A Numerical Time Integration Procedure for Secondary Dendrite Arm Spacing in Hyper-Peritectic Steel Alloys

A numerical time integration procedure for the calculation of the secondary dendrite arm spacing (SDAS) in FeC hyper-peritectic alloys is presented, a preferred group of low-carbon casting steel. The procedure incorporates a three-stage thin arm dissolution model, which is solved at each time step using Newton–Raphson iteration. This is coupled to a coarsening model based on the integral forms of the dissolution model, which are solved using Gaussian quadrature, as well as a growth model for solid fraction evolution. The procedure can easily be embedded into numerical models for solidification, in which the space–time evolution of the SDAS is required for determining the dynamic permeability in the mushy zone. Higher order approximations for both growth and solute concentration evolution can easily be incorporated. Temperature dependence of thermophysical parameters is taken into account using inter-dendritic solidification empirical models, and an alloy-specific peritectic reaction constant is used to determine the isothermal peritectic holding time. The procedure is validated against experimental data presented in literature. Various cases of SDAS as a function of local solidification time, cooling rate and carbon composition are investigated. The method is compared to experimental results of SDAS obtained from test castings of a hyper-peritectic steel alloy and can be used to iteratively determine the alloy-specific peritectic reaction constant by comparing the solid fraction evolution during the peritectic reaction with that found from the experimental cooling curve.