Theoretical model of eutectic growth of chromium white cast iron under pressure

The stability of solid-liquid interface affects the morphology of microstructure and determines the final properties of materials. The expression of the effect of pressure on solidification interface stability is still qualitative and incomplete, in which only the effect of pressure on diffusion coefficient and solute partition coefficient is considered. Due to the lack of thermodynamic expressions for temperature, pressure and concentration of the system, it is still difficult to fully and systematically understand the effect of pressure on the stability of solidification interface.

The total undercooling △ t of eutectic solidification consists of four parts: thermal undercooling △ TM, curvature undercooling △ TR, solute undercooling △ TC and dynamic undercooling △ TK

According to Clausius Clapeyron equation, the effect of pressure on thermal supercooling is calculated

According to young Laplace, the relationship between additional pressure and curvature supercooling is obtained, and Gibbs Thomson effect can be expressed as:


Γ—— Gibbs Thomson parameter.

If there is no convection and only diffusion during solidification, the change of composition undercooling is mainly controlled by solute diffusion rate and growth rate


M — slope of liquidus;

ɑ L — curvature constant Γ sin θ;

λ—— Average eutectic spacing.

Because of the pressure, the melting point of the alloy increases, i.e Δ TP > 0 indicates that the dynamic undercooling of the alloy melt increases with pressure solidification.

By substituting the formula, we can get:

The radius of curvature RS is an important criterion to evaluate the stability of the growth interface. The higher the stability of the interface is, the larger the curvature radius of the interface is, and the lower the tendency of the interface evolution to dendrite is

The equilibrium liquid concentration equation under pressure can be simplified as:

The effective distribution coefficient K of eutectic solidification is the same as that assumed by most models ɑ= k β < The difference is that the addition of Cr to the molten iron will dissolve in austenite first, and the excess CR will dissolve in ferrite and form carbide. The effective distribution coefficient of Cr between austenite and liquid phase is very different from that of Cr between carbide and liquid phase. At the same time, the influence of pressure on the effective distribution coefficient is shown in the formula


K p — system pressure change Δ The effective partition coefficient of solute at p;

Δ V — the change of molar volume of solute component from liquid to solid.

In conclusion, the effect of effective solute partition coefficient on solid-liquid interface in chromium white cast iron can not be ignored. Therefore, the equivalent partition coefficient of Cr element in the eutectic growth process under pressure is defined as 𝑘 e:

For chromium white cast iron, △ V △ P / RTM > 0, after calculation, the equivalent distribution coefficient in eutectic phase decreases due to pressure.

By substituting the formula, we can determine the relationship between the pressure P, △ T and RS in the process of eutectic alloy solidification under pressure. It can be concluded that with the increase of pressure, the total undercooling △ t of eutectic solidification increases, and the radius rs of eutectic dendrite tip decreases, so that solute atoms are easily enriched in front of solidification interface. The insufficient solute diffusivity and unstable solid-liquid interface lead to the appearance of non-equilibrium microstructure. With the solidification, especially under pressure, the solid-liquid interface will be disturbed and become unstable, resulting in the change of the final microstructure of eutectic structure, from straight strip to tree and dendrite. Considering the temperature gradient, the pressure makes the unstable interface experience more undercooling at its position and further grow, leading to the breakthrough of plane growth.

From the above analysis, it can be seen that the supercooling at the front of the solid-liquid interface increases and becomes unstable due to the pressure, which leads to the breakthrough of the plane growth and the transformation of the phases in the eutectic structure from cooperative growth to alternate competitive growth. This explains that the edge of strip eutectic carbides fluctuates with the increase of pressure, austenite and carbides grow alternately, and carbides show dendritic protrusion.

However, when the pressure increases to more than 100 MPa, the final morphology of eutectic carbide is not dendritic, but short rod or equiaxed. This is due to the fact that Cr white cast iron belongs to the alloy with volume shrinkage during crystallization during pressure casting. Under the condition of constant crystallization temperature, the melting point of the alloy increases and the undercooling increases correspondingly, which will lead to the increase of crystal growth rate. Under pressure, dendrites are formed in the undercooled liquid metal along the three-dimensional direction. However, the diffusion coefficient decreases sharply with the increase of pressure, and the length of dendrite arm is limited, resulting in the formation of a stable solute rich layer in front of the solid-liquid interface and greater composition supercooling. When the pressure increases further, new nuclei will be formed, which will further restrict the growth of the second dendrite arm. Therefore, the short rod and equiaxed grains become the final morphology of eutectic solidification structure of Cr white cast iron.