Dendritic needle network modeling of the Columnar-to-Equiaxed Transition. Part II: three dimensional formulation, implementation and comparison with experiments

International audienceThe dendritic needle network (DNN) model tracks the diffusion-controlled growth of branches in the hierarchically structured dendritic network, thereby bridging the well-separated scales traditionally simulated by phase-field and coarse-grained models. In particular, the DNN model relaxes the assumptions on the dendrite growth kinetics and grain structures commonly used in the coarse-grained models. In part I of this paper, we proposed a two-dimensional (2D) version of the DNN model and applied it to investigate the Columnar-to-Equiaxed Transition (CET) to clarify the influence of these assumptions on the prediction of the CET. In order to overcome the limitations inherent in a 2D model, part II presents here a fully three-dimensional (3D) version of the DNN model and its application to the CET. After validation of the 3D model, we perform simulations to study the solidification of Al-7wt.%Si alloy and compare the results to the experimental measurements conducted on board of the International Space Station (ISS) in the framework of the CET in SOLidification processing project. The comparison shows that the present 3D DNN model is able to provide quantitative prediction of the position and the type of CET at experimental time and lengthscales, without any adjustable parameters

Stress fields induced by a non-uniform displacement discontinuity in an elastic half plane

This paper presents the exact closed-form solutions for the stress fields induced by a two-dimensional (2D) non-uniform displacement discontinuity (DD) of finite length in an isotropic elastic half plane. The relative displacement across the DD varies quadratically. We employ the complex potential-function method to first determine the Green\u27s stress fields induced by a concentrated force and then apply Betti\u27s reciprocal theorem to obtain the Green\u27s displacement fields due to concentrated DD. By taking the derivative of the Green\u27s functions and integrating along the DD, we derive the exact closed-form solutions of the stress fields for a quadratic DD. The solutions are applied to analyze the stress fields near a horizontal DD in the half plane with three different profiles: uniform (constant), linear, and quadratic. The same methodology is applied to an inclined normal fault to investigate the effect of different DD profiles on the maximum shear stress in the half plane as well as on the normal and shear stresses along the fault. Numerical results demonstrate considerable influence of the DD profile on the stress distribution around the discontinuity

Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvation-layer interface condition

We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics (Gibbs free energies, entropies, and heat capacities) in numerous polar solvents. We are also able to predict ion solvation free energies in water–co-solvent mixtures over available concentration series. The first modification to the classical dielectric Poisson model is a perturbation of the macroscopic dielectric-flux interface condition at the solute–solvent interface: we add a nonlinear function of the local electric field, giving what we have called a solvation-layer interface condition (SLIC). The second modification is including the microscopic interface potential (static potential) in our model. We show that the resulting model exhibits high accuracy without the need for fitting solute atom radii in a state-dependent fashion. Compared to experimental results in nine water–co-solvent mixtures, SLIC predicts transfer free energies to within 2.5 kJ/mol. The co-solvents include both protic and aprotic species, as well as biologically relevant denaturants such as urea and dimethylformamide. Furthermore, our results indicate that the interface potential is essential to reproduce entropies and heat capacities. These and previous tests of the SLIC model indicate that it is a promising dielectric continuum model for accurate predictions in a wide range of conditions