In the October 2016 issue of Industrial Heating, we reported on a simulation tool called CarbTool© that successfully predicts the carbon-concentration profiles of steel parts. Our focus then was on gas carburization. In this issue, we will focus on the simulation work being done with this technology in the area of low-pressure carburization (LPC), also referred to as vacuum carburization.


Researchers at the Center for Heat Treating Excellence (CHTE) at Worcester Polytechnic Institute (WPI) in Massachusetts are perfecting carbon-concentration profile predictions through enhancements to CarbTool©, its simulation software. The models they are developing can be used to optimize industrial carburizing parameter processes, eliminating much of the trial and error currently happening in the industry and saving time and money.

Low-pressure carburizing (LPC) is gaining popularity because there is less distortion with this process, and it is environmentally friendly.[4,7] A typical LPC process may include a few boost-diffuse cycles (Fig. 1). More cycles are preferred by some manufacturers to avoid soot on the surface.[16]

Figure 2 shows the modeling process of carburizing. Carbon atoms are transferred to the surface from the atmosphere, which is described as the flux.[1,2,10]

Carbon-Concentration Profile Predictions Equation 1 (1)

where J is the carbon flux, β is the mass-transfer coefficient, Cp is the carbon potential and Cs is the surface carbon concentration.

Diffusion of the carbon into the bulk is modeled with Fick’s Law.[1,2,5]

Carbon-Concentration Profile Predictions Equation 2 (2)

where Dc is the carbon diffusivity, which is a function of temperature and carbon concentration, and x is the distance from the surface.[1,2]

Mass balance will be built in a short time.

Carbon-Concentration Profile Predictions Equation 3 (3)

In low-pressure carburizing, carbon flux was used for the simulation. Empirical data was used for calculation.

Carbon-Concentration Profile Predictions Equation 4 (4)

Simulation Research

In most cases, the simulation fits the experimental results pretty well (Fig. 3).[6] 5120 and 4320 alloys were used for the modeling. The empirical carbon flux was effective for the simulation of these two alloys. The simulation data and experimental profile almost overlapped.

However, the prediction does not work well with 9310 steel. The LPC process for 9310 steel was designed and compared with the experimental result. The experiment parameters are presented in Table 1. Figure 4 shows the concentration profiles.

The recipe for 9310 LPC process

In the simulation process, the carbon flux is calculated with the fitting of the experimental results. In Figure 4, with the input of carbon flux (1.63E-06), the concentration profile is not close to the experimental results. Carbon flux is the boundary condition with CarbTool. It is sensitive to gas temperature, pressure and the surface condition. The gas temperature and pressure remain constant. The surface of the steel is well cleaned.

Carbides may form on the surface of the 9310 samples, which will slow down the absorption of the carbon atoms toward the bulk. Figure 5 shows the solubility of 9310 at 927°C which is about 1.0 wt%. Beyond the concentration, carbides start to precipitate, as does the graphite.

The model needs to be optimized to better simulate the process. A thin layer of carbon deposit and carbides form during the LPC boost step.[8,16,17] The carbon deposit is made up of hydrocarbons containing radicals.[12]

Minsu Jung, Sehoon Oh and Young Kook Lee modeled the process with a carbon-potential value, which equals the maximum solubility of the carbon in austenite.[7] P. Kula and R.Pietrasik have developed a boundary condition that uses the multicycle boost-diffuse steps for the LPC process.[12] In this method, constant carbon concentration was used, and the boost step was extended because of the carbon deposit.[11,16]

CHTE Experiments

To investigate the reaction during the LPC process of 9310, two cycles are designed with boost steps only, which last for 20 minutes and 60 minutes. There are no carbides found with our previous experiments because the carbides are dissolved during the diffusion step. The testing with boost step only reveals the surface condition.

Figure 6 presents the carbon concentration profile for 9310 after a LPC process. For the process with 20-minute boost, surface carbon concentration is about 0.80 wt%. The surface carbon concentration of the other process is as high as 1.80 wt%, which leads to the carbide precipitation. The carbides can affect the absorption of carbon into the steel.

Several experiments have been conducted to study the phase development at part surfaces. The samples with only the boost stages for 20 and 60 minutes were analyzed for surface microstructural development and concentration profiles. The XRD is used for surface-phase identification. The samples were well cleaned before the XRD testing. Figures 7 and 8 present the testing for both 20- and 60-minute processes. A strong peak of graphite and carbides are found at the surface area. The 60-minute boost step generates stronger carbide peaks than the 20-minute boost step. More carbides are found.

After a 15µm layer is removed from the surface, the graphite peak disappeared in XRD. Carbides are rarely found for 20-minute boost, but they are seen after the 60-minute boost step.

Model Development

R. Gorockiewicz has studied the kinetics of the LPC process.[17] The carbon deposit formed after the five-minute boost process. The hydrocarbon deposit is also the carbon source for carburizing during the diffuse step.[12,17]

P. Kula, R. Pietrasik and K. Dybowski did the Armco foil testing (Fig. 10).[16] The surface carbon concentration of Armco reaches 1.23 wt% after 5 minutes of carburizing at 950°C. It increases to 1.39 wt% after 120 minutes of carburizing, which is almost the same as the 15-minute process. The result indicates the maximum carbon concentration that can be achieved in LPC is 1.39 wt% at 950°C. The carbon potential can be applied for the simulation.

Assume the carbon deposit is providing a carbon-atom source for the LPC process. The carbon activity is related to the pressure and the temperature of the atmosphere, which is constant. When there is a balance at the surface during the carburizing process:

Carbon-Concentration Profile Predictions Equation 5 (5)

The mass transfer coefficient can be calculated as:

Carbon-Concentration Profile Predictions Equation 6 (6)

The enhanced model is verified with more alloys by LPC. Figure 11 shows the simulation of 9310, which failed to simulate with the previous model. It has been successfully modeled with the current model. 8620 cycles are also modeled, and they can also meet the experimental results (Fig. 12).


CarbTool© is an effective model to predict carbon-concentration profiles during low-pressure carburizing. However, 9310 steel predictions are inconsistent. Experiments have been conducted to understand why. Like the diffusion step, boost-only LPC process keeps the carbides and graphite on the surface without dissolving into the bulk.

The analysis from both XRD and SEM has proven that carbides and graphite are present on the surface. These phases impede the diffusion of carbon atoms into the steel.

The boundary condition for simulation of the LPC process has been optimized. A mass-transfer coefficient is calculated, and a nominal carbon potential is used for the simulation. With the novel model, the simulation meets the experimental results.


We would like to thank the members of CHTE for their support during the project.


For more information: If you are interested in learning more about this research study or about CHTE and its other projects, please visit, call 508-831-5592 or e-mail Richard Sisson at or Lei Zhang at


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