By Laurentiu Nastac
The purpose of Modeling and Simulation of Microstructure Evolution in Solidifying Alloys is to explain in a transparent mathematical language the physics of the solidification constitution evolution of forged alloys. The options and methodologies awarded right here for the net-shaped casting and the ingot remelt techniques will be utilized, with a few differences, to version different solidification tactics resembling welding and deposition processes.
Another goal of the e-book is to supply simulation examples of the solidification constitution modeling in a few an important advertisement casting applied sciences in addition to to supply useful concepts for controlling the constitution formation through the solidification strategies.
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Extra resources for Modeling and Simulation of Microstructure Evolution in Solidifying Alloys (Mathematics & Its Applications)
419) and (4-20) was used to compute the curvature undercooling. % Nb alloy in Figs. 4-13a to 4-14c. % Sn alloy cast in microgravity conditions  are presented in Fig. 4-14. Note from Fig. 4-14 the sharp CET that takes place at approximately 2/3 of the sample height where the thermal gradient in the mushy region is less than about 3000 K/m. The CET is sharp because of faster growth of equiaxed dendrites that have nucleated in the undercooled liquid ahead of the columnar front. % Nb is shown in Fig.
3 SOLUTION METHODOLOGY The solidification process is governed by Eqs. (4-3) to (4-8) and a stochastic model for nucleation and growth. The numerical procedures for calculating the nucleation and growth, temperature and concentration fields as well as the growth velocity of the S/L interface during dendritic solidification are described in details below. Chapter 4. Stochastic/Mesoscopic Modeling 35 A. Stochastic Model for Nucleation and Growth. The structure of the stochastic model is similar to that described in Ref.
I) The Latent Heat Method is the most accurate method that can be used in HT-SK codes. The drawback of this method is a much longer computational time. (ii) Assuming a constant heat transfer throughout the micro-solidification path, the Micro-Latent Heat Method and MicroEnthalpy Method can be used with enough accuracy instead of the Latent Heat Method or Enthalpy Method. 3% was calculated in the prediction of recalescence temperature and solidus temperature, with respect to the LHM. A max. 5% error in the prediction of recalescence rate, solidification time, and temperature of eutectic undercooling was also obtained.