## Numerical analysis of additive manufacturing (3D printing) systems By Bruno Carpentieri, 11 April 2024. **Abstract.** _Additive Manufacturing (AM), or 3D printing, is defined as the process of joining materials to make objects from a computer model. Although AM technology is modernising manufacturing processes in almost every sector where it is applied, especially those requiring low volume production, high design complexity and the ability to change designs frequently, it is not yet considered to be mature enough to be employed routinely in modern industry, due to various technological challenges and drawbacks. The technology has been established for almost two decades; however, its optimisation is still performed by trial and error experimentation. Recently, numerical modelling approaches have been employed for process optimisation. ._ ###### Background Industry 4.0 is the term that describes the Fourth Industrial Revolution, an ongoing automation effort that, in the coming years, is going to radically innovate industrial processes using advanced smart technologies. Additive manufacturing (AM) or 3D printing (3DP) is considered one of the key drivers of this revolution, together with industry Internet of Things (IoT), cloud computing, big data, cyber security, augmented and virtual reality, cyber-physical systems and robotics, and other important technologies. In the Standard Terminology for Additive Manufacturing documentation (ASTM F2792), AM is defined as the process of joining materials to make objects from 3D models, usually layer upon layer, using Standard Tessellation Language (STL) files that describe the geometry of the object. Some massive advantages of AM over traditional manufacturing are that, in addition to customary requirements such as low cost and excellent quality, it can ensure high product customisation and complicated design, there are much faster lead times from prototyping to production and delivery of parts, and it requires shorter life cycles, less material waste and reduced manufacturing skills. The feasibility of AM was demonstrated for the first time in 1981 by Hideo Kodama in the article titled _"Automatic method for fabricating a three-dimensional plastic model with photo-hardening polymer"_. The SLA-1 Stereolithography (SLA) printer, constructed in 1987 by the company 3D Systems, is considered the first commercially successful 3D printing device. An important breakthrough in the history of 3D printing was the development of a self-replicating fabricating system that was capable of manufacturing its own components, at the University of Bath in 2005. Since then, several small and large businesses have been launched in the AM field, such as Makerbot (2009), Form Labs (2011), Micro (2014), Cellink (2015) and HP Fusion Jet 3D printer (2016). Over the last decade, AM technology has contributed to modernising manufacturing processes in almost every sector where it was applied, especially those requiring low volume production, high design complexity and the ability to change designs frequently. In the aerospace industry, for example, a reduction in product lead time of 30% to 70% was obtained and reduced manufacturing costs of lowvolume parts of 30% to 35% were obtained. In the healthcare industry, AM technology enables the fabrication of complex anatomical parts from computed tomography images and to assists the precise presurgical planning for very delicate operations, like the separation of Siamese twins. In architectural and jewelry modelling, much higher resolution, free design and object customisation is possible compared to traditional manufacturing solutions. <center><img width=600 src="C:\Users\bruno\Dropbox\Obsidian_Notes\000-publish\Blog\Images\SLA1.png"></center> _Figure 1. The SLA-1 laser stereolithography machine, built in 1987, is considered the first 3D printing device._ AM processes are controlled by many process parameters (printing speed, layer thickness, laser power, spot diameter, powder mass stream, scanning space, particle size or packing density, etc.) that affect the layer generation and material preparation, and can greatly influence the microstructure and mechanical properties of AM-fabricated parts. Optimisation of the printing process can help reduce the high production costs and (sometimes) long build times, enhance the quality of the final products by preventing porosity, void formation and layering errors, deal with anisotropies in microstructures, face the challenges of small build volumes and diseconomies of scale. Although the technology has been established for almost two decades, its optimisation is still performed mainly by trial and error experimentation, which remains a lengthy and expensive process. High-fidelity simulations and in situ monitoring using smart sensors and image data are two promising approaches for non-destructive evaluation of internal component geometries and thorough assessments of part quality and process reliability. However, these both require the development of innovative and efficient computational tools. ###### Physics-based simulation modelling Recently, physics-based simulations have been used to perform process optimisation with minimal trial and error experiments. By simulation modelling, we refer to the theory-based approach in which a model is built using physical laws that describe the causal relationships between a set of controllable inputs and a set of target physical variables. The model is often solved using numerical methods, except if a closed form solution of the resulting set of equations is available. The physical phenomena associated with AM processes include melting and solidification, fluid flow, heat and mass transfer, the appropriate description of the heat source, temperature-dependent material properties, microstructural changes, thermal and transformation strains, vaporization, radiation, in addition to the crystallographic texture of the produced parts. Since the quality of a part using a certain combination of process parameters remains uncertain until it is finally printed, it is essential to simulate the kinetics of the phase transformation that takes place during the build process and/or in samples subjected to heat treatment. In the last decade, different types of AM processes have emerged, such as selective laser melting (SLM) and electron-beam melting (EBM). By using a high-power laser source to melt metal powder layer-by-layer, it allows fabricating nearly fully-dense parts (up to 99.9%) as well as complex metallic lattice structures, that are impossible to obtain through traditional manufacturing techniques. The equations of the SLM process model the melt pools, the deposited metal powder and the surrounding air, by mass, momentum and energy conservation laws. The liquid metal is modelled as an incompressible Newtonian fluid while the molten pool flow is assumed to be a free-surface laminar flow (the viscous stresses are assumed to be zero). In the process of deposition of new layers of material, thermal cycles are induced while heat is conducted away from the recently solidified material through the already sintered layers and surrounding powder. Heat produced by laser beam dissipates from the powder bed by conduction, convection, and radiation. The underlying physics is modelled by using partial differential equations. These thermal cycles can influence the microstructure and phase transformation behaviour, and in turn they can modify the crystallographic texture, typically leading to complex distributions of microstructures and properties in the finished parts. Hence, AM processes involve complex multiphysics phenomena. In order to achieve optimal properties, the complete deposition process must be optimised and, given its complexity, this optimisation can be effectively conducted using numerical simulations. <center><img width=600 src="C:\Users\bruno\Dropbox\Obsidian_Notes\000-publish\Blog\Images\AMsimulation.png"></center> _Figure 2. Simulations of the selective laser melting (SLM) or laser powder bed fusion (LPBF) technique using the finite element method typically involve the analysis of various time-dependent phenomena that evolve over the course of the additive manufacturing process, including thermal cycling, residual stresses, strains, and microstructure. Such simulations aim to optimize process parameters to achieve desired part quality, minimize defects, and understand the underlying physics._ ###### Data-driven simulation modelling Although physics-based simulation models are generally very powerful in understanding the behaviour of the system, they can sometimes fail to accurately reveal the macroscale properties of printed parts or the mechanisms leading to the formation of microstructures, due to limited theory and simplified assumptions, large numbers of variables and parameters involved in complex AM processes and, sometimes, a lack of robust numerical solvers. In these difficult situations, data-driven models can be used to find correlation relationships between two sets of controlled inputs and output variables, without the effort of explicitly describing their causal pips. Data-mining techniques can be applied to predict future data patterns by analysing the properties of available datasets. Genetic algorithms and artificial neural networks can map associations between two datasets by minimising a cost or error function and then making predictions on the future behaviour of the target system. In the last decade or so, machine learning (ML) algorithms have become widespread and popular in several scientific fields, including medical diagnostics, self-driving cars, natural language processing, image recognition, website recommendations, solid-state materials science and finance. They are more established modelling techniques in areas like bioinformatics and chemistry. Although their use in AM is only several years old, a number of research projects are currently underway to apply data-driven approaches to tackle some of the challenges in process optimisation of metal AM. Such challenges include: finding the correlation between process parameters (melt pool geometries, layer thickness, laser power, scan speed) and resultant mechanical material properties (e.g. porosity, modulus of elasticity, tensile properties, strength, toughness) that largely influence the final product quality. Other challenges are: designing novel alloys or high-performance metamaterials (that would be impossible to design manually), optimising the material distribution within a given design space, subject to specific loads and constraints, dealing with in situ images and acoustic emissions during printing and detecting defect formation in real time. They can also be used in predicting the geometric deviation based on design geometry after training and to provide guidance for geometric error compensation. By using convolutional neural networks (CNN) on a training dataset of mechanical properties calculated by FE models, researchers were able to create novel microstructure patterns of a composite metamaterial that resulted in being 25 times tougher (in material science, toughness is defined as the amount of energy that a material can absorb per unit volume without fracturing) and approximately 2 times more resistent than the stiff material, and 40 times tougher and more than 100 times stronger than the soft material. It took about 5 days to calculate the mechanical properties by FE simulation and only 10 hours to train the data by CNN. Once the training process was completed, billions of designs were screened in hours, whereas the same prediction by FE would take years of simulation. In topology optimisation, trained CNN models have predicted almost the same optimised structures that were computed by the FE-based Solid Isotropic Material with Penalisation (SIMP) method, one of the most popular mathematical methods for AM mechanical problems, but nearly 20 times faster. To date, FE-based methods are the most widespread computational tools implemented in topology optimisation software, both commercial and academic. After the training, the method was able to predict 3D structures almost instantaneously with an average binary accuracy of 96.2% and an overall 40% reduction in time, compared to SIMP. In other AM applications, multi-scale CNN has been used to design a system for the autonomous detection and classification of powder spreading defects that could potentially lead to warping, swelling and even build failures, solely based on the images captured during the SLM process and without human intervention. The general applicability of CNN and other ML methods to different applications, without requiring specific knowledge of the underlying problem makes data-driven modelling computationally appealing to use and a key simulation tool for Industry 4.0, one that could lead to significant savings in terms of research and development efforts. Recently, the spin-off Artificial intelligence (AI) company ‘Intellegens’ from the University of Cambridge, has created a machine learning algorithm, called Alchemite, for fast training of deep neural networks that has enabled much faster and less expensive design of novel AM materials. It has been estimated that the toolset has saved about US$10 million and 15 years in research and development costs for the analysis of databases of existing materials and for designing new alloys to be used for the 3D printing of high-performance jet engine components required in the aerospace industry. However, the literature on data-driven AM simulations focuses mainly on design and on the engineering aspects of AM processes. Applications for the study of other technological and scientific aspects of AM, such as microstructure analysis, property prediction, topology optimisation and new alloy design, are still at an early stage and have only been partly explored. For example, many studies in topology optimisation use deep learning approaches, focussing on 2D structures, while the design of 3D structures is clearly more relevant to AM. Likewise, the symbiosis of state-of-the-art ML and AM techniques in material design and the great potential of the data that can be extracted from the correlation maps between process parameters and microstructure properties have not been fully exploited. Seeking new data acquisition methods and developing better search algorithms which require minimalist datasets, and exploring new ML applications, are indicated as being some of the future research directions in this massive and fast growing field of AM. <center><img width=600 src="C:\Users\bruno\Dropbox\Obsidian_Notes\000-publish\Blog\Images\AMsimulation1.png"></center> _Figure 3. An example of finite element models analysis from our team’s work: temperature field distribution during sintering of a) 9th, b) 28th a c) 49th layer, d) colour legend._ ###### Innovation, urgency and impact towards a sustainable development Additive manufacturing has been classified by the European Union as a Key Enabling Technology for future sustainable production and represents one of the pillars of Industry 4.0. Numerous companies have now adopted AM, and the European Union and governments Europeans are financing projects and initiatives in this sector. We mention the initiative lasting 4.5 years (January 2013-June 2017) and worth 1.88 million euros called _"Additive Manufacturing Aiming Towards Zero Waste and Efficient Production of High-Tech Metal Products"_ funded by the Agency European space, and the strategic program called _"Solutions Industrie du Futur"_ undertaken by French government in April 2021 which aims to accelerate the development of AM in France. AM technology it offers opportunities for innovation and competitiveness for local businesses, allowing them to develop products lighter, more efficient and personalized. Through the optimization of AM processes and the integration of new techniques, local companies could improve their productivity, reduce production costs and expand their range of product offerings. The adoption of advanced AM solutions could be attractive external investments and strategic partnerships, contributing to the growth of the local industrial ecosystem and to the creation of new qualified jobs in the engineering, production and research sectors. Adopting AM, however, requires much more than that the simple purchase of production machines additive manufacturing and their integration into workflows existing. It may require a transformation global business model (the so-called value chain), design innovation, the digitalization and process simulation, the supply chain restructuring, one careful selection of materials, careful management of the product life cycle, post-processing treatment, control certification quality, training and development of new ones skills. Although the AM found a significant success in some industrial sectors specific and specialist, it is not traditionally still considered a production technology of large scale. Its use in the production of end-use products for high-energy industries energy consumption, such as automotive and aerospace, is still limited. These sectors often require the large-scale production of components and materials with specific mechanical properties, of long life and high resistance in extreme conditions. Compared to traditional manufacturing processes for these types of applications, additive manufacturing must overcome shortcomings and limitations in terms of speed, scalability and cost efficiency, and may not always be able to meet the stringent requirements of high performance generally required in these sectors. The potential of AI-based techniques in optimization of additive manufacturing processes may offer an efficient and fast solution for component design optimized, significantly contributing to reducing costs and improving the overall efficiency of the process of additive manufacturing. Research in this field is growing rapidly and is focused on the development of new approaches to acquire data, more efficient search algorithms that require fewer experiments and the exploration of new applications of machine learning. The results of these studies will lead to innovative solution methods that enable to simulate a wider range of parameters and perform faster predictions of material properties and design, as well as contribute to the ultimate goal of developing smart or intelligent AM solutions in the near future • ##### References Effect of cyclic loading on microstructure and crack propagation in additively manufactured biomaterial Co–Cr–Mo alloy - B. R. C. Saraiva, L. Novotný, B. Carpentieri, T. F. Keller, M. Fáberová, R. Bureš, S. F. Rodrigues, J. R. de Barros Neto, L. H. M. Antunes, M. Masoumi, H. F. G. de Abreu, M. Béreš - Journal of Materials Research and Technology 26, 3905-3916, 2023. DOI: https://doi.org/10.1016/j.jmrt.2023.08.185 Effect of interlayer time interval on residual stress distribution in Ti6Al4V alloy manufactured by laser powder bed fusion - L. Novotný, M. Béreš, B. Carpentieri - Science and Technology of Welding and Joining, 1-11, 2023. DOI: https://doi.org/10.1080/13621718.2023.2184105 Numerical Analysis of Residual Stresses in Additively Manufactured Materials - L. Novotny, M. Béreš, B. Carpentieri, H. F. G. Abreu - ECS Transactions 107 (1), 1761, 2022. https://doi.org/10.1149/10701.1761ecst Thermal Analysis and Phase Transformation of Ti6Al4V Alloy Fabricated by Direct Metal Laser Sintering - L. Novotný, B. Carpentieri, M. Bereš, H. F. G. De Abreu - 2021 International Applied Computational Electromagnetics Society Symposium (ACES), 2021. https://ieeexplore.ieee.org/abstract/document/9528824