Continuous Casting

1. Continuous Casting: Introduction
2. Temperature Control
3. Mold Oscillation Settings
4. Heat Flux in the Mold
5. Heat Flux in the Secondary Cooling Zone
6. Critical Strain During Continuous Casting
7. Bulging Strain
8. Bending and Straightening Strain
9. Misalignment Strain
10. Combined Strain in the Strand
11. Internal Crack Formation Through Hot Tearing
12. Transverse Cracking
13. Microsegregation
14. Continuous Casting Simulation

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Segregation of alloy elements in continuous castings is termed microsegregation when it takes place over distances the order of the dendrite arm spacing (typically 50–400 µm). Microsegregation results because the composition of the solid forming is different in from the liquid from which it forms (generally less rich in solute). The excess solute is thereby rejected into the liquid, into the narrow spaces between the dendrite arms.

Microsegregation can be analyzed quantitatively using either an analytical model or a computational model. For this purpose the Clyne-Kurz model which takes into account the solute diffusion in the solid phase is employed.

Clyne - Kurz model

This model can be used to calculate the brittle temperature range ΔT_B as well as the liquidus and solidus temperature, T_L and T_S. The brittle temperature range can be expressed as follows:

ΔT_B = LIT – ZDT = T_L(f_s = 0.9) – T_S(f_s = 0.99)

To determine the solid fraction (f_s), the equilibrium solid concentration () needs to be calculated:

where C₀ is the initial concentration, k is the equilibrium redistribution coefficient and Ω is a parameter expressing the degree of back diffusion of solute element described as:

α is related to the appropriate secondary dendrite arm spacing λ and can be expressed as:

D_s is the solute diffusion coefficient in the solid and t_f is the local solidification time:

where ΔT_s is the solidification temperature range and is the cooling rate. The secondary dendrite arm spacing, λ, is a function of cooling rate and can be written as:

B and n are experimental constant parameters with values of 319.4 and 0.378, respectively. There exist numerous correlations between local cooling rate and secondary dendrite arm spacing: the one here is only valid for (low-alloyed) steels. The liquidus temperature can be calculated using the following equation considering the chemical composition of the steel:

The solidus temperature can be calculated using an empirical formula:

T_s = T_f – 415.5%C – 12.3%Si – 6.8%Mn – 124.5%P – 183.9*%S

Summary of parameters used in the derivation:

brittle temperature range, ΔTB / °C	dendrite spacing coefficient, α
liquidus temperature, TL / °C	secondary dendrite arm spacing, λ /μm
solidus temperature, TS / °C	solute solid diffusion coefficient, Ds / m2 s−1
solid fraction, fs	local solidification time, tf / s
equilibrium solid concentration,	solidification temperature range, ΔTs / °C
initial concentration, C0	cooling rate, , / °C s-1
equilibrium redistribution coefficient, k	empirical constants, B and n
degree of back diffusion, Ω

References

• AISE,  The Making, Shaping and Treating of Steel - Casting Volume CD, The AISE Steel Foundation,  
• Bernhard, C & Sjökvist, T, Die interaktive Stranggießsimulation auf www.steeluniversity.org Berg- und Hüttenmännische Monatshefte, SpringerWienNewYork, 0005-8912 
• Clyne, TW and Kurz, W,  Metall. Trans. A, ,  

External Links

• MATTER > Solidification > Redistribution 

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