Low-pressure carburizing in combination with high pressure gas quenching is becoming an application of choice for case hardening of steel parts[1],[2],[3]. This process offers an environmentally-friendly alternative to standard atmosphere carburizing and oil quenching. Furthermore, low pressure carburizing and gas quenching allows more control options with increased levels of automation and process flexibility. Finally, changes in quenching intensity are possible by changing gas pressure or gas velocity.

The recent growth of high pressure gas quenching technology is mainly due to the improvement of the vacuum heat treatment installations which today achieve productivities equivalent to their atmosphere carburizing counterparts[4]. A large part of the improvement is in the quenching process itself. Quenching pressures have risen to 20 bar from the 6 bar in the early 1990's. It is generally agreed that high pressure gas quenching performed in a separate cold chamber improves cooling capacity[5].

## Need for Further Improvement

Despite the technological developments mentioned above, the cooling rates for many materials remain below those of oil quenching[6]. Core hardness and other issues are a concern when quenching low-alloyed steel grades, large parts, or massive loads. Quenching with helium offers a possible route to increased cooling rates, however some experimental results have shown that under certain conditions helium fails to achieve heat transfer performance superior to that of nitrogen[7]. Thus, optimization of the cooling efficiency of gas quenching still remains necessary. Use of the Air Liquide model has already led to development of high cooling performance in gas mixtures of carbon dioxide and helium[8]. Control of the quenching process, with use of step or staged quenching, is possible as well.## Gas Quenching - Physical Description

Quenching of steel parts is a fast cooling operation that generates specific crystalline structures through phase transformations. This results in improved mechanical properties. In order to define an efficient numerical simulation strategy for this process, an understanding of all of the physical phenomena involved is needed.In high pressure gas quenching process, parts are cooled by a high velocity flow of pressurized gas. Therefore, heat transfer, both inside the steel part (thermal conduction) and between the part and the gas (conduction, convection and radiation), is the key mechanism that drives the material transformations. However, all phenomena involved in quenching are interdependent (Fig. 1).

Heat transfer between the gas and the parts depends to a large extent on the gas flow. Thus as the heat exchange influ-ences the gas temperature, it also modifies the gas flow itself. The heat exchange between the gas and the parts also de-pends on the part's surface temperature, which decreases during the process due to the heat exchange.

The resulting metallurgical structure is linked to the cooling rates achieved inside the part. For martensitic quenching of carburizing steel grades, a sufficiently high cooling rate from the very beginning of quenching avoids formation of ferrite-pearlite structures having poorer mechanical properties than martensite. The phase transformations also influence the temperature change over time inside the part. Indeed the physical properties (i.e. heat conductivity, heat capacity) greatly differ from one phase to another. Besides, the phase transformation of austenite to martensite is exothermic, further which retards cooling.

In addition, the steel microstructure modification reduces the steel density (causing expansion). This effect, combined with thermal contraction, generates mechanical distortion and stresses in the steel part. In return, mechanical stresses affect the phase transformations.

## Simplified Model Overview

The detailed modeling of all the physical phenomena involved in the quenching process requires complex and time-consuming computations. The approach presented here is intended to allow fast computations. The main purpose of the developed model is to predict the temperature change over time inside a steel part and to assess the final hardness, as a function of the process parameters.
An analysis of the interdependent physical phenomena shows that heat conduction in the steel part and heat transfer between the parts and the gas are of major importance for the process simulation (Fig. 2). Indeed they link the gas flow characteristics with the final metallurgical and mechanical properties of the steel parts. While these must be computed in detail, other factors can be computed by using simplified models or neglected.

## Simplified Model Overview

The detailed modeling of all the physical phenomena involved in the quenching process requires complex and time-consuming computations. The approach presented here is intended to allow fast computations. The main purpose of the developed model is to predict the temperature change over time inside a steel part and to assess the final hardness, as a function of the process parameters.
An analysis of the interdependent physical phenomena shows that heat conduction in the steel part and heat transfer between the parts and the gas are of major importance for the process simulation (Fig. 2). Indeed they link the gas flow characteristics with the final metallurgical and mechanical properties of the steel parts. While these must be computed in detail, other factors can be computed by using simplified models or neglected.

## Physical Properties of the Gas

In the model the physical properties of six gases (Air, H2, He, N2, Ar, CO2) are evaluated using a database taking into account the variations of the physical properties with pressure and temperature[10].
Moreover, the physical properties of gas mixtures can be computed based on the properties of the pure gases. The density r is computed as the mean of the density of each component of the mixture weighted by the volume fraction. The specific heat CP is computed in the same way but mass fractions are used to compute the weighted mean. The computation of the mixture dynamic viscosity µ and heat conductivity k requires the computations of the viscosity parameters Fij (Formula 1).

The knowledge of those properties is mandatory in order to determine the heat transfer.

## Heat Transfer at the Part Surface

The heat transfer at the surface of the steel parts is due to conduction, convection and radiation. In our simplified model, the radiant heat transfer has been neglected. This is due to the fact that radiant heat flux decays very quickly as it is proportional to TS4 where TS is the part surface temperature. This is justified in industrial quenching installations by the fact that most parts are surrounded by other hot parts, thus the net radiant heat exchange is negligible, especially if the quenching gas is transparent.Conduction and convection at the part's surface in the gas are lumped into the heat transfer coefficient h. The heat flux j is then computed using the formula j = h(Ts-Tg), where TG is the gas temperature. In general, the determination of h requires calculating the gas flow. In order to avoid this complex and time consuming computation, h is calculated from experimental data. Since empirical formula are adapted to specific geometries this study focused on parts having a cylinder shape and aligned with the gas stream[13].

The experimental correlations give the dimensionless Nusselt number Nu, which is linked to h by the expression Nu = hDh/k where DH is the hydraulic diameter that characterizes the free section through the load. For highly turbulent regimes the correlation used is Formula 3.

K being a parameter dependent on the cylinders shape [13] (K=1 for long cylinders). Re and Pr are respectively the Reynolds number characterizing the flow and the Prandtl number characterizing the gas diffusivities. Formula 4.

## Heat Conduction Inside the Part

The heat conduction within the steel mass is modeled according to Fourier's law j¢ = k°'t. This expression (Formula 5) of the heat flux is used to compute the temperature field inside the steel part by solving the heat equation [14].
The steel's physical properties r, CP, k are variable with the temperature. The influence of the phase transformations on the temperature evolution is not taken into account since the effect on hardness is negligible. The validity of this simplifying assumption has been checked by experiment.

## Hardness Prediction

The exact computation of the steel hardness at the end of the quenching requires the knowledge of its microstructure and consequently the computation of the phase transformations that have taken place in the steel part. These computations re-quire the knowledge of precise continuous cooling-transformation (CCT) or time-temperature-transformation (TTT) diagram for each steel grade. Although CCT and TTT diagrams are not represented in the model, the computed cooling curves can be compared with specific CCT diagrams in order to determine the present phases and the hardness.
Under the assumption that the temperature evolution weakly depends on the steel part's properties, the cooling rate can be directly related to the Jominy distance (distance from the quenched end).

## Model Software

The information presented above has been incorporated into a user-friendly software called "QuenchAL". This software includes a specific module (Fig. 4), which computes gas mixture properties as well as a module dedicated to optimization of the quenching process parameters with regard to heat transfer coefficients.
Finally, a simulation module allows the computation of the temperature changes over time inside cylindrical parts by solving the heat equation via a 2D finite volume method. The average cooling rates and the final hardness in terms of equivalent Jominy distance can be evaluated using the simulation module. Generally the computation time can be kept within a few minutes with a personal computer.

## Validation - Temperature Prediction

In order to validate the model, computed temperature curves have been compared to experimental temperature data. A load of 16MnCr5 cylinders (Fig. 5) has been quenched in an industrial facility in order to validate the model. The load is equipped with a data recorder linked to thermocouples inserted in the core of several sample cylinders.The average cooling rates between 1475°F (800°C) and 930°F (500 °C) are given in Table 1. This criterion is equiva-lent to the lambda-value, which characterizes the severity of gas quenching[6]. Good agreement results from this compari-son as well. It is to be noticed that those results have been obtained without taking the exact steel grade composition into account.

## Validation - Hardness Prediction

The ability of the software to predict the effect of quenching parameters on the final hardness has been validated in tests using production parts of 27MnCr5 quenched in nitrogen at 18 bar. As a first step, an equivalent cylinder diameter of the same material was selected so that its hardness range would correspond to the measured core hardness values for the original geometry in production conditions (Fig. 7).The hardness has been determined using the Jominy curve and the Jominy distances issued from the simulation. Experimental and simulation hardness results are given in Table 2.

## Improvement of Gas Quenching Technology

The developed model can be used to determine feasibility of gas quenching on samples from a given steel grade, using metallurgical data on the steel grade. If the steel grade's CCT diagram is supplied, the cooling curve predicted by the model can be used to determine the metallurgical phases obtained and the corresponding hardness. For example, the cooling at the core of a ¾" (20 mm) diameter cylinder quenched under nitrogen at 10 bar and 20 bar is simulated (Fig. 8).
Equivalent Jominy distance ranges between 7 and 9 mm for the simulated quenching conditions (except for the edges). The corresponding hardness range can be read on the steel's maximum and minimum Jominy curve (see NF EN 10083-3). Therefore, depending on the steel grade, the hardness reached with this set of working conditions (steel grade, part geometry, quenching gas and pressure) may be in the 29 - 49 HRC range.

## Optimization of Gas Quenching Conditions

The model can be used to compare the relative cooling efficiency of a given set of quenching parameters, expressed through the heat transfer coefficient. The interest of this approach is that it does not require the full computation of a cooling curve. Indeed it only characterizes the cooling efficiency at a specific part surface temperature.
"QuenchAL" can be used for the optimization of binary gas mixtures with regard to cooling capacity. For example, the heat transfer coefficient for CO2 - He mixtures (having helium volume fractions varying from 0 to 100%), at different pressures was calculated (Fig. 10).

## Control Options

Step or staged quenching is seen as a promising alternative allowed by gas quenching for improved distortion control. By a decrease in gas quenching pressure or gas velocity at an intermediate stage of quenching, the cooling can be considerably slowed down improving homogenization of part temperature before martensitic transformation.
A 1 9/16" (40 mm) diameter part has been simulated for 20 bar nitrogen quenching until surface temperature reaches 660°F (350°C), followed by 2 bar nitrogen quenching (Fig. 11). The homogenization is highlighted by the computed cooling curves superimposed on the CCT diagram.

## In Summary

In the presented study, high pressure gas quenching has been simulated using a simplified model. A user-friendly soft-ware based on this model has been developed. This software includes gas properties database and gas mixtures prop-erties model. Besides, a specific module allows comparison of the relative cooling efficiency for different quenching gas and conditions.The software for a cylindrical geometry is able to perform fast simulations of a quenching cycle (less than 10 minutes on a personal computer). Despite important simplifying assumptions, the model is able to take into account the main process parameters such as quenching pressure, gas composition and velocity. In the future, the model can be extended to other standard geometries. In the meantime, the equivalent cylinder approach allows preliminary estimation of quenching parameters influence for most types of parts.