Heat treaters want an effective simulation tool that predicts the carburization performance of a variety of steels. At the Center for Heat Treating Excellence (CHTE) at Worcester Polytechnic Institute (WPI) in Massachusetts, researchers are perfecting carbon-concentration profile predictions through enhancements to CarbTool©, its simulation software.


Researchers at CHTE have been working on gas and vacuum carburizing models that can be used to optimize industrial carburizing-parameter processes, eliminating much of the trial and error currently happening in the industry. This report will focus on gas carburization. As part of the research process, CarbTool® predictions were compared with industrial experimental results of four types of steels heat treated by gas carburization.

CarbTool® – Carburizing Simulation Tool

The solution algorithm used in CarbTool is based on the finite-difference method (FDM), and the code is developed using Microsoft Visual C++ in Window OS. Users can specify the carbon potential or a flux at the surface between gas and steel.[1]

The output of CarbTool is the carbon-concentration profile. Users input carburization parameters, such as temperature, time and carbon potential or flux. After a quick simulation, the carbon profile along the distance below the surface can be plotted, with the case depth determined according to a user-defined value.

CarbTool has two modules: gas carburizing and vacuum carburizing. Gas carburization functions include:

  • Variable operating temperature
  • Constant mass-transfer coefficient
  • Variable carbon potential
  • Single boost-diffuse process
  • Data export of carbon profile at certain interval and final time
  • Effective case-depth indication at 0.35 wt.% carbon or other user-defined condition

Gas Carburizing Model

Gas carburizing is a complex phenomenon that involves three distinct stages: 1) carbon transport from the atmosphere to the steel surface; 2) surface chemical reactions and absorption; 3) diffusion of the absorbed carbon atoms toward the bulk of the steel down the chemical-potential gradient.[2]

Total carbon transfer from the atmosphere to the steel is thus determined by a rate-limiting process, which kinetically becomes the rate-controlling stage of carburizing. Figure 1 shows the mechanisms of carbon transfer during carburizing and the primary control parameters: the mass-transfer coefficient (β) defining carbon atoms, flux (J) from the atmosphere to the steel surface and the coefficient of carbon diffusion in steel (D) at austenizing temperatures.[1]

Mass-Transfer Coefficient

A constant value for the mass-transfer coefficient is applicable for most cases because once the carbon potential approaches the near-solubility limit in austenite with carbon content greater than 0.5 wt.%, the value of β becomes consistent with temperature and has little relation with gas compositions.[4]

The carbon potential of the carburizing atmosphere is set as the boundary condition, which defines the physical problem. The mass balance of the steel is:


Diffusivity Development

Diffusivity data of 10XX, 51XX, 86XX and 48XX series steels in the current version of CarbTool was experimentally measured by O.K. Rowan.[1] Diffusivities of other alloys were built-in based on the experience reference data. The comparison of different alloys’ diffusivity is presented in Figure 2. These curves are almost parallel to each other, so the diffusivity of one alloy should be proportional to that of another alloy. For example, 10XX and 51XX can be expressed as k in the following equation; k is dependent on carbon concentration.


From the flux balance condition at the steel interface and the continuity equation of the mass accumulation within the solid, the rate at which the total flux over the carburizing time is:


where x0 is the initial condition of the interface between the two components of the diffusion couple, x is the depth beyond which no concentration gradient exists and t is the diffusion time.

Assuming the isotropic media, based on Fick’s first law:


By equating the previous two equations, the expression of diffusion coefficient from the carbon profile can be derived.[7]


Based on this equation, two carbon profiles treated in the same carbon potential and temperature but different time are required. There are two parts: the negative inverse of the slope of any position on the carbon profile and the differentiation in terms of time-integrated area under the corresponding section.[2]

To develop the diffusivity, samples of each alloy can be treated in a carbon potential of 1.1 wt.% at three different temperatures. Samples were kept for 1 hour, 2 hours and 3 hours separately at each temperature.

Case Study


In one study, a series of steels were to be carburized for mechanical testing. The carbon profiles were achieved by gas carburizing in endogas. CarbTool modeling was used to revise the processes to achieve the same surface carbon concentration and effective case depth.

Three materials are selected for the gas carburizing process. Table 1 shows the chemistries (AISI and UNS). The carburizing objectives are as follows:

  • Case depth: 0.035 inch (0.9 mm) at C = 0.35 wt.%
  • Surface carbon: 0.80 ± 0.05% for 8620 and 5120
  • 0.70 ± 0.05% for 4320

Test samples were gas carburized in an industrial furnace using a boost-and-diffuse method. Samples were heated up to 1700°F and held 3.5 hours in endothermic gas at carbon potential of 0.95%, then diffused at 1550°F for one hour in carbon potential of 0.8%, quenched in oil at 140°F and tempered at 350°F for two hours. Figure 4 shows the process schematic.


The carbon depth-profile measurements of the carburized parts were performed using an optical emission spectrometer (OES). Modeling was calculated by inputting the parameters of boost-and-diffuse cycles. Figure 5 shows the measured results and model predictions from CarbTool. These results agreed very well, which verified the effectiveness of CarbTool on predicting gas carburizing.

The accuracy of CarbTool was demonstrated in Table 2. CarbTool’s calculated surface concentration is compared with the measured result. The effective case depth is also compared for experimental and simulation results. They match each other well.

Key Conclusions and Benefits

  • CarbTool is effective in predicting the carbon profile for gas carburizing and vacuum carburizing.
  • Carburization modeling helps heat treaters better understand the effects of process parameters on the diffusion process, distribution of carbon concentration, and effective case depth and hardness.
  • Effective modeling saves time and money over experimental trials.
  • The model will give engineers the ability to optimize material, process and design for best results.


CHTE member Timken Inc. provided the raw materials and intellectual support for this research project. Carburization heat treatments were performed at Bodycote Inc. and Surface Combustion Inc. All are CHTE members. Their support is greatly appreciated.

Lei Zhang is a graduate student and CHTE researcher at Worcester Polytechnic Institute. Richard D. Sisson Jr. is the George F. Fuller Professor of Mechanical Engineering and technical director of CHTE at WPI.


For more information:  If you are interested in learning more about this research study or about CHTE and its other projects, please visit www.wpi.edu/+chte, call 508-831-5592 or e-mail Richard Sisson at sisson@wpi.edu or Lei Zhang at zhanglei@wpi.edu


  1. O. Karabelchtchikova, Fundamentals of Mass Transfer in Gas Carburizing, Ph.D. Dissertation, Worcester Polytechnic Institute, 2007
  2. O. Karabelchtchikova, Carburization Process Modeling and Sensitivity Analysis using Numerical Simulation, MS&T ‘06: Materials Science and Technology 2006 Conference and Exhibition, 2007
  3. V.A. Munts, A.P.B., Rate of Carburizing of Steel, Met. Sci. Heat Treat. (English Translation of Metallovedenie i Termicheskaya Obrabotka Metallov), 1980, Vol 22 (No. 5-6), p 358-360
  4. Ya. Baran, and J.L. Gyulihandanov, Vysokotemperaturnaya nitrotsementatsiya spietchenykh staliv vysokoy plotnosti, MITOM, 1986, Vol 9, p 8-10 (in Russian)
  5. W. Grafem, and B. Edenhofer, Acetylene low–pressure carburizing – a novel and superior carburizing technology, Heat Treatment of Metals, 1999, Vol 4, p 79-85
  6. P. Kula, R. Pietrasik, and K. Dybowski, Vacuum carburizing - process optimization, 13th International Scientific Conference on Achievement in Mechanical and Materials Engineering, 2005, Poland
  7. O. Karabelchtchikova, and R.D. Sisson, Carbon Diffusion in Steels: A Numerical Analysis Based on Direct Integration of Flux, J. Phase Equilib. Diff., 2006, Vol 27 (No. 6), p 598-604