadium and titanium. The composition can also incorporate molybdenum, zirconium, boron, aluminium, nitrogen and rare-earth elements [144‐146]. These steels find extensive applications in petrochemical transportation, pipelines, automotive, aircraft and railways for example in Fig. 19.
Fig. 19
Example HSLA application, a Local Buckling for construction, b High-altitude Escape Solid Motor for spacecraft and c Bogie for railway [147‐149]
This review prioritizes the meso-scale in its analysis of WAAM, positioning it as the critical link between process parameters and final component properties. Meso-scale simulation strikes an optimal balance, capturing essential phenomena such as residual stress, distortion, and phase transformations through thermal history without the computational intractability of detailed micro-scale models. While micro-scale approaches are indispensable for fundamental research, they remain largely confined to small volumes due to extreme computational costs. Conversely, faster macro-scale methods, despite their industrial adoption, often lack the resolution for accurate local predictions, as their simplified models cannot fully capture the process’s physical complexities.
3.1 Experimental investigation on HSLA and HSLA-WAAM
HSLA steels typically characterised by low cost, excellent processability and satisfactory mechanical property indicators. Current research on HSLA steels concentrates on:
Thermo-Mechanical Controlled Processing (TMCP): This process combines controlled rolling with accelerated cooling to refine grains and tailor precipitation which deliver high strength and toughness at low carbon for good weldability. Different process parameters of TMCP produce distinct microstructures explaining the reasons that S460 and S690 retain strength differently at elevated temperatures even though both are TMCP steels [150]. Recent work on lean Nb–Ti pipeline plates in the API X60–X70 range shows that fine-grained ferritic microstructures with proper controlled rolling and cooling conditions for each grade [151].
Weathering steel: A588 weathering steel gains corrosion resistance from its Cu–Cr–Ni patina, but in fire its strength drops slightly more than standard A709/A992 and the patina offers little heat protection. After exposure up to 650 °C, air or water cooling generally restores properties, rapid quenching from 815 °C can raise strength but cause brittleness [152].
Dual-phase (DP) steels: DP steels have a mix of ferrite and martensite phases, which gives them a good balance of strength and formability. This combination makes them suitable for applications where both properties are important [153‐155].
Transformation-induced plasticity (TRIP) steels: A type of material that offers high strength and ductility due to metastable austenite transforming into martensite. These characteristics make TRIP steels ideal for applications requiring high impact strength levels [156‐158].
Bainitic steels: This type is characterized by unique microstructures, combination of high strength and toughness. These steels are suited for a variety of applications where balanced between strength and ductility is critical [159‐162].
Quenched and tempered (Q&T) steels: A specialized category of steel that has undergone a specific heat treatment designed to optimize strength and toughness. Due to their reliability to endure high stress and dynamic loads, these steels are extensively utilized in various engineering and construction projects [163, 164].
The automotive industry is one of the biggest users of HSLA steels and for example, uses HSLA-65 steels in the springback [165]. In the energy sector, the industry uses HSLA steels for pipeline projects. HSLA grades microalloyed with niobium and titanium are engineered to withstand high pressures and harsh service environments. They are also widely used for structural components in the marine and construction sectors. [166, 167].
The construction industry relies on HSLA steels, particularly for bridges and tall buildings. Major skyscrapers in cities are increasingly using HSLA steels for better height safety [168]. In shipbuilding, especially for naval vessels, HSLA steels are incorporated into their designs. These steels offer strength and toughness while reducing the overall weight of the ships which is crucial for military performance and durability. ASTM A572 HSLA steel is a common tower material that provides structural capacity for larger turbines and delivers durable service under wind, weather and temperature variations [169, 170].
The WAAM process utilizing HSLA steel has emerged as a promising technology for producing large structural components with high deposition rates and geometric flexibility [171, 172]. It involves understanding the influence of process parameters, microstructure evolution and mechanical properties to optimize the manufacturing process [173]. WAAM particularly through techniques such as Cold Metal Transfer (CMT) and conventional gas metal arc welding (C-GMAW), facilitates the production of large and complex structures [174]. Due to strength characteristics of HSLA, this additive manufacturing process offers significant design flexibility while minimizing material usage.
In HSLA-WAAM, the cooling rate, tempering time and temperatures during layer reheating determine phase transformation. This variation influences mechanical properties such as microhardness and tensile strength [175]. Repeated reheating and cooling also produces ferritic morphologies which are acicular ferrite, quasi-polygonal ferrite and Widmanstätten ferrite which can vary within the build direction [176]. This is due to changes in the heat accumulation and dissipation conditions as the deposition layer increases. The process of HSLA-WAAM involves complex solidification and phase transition, which is sensitive to local heat accumulation [177, 178]. Consequently, variations in ductility can be seen due to the multiple thermal cycles experienced during the WAAM process [179]. Research shows that WAAM-HSLA steel can exhibit yield strengths greater than 840 MPa and elongations exceeding 16%. The tensile strength can reach up to 1200 MPa with significant improvements in hardness and ductility. The components also exhibit excellent low-temperature toughness and high energy absorption efficiency [180].
Recent studies show that WAAM can fabricate functionally graded HSLA with location-specific properties by adjusting heat input, interpass temperature and filler composition. A double-wire bypass plasma arc setup has been proposed as a practical way to induce material gradient within a single-pass clad, producing hardness–toughness gradients along the cladding direction. This expands WAAM’s adaptability for parts that need wear-resistant surfaces with tougher substrates or smooth transitions between dissimilar regions [181]. Another research study on Ultracold-WAAM using HSLA steel. This variant reduces process temperatures and increases cooling rates, preserving the high mechanical strength and ductility of HSLA steel parts. Other study uses a different technique by combining HSLA-WAAM with interlayer friction stir processing to improve the quality of components. It reduces porosity and refine grain size, improving mechanical properties [182].
3.2 Meso-scaled numerical computation on HSLA and HSLA-WAAM
Numerical computation of HSLA steels involves accurate models and strong calibration techniques to predict how the material behaves under different conditions. To capture the behaviour of these alloys, several categories of models have been developed, including:
Yield Criteria: To capture plastic deformation, advanced yield criteria such as the Hill model are often required to account for the anisotropic behaviour observed in some HSLA steels. This approach has been successfully applied to predict the anisotropic yielding in HSLA-WAAM components [183, 184].
Constitutive and Hardening Models: These models describe the materials stress–strain relationship after yielding. While simple isotropic hardening models are sometimes used, more advanced models that combine isotropic and kinematic hardening are needed to accurately simulate the non-linear mechanical behaviour and cyclic loading effects common in WAAM [185‐188].
Microstructure Evolution Models: These models predict how the microstructure changes in response to thermal and mechanical loads. For hot deformation processes in WAAM, Dynamic Recrystallization (DRX) models are important [189]. Additionally, kinetics models are even more critical, as they predict the evolution of phases during the rapid cooling and reheating cycles, which ultimately determines the final material properties [190, 191].
These models provide the framework needed to predict HSLA steel behaviour across actual loads and temperature. However, the accuracy of these models depends on identifying parameters for the specific steel grade, product form and thermal history. In practice, this requires calibrating the models against actual datasets. Common experimental methods used to generate calibration data include:
Uniaxial Tensile Tests: These tests provide stress–strain data, such as yield strength, ultimate tensile strength and elongation. This data is important for calibrating plasticity, isotropic hardening and anisotropic yield criteria [192‐194].
Compression Tests: Compression tests are particularly important for processes involving high temperatures. They are used to characterize the material’s flow stress and to determine the critical strain for the initiation of dynamic recrystallization [195, 196].
Microstructural Characterisation: Advanced process such as Electron Backscatter Diffraction (EBSD) and Transmission Electron Microscopy (TEM) is used to quantify microstructural features. This provides essential data on grain size, phase fractions and dislocation density needed to calibrate and validate microstructure evolution models [197, 198].
The identified parameters can be used to validate the numerical method. The most common validation technique is the direct comparison of simulation predictions with new experimental data [199‐201]. The accuracy of a model is evaluated by comparing predicted stress–strain curves, failure points or microstructures with the validation experiments. For complex WAAM components, this involves comparing the predictions from an FEA with measurements from a physical component [202, 203]. For applications involving cyclic loading, specialized experiments such as fatigue tests are used to validate the models ability to predict component life with results compared directly against experimental fatigue data [204, 205].
One study proposed a combined experimental–numerical methodology to generate Multiple Cycle Continuous Cooling Transformation (MC-CCT) diagrams specifically for HSLA steels in AM applications [206]. Another developed a validated thermo-mechanical model using ABAQUS and a FORTRAN subroutine to investigate the effect of interpass hammering on residual stress in HSLA-WAAM components [207]. At the structural scale, a research examined WAAM-fabricated HSLA steel columns by assessing geometric accuracy and performing mechanical testing to predict their load-bearing performance by using numerical computation [208]. Finally, a design-focused study used a DED-Arc process to redesign a railway bogie, creating a functionally graded structure with HSLA steel in critical regions and validating the design through simulation and optimization [209]. While the reviewed studies represent important advancements, a significant gap remains in developing an integrated computational framework to predict and control the formation of multiphase microstructures in HSLA-WAAM.
3.3 Research prospect for HSLA-WAAM using Meso-scaled numerical computation
To quantify the existing research landscape, a bibliometric analysis was conducted using the Scopus database for the period of 2020 to mid-2025, with the results summarized in Table 2. There are 4,239 publications on WAAM, indicating extensive research in this area. Searching for articles using the combined keywords "wire arc additive manufacturing, Numerical Computation and High Strength Low Alloy (HSLA)," only 4 articles were identified. However, only 1 study covers the transformation cycle. This shows a gap in research regarding WAAM simulations for HSLA steels.
Table 2
Publication based on Scopus database (2020 to mid-2025)
Keywords
Publication 2020 – mid 2025
Wire Arc Additive Manufacturing (WAAM)
4239
WAAM AND Numerical
324
WAAM AND High Strength Low Alloy
189
WAAM AND Numerical Computation
13
WAAM AND Numerical Computation AND High Strength Low Alloy
3
WAAM AND Numerical Computation AND High Strength Low Alloy AND Transformation cycle
1
Review of these few publications highlights the current research boundary that is the creation of functionally graded components with tailored to location specific properties. Achieving this requires a deeper study of the entire process structure and Fig. 20 illustrates a conceptual framework for this challenge. Such a system requires the integration of multiple inputs, including material composition, Continuous Cooling Transformation (CCT) and Time–Temperature-Transformation (TTT) diagrams and targeted pre-experimental data for calibration. This input is incorporated into the WAAM simulation and adjusted to match the experimental result. A critical prerequisite for this, however, is the development of CCT/TTT diagrams specifically for the non-isothermal and rapid thermal cycles inherent to the WAAM process, as existing diagrams are often inadequate. The complex thermal cycles in WAAM are important to predict phase transformations accurately [210, 211]. This highlights the importance of conducting studies to produce TTT and CCT for HSLA-WAAM applications.
Fig. 20
Simulation-informed multiphase material properties for HSLA-WAAM
A thorough knowledge of phase transformations during HSLA-WAAM is critical for controlling the microstructure and mechanical properties of the final component. The process is characterized by complex thermal cycles in which initial layers undergo rapid cooling, leading to the formation of martensitic or bainitic phases, while subsequent layer depositions reheat these underlying regions, causing tempering and microstructural changes [212].To model these phase transformations, kinetic models such as the Johnson–Mehl–Avrami-Kolmogorov (JMAK) equation as in Eq. (12) is often use to predict the extent of diffusional phase changes [213, 214]. These models consider the isothermal state to predict the formation of varied phases such as ferrite, pearlite, bainite and martensite [215].
where y is the phase fraction, k is the nucleation and growth rate depend on temperature and n is the time exponent.
To adapt the JMAK model for the non-isothermal conditions of WAAM, an additivity rule is required. This approach allows for the prediction of non-isothermal CCT behaviour based on data from isothermal TTT diagrams [216‐218]. The underlying principle, known as additivity rule, is illustrated in Fig. 21. The continuous cooling curve is discretized into a series of short, isothermal time steps. At each step, the fraction of transformation is calculated and these fractions are summed to predict the final phase after cooling [219, 220]. While this method provides a framework for non-isothermal analysis, its accuracy is entirely dependent on the availability of high-quality TTT data that is relevant to the specific alloy and thermal conditions of the process [221]. This highlights a further research gap the lack of comprehensive TTT and CCT diagrams generated specifically for the rapid cooling rates and repeated thermal cycles experienced by HSLA steels in the WAAM process.
Fig. 21
Rate of transformation during continuous cooling based on the TTT data using step function [222]
Maintaining a consistent cooling rate during the WAAM deposition process is challenging due to continuous layer-by-layer deposition and fluctuating thermal conditions [223, 224]. The complexity of the non-isothermal kinetics arises from heterogeneous nucleation in reheated zones, variable phase growth rates caused by spatial thermal gradients and the repeated tempering of previously deposited material [225]. To overcome these limitations, advanced models such as the proposed "unified JMAK" model extend the Avrami kinetics to control variable thermal conditions, as shown in Eq. (13). This model incorporates correction factors that account for both linear and non-linear cooling paths.
where X is the maximum phase fraction achievable at a given cooling rate CR, k and n are the kinetics parameters for nucleation growth with function to both cooling rate and temperature, T and t is time in seconds.
A mathematical models can be used to connect process thermal, chemical composition and final mechanical properties. A prominent example is the Maynier hardness model, which predicts the hardness of the final multiphase microstructure based on the alloy composition and the cooling rate [226‐228]. The model first calculates the hardness of each potential phase using empirical relations Eq. (14–16) and then calculates the final bulk hardness using a rule of mixtures Eq. (17). This data is then used to map phase fractions in CCT diagrams.
While \({\upzeta }_{\mathrm{f}}, {\upzeta }_{\mathrm{p}}, {\upzeta }_{\mathrm{b}}, {\upzeta }_{\mathrm{m}}\) are phase fractions of ferrite, pearlite, bainite and martensite, \({\mathrm{HV}}_{\mathrm{f},\mathrm{p}},\mathrm{ H}{\mathrm{V}}_{\mathrm{b}},\mathrm{ H}{\mathrm{V}}_{\mathrm{m}}\) are hardness from ferrite/pearlite, bainite and martensite, respectively.
Ultimately, the goal of this research is to create predictive method that estimates the final mechanical properties of additively manufactured HSLA components before the fabrication. The simulation-informed methods employ pre-experimental analysis of calculated hardness to estimate tensile strength as in Eq. (18) [229, 230].
where \({\sigma }_{UTS}\) is tensile strength, HV is hardness and \({\mathrm{a}}_{1}\), \({\mathrm{a}}_{0}\) are constants for HSLA steel.
Consequently, CCT diagrams in WAAM often miscalculate transformation kinetics, leading to inaccurate predictions of phase fractions and mechanical properties such as hardness [231]. Targeted experiments are important to provide the high reliability data including measured thermal histories, microstructural phase fractions and hardness which serves as the basis for calibration and final validation [232, 233]. This concept is taken further by advanced data-driven techniques such as Physics-Informed Neural Networks (PINNs). A PINN can be trained to learn the complex relationships between process inputs and material outputs by integrating both experimental data and the governing equations of physics [234]. The proposed model would be structured to map main inputs such as the alloy composition and cooling rate which giving the output on the phase fractions and mechanical properties such as hardness and tensile [235, 236]. Crucially, the network learning process is constrained by the empirical formula.
The training strategy for such a model is a critical two-stage process as in Fig. 22. First, the PINN is pre-trained on a large volume of data generated from the CCT diagrams and Maynier equations [237]. This step teaches the model the fundamental metallurgical relationships of the system [238]. Subsequently, the model is optimized using the smaller, high-value set of targeted experimental data from actual WAAM builds. This step calibrates the model, correcting for the inaccuracies of the standard CCT data and teaching it the true material response under real-world WAAM conditions [239]. The resulting validated PINN can accommodate process variations and deliver the rapid, accurate property predictions required for a simulation-informed design framework in HSLA-WAAM. To execute this integrated strategy, this work proposes a Hybrid PINN. Compared to traditional PINNs, the proposed hybrid approach combines the knowledge from three complementary sources which are governing physicals law, established empirical models and data-driven experimental or simulation WAAM.
Fig. 22
Conceptual Hybrid PINN in modified CCT to predict material properties
Figure 23 illustrates different material properties in the flange where multiphases are intentionally produced at different locations to optimize performance [240‐242]. A hard and wear-resistant martensite could be formed on the surface layers, while the core could be composed of tougher and more fatigue-resistant bainite [243, 244]. The ability to manufacture such multiphase components would be highly impactful for industries such as pipeline and construction, where there is high demand for materials with an optimal balance of strength, toughness and ductility [245‐247]. For critical components as an example high-pressure pipe flange, a functionally graded design resolves the problem between wear resistance and fracture toughness. Stress analysis often identifies the inner bore as a high-wear, crack-prone site [248]. A hard, wear-resistant martensitic microstructure is therefore selectively formed on this inner surface, with its brittleness managed by the tempering effects of subsequent layers [249]. The outer part of the component is then composed of tougher bainitic microstructures to provide the toughness and fracture resistance [250, 251]. This targeted approach achieves an optimal balance of properties unattainable in a uniform material. However, achieving this level of control is currently hindered by the lack of validated simulation tools. Therefore, the development of an integrated computational framework capable of predicting and optimizing the formation of multiphase microstructures in HSLA-WAAM remains a critical research gap and the primary motivation for the work that follows.
Fig. 23
Example of an optimized flange design for abrasion and impact resistance
WAAM is a process influenced by several factors such as heat accumulation, interlayer temperature and accuracy of prior layer deposition, all of which have an important impact on the stability of the final component. Examining current patterns offers valuable insights for future research. Data obtained from Scopus is used to assess publication characteristics, including quantity and quality over the last ten years. The most significant discoveries are as follows:
WAAM research grew from 378 articles in 2020 to 1041 in 2024, marking over 160% increase in four years. “High strength alloy”, “High-strength steel” and “numerical computation” emerged as frequent keywords in this period, appearing 136, 76 and 7 times respectively.
Emerging post-2023 research trends in HSLA focus on advanced high-strength steels, including micro-alloyed HSLA, dual-phase, TRIP, bainitic and Q&T steels. These advanced steels are recognized for their blend of high strength, formability and toughness, essential for application in industries.
Numerical computation plays a key role in improving WAAM process efficiency and quality, especially for HSLA steel. The intricate connection between process parameters and material properties is studied through simulation. The development of accurate models and calibration methods are crucial to determine the mechanical behaviour of HSLA steels.
A fundamental challenge is that no single simulation method can currently capture the full macro-, meso- and micro-scaled nature of the WAAM process efficiently.
Only four articles were identified from 2020 to mid-2025 that integrate numerical computation with HSLA-WAAM. These studies primarily focus on macro- to meso-scale analysis, with only one investigating into cooling cycles and phase transformation.
Despite rapid progress in experimental HSLA-WAAM, micro-scale simulation design for phase-transformation kinetics remain limited and further integration with artificial intelligence may uncover new research directions.
Conventional metallurgical models such as CCT/TTT diagrams and isothermal kinetic models inaccurately represent the repeated heating and cooling of WAAM process.
There is a lack of studies on using material simulation software to accurately model the complex physics of material solidification and phase transformations that occur during the WAAM thermal cycles.
The potential to transform future research lies in developing more complex and exact models that can predict outcomes under a wide range of conditions. Future research should focus on integrating FEM, experimental data and AI tools with analytical equations. Combining all of these with macro-, meso- and micro-scaled approaches in WAAM research has the potential to revolutionize the manufacturing sector, allowing for the production of complex components with improved material performance. Some recommendations of concepts for future research are as follows:
Functional grading in WAAM steel can be achieved by adjusting process parameters which enables the customization of material properties for specific needs. Material modelling of HSLA steel centres on understanding process parameters, microstructure evolution and mechanical properties for process optimization.
WAAM process involves non-isothermal conditions, phase transformations, microstructural development and mechanical properties of steel components. Understanding and simulating non-isothermal conditions are vital for enhancing WAAM and achieving desired final properties.
Advanced simulation tools can effectively model transformation and microstructural changes during WAAM. This assists in the prediction of process parameters that affect the microstructure and mechanical properties.
The formation and growth on a micro-scale during the WAAM process are important for understanding microstructural evolution and optimizing process parameters to achieve desired material properties.
Simulating grain growth and nucleation during solidification with thermal models can provide a better understanding of microstructural development throughout the WAAM process.
There is a critical need for comprehensive experimental datasets. These including detailed cooling rates, microstructure formation and mechanical properties data which are essential for the rigorous calibration and validation of the computational models.
While experimental correlation is typically deployed to evaluate mechanical properties, recent advancements in PINN for material modelling particularly in mechanical properties show significant promise. PINN can be included for identifying phase transformation and gaining insights into microstructural changes in steels using CCT and TTT diagrams.
The development of Hybrid PINNs represents a future direction, allowing the rapid prediction of multiphase microstructures and properties for the simulation-driven design of functionally graded HSLA components.
Acknowledgements
The authors would like to express their gratitude to the staff member of Smart Manufacturing Research Institute (SMRI) as well as the staff of Welding Laboratory and Advanced Manufacturing Laboratory at Universiti Teknologi MARA (UiTM) in Shah Alam, Malaysia. This project was funded by Ministry of Higher Education (MOHE) in Malaysia under Hadiah Latihan Persekutuan (HLP) with offer Cuti Belajar Bergaji Penuh Tanpa Biasiswa (CBBPTB). This internationally collaborated research was conducted under the Adjunct Professor Senior Research Fellow at Universitas Sumatera Utara (USU) in Medan, Indonesia and West University in Trollhättan, Sweden.
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A focused review on numerical computation in wire arc additive manufacturing for high strength low alloy steels: past insights and potential opportunities
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