Sergio D. Felicelli

Simulation of freckles during vertical solidification of binary alloys

A mathematical model of solidification that simulates the formation of channel segregates or freckles is presented. The model simulates the entire solidification process starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. Predictions of the pattern and location of channels in different cooling situations are in good agreement with experimental observations.

Numerical model for dendritic solidification of binary alloys

Abstract A finite element model capable of simulating solidification of binary alloys and the formation of freckles is presented. It uses a single system of equations to deal with the all-liquid region, the dendritic region, and the all-solid region. The dendritic region is treated as an anisotropic porous medium. The algorithm uses the bilinear isoparametric element, with a penalty function approximation and a Petrov-Galerldn formulation. Numerical simulations are shown in which an NH4Cl-H2O mixture and a Pb-Sn alloy melt are cooled. The solidification process is followed in time. Instabilities in the process can be clearly observed and the final compositions obtained.

Process Modeling in Laser Deposition of Multilayer SS410 Steel

Summary of Original Contributions Although higher travel speeds seem to be beneficial for theuniformity of the microstructure and hardness of the material, thiscan only be achieved with careful control of other process param-eters. The main contribution of this work is to show the need tocontrol laser power in order to obtain the desired results. This wasnot addressed in Costa et al. 12 and other modeling works 7because the liquidus temperature of the alloy was used as bound-ary condition in newly deposited elements, hence the effect oflaser power is missed. Actually, measurements of the temperaturein the molten pool have shown that the liquid is significantlysuperheated 3 . As illustrated in Fig. 5, the power must be ad-justed not only from layer to layer, but also during depositionalong a same layer in order to avoid edge effects. Insufficient laserpower may result in porosity due to lack of fusion, while exces- Fig. 9 Volume fraction of austenite at the time instant after the tenth layer is deposited.

Macrosegregation patterns in multicomponent Ni-base alloys

A mathematical model of the dendritic solidification of multicomponent alloys, that includes thermosolutal convection and macrosegregation, is presented. The model is an extension of one previously developed for binary alloys. Numerical simulations are given for ternary and quaternary Ni-base alloys, and the evolution of macrosegregation during solidification is studied. The results show that the segregation patterns vary greatly with cooling conditions, adopting several shapes and levels of intensity. Calculations of segregation in rectangular molds and in molds with smooth and abrupt variations of the cross sections exhibit significant differences in the distribution of macrosegregation due to the change in geometry. In addition, the segregation patterns are found to be particularly sensitive to the values of the equilibrium partition coefficients of the alloy components.

Three-dimensional simulations of freckles in binary alloys

Abstract A tridimensional finite-element model was developed to calculate the thermosolutal convection and macrosegregation during the solidification of dendritic alloys. A single set of conservation equations is solved in the mushy zone, all-liquid, and all-solid regions without internal boundary conditions. The model is applied to simulate the directional solidification of a Pb–Sn alloy in cylinders of square and circular cross section. The calculations are started from an all-liquid state and the evolution of convection, solute and energy transport, and the mushy zone growth are followed in time. The results show details of the channels, which result in freckles, that are not observable in existing two-dimensional simulations. Several qualitative features of channels and freckles previously observed in experiments with transparent systems, like chimney convection, preference of channels to be on surfaces, and enhanced solid growth at the channel mouth (“volcanoes”) are successfully reproduced.

Thermosolutal convection during dendritic solidification of alloys: Part i. Linear stability analysis

This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state .e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips,GL,vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1g,0.5g, 0.1g, and 0.01g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤GL≤ 100 K-cm-1).

Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection

A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10−4g0 (g0=980 cm·s−1) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤Gl≤100 K·cm−1 at solidification velocities of 2 to 8 cm·h−1.

Finite element analysis of directional solidification of multicomponent alloys

A finite element model of dendritic solidification of multicomponent alloys is presented that includes solutal convection and is an extension of a previously developed model for solidification of binary alloys. The model is applied to simulation of the solidification of ternary and quaternary Ni‒based alloys. The role of solutal convection in the macrosegregation and the formation of freckles is analysed. Calculations show the effects of geometry and material properties on the convection patterns and the attendant segregation.

Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

A cellular automaton (CA){flnite element (FE) model and a phase fleld (PF){FE model were used to simulate equiaxed dendritic growth during the solidiflcation of hexagonal metals. In the CA{FE model, the conservation equations of mass and energy were solved in order to calculate the temperature fleld, solute concentration, and the dendritic growth morphology. CA{FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidiflcation of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton{Glicksman{Kurz (LGK), showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 (approximated with the binary Mg{8.9 wt% Al) illustrates the di‐culty of modeling dendrite growth in hexagonal systems using CA{FE regarding mesh-induced anisotropy and a better performance of PF{FE in modeling multiple arbitrarily-oriented dendrites growth.

Experimental and Numerical Study of the LENS Rapid Fabrication Process

Several aspects of the thermal behavior of deposited stainless steel 410 (SS410) during the laser engineered net shaping (LENS™) process were investigated experimentally and numerically. Thermal images in the molten pool and surrounding area were recorded using a two-wavelength imaging pyrometer system, and analyzed using THERMAVIZ™ software to obtain the temperature distribution. The molten pool size, temperature gradient, and cooling rate were obtained from the recorded history of temperature profiles. The dynamic shape of the molten pool, including the pool size in both travel direction and depth direction was investigated, and the effect of different process parameters was illustrated. The thermal experiments were performed in a LENS™ 850 machine with a 3 kW IPG Photonics laser for different process parameters. A three-dimensional finite element model was developed to calculate the temperature distribution in the LENS™ process as a function of time and process parameters. The modeling results showed good agreement with the experimental data.