«Keywords: Heat Treatment Simulation, Vacuum Carburization, Gas Quenching, High Alloy Steel, Residual Stress, Distortion Abstract Aerospace ...»
Predicting Distortion and Residual Stress in a Vacuum Carburized and Gas
Quenched Steel Coupon
A. Freborg, B. Ferguson and Z. Li
Deformation Control Technology, Cleveland, Ohio USA
Keywords: Heat Treatment Simulation, Vacuum Carburization, Gas Quenching, High Alloy
Steel, Residual Stress, Distortion
Aerospace transmission components are typically manufactured from high strength, case
carburized alloy steels such as AMS 6308 (Pyrowear®53). The combination of carburization and quench hardening of these steels produces residual compressive surface stresses and high surface hardness, thus enhancing both surface durability and fatigue resistance. The hard case, coupled with a tough non-carburized core, provides the foundation upon which additional processing can further improve surface fatigue response. An internal state variable (ISV) material model for carburized and heat treated gear steels has been implemented into the DANTE heat treatment simulation software for the purpose of engineering microstructural, residual stress and distortion response to meet specific steel component application requirements. This paper describes the use of heat treatment simulation to engineer residual stress and distortion response in an AMS 6308 alloy steel coupon to subsequently be used for fatigue testing. The criticality for accurate use of process-descriptive boundary conditions is presented in the context of vacuum carburizing and gas quenching. Model predicted residual stress and distortion response for a tapered, notched coupon are validated against x-ray diffraction and dimensional physical testing.
Introduction Precision engineered gears are a critical component in rotorcraft transmission systems.
These gears provide transfer of power from the horizontal drivetrain to vertically mounted rotor shafts, enabling high speed and torque with non-parallel input and output. The increasing performance requirements in both military and commercial rotorcraft necessitate improvement in transmission power density (horsepower/lb) capabilities. This provided the incentive for steel manufacturer’s to shift aerospace steel production and processing towards use of specialized high strength alloy steels. These steels are characterized by a combination of high strength and high toughness, and are noted for their combined use of a carburized case and fine alloy carbide dispersions to achieve these properties. [1-3] Carburizing steels with high alloy content are both an attractive and economically affordable alternative to addressing challenges related to the durability and power density of components used in transmission gears. The carburized case provides high strength and wear resistance, while the non-carburized core maintains the strength and hardenability achieved through alloying while offering a combination of toughness, ductility during impact or impact resistance, and an overall high resistance to fatigue. All of this is made possible due to the low carbon content in the matrix. The influence of a fine dispersion of alloy carbides helps in providing improved fatigue resistance by inhibiting the motion of dislocations.
Maximizing and characterizing fatigue strength of these mechanical elements is therefore essential to increasing transmission performance. Current efforts towards maximizing high cycle fatigue (HCF) performance involve research into the effects of heat treatment residual stress, post heat treatment processes for increasing surface compressive stresses, and various means of enhancing gear surface finish. However, a means of quantifying these improvements from the perspective of quantifiable design metrics has been difficult, specifically due to the need to address complex part geometries such as contour surfaces, edges, and root bottoms of the gear teeth. Residual stress generated during heat treatment of these components is a critical element affecting potential fatigue life, as surface residual compression or tension affects local loading stresses experienced in the gear through the mechanism of superposition.  The magnitude and location of such compressive stresses affect the dynamic stresses experienced locally by the part during service. Additionally, section size changes, gear root geometry, and non-uniformities in heat treatment quenching operations may also contribute to local part distortion and require subsequent grinding or machining to eliminate.
Quantifying and predicting these residual stress and distortion responses remains a substantial challenge to the manufacturing engineer. Recent advancements in quantitative process simulation (modeling) have made it possible to study in situ the combined effects of carbon mass diffusion, heat treatment thermal strains, and strains produced from metallurgical phase changes. Developed in part by DCT Inc. in a US Dept. of Energy sponsored research project, DANTE® (Distortion ANalysis for Thermal Engineering) is a finite element based software tool that calculates the residual stress, dimensional change, hardness and metallurgical phase volume fractions of steel parts as a result of heat treatment.  The DANTE database includes mechanical and thermal property data for steel microstructural phases as functions of temperature and rate, as well as the necessary phase transformation kinetics parameters to address both heating and cooling transformations.  Aerospace transmission components are typically manufactured from high strength, case carburized alloy steels such as AMS 6308 (Pyrowear®53, X53). The impetus for the study presented here was the development of a simple, notched four-point bending fatigue coupon which could be used to characterize residual stresses, distortion, and surface effects in the AMS 6308 carburizing steel for the US Navy and Army.  Steel for physical experiments was acquired by DCT Inc (Cleveland, Ohio, USA). The certified chemical composition of the acquired steel is summarized in Table 1.
Table 1 Chemistry for AMS 6308 steel used for experiments C Mn Si Cr Ni Mo Cu V 0.10 0.35 1.00 1.00 2.00 3.25 2.00 0.10 The notched coupon was designed specifically to maximize resulting loading stress in the notch center by creating a plane strain condition in the notch by use of a “funnel” geometry.
Although the fatigue response of this coupon is not discussed this paper, the geometry, directional carburization, and quenching/tempering response (distortion and residual stress) of this part are integral for subsequent fatigue studies, and are the basis for the paper presented here.
Figure 1 shows a dimensional schematic and photograph (inset) of the coupon and funnel notch geometry.
Figure 1 Geometry and photograph of AMS 6308 funnel notched bend coupon
For the subsequent fatigue study, the AMS 6308 steel was directionally carburized, gas quenched, cryogenically treated, and double tempered. This paper will discuss the use of heat treatment simulation to predict residual stress and distortion response of this coupon to the ascribed heat treatment. The criticality of accurate, process-descriptive boundary conditions, as presented in the context of vacuum carburizing and gas quenching, will be shown, and predicted residual stress and distortion response are validated against x-ray diffraction and dimensional measurement.
Prior to heat treatment, a series of notched coupons were fabricated from the certified AMS 6308 steel through saw cutting and plunge EDM. The coupons were then heat treated using the process sequence outlined in Table 2.
The primary objective of this study was to develop a quantitative prediction of residual stress and distortion for the AMS 6308 coupon to facilitate further engineering analysis in subsequent fatigue studies. Therefore accurate predictions of cross sectional residual stresses in the coupon, as well as coupon dimensional response in heat treating, were essential. As discussed in the introduction, a DANTE heat treatment simulation for the vacuum carburizing, gas quenching and deep freeze processes was undertaken for this direct purpose.
The heat treatment simulation model used a one-quarter symmetry section taken from the full bend coupon geometry, as shown in Figure 2a.
Figure 2 Solid model and finite element mesh used for heat treatment simulation of the funnel notched coupon Because the multiple boost and diffuse cycles in vacuum carburizing introduce a multiple sequence of highly localized carbon gradients during the carburization cycle, and to accurately account for the final surface carbon gradient in the coupon, a fine mesh is required on the top flat surfaces and in the funneled notch, corresponding to surfaces receiving the carburization. The finite element mesh consisted of 39,078 nodes and 35,350 hexahedral elements. The model mesh is shown in Figure 2b.
Specification called for an effective carburized case depth of 1.0mm (0.0394”), defined as HRC 50. The coupon is carburized only on the top face, including the notch (see Figure 2a).
Side and bottom faces are masked. Figure 3 shows the achieved case hardness profile as measured in the notched root corner and on one of the flat carburized surfaces. The plot also shows the DANTE model predicted carbon and hardness profiles at these locations, with the addition of the predicted profile at the notch center. Figure 4 shows the associated Knoop microhardness indents in metallographic sections taken at these locations (ASTM E29).
Figure 3 Measured microhardness profile and model predicted carbon profile for the funnel notch coupon
Carburization was modeled using mass diffusion model. The vacuum carburizing process consisted of a sequence of paired boost and diffuse cycles designed to successfully achieve
1.0mm effective case depth, as shown in Figures 3 and 4. The specific cycle pressures and times are proprietary to the heat treater, and are not given here. However, they were shared with the authors for use in the carburizing model for this study. The predicted carbon profiles in the gear root and flat surfaces, as calculated from the DANTE carburization model, are also plotted and shown in Figure 3 relative to the associated microhardness profiles. The model shows the internal carbon gradient extending from the surface, with predicted carbon of 0.002 wt. pct. at
1.00mm with an associated HRC 50. This conforms well with reported literature data.  The DANTE heat treatment model also enables visualization of the internal carbon gradient at cross sectional locations of interest. Specifically, localized carbon build-up or dispersion at corners and radii are readily visualized. For the notched coupon, Figure 5 shows the internal carbon profiles in both the notch and flat areas. A slight dispersion in the carbon distribution in the notch can be seen visually, which conforms with the slight notch microhardness drop witnessed in the Figure 3 microhardness profile at 0.20mm depth.
Figure 5 Carbon profile on a) Outer surfaces and b) Inner cross section of the heat treated AMS 6308 coupon, as predicted by the DANTE mass diffusion carburization model Gas Quenching Thermal Boundary Conditions The carburized notched coupons were hardened by gas quenching in a vacuum chamber pressurized to 10 bar with nitrogen quench gas. Prior experience in both physical experiments and simulation of gas quenching of commercial parts has shown a high degree of localized cooling sensitivity for convection cooling in gas quenching.  Consequently, for these simulations it was necessary to fit local convection cooling heat transfer coefficients for the coupon surfaces by employing cooling curve data provided by the gas quench heat treater – Solar Atmospheres. Solar provided cooling data from a thermocoupled test block placed in the array of the parts during processing. A photograph of this arrangement is shown in Figure 6.
The test block consisted of a hollow, square tube of 304 stainless steel, with wall thickness of 3.175mm. Three thermocouples were inserted, measuring inside wall temperature of the top, side and bottom faces. These data were used in conjunction with a simple finite element thermal model to determine heat transfer coefficients of the top, side and bottom surfaces. Model thermal response for the fit data is plotted against the measured thermocouple data in Figure 7.
The data showed a 15 second thermal response time at the beginning of the gas quench as the chamber is pressurized. The data indicated a difference in thermal response between the coupon top and its sides/bottom. Average heat transfer coefficients (htc) for each location were determined, and fit to the thermocouple test block data as shown in Figure 7.
Figure 7 DANTE thermal model fit to gas quench thermocouple data obtained from test block shown in Figure 9 The average gas quench convection heat transfer coefficients for the two locations are given in Table 3.
Application of the gas quench heat transfer coefficients was made assuming a constant value over the variable temperature range of the convective nitrogen media. Prior investigations have shown that the temperature dependent gas properties (i.e. kinematic viscosity, thermal conductivity) have only second order influence on htc, and a constant htc can be assumed. [10, 11]
Physical Results and Simulation Validation
The end use of the heat treated Pyrowear53 coupons as bending fatigue test samples necessitated physical characterization of heat treatment residual stress and distortion. Residual stresses were physically characterized at five (5) locations on the coupon (see Figure 8), and distortion was measured both in axial and transverse directions, as the coupon exhibited both bowing in the axial direction and bulging (crowning) in the transverse direction on the carburized surface.
Figure 8 Locations for surface (1-5) and depth (5) x-ray diffraction residual stress measurements Physical test results and corresponding, validated heat treatment simulation predictions will be discussed in terms of metallurgical phase volume fraction, axial residual stresses, and dimensional change.