Additive manufacturing (AM) is an emerging technology that fuses deposited powder materials together layer-by-layer using a localized heat source to create an arbitrarily complex geometry. This technology is an inherently multiphysics problem, involving the simultaneous evolution of fluid flow, heat transfer, free surface, laser-material interaction and material phases including solid, liquid and gas. Multiphysics and multiphase models are typically used to understand the dominant physics driving AM processes through high fidelity simulations resolving the individual powders as they melt onto the substrate. However, these types of high fidelity models have not been applicable to modeling directed energy deposition (DED) process, where powders are delivered through the ambient vapor onto the substrate by a nozzle and subsequently fused. This paper presents a novel multiphase thermo-fluid formulation for modeling DED processes. A diffuse level set formulation coupled with the Navier–Stokes, energy conservation and radiative transport equation allows us to model complex free surface, fluid flow, thermal and laser interaction evolution. In addition, our formulation enables us to resolve the vapor flow field and its effect on deposited material during AM processes. The accuracy of our proposed method is assessed by comparing with literature solutions and experimental benchmarks. Our proposed formulation is then used to model simple DED processes that enable us to visualize the entrainment of powder particles into the melt pool. This process elucidates the dominant physical forces that can drive powders into the melt pool as well as their effect on the melt pool evolution within DED processes.

In the NIST additive manufacturing benchmark (AM-Bench) experiments, melt pool geometry, cooling rates, surface topography, and dendritic microstructure in laser melted Inconel 625 were used to challenge and validate computational models of the melting and solidification process. To this end, three thermal models incorporating different physics are compared with the experimental data. It is identified that the heat convection enhanced by the thermocapillary flow inside the melt pool and heat loss caused by vaporization play pivotal roles to guarantee the accuracy of the predictions, and thus should be considered in the thermal model. Neglecting fluid flow and vaporization leads to nearly 100% difference in cooling rate during solidification, and 20% difference in cooling rate after solidification from the results. With the most accurate thermal model, surface topographies of the melt tracks are predicted and quantitatively analyzed. Using the Kurz-Fisher model, the primary dendrite arm spacing is predicted based on the thermal gradient and solidification rate predictions, while elemental segregation is predicted using the Scheil-Gulliver model and a non-equilibrium solidification model. Additionally, it is shown that increasing scan speed inhibits elemental microsegregation.

Process−property relationships in additive manufacturing (AM) play critical roles in process control and rapid certification. In laser-based directed energy deposition, powder mass flow into the melt pool influences the cooling behavior and properties of a built part. This study develops predictive computational models that provide the microhardness of AM components processed with miscible dissimilar alloys, and then investigates the influence of varying process parameters on properties in experiments and modeling. Experimentally-determined clad dilution and microhardness results of Ni-based superalloy Inconel 718 clads deposited onto 1045 carbon steel substrates are compared to the values from a computational thermo-fluid dynamics (CtFD) model. The numerical model considers the fluidic mechanisms of molten metal during powder deposition and the resulting transient melt pool geometry changes. The model also handles the change in thermo-physical properties caused by the composition mixture between the powder and substrate materials in the melt pool. Based on the computed temperature and velocity distributions in the melt pool, cooling rate, dilution of the melt pool and microhardenss are evaluated. The capability to predict thermal histories in such models is calibrated and validated with experimental thermal imaging and microstructures of additive manufactured clads. In addition, the roles of cooling rate and alloy composition on the microhardness are examined. The results show that variation in microhardness is dominated by composition mixture between the powder and substrate materials, rather than cooling behavior or dendrite arm spacing at liquid-solid interface in laser deposited Inconel 718 on AISI 1045 carbon steel.

Metal powder-based Additive Manufacturing (AM) processes are increasingly used in industry and science due to their unique capability of building complex geometries. However, the immense computational cost associated with AM predictive models hinders the further industrial adoption of these technologies for time-sensitive applications, process design with uncertainties or real-time process control. In this work, a novel approach to accelerate the explicit finite element analysis of the transient heat transfer of AM processes is proposed using Graphical Processing Units. The challenges associated with this approach are enumerated and multiple strategies to overcome each challenge are discussed. The performance of the proposed algorithms is evaluated on multiple test cases. Speed-ups of about 100 ×–150 × compared to an optimized single CPU core implementation for the best strategy were achieved.

A novel multi-phase flow formulation using a level-set-based interface-capturing approach is proposed, focusing on addressing numerical challenges associated with the modeling of surface tension. The surface tension is handled through the continuum surface force model. The residual-based variational multiscale (RBVMS) formulation is employed to solve the coupled Navier–Stokes and level-set convection equations. The RBVMS formulation is discretized using either standard low-order finite elements, or Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS), which are higher-order accurate and smooth. The proposed method is applied to the simulation of 3D bubbles moving in viscous liquids with large density and viscosity ratios representative of common two-phase flow systems. The accuracy of the proposed method is assessed by comparing the results with analytical solutions, experimental data, and computational results, reported in the literature. In all cases IGA showed superior performance to standard finite elements; this superiority is attributed to the higher-order accuracy of IGA and its ability to directly and accurately compute, using smooth NURBS functions, the curvature term, which is a key ingredient the surface tension formulation. For single-bubble rising problems, the proposed approach produced accurate predictions of the terminal bubble shape, velocity and Reynolds number. The advanced nature of the new multi-phase flow formulation is demonstrated with a simulation of merging of two bubbles in the presence of a deforming free-surface.

Many important industrial processes, such as additive manufacturing, involve rapid mass, flow and heat transport between gas, liquid and solid phases. Various associated challenges, such as the large density ratio between gas and condensed phases, make accurate, robust thermal multi-phase flow simulations of these processes very difficult. In order to address some of the associated challenges, a computational framework for thermal multi-phase flows is developed based on the finite element method (FEM). A unified model for thermal multi-phase flows similar to the models widely used in the manufacturing community is adopted. The combination of the level-set method and residual-based variational multi-scale formulation (RBVMS) is used to solve the governing equations of thermal multi-phase flows. Phase transitions between solid and liquid phases, i.e., melting and solidification, are considered. Interfacial forces, including surface tension and Marangoni stress, are taken into account and handled by a density-scaled continuum surface force model. A robust fully coupled solution strategy is adopted to handle various numerical difficulties associated with thermal multi-phase flow simulations, and implemented by means of a matrix-free technique using Flexible GMRES. The mathematical formulation and its algorithmic implementation are described in detail. Four numerical test cases are presented to demonstrate the capability of the proposed formulation. The first case is a benchmark example of solidification of aluminum in a graphite mold, the second case is a thermo-capillary droplet migration problem, the third case is a spot laser melting problem, and the fourth case is the melting of metal with an interior gas bubble. The computational results are compared with analytical, experimental and simulation data from other researchers, with good agreement in cases where such data is available.

The level set method for modeling multi-fluid interfaces gives a simple approach for the simulation of multiphase flow problems. However, many of the components of this method, such as the redistancing of the level set function and discretization of the singular surface tension force, become more difficult on unstructured meshes in a control volume framework; furthermore, these operations are shown to lead to errors in conservation of mass of the individual phases, as well as unphysical currents near the interface. This paper presents a novel formulation for the level set method combined with a balanced-force algorithm using a control volume finite element method (CVFEM) for unstructured grids. A diffuse interface description is used, allowing a straightforward inclusion of surface tension forces; we show that by consistently evaluating the pressure gradient and surface tension, we are able to discretely balance these two forces and suppress any parasitic currents given a prescribed curvature. By converting the redistancing equation to a form that is suitable for CVFEM and enforcing a constraint directly linked with the phase fraction in each cell, we are able conserve mass and preserve the shape of the interface to a high degree of accuracy in multiphase flow problems with high density and viscosity ratios. The accuracy of the of our proposed method is assessed by comparing with benchmark results from the literature.

This paper presents our latest work on comprehensive modeling of process-structure-property relationships for additive manufacturing (AM) materials, including using data-mining techniques to close the cycle of design-predict-optimize. To illustrate the process-structure relationship, the multi-scale multi-physics process modeling starts from the micro-scale to establish a mechanistic heat source model, to the meso-scale models of individual powder particle evolution, and finally to the macro-scale model to simulate the fabrication process of a complex product. To link structure and properties, a high-efficiency mechanistic model, self-consistent clustering analyses, is developed to capture a variety of material response. The model incorporates factors such as voids, phase composition, inclusions, and grain structures, which are the differentiating features of AM metals. Furthermore, we propose data-mining as an effective solution for novel rapid design and optimization, which is motivated by the numerous influencing factors in the AM process. We believe this paper will provide a roadmap to advance AM fundamental understanding and guide the monitoring and advanced diagnostics of AM processing.

In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments.

Selective Electron Beam Melting (SEBM) is a promising powder-based metallic Additive Manufacturing (AM) technology. However, most powder-scale modeling efforts are limited to single track process, while it is also difficult to experimentally observe the interaction between tracks and layers. In this study, we develop an integrated modeling framework to investigate the SEBM process of multiple tracks and multiple layers. This approach consists of a Discrete Element model of powder spreading and a Computational Fluid Dynamics (CFD) model of powder melting. These two models exchange 3D geometrical data as a cycle to reproduce the manufacturing process of multiple tracks along various scan paths in multiple powder layers. This integrated modeling approach enables further understanding of how current tracks and layers interact with previous ones leading to inter-track/layer voids. It also incorporates more influential factors, particularly the layer-wise scan strategy. The inter-layer/track voids due to the lack of fusion are systematically discussed in light of our simulation results which qualitatively agree with experimental observations in literature.

Metallic powder bed-based additive manufacturing technologies have many promising attributes. The single track acts as one fundamental building unit, which largely influences the final product quality such as the surface roughness and dimensional accuracy. A high-fidelity powder-scale model is developed to predict the detailed formation processes of single/multiple-track defects, including the balling effect, single track nonuniformity and inter-track voids. These processes are difficult to observe in experiments; previous studies have proposed different or even conflicting explanations. Our study clarifies the underlying formation mechanisms, reveals the influence of key factors, and guides the improvement of fabrication quality of single tracks. Additionally, the manufacturing processes of multiple tracks along S/Z-shaped scan paths with various hatching distance are simulated to further understand the defects in complex structures. The simulations demonstrate that the hatching distance should be no larger than the width of the remelted region within the substrate rather than the width of the melted region within the powder layer. Thus, single track simulations can provide valuable insight for complex structures.

Additive manufacturing (AM) of titanium alloys is a rapidly growing field due to an increase in design flexibility of parts. However, AM parts are highly anisotropic in material microstructure and mechanical behavior due to the change of the local processing conditions in the build-up process. This study follows a link chain model to investigate the relationships between process parameters, cooling rate, porosity and mechanical behavior. The aim of this work is to present a framework that is inspired by the three-link chain model. The framework combines theoretical, computational and experimental approaches. We demonstrate this by using an in-house thermal simulator to link predicted cooling rates with micrographs describing experimental shape descriptors to develop a relationship between solidification cooling rate and porosity geometry. Finally, representative volume elements from predicted porosity maps allow for a prediction of mechanical properties at localized areas. The capability of being able to predict mechanical behavior of titanium alloys is demonstrated for the directed energy deposition process.

A concurrent multiscale method is developed to model time-dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved. Ensuring this energetic consistency among scales enables the implementation of high fidelity physics-based models at critical locations within the coarse-scale to temporally and spatially resolve highly complex and localized phenomena. To achieve this, only Neumann boundary conditions are applied over the fine scale domain, ensuring a conservative formulation. The coarse-scale solution is used to reconstruct these Neumann boundary conditions on the fine scale, which are then used to evolve a separate system of governing equations. The results on the fine scale are then sent back to the coarse scale through an energy-based homogenization scheme. Transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness, including the coupling of a phase field model at the fine scale to a coarse-scale heat equation.

Additive manufacturing (AM) methods for rapid prototyping of 3D materials (3D printing) have become increasingly popular with a particular recent emphasis on those methods used for metallic materials. These processes typically involve an accumulation of cyclic phase changes. The widespread interest in these methods is largely stimulated by their unique ability to create components of considerable complexity. However, modeling such processes is exceedingly difficult due to the highly localized and drastic material evolution that often occurs over the course of the manufacture time of each component. Final product characterization and validation are currently driven primarily by experimental means as a result of the lack of robust modeling procedures. In the present work, the authors discuss primary detrimental hurdles that have plagued effective modeling of AM methods for metallic materials while also providing logical speculation into preferable research directions for overcoming these hurdles. The primary focus of this work encompasses the specific areas of high-performance computing, multiscale modeling, materials characterization, process modeling, experimentation, and validation for final product performance of additively manufactured metallic components.

Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction–advection–diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.