8 Search Results

Here, we investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $$\textit{V}$$ decreases in time $$\textit{t}$$ as a power law $$V ~t^{–2/3}$$, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width $$Λ ≈ 5l_D$$, where $$l_D$$ is the diffusion length, needle crystals grow with a constant $$V < V_s$$, where $$V_s$$ is the free-growth needle crystal velocity, and approaches $$V_s$$ in the limit $$Λ \gg l_D$$.

Understanding rapid solidification behavior at velocities relevant to additive manufacturing (AM) is critical to controlling microstructure selection. Although in-situ visualization of solidification dynamics is now possible, systematic studies under AM conditions with microstructural outcomes compared to solidification theory remain lacking. Here we measure solid-liquid interface velocities of Ni-Mo-Al alloy single crystals under AM conditions with synchrotron X-ray imaging, characterize the microstructures, and show discrepancies with classical theories regarding the onset velocity for absolute stability of a planar solid-liquid interface. Experimental observations reveal cellular/dendritic microstructures can persist at velocities larger than the expected absolute stability limit, where banded structure formation shouldmore » theoretically appear. We show that theory and experimental observations can be reconciled by properly accounting for the effect of solute trapping and kinetic undercooling on the velocity-dependent solidus and liquidus temperatures of the alloy. Further theoretical developments and accurate assessments of key thermophysical parameters - like liquid diffusivities, solid-liquid interface excess free energies, and kinetic coefficients - remain needed to quantitatively investigate such discrepancies and pave the way for the prediction and control of microstructure selection under rapid solidification conditions.« less

We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Lambda and tip radius rho. While rho shows a good agreement between experimental measurements and dendrite growth theory, with rho similar to V-1/2, Lambda is observed to increase with V (partial derivative Lambda/partial derivative V > 0), in apparent disagreement withmore » classical scaling laws for primary dendritic spacing, which predict that partial derivative Lambda/partial derivative V <0. We show through simulations that this trend inversion for Lambda(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of partial derivative Lambda/partial derivative V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.« less

We study microstructure selection during during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. Here we explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ~V^$$-$$1/2, Λ is observed to increase with V (∂Λ/∂V > 0), in apparent disagreement with classical scaling laws for primarymore » dendritic spacing, which predict that ∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. Lastly, we explain the observed inversion of ∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.« less

Here, we present a three-dimensional (3D) formulation of the multiscale Dendritic Needle Network (DNN) model for dendritic microstructure growth. This approach is aimed at simulating quantitatively the solidification dynamics of complex hierarchical networks in spatially extended dendritic arrays, hence bridging the scale gap between phase-field simulations at the scale of a few dendrites and coarse-grained simulations on the larger scale of entire polycrystalline structures. In the DNN model, the dendritic network is represented by a network of branches that interact through the solutal diffusion field. The tip velocity V(t) and tip radius ρ(t) of each needle is determined by combiningmore » a standard solvability condition that fixes the product ρ²V and a solute flux conservation condition that fixes the product ρV² in 2D and ρV in 3D as a function of a solutal flux intensity factor ℱ(t). The latter measures the intensity of the solute flux in the dendrite tip region and can be calculated by contour (2D) or surface (3D) integration around the tip of each needle. We first present an extended formulation of the 2D DNN model where needles have a finite thickness and parabolic tips. This formulation remains valid for a larger range of tip Péclet number than the original thin needle formulation and is readily extended to 3D needles with paraboloidal tips. The 3D DNN model based on this thick-needle formulation is developed for both isothermal and directional solidification. Model predictions are validated by comparisons with known analytical solutions that describe the early transient and steady-state growth regimes. We exploit the power of the DNN model to characterize the competitive growth of well-developed secondary branches in 3D on the scale of the diffusion length. The results show that the length of active secondary branches increases as a power law of distance behind the tip with an exponent in good quantitative agreement with experimental measurements. Finally, we apply the model to simulate the three-dimensional directional solidification of an Al-7wt% Si alloy, which we directly compare to observed microstructures from microgravity experiments onboard the International Space Station. The predictions of selected microstructural features, such as dendrite arm spacings, show a good agreement with experiments. The computationally-efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at length and time scales relevant to solidification experiments and processes.« less

Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study

We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. The focus is on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. Here, the computationally efficient DNN model opens new avenuesmore » for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.« less