Twin-roll casting (TRC) is a process in which liquid metal is introduced directly between counter-rotating water-cooled rolls, where it solidifies and is rolled to a strip having final thickness of 3 to 8 mm. TRC for aluminum is best suited to those alloys having a narrow freezing range with little susceptibility to hot tearing, such as 1XXX, 3XXX, 5XXX, and 8XXX. TRC offers advantages over conventional DC casting followed by hot and cold rolling for these alloys due to its lower capital cost, and decreased downstream processing operational cost and energy consumption, since hot rolling is not required. The microstructure formed in the strip must be carefully controlled, because as a near-net shape product used mostly for non-age-hardenable alloys, there is limited opportunity to modify it by subsequent processing. In particular, the near-surface microstructure has a strong effect on performance in forming applications. In this article, we present a computational model of TRC, and validate it for AA1050 aluminum alloy in a production environment. The novel aspect of this work is that the model is used to predict the final microstructure and crystallographic texture of the cast strip. The model is validated in plant trials for strip cast at a range of thicknesses, casting speeds, and caster setup by comparing the predicted microstructure, texture, and process outcomes such as roll separating force and forward slip to their corresponding measured values. We then apply the validated model to explore process parameters outside the standard practices, including feed inlet setback, casting speed, metal inlet temperature, and changing roll material to demonstrate how the microstructure and texture can be controlled via these parameters.

We report on a dendrite orientation transition (DOT) discovered in the Al-Ge system by conducting isothermal solidification experiments in thin samples under slow cooling conditions. The DOT was revealed using a combination of in situ X-radiography imaging and post-mortem electron backscatter diffraction. In Al-20 wt% Ge the primary arms grow along (100), whereas in Al-46 wt% Ge the primary arms grow along < 110 >. At an intermediate composition of Al-29 wt% Ge, we observe both directions growing simultaneously. Phase-field simulations in which the solid-liquid interfacial energy anisotropy was systematically varied to correspond with the composition changes reproduced the experimentally observed microstructures. The remarkable agreement between the experimental observations and the simulations provides strong evidence that the DOT in this alloy system is caused by modification of surface energy anisotropy with increasing Ge content. Furthermore, we show that the confinement due to the thin sample geometry influences the selection of the primary growth directions, so that different growth morphologies develop depending on the orientation of the crystal in the sample. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The determination of the shape of a solid crystal in equilibrium with its melt was first described by Wulff using a geometric construct. Mathematical descriptions were later developed. In this note, some of the various methods used to compute the Wullf shape are described. Particular attention is paid to the determination of forbidden orientations for crystals with large anisotropy, and the calculation of their Wulff shapes. 1 Wulff’s construction Wulff proposed without proof that the equilibrium shape of crystal suspended in its melt could be obtained using the following geometric construction. Begin with a polar plot of the surface energy γs`(n), where n is a unit vector in a direction defined in the crystal coordinate system r = nγs`(n) (1) The Wulff shape is constructed by placing a plane perpendicular to n at each point on the surface defined by r. The locus of all of the interior points of these tangent planes is the Wulff shape. It should be obvious that if γs` is isotropic, then the Wulff shape is a sphere, coinciding with the polar plot. Let us illustrate this with two examples in 2-D, for a crystal having four-fold symmetry. Suppose that the anisotropic surface energy γs` is given by γs`(θ) = γ 0 s` [1 + ε4 cos(4φ)] (2) where ε4 is a measure of the strength of the four-fold anisotropy. Fig. 1 illustrates the Wullf construction for ε4 = 0.05 and 0.12. Consider first the case ε4 = 0.05, presented in Fig. 1(a). The polar plot of γs`, normalized by γ0 s`, is plotted in red. In the upper half plane, the perpendicular planes (actually, lines in 2-D) are shown as dashed black lines for several points on the gamma plot in the upper half-plane. The Wulff shape is then shown in blue. Because the anisotropy for this case is just 5%, the deviation of the Wulff shape from the gamma plot is fairly small. Fig. 1(b) shows the more interesting case ε4 = 0.12. The larger value of anisotropy leads to much larger deviation of the Wulff shape from the gamma plot. One can also see at the intersection of the Wulff shape with the coordinate axes, the construct produces a shape where a radial line intersects the Wulff shape at multiple points. The triangular-shaped regions outside of the inner convex hull, sometimes called “ears’,” correspond to orientations that cannot be part of the equilibrium shape, sometimes called “forbidden orientations.”

This article describes the interaction of thermodynamics, heat transfer, and mass transfer in solidification processes. The thermodynamics and equilibrium of solutions is discussed, including methods for computation of equilibrium phase diagrams. The resulting relations between temperature and composition are used in the analysis of heat and mass transfer processes associated with solidification. We then consider morphological stability of the moving interface, to demonstrate the physics that leads to microstructural pattern formation. Finally, some computational methods for microstructures are discussed, including examples of solidification in binary alloys.

Due to the variations in the local solidification conditions in typical industrial casting processes, dendrites grow under transient rather than steady-state conditions. In this study, the phase-field method was used to study the evolution of secondary dendrite arms of Fe-0.3 wt.% C alloy during transient directional solidification imposed by decreasing the pulling velocity. We find that the dendrite under transient growth conditions is different from the steady-state dendrite, with smaller selection parameter e and the dendrite envelope inside the parabola scaled by the tip radius. The secondary arms undergo a ripening process in which other secondary arms remelt by shrinking from their tips, rather than by detachment from the primary stalk. The surviving arms are finer than those found under steady-state growth conditions, and the size of the surviving arms decreases with decreasing growth velocity.

This study investigates the use of interface Peclet number P=w/(Dl/Vtip), to determine the interface width (w) used in phase-field simulations, where Dl is the liquid diffusivity and Vtip is the tip velocity. The maximum simulation interface width (wmax) under varied growth conditions was analysed via convergence analysis and it was found that there is a limit of P for the maximum interface width at various velocities. Converged results can be obtained only when w<wmax=0.075Dl/Vmax where Vmax is the maximum growth velocity during transient solidification. The effect of the inclusion of finite solid diffusivity on the P limit in selecting wmax was analysed, and little influence was observed.

In directional solidification experiments on hypoperitectic Cu-Sn alloys at low velocity and high thermal gradient, both lamellar and fibrous coupled peritectic growth patterns have been observed. Two phenomena that had not been observed in previous experiments on other alloy systems are investigated here with the help of different modeling approaches. The mean volume fraction of primary phase alpha,(g) over bar (alpha), as determined by X-ray microtomography, decreases with solidification distance over the entire length of the coupled zone, but is always much larger than that expected from the equilibrium phase diagram. Moreover, oscillations in (g) over bar (alpha), with a spatial periodicity approximately equal to the lamellar spacing are also observed. The first observation is explained semi-quantitatively by a simple ID diffusion model, which reveals that the onset of coupled growth occurs during the initial transient of the primary phase planar front growth. A two-dimensional phase-field model is used to monitor the subsequent microstructure evolution, and shows that the lamellar structure exhibits collective 1-lambda oscillations. In agreement with previous studies, it was found that these oscillations lead to stable coupled growth only for a limited range of the control parameters. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Various physical interfacial phenomena occur during the process of welding and influence the final properties of welded structures. As the features of such interfaces depend on physics that resolve at different spatial scales, a multiscale and multiphysics numerical modeling approach is necessary. In a collaborative research project Modeling of Interface Evolution in Advanced Welding, a novel strategy of model linking is employed in a multiscale, multiphysics computational framework for fusion welding. We only directly link numerical models that are on neighboring spatial scales instead of trying to link all submodels directly together through all available spatial scales. This strategy ensures that the numerical models assist one another via smooth data transfer, avoiding the huge difficulty raised by forcing models to attempt communication over many spatial scales. Experimental activities contribute to the modeling work by providing valuable input parameters and validation data. Representative examples of the results of modeling, linking and characterization are presented.

During welding, work-pieces are melted to form a weld pool and are joined upon solidification. The quality of the welded product is largely determined by the solidified microstructure and solute distribution. In recent years phase-field (PF) models have been developed to simulate solidification structure evolution and microsegregation. However many input data for the PF simulations are difficult to measure, including at the nanoscale the solid-liquid interfacial energy and its anisotropy, and at the macroscale the solidification conditions. In this study, an integrated scheme is proposed to resolve the above challenges by linking nanoscale molecular dynamics modelling (MD) and mesoscale front tracking (FT) modelling to the PF modelling. The approach is demonstrated in a case study in which the solidified structures and solute distributions are simulated in the weld pool for Fe-0.3wt. %C steel.

In Part I of this article, the role of the Zn content in the development of solidification microstructures in Al-Zn alloys was investigated experimentally using X-ray tomographic microscopy. The transition region between \({\langle{100}\rangle}\) dendrites found at low Zn content and \({\langle{110}\rangle}\) dendrites found at high Zn content was characterized by textured seaweed-type structures. This Dendrite Orientation Transition (DOT) was explained by the effect of the Zn content on the weak anisotropy of the solid–liquid interfacial energy of Al. In order to further support this interpretation and to elucidate the growth mechanisms of the complex structures that form in the DOT region, a detailed phase-field study exploring anisotropy parameters’ space is presented in this paper. For equiaxed growth, our results essentially recapitulate those of Haxhimali et al.[1] in simulations for pure materials. We find distinct regions of the parameter space associated with \({\langle{100}\rangle}\) and \({\langle{110}\rangle}\) dendrites, separated by a region where hyperbranched dendrites are observed. In simulations of directional solidification, we find similar behavior at the extrema, but in this case, the anisotropy parameters corresponding to the hyperbranched region produce textured seaweeds. As noted in the experimental work reported in Part I, these structures are actually dendrites that prefer to grow misaligned with respect to the thermal gradient direction. We also show that in this region, the dendrites grow with a blunted tip that oscillates and splits, resulting in an oriented trunk that continuously emits side branches in other directions. We conclude by making a correlation between the alloy composition and surface energy anisotropy parameters.

The Phase-Field Crystal (PFC) model represents the atomic density as a continuous function, whose spatial distribution evolves at diffusional, rather than vibrational time scales. PFC provides a tool to study defect interactions at the atomistic level but over longer time scales than in molecular dynamics (MD). We examine the behavior of the PFC model with the goal of relating the PFC parameters to physical parameters of real systems, derived from MD simulations. For this purpose we model the phenomenon of the shrinking of a spherical grain situated in a matrix. By comparing the rate of shrinking of the central grain using MD and PFC we obtain a relationship between PFC and MD time scales for processes driven by grain boundary diffusion. The morphological changes in the central grain including grain shape and grain rotation are also examined in order to assess the accuracy of the PFC in capturing the evolution path predicted by MD.

The project Modelling of Interface evolution in advanced Welding (MIntWeld) is a 4-year international research project funded by the European Commission under their FP7 programme. Its main target is to develop a numerical toolbox which can be used to predict the evolution of interfaces during welding. There are various interfaces involving multiple phenomena and different spatial scales, which can be simulated using corresponding numerical modelling methods respectively. The modelling methods include quantum dynamics, molecular dynamics, phase field, phase field crystal, computational fluid dynamics, phase transformation and heat transfer, thermodynamics, continuum mechanics and life and defects prediction. Although each modelling method is based on different physical theories and involves different scales, they are not isolated. Therefore, this project aims to design a common framework which couples each model with the upstream and/or downstream model at the relevant neighbouring length scales. The data exchange framework which underpins the coupling of the models is described, and typical examples addressing the solution to the challenges faced, such as those of data interpolation between one discretisation of the computational domain and another, are discussed. Initial successes from the model-linking efforts of the authors are also presented.

With a few exceptions, phase-field simulations of dendritic growth in cubic materials have been modeled using simple expressions for the interfacial energy anisotropy and with strong anisotropy. However, recent experimental results show that the Dendrite Orientation Transition (DOT) observed in Al-Zn alloys by Gonzales and Rappaz [Met. Mat. Trans. A37 (2006) 2797] occurs at weak anisotropy, and modeling these results requires at least two anisotropy parameters. In the present work, we solve the corresponding phase-field model on an adaptive grid, after measuring and compensating for the grid anisotropy. A systematic scan of equiaxed growth simulations was performed in the range of the anisotropy parameter space where the transition is expected. We find separate domains of existence of ⟨100⟩ and ⟨110⟩ dendrites, similar to those previously reported by Haxhimali et al. [Nat. Mat. 5 (2006) 660] for pure materials. In the so-called hyperbranched regime, lying between the ⟨100⟩ and ⟨110⟩ regions, we observe a competition between ⟨100⟩ and ⟨110⟩ growth directions, but no seaweed structures. Directional solidification simulations showed the stabilizing effect of the thermal gradient on the twofold splitting of ⟨110⟩ dendrites, and the importance of the choice of anisotropy parameters. We also found a strong dependence between the orientation of the crystal axes with respect to the thermal gradient and the actual growth direction. Finally, 3-dimensional seaweed microstructures were modeled for the first time, demonstrating that this pattern is a result of not only the values of anisotropy parameters, but also a consequence of directional solidification.

We employ a recently developed model for the adaptation of cortical bone in response to mechanical loading to study the effect of loading frequency on the computed response, and we compare our results to previous experimental measurements on rat ulnae. We represent the cortical bone as a poroelastic material with orthotropic permeability. Bone adaptation in the model is related to a mechanical stimulus derived from the dissipation energy of the poroelastic flow induced by deformation. We account for a non-locality in the mechanotransduction of osteocytes present in the lacunae by using a “zone of influence.” Calculations are done using the finite element method applied to a rat ulna whose geometry is obtained from micro-computed tomography images. We show that the change in the second moment of inertia of the cross-section increases non-linearly and saturates at higher frequency range. The numerical results are then compared quantitatively to experimental data from the literature. Finally, we examine the role of local narrowing of intramedullary canal in our specific ulna in the development of local irregularities in growth.

We present a finite element study of a poroelastic rectangular beam subjected to oscillatory bending loads. This geometric model is chosen for simplicity, as an idealized representation of cortical bone. We then propose the use of the dissipation energy of the poroelastic flow as a mechanical stimulus for bone adaptation, and show that it can predict the effect of frequency of the applied load. Surface adaptation in the model depends on the weighted average of the mechanical stimulus in a "zone of influence" near each surface point, in order to incorporate the non-locality in the mechanotransduction of osteocytes present in the lacunae. We show that the dissipation energy stimulus and the resulting increase in second moment of inertia of the cross section increase linearly with frequency in the low frequency range (less than 10 Hz) and saturate at the higher frequency range (greater than 10 Hz). Similar non-linear adaptation frequency response also has been observed in numerous experiments. Our framework is readily extended to the modeling of cortical bone using actual bone geometries.

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foamlike behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.