Search

The prediction of the equilibrium and metastable morphologies during the solidification of Ni-based superalloys on the mesoscopic scale can be performed using phase-field modeling. In the present paper, we apply the phase-field model to simulate the evolution of solidification microstructures depending on undercooling in a quasi-binary approximation. The results of modeling are compared with experimental data obtained on samples of the alloy Inconel 718 (IN718) processed using the electromagnetic leviatation (EML) technique. The final microstructure, concentration profiles of niobium, and the interface-velocity–undercooling relationship predicted by the phase field modeling are in good agreement with the experimental findings. The simulated microstructures and concentration fields can be used as inputs for the simulation of the precipitation of secondary phases.

Tool steels are martensitic steels alloyed with carbide forming elements, thus having high strength, hardness and wear resistance. These characteristics, however, make them costly materials to shape into complex geometries. Laser powder bed fusion (PBF-LB) enables the consolidation of near-net-shape complex shapes from powders, which is a highly resource efficient way of producing tools. However, processing tool steels with PBF-LB is problematic due to hardening and segregation generated during the process leading to high stresses and eventually to cracking. To diminish these problems, we utilized a tailored high temperature building platform in PBF-LB to process gas atomized high carbon tool steels such as K110, S600 and 1.4122. Calphad method was used to evaluate the stress formation and cracking tendency of these alloys. The microstructure, hardness and tendency to form residual stresses of the manufactured samples were characterised. Properties comparable to conventionally manufactured quenched and annealed tools steels were achieved.

Nearly all commercially available alloys have been developed for manufacturing processes other than additive manufacturing. Most of those alloys are not suitable for laser powder bed fusion (L-PBF) processing due to the non-weldable nature of the alloys developed for casting, forging, and machining. Even some weldable alloys can be difficult to produce with L-PBF because the characteristics of L-PBF, such as highly concentrated heat input and the extremely high cooling rate, can lead to very high residual stresses and cracking. In order to speed up the development process of new alloys for additive manufacturing, a powder-free evaluation method was used to evaluate the materials processing window and susceptibility to cracking. Single tracks were scanned with an L-PBF machine onto H13 steel substrates. The substrate condition was varied, and its effect on melt pool geometry and cracking behavior was evaluated. The results clearly show that thermal history of the substrate influences its thermal conductivity, affecting melt pool volume. Melting point of the substrate was not found as significant factor as thermal conductivity on melt pool dimensions. Cracking type was noted to differ between substrates. If printability is assessed without powder, the substrate microstructure should be similar to rapidly solidified material. It is recognized that single-track tests are not adequate in terms of residual stress evaluation, but they can give valuable information about materials’ melting, segregation, and micro-scale cracking behavior.

Microstructure is the origin of the properties and performance for additively manufactured metals. Rapid solidification enable the formation of various grain/phase structures as well as solute segregation and initial dislocation structures that all contribute to the properties of the alloy. We present the following methods in this work. An effective way to approach process-structure-properties linkage in rapid solidification is to utilize a phase field solidification model coupled with a thermomechanical crystal plasticity. This allows us to assess both intra-grain/polycrystal level dislocation/stress heterogeneities introduced during solidification and residual stresses. Single-track laser melting is a method to analyze materials printability. In this scope, crystal plasticity is a tool to investigate heterogeneities and cracking tendency of solidified microstructures during cooling. Finally, at the part level it is possible to utilize homogenized/embedded crystal plasticity models to provide the thermomechanical response of the material. We review the pre-mentioned multiscale model outputs, interactive dialogue, and opportunities.

Rapid solidification kinetics of dilute Al–Cu alloys is simulated using a quantum mechanics based bond-order potential (BOP), in free solidification conditions, to determine kinetic and thermodynamic properties of solidification, as well as point defects and chemical ordering of the solidified structures. We measure the anisotropic kinetic coefficient, anisotropic solid–liquid interface energy, as well as solute trapping kinetics in terms of partition coefficient versus velocity and solute drag coefficient. Furthermore, solid–liquid interface free energy and its anisotropy are measured in equilibrium simulations, showing reasonably good agreement with previous studies. We also verified the self-consistency of the MD simulations, by comparing the interfacial temperature vs. velocity to that predicted by the continuous growth model. These solid–liquid interface properties are important for quantitative parametrization of larger scale solidification modeling techniques such as phase field models. We also investigated the point defect content, local chemical ordering, and local crystalline structures in the rapidly solidified samples. We found clustering of solute with vacancies, whereas copper atoms repelled each other in these dilute alloy simulations. In addition to vacancies, a large number of interstitials were found. In solidification velocities approaching the complete solute trapping regime, we found that the vacancies and interstitials formed in conjunction, i.e. as Frenkel pairs. Finally, in addition to FCC, we detected BCC and HCP phases, where the latter two were accompanied by an increase in local copper content. Understanding the formation of point defects and their relationship to chemical ordering is an important step towards controlling the formation of pre-precipitates and precipitates, which are an important strengthening mechanism for aluminum–copper alloys.

Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline orientation. As these defects critically affect the material’s mechanical properties and performance features, it is important to understand the defect formation mechanisms, and how they depend on the solidification conditions and alloying. To illuminate the formation mechanisms of the rapid solidification induced crystalline defects, we conduct a multiscale modelling analysis consisting of bond-order potential-based molecular dynamics (MD), phase field crystal-based amplitude expansion simulations, and sequentially coupled phase field–crystal plasticity simulations. The resulting dislocation densities are quantified and compared to past experiments. The atomistic approaches (MD, PFC) can be used to calibrate continuum level crystal plasticity models, and the framework adds mechanistic insights arising from the multiscale analysis. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Rapid solidification experiments on thin film aluminum samples reveal the presence of lattice orientation gradients within crystallizing grains. To study this phenomenon, a single-component phase-field crystal (PFC) model that captures the properties of solid, liquid, and vapor phases is proposed to model pure aluminium quantitatively. A coarse-grained amplitude representation of this model is used to simulate solidification in samples approaching micrometer scales. The simulations reproduce the experimentally observed orientation gradients within crystallizing grains when grown at experimentally relevant rapid quenches. We propose a causal connection between formation of defects and orientation gradients.

Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) of Aziz et al. [1] is a popular sharp interface theory. By modulating the so-called anti-trapping current and using asymptotic analysis, we show how to quantitatively map the thin interface behavior of an ideal dilute binary alloy phase field model onto the CGM kinetics. We present the parametrizations that allow our phase field model to map onto the sharp interface kinetics of the CGM, both in terms of partition coefficient k ( V ) and kinetic undercooling. We also show that the mapping is convergent for different interface widths, both in transient and steady state simulations. Finally we present the effect that solute trapping can have on cellular growth in directional solidification. The presented treatment for solute trapping can be easily implemented in different phase field models, and is expected to be an important feature in future studies of quantitative phase field modeling in quasi-rapid solidification regimes, such as those relevant to metal additive manufacturing.

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-diffusion are quantitatively consistent with earlier theoretical work, with grain boundary energy being controlled through a simple solid-solid interaction parameter. Moreover, when considering polycrystalline aggregates and their coarsening, we show that the kinetics follow the expected parabolic growth law. Finally, we demonstrate how this vector order parameter model can be used to describe nucleation in polycrystalline systems via thermal fluctuations of the vector order parameter, a process that cannot be treated consistently with multiphase or multi-order-parameter based phase field models. The presented vector order parameter model serves as a practical and efficient computational tool for simulating polycrystalline materials. We also discuss the extension of the order parameter to higher dimensions as a simple method for modeling multiple solid phases.

Fatigue remains a challenge especially for high end metal AM parts and materials. From a design perspective, the fatigue limit of an AM solution can be improved upon by optimizing the manufacturing process for a certain material and part. In addition, improved accuracy of design methodologies aids in capturing the features critical for fatigue and quantifies their significance to desired part lifetime as well as providing a basis for their avoidance. In current work we present an overall concept merging thermomechanical process and powder bed solidification modeling to micromechanical analysis of fatigue of the resulting material microstructure. Material features critical to fatigue, particularly surface roughness, internal defects such as porosity and cracks and on the other hand inclusions, can be assessed directly on the basis of AM part microstructure with respect to the resulting fatigue limit. Case analyses consist of maraging steel and nickel alloys. The overall scheme provides a basis for optimization of metal AM solutions against fatigue and multiscale modeling founded basis for fatigue design.

Rapid solidification gives rise to solute trapping, which decreases solute partitioning and alters equilibrium solidification velocity-undercooling relationships. These effects influence microsegregation, solidification morphology, and the emergent microstructure length scales. Here, we review solute trapping and solute drag in rapid solidification in terms of theory, simulation methods, and experimental techniques. The basic theory to describe solute trapping is contained in the continuous growth model. This model breaks down at high solidification velocities, where solidification transitions abruptly to complete trapping, a limit that can be captured with the local nonequilibrium model. Solute trapping theories contain unknown parameters. Their determination from atomistic simulations or pulsed laser melting experiments is discussed. Microstructural evolution in rapid solidification can be readily investigated with the phase-field method, various alternatives of which are presented here. Uncertainties related to kinetic parameters and heat transfer during rapid solidification can be studied by comparing phase-field simulations to dynamic transmission electron microscopy observations.

Selective laser melting (SLM) is a novel manufacturing technique for producing complex parts, with unique mechanical properties that result from rapidly solidified structures. For SLM of austenitic 316L stainless steel, the reported mechanical properties have a large scatter, which reflects an incomplete understanding and control of the process-structure-properties linkage. This paper demonstrates how material micromechanical behavior --- including length scale dependent yield strength and hardening --- is linked to rapid solidification microstructure, and how this structure emerges from typical SLM process conditions. This linkage is produced by concurrently coupling phase field simulations with crystal plasticity modeling. In particular, the evolution of rapidly solidified SLM microstructures is described with a quantitative phase field model with imposed solute trapping kinetics. A range of process conditions are considered by varying the thermal gradient and pulling speed driving solidification. The phase field model can predict morphological transitions (dendritic-cellular-planar), microsegregation, and emergent microstructure length scales, as function of process conditions. Both 2D and 3D phase field simulations are conducted, yielding microstructure morphologies and cell spacing Vs. cooling rate data that are in good agreement with the available experiments in the literature. Micromechanical response of domains characterized by cellular subgrain solidification structures, generated from phase simulations, are analyzed with a Cosserat crystal plasticity model which includes calibrated length-scale and hardening effects, and a realistic description of solid solution strengthening. It is shown that length scale characteristics (cell spacing and grain size) and solute segregation greatly influence the overall hardening behavior, and also affect plastic localization and evolution of geometrically necessary dislocation (GND) type hardening. We conclude with a study of the micromechanical behavior of a polycrystalline structure, focusing on the effects of cell spacing and grain size, and the relative orientation between crystalline lattices and cells. Our results suggest that the material strength is more sensitive to the cell spacing (microstructural length scale) than to the magnitude of solute segregation. The concurrently coupled phase field-crystal plasticity modeling scheme is presented as a proof-of-concept for systematically investigating and discovering new compositions, processes and microstructures for additive manufacturing of metals.

Phase field (PF) models are one of the most popular methods for simulating solidification microstructures due to their fundamental connections to the physics of phase transformations. However, these methods are numerically very stiff due to the multiple length scales in a solidifying material, from the nanoscopic solid-liquid interface, to dendritic structures on the order of hundreds of microns. While this problem can be greatly alleviated by thin-interface analytical treatments of the PF equations, additional numerical methods are required to explore experimentally relevant sample sizes and times scales. It was shown about 18 years ago that the use of dynamic adaptive mesh refinement (AMR) can alleviate this problem by exploiting the simple fact that the majority of the solidification kinetics occur at the solid-liquid interface, which scales with a lower dimensionality than the embedding system itself. AMR methods, together with asymptotic analysis, nowadays provide one of the most efficient numerical strategies for self-consistent quantitative PF modelling of solidification microstructure processes. This paper highlights the latest developments in the AMR technique for 3D modelling of solidification using classical phase field equations. This includes a move away from finite element techniques to faster finite differencing through the use of dynamic mini-meshes which are each associated with each node of a 3D Octree data structure, and distributed MPI parallelism that uses a new communication algorithm to decompose a 3D domain into multiple adaptive meshes that are spawned on separate cores. The numerical technique is discussed, followed by demonstrations of the new AMR algorithm on select benchmark solidification problems, as well as some illustrations of multi-phase modelling using a recently developed multi-order parameter phase field model.

A coupled phase field and crystal plasticity model is established to analyze formation of dislocation structures and residual stresses during rapid solidification of additively manufactured 316L stainless steel. The work focuses on investigating the role of microsegregation related to the intra-grain cellular microstructure of 316L. Effect of solidification shrinkage is considered along with dislocation mediated plastic flow of the material during solidification. Different cellular microstructures are analyzed and the characteristics of the cell core, boundary and segregation pools are discussed with respect to heterogeneity of dislocation density distributions and residual stresses. Quantitative comparison with experimental data is given to evaluate the feasibility of the modeling approach.

Single track scanning is a widely used method to evaluate the effects of rapid solidification of metals and to analyze their printability. Microstructure level stresses play a dominant role in causing material failure during deposition or poor performance on the finished product. This work formulates a thermomechanical crystal plasticity model capable of presenting microscale level evolution and residual state of stresses and strains in a single track event of selective laser melting. The present novel thermomechanical model is a vital piece of an overall workflow to analyze material properties and more complex performance inherent and dependent on the microstructure scale phenomena. The results show effectiveness of the model in addressing microscale residual stress heterogeneities dependent on the melt pool area thermal and microstructural evolution, including micromechanical phase transformations, and their interaction with the surrounding matrix on the studied H13 tool steel. The method is found exceptionally robust in terms of predicting microstructural residual stresses and deformation, while its greatest limiting feature is the requirement of prior solidified microstructure as an input for the computations.

We describe herein a nanocellulose-alginate hydrogel suitable for 3D printing. The composition of the hydrogel was optimized based on material characterization methods and 3D printing experiments, and its behavior during the printing process was studied using computational fluid dynamics simulations. The hydrogel was biofunctionalized by the covalent coupling of an enhanced avidin protein to the cellulose nanofibrils. Ionic cross-linking of the hydrogel using calcium ions improved the performance of the material. The resulting hydrogel is suitable for 3D printing, its mechanical properties indicate good tissue compatibility, and the hydrogel absorbs water in moist conditions, suggesting potential in applications such as wound dressings. The biofunctionalization potential was shown by attaching a biotinylated fluorescent protein and a biotinylated fluorescent small molecule via avidin and monitoring the material using confocal microscopy. The 3D-printable bioactivated nanocellulose-alginate hydrogel offers a platform for the development of biomedical devices, wearable sensors, and drug-releasing materials.

Erosion-corrosion, the combined loss of material due to combined effects of particle erosion and electrochemical corrosion, has due to its complexity largely evaded modeling efforts. Assessment of the synergy between erosion and corrosion leading in extreme conditions to far greater material losses than for the mechanisms individually has proven elusive. Various analytical and semi-empirical approaches have been proposed with varying degree of success, but it has been a typical outcome that the predictive capabilities or transferability of such modeling efforts have been less than desirable. In current work this aspect is addressed and improvement is seeked by introducing a concept merging computational fluid dynamics (CFD) and the point defect model (PDM) to a micromechanical finite element (FE) formulated wear model. The implemented approach is utilized to study erosion-corrosion in a stirring tank configuration where flow velocity, abrasive particle type, solution chemistry, temperature and pH are varied. In order to investigate model performance experimental work supplemented by a detailed characterization regime is performed to produce a dataset for model validation for a wear resistant steel with two different abrasives, quartz and chromite particles. The respective experiments indicative of industrially relevant erosion-corrosion conditions are modelled and the Results are directly compared to model predictions. The erosion-corrosion model is found to produce satisfactory results in relation to the validation tests and predict the main trends of the experimental dataset appropriately. The capabilities and approximations underlying the introduced erosion-corrosion model are evaluated, discussed and future development needs identified.

A binary alloy multi-order parameter phase field model is used to study rapid solidification in Al-Cu under conditions corresponding to recent dynamic transmission electron microscopy (DTEM) experiments. The phase field model’s sharp interface limit is set through a recent matched asymptotic analysis to follow the solute trapping and interface undercooling kinetics of the Continuous Growth Model (CGM). The phase field model convergence to the CGM sharp interface model is investigated, and based on this an optimal interface width is chosen to simulate the DTEM experimental conditions. The temperature distribution used in the phase field simulations is taken from an analytic expression extracted from experiments. Simulated solidification structures are compared to experiments, including time-resolved DTEM images and post-mortem TEM-based image quality and orientation maps. We find that the large scale morphological features of the simulated microstructures are in good agreement with the experiments, and the corresponding concentration profiles that emerge are in qualitative agreement with experiments. These results show that phase field simulations, informed with DTEM experiments, provides a promising framework to investigate rapidly solidified microstructure evolution and solute segregation, and to calibrate hard-to-determine solidification parameters.

A major challenge in additive manufacturing is to relate process parameters and microstructure. This relation can be explored with phase field method coupled to a larger scale heat transfer model. Phase field method is the state-of-the-art method to simulate the kinetics of solidification, including the development of microstructural features including grain morphology, solute distribution, and formation of metastable phases. In this work we study the selective laser melting (SLM) of a nickel based superalloy. Taking into account the major segregating chemical elements, the solidification patterns are modeled using the phase field method. The large scale heat transfer model is used to estimate the temperature distribution and history, specifically thermal gradients and cooling rates.

Cellulose-based materials are a promising biomaterial candidate for certain medical applications, such as wound-care products. We studied the potential of nanocellulose-based hydrogels for use as pastes in the 3D printing of structures with special functionality for medical applications. We used computational fluid dynamics (CFD) to relate the rheological properties of the paste and the printing parameters to the resolution and quality of the printed specimen. The considered printing paste was two times microfluidized bleached kraft pulp pretreated with TEMPO-mediated oxidation. Transient and steady-state rheometry was carried out to obtain parameters for rheological modelling, and capillary viscosimetry was used to verify the limiting behavior at very high shear rates. 3D printing experiments were carried out for validation, to determine the dependency between operating pressure and mass flow within the nozzle, as well as the printing speed and line resolution at constant operating pressure. Different levels of rheological description were considered for explaining the observed flow behavior. These include models with both instantaneous and history-dependent response to the flow conditions. We implemented separate CFD models for the flow conditions inside the printing head and during the deposition. Volume of fluid method was used to describe the interaction between the hydrogel and the surrounding air. The calculations were performed with the open source CFD package OpenFOAM. The rheometry showed that, under steady-state conditions, the nanocellulose hydrogel accurately follows power-law fluid behavior. However, transient experiments indicated that thixotropy plays a significant role in situations with rapidly varying shear rates. The CFD analysis of the printing head revealed that practical shear rates can reach much higher values than ones considered in conventional rheometry. The effect of thixotropy on the flow was studied both inside the printing head and during deposition. We demonstrated the feasibility of the models to describe the main elements of the 3D printing process. The models can be used to study the sensitivity of the printing resolution and specimen quality on the material properties and the printing parameters.

This work demonstrates an accurate model for solidification of WC-Co powder in thermal spray deposition, where particles-Typically metal or ceramic powder-are heated and propelled towards a substrate, leading to a thick and lamellar coating. The WC tends to dissolve partially while the cobalt is molten in flight, and upon impact, the cobalt solidifies rapidly. This leads to a microstructure with WC particles decreased in size, and the matrix phase-originally pure cobalt-is accompanied with tungsten semicarbide and Co-W-C carbide phases, which embrittles the coating. A simple diffusion model is used to model dissolution of WC in liquid cobalt during solidification, with a cooling rate typical to thermal spray deposition. We use a 2D phase field method to simulate the rapid solidification of WC particles immersed in liquid cobalt. We assume that the dendrites nucleate randomly in the liquid cobalt. Phase field simulations are used to predict a heterogeneous distribution of dendrites, their sizes, morphologies, alloying element distribution, and competitive growth of different phases. Our work presents a model that can be used to generate virtual microstructures of thermal spray coatings, and additionally, the model can be employed to model other powder consolidation and sintering processes, such as selective laser sintering.

The freedoms of additive manufacturing (AM) go beyond geometry, with metal AM it is possible to tailor powders, alloys, microstructures as well as processes and manufacturing parameters, to name a few. It is expected that with global data-driven optimization it becomes possible to tailor product and application specific metal AM solutions, subsequently significantly improving the competitiveness of respective AM products. In current work integrated computational materials engineering and machine learning (ML) are utilized to create a workflow for optimization of metal AM solutions. Physics-based models aid in the delivery of ML training data, and the resulting data-driven models are suited for fast and thorough optimization of metal AM products. Use case is presented with different performance metrics targeting critical product material properties which are optimized across the metal AM process to product performance chain.

Selective Laser Melting (SLM), a type of Additive Manufacturing (AM), is versatile manufacturing method especially for rapid prototyping. One big issue with the method is components material integrity. Various types of defects can be left inside the material after sintering process. These defects often have derogative effect on materials fatigue life time. In this paper different material defect types are identified from Scanning Electron Microscope (SEM) images. Defected areas are transferred to Finite Element Models (FEM). Simple uniaxial tension test is performed to the models and results are incorporated into low cycle fatigue life time prediction. Residual stresses play also significant role in material endurance. Simple process model in created in order to predict residual stress levels.

Interface structures are a key feature in developing modern composite material solutions with ever improved performance. To that effect, we present a nano-microstructural modeling approach for the WC-Co system which can include the interface structures of WC-Co and various other phases present in the microstructure, utilising a methodology which combines imaging based and synthetically generated nano-microstructures into an effective interface model for predicting the behavior and properties of the resulting composite material. The effective model comprises of a local model of the WC-Co interface interacting with a larger scale model of the WC-Co microstructure. The interface model consists of either layered modeling of the different phase structures (phases of WC, films due to doping of cemented carbides, binder phase and microstructure, segregated and carbide structures within the binder such as gamma or eta phases, oriented and/or gradient structures etc.) or utilization of locally defined spatial morphologies and properties in three-dimensional models. In this current work, two approaches are made available and demonstrated. Firstly, commonly identified interface structures can be assessed with the methodology via creation of synthetic carbide-carbide, carbide-binder or related microstructural characteristics. Secondly, the use of phase field analysis generated interface solute concentrations are used as an input from accompanying work by the authors. The results provide a linkage between the interface character of cemented carbide microstructures and their properties, for example with respect to compressive strength, fracture toughness and wear resistance. The results demonstrate the obvious importance of interface character and properties with respect to resulting material properties, and describe a toolset towards systematic inclusion of these features in a materials-by-design type of material development. The methodology presents a multiscale formalism for carrying out performance and application driven evaluation and tailoring of composite interfaces and mesostructures, carried out on the basis of the emerging engineering material properties.

Fatigue remains a challenge especially for high end metal AM parts and materials. From a design perspective, the fatigue limit of an AM solution can be improved upon by optimizing the manufacturing process for a certain material and part. In addition, improved accuracy of design methodologies aids in capturing the features critical for fatigue and quantifies their significance to desired part lifetime as well as providing a basis for their avoidance. In current work we present an overall concept merging thermomechanical process and powder bed solidification modeling to micromechanical analysis of fatigue of the resulting material microstructure. Material features critical to fatigue, particularly surface roughness, internal defects such as porosity and cracks and on the other hand inclusions, can be assessed directly on the basis of AM part microstructure with respect to the resulting fatigue limit. Case analyses consist of maraging steel and nickel alloys. The overall scheme provides a basis for optimization of metal AM solutions against fatigue and multiscale modeling founded basis for fatigue design.