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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.

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.

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.

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.