Model for Transition from Upper to Lower Bainite

Abstract

An attempt is made to model the transition from upper to lower bainite in steels, based on the hypothesis that bainitic ferrite grows with a supersaturation of carbon in solid solution. The theory involves a comparison between the time required to reject the excess carbon into the residual austenite by diffusion and the time required to obtain a detectable degree of cementite precipitation in the bainitic ferrite. If the precipitation process is relatively rapid, then it is assumed that lower bainite is obtained. The results are found to be in broad agreement with published experimental data.

This paper introduces a computational model to predict the temperature-dependent shift between upper and lower bainite in steel alloys. It is proposed that the transition is governed by a kinetic competition between the time needed for carbon to diffuse out of ferrite and the time required for carbide precipitation to occur within it. When carbon leaves the ferrite quickly, upper bainite forms, whereas rapid precipitation within the ferrite leads to lower bainite. By applying Avrami equations and empirical tempering data, it becomes possible to quantify these rates to estimate the transition temperature. It is demonstrated that this model aligns well with experimental observations regarding how carbon concentration influences steel microstructure.

Materials Science and Technology, Vol. 6, 1990, pp. 592-603.

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Core Concept

In metallurgy, we recognise that the final morphology of bainite is not a stochastic occurrence, but a deterministic result of a kinetic "race." When a plate of bainitic ferrite forms, it does so through a mechanism that initially traps a supersaturation of carbon within the iron lattice. This state is thermodynamically unstable.

The carbon has two competing pathways to alleviate this supersaturation. The specific microstructure we observe - upper or lower Bainite - is dictated by which of these two independent kinetic processes reaches its completion first.

The Two Primary Actors in the Race:

• Decarburisation: The "Escape" process. Carbon atoms diffuse out of the supersaturated ferrite plate and into the surrounding residual austenite.
• Precipitation: The "Trap" process. Carbon atoms remain within the ferrite and react to form discrete carbide particles (such as cementite or $\epsilon$-carbide).

To understand who wins the race, we must evaluate the "stopwatches" or time constants ($t_d$ for decarburisation and $t_{\theta }$ for precipitation) governing each process.

Decarburisation is the process by which excess carbon is rejected from the ferrite lath. The time required for this escape, $t_d$, is mathematically modelled by considering the diffusion distance and the chemical potential gradients at the interface. According to the model for supersaturated ferrite plates of thickness $w$, the time $t_d$ is given by:

• Plate Thickness ($w$): The distance carbon must travel. Critically, $t_d$ is proportional to $w^2$; thus, doubling the plate thickness quadruples the time required for the carbon to escape.
• Concentration Gradients ($\overline{x},x^{\alpha \gamma },x^{\gamma \alpha }$): Determined by the difference between average concentration ($\overline{x}$) and equilibrium concentrations in ferrite ($x^{\alpha \gamma }$) and austenite ($x^{\gamma \alpha }$).
• Diffusivity ($D$): The mobility of atoms within the lattice.

Precipitation

If carbon atoms cannot migrate quickly enough, they reach a critical incubation point and precipitate in situ. This is governed by $t_{\theta }$ (or $t_e$ for $\epsilon$-carbide).

The kinetics are described using Avrami-type equations, where volume fraction $\xi \left(t\right)$ is a function of time and temperature.

Upper versus lower bainite

The transition occurs at the Lower Bainite Start temperature ($L_s$), where $t_d=t_{\theta }$.

Influence of temperature

Temperature influence is non-linear:

• The C-Curve of Decarburisation: The $t_d$ curve typically exhibits a "C-shape" due to the balance of mobility and driving force.
• The 0.32 wt% C Boundary: In steels with less than 0.32 wt% C, $t_d$ is always shorter than $t_{\theta }$, so only Upper Bainite forms.
• The $L_s$ Intersection: Below this point, the "trap" is faster than the "escape."

Synthesis

The identity of bainite is a frozen record of a high-speed kinetic competition.