Modeling and Simulation of Microstructure Evolution for Additive Manufacturing of Metals: A Critical Review

Abstract Beam-based additive manufacturing (AM) of metallic components is characterized by extreme process conditions. The component forms in a line-by-line and layer-by-layer process over many hours. Locally, the microstructure evolves by rapid and directional solidification. Modeling and simulation is important to generate a better understanding of the resultant microstructure. Based on this knowledge, the AM process strategy can be adapted to adjust specific microstructures and in this way different mechanical properties. In this review, we explain the basic concepts behind different modeling approaches applied to simulate AM microstructure evolution of metals. After a critical discussion on the range of applicability and the predictive power of each model, we finally identify future tasks

A new approach of preheating and powder sintering in electron beam powder bed fusion

Preheating is an essential process step in electron beam powder bed fusion. It has the purpose of establishing a sintered powder bed and maintaining an elevated temperature. The sintered powder bed reduces the risk of smoke and in combination with the elevated temperature improves the processability. Today, the line-ordering preheating scheme is widely used. This scheme does not take the previously built layers into account and results in an inhomogeneous elevated temperature and consequently in a variety of sinter degrees, which is disadvantageous for the process. The main challenge is now to modify this scheme to establish a homogeneous temperature distribution. This study addresses this challenge and analyses as well as optimises this scheme. A GPU-parallelised thermal model reveals a heterogeneous temperature distribution during preheating because of varying thermal conditions within a build job. In addition, a work-of-sintering model predicts that the sinter degree of the current powder layer on top of previously consolidated material is smaller than on top of the surrounding powder bed. This work aims to invert this trend to improve powder re-usage and material consolidation. Consequently, this work proposes an extension of the current scheme, compensating for the specific energy loss with local adjustments to the energy input. This adaption results in a uniform temperature distribution and advantageous sintering. Applying the proposed numerical model proves to be an effective method to analyse the evolving process conditions and tailor the local energy input, thereby improving the efficiency of the preheating step

A CALPHAD-Informed Enthalpy Method for Multicomponent Alloy Systems with Phase Transitions

Solid–liquid phase transitions of metals and alloys play an important role in many technical processes. Therefore, corresponding numerical process simulations need adequate models. The enthalpy method is the current state-of-the-art approach for this task. However, this method has some limitations regarding multicomponent alloys as it does not consider the enthalpy of mixing, for example. In this work, we present a novel CALPHAD-informed version of the enthalpy method that removes these drawbacks. In addition, special attention is given to the handling of polymorphic as well as solid–liquid phase transitions. Efficient and robust algorithms for the conversion between enthalpy and temperature were developed. We demonstrate the capabilities of the presented method using two different implementations: a lattice Boltzmann and a finite difference solver. We proof the correct behaviour of the developed method by different validation scenarios. Finally, the model is applied to electron beam powder bed fusion—a modern additive manufacturing process for metals and alloys that allows for different powder mixtures to be alloyed in situ to produce complex engineering parts. We reveal that the enthalpy of mixing has a significant effect on the temperature and lifetime of the melt pool and thus on the part properties.German Research Foundation (DFG

Predictive Simulation of Process Windows for Powder Bed Fusion Additive Manufacturing: Influence of the Powder Bulk Density

The resulting properties of parts fabricated by powder bed fusion additive manufacturing processes are determined by their porosity, local composition, and microstructure. The objective of this work is to examine the influence of the stochastic powder bed on the process window for dense parts by means of numerical simulation. The investigations demonstrate the unique capability of simulating macroscopic domains in the range of millimeters with a mesoscopic approach, which resolves the powder bed and the hydrodynamics of the melt pool. A simulated process window reveals the influence of the stochastic powder layer. The numerical results are verified with an experimental process window for selective electron beam-melted Ti-6Al-4V. Furthermore, the influence of the powder bulk density is investigated numerically. The simulations predict an increase in porosity and surface roughness for samples produced with lower powder bulk densities. Due to its higher probability for unfavorable powder arrangements, the process stability is also decreased. This shrinks the actual parameter range in a process window for producing dense parts

Tensor Constructions of Open String Theories I: Foundations

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A_\infty algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a spacetime interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.Comment: 62 pages, LaTe

New Grain Formation Mechanisms during Powder Bed Fusion

Tailoring the mechanical properties of parts by influencing the solidification conditions is a key topic of powder bed fusion. Depending on the application, single crystalline, columnar, or equiaxed microstructures are desirable. To produce single crystals or equiaxed microstructures, the control of nucleation is of outstanding importance. Either it should be avoided or provoked. There are also applications, such as turbine blades, where both microstructures at different locations are required. Here, we investigate nucleation at the melt-pool border during the remelting of CMSX-4® samples built using powder bed fusion. We studied the difference between remelting as-built and homogenized microstructures. We identified two new mechanisms that led to grain formation at the beginning of solidification. Both mechanisms involved a change in the solidification microstructure from the former remelted and newly forming material. For the as-built samples, a discrepancy between the former and new dendrite arm spacing led to increased interdentritic undercooling at the beginning of solidification. For the heat-treated samples, the collapse of a planar front led to new grains. To identify these mechanisms, we conducted experimental and numerical investigations. The identification of such mechanisms during powder bed fusion is a fundamental prerequisite to controlling the solidification conditions to produce single crystalline and equiaxed microstructures

New Grain Formation by Constitutional Undercooling Due to Remelting of Segregated Microstructures during Powder Bed Fusion

A microstructure has significant influence on the mechanical properties of parts. For isotropic properties, the formation of equiaxed microstructures by the nucleation of new grains during solidification is necessary. For conventional solidification processes, nucleation is well-understood. Regarding powder bed fusion, the repeated remelting of previous layers can cause nucleation under some conditions that are not explainable with classical theories. Here, we investigate this nucleation mechanism with an unprecedented level of detail. In the first step, we built samples with single crystalline microstructures from Ni-base superalloy IN718 by selective electron beam melting. In the second step, single lines with different parameters were molten on top of these samples. We observed a huge number of new grains by nucleation at the melt-pool border of these single lines. However, new grains can only prevail if the alignment of their crystallographic orientation with respect to the local temperature gradient is superior to that of the base material. The current hypothesis is that nucleation at the melt-pool border happens due to remelting microsegregations from former solidification processes leading to constitutional undercooling directly at the onset of solidification. This study offers the opportunity to understand and exploit this mechanism for different manufacturing processes