Validation of VrHeatTreat Software for Heat Treatment and Carburization John Goldak a, Jianguo Zhou a, Stanislav Tchernov a, Dan Downey a, a Goldak Technologies Inc, Ottawa, Canada December 12, 2007 1 Summary This note describes a simulation of the conventional atmosphere carburization (AC) heat treating process of a disk specimen for low AC 0.70% C described in Zimmermann et al [1]. The simulation was done with the VrHeatTreat software [2]. The computed and experimental data were compared to validate VrHeatTreat. This simulation modelled the evolution of the transient temperature, carbon composition, microstructure evolution, displacement, strain and stress during furnace heating, carburization and quenching. The analysis was 3D non-linear coupled and transient. The mesh, which had 96,240 eight-node brick elements, was graded such that the smallest elements on the surface had a thickness of 4.9 microns. A total of 196 time steps were analyzed. The time steps were graded separately during heating and quenching to keep the maximum temperature increment in all time steps to less than 25 C. The time steps were also graded during carburizing to capture accurately the growth of the carburized layer. The 3D solute diffusion equation for the conservation of carbon was solved during carburization for the full specimen. During the first stage of carburization from 1500 s to 12300 s, the surface carbon was prescribed to a value of 0.7 % carbon. During a second stage of carburization from 12300 s to 13500 s, the flux of carbon on the surface was prescribed to zero. At all times, the evolution of the microstructure was computed for the full specimen. At all times the evolution of displacement, strain, stress was computed. The stress-strain analysis used the stress-strain curves or functions for each phase at each Gauss point for all times. The stress analysis was visco-elasto-plastic. Zimmermann et al [1] only present experimental data taken on the specimens after heat treatment was completed. This note describes the evolution of all fields in the disk as a function of time and space. The good agreement found between the end state of the simulation predicted by VrHeatTreat and the experimental results for the end state published [1] is strong evidence that VrHeatTreat model is valid. 1
2 VrheatTreat Software The main features of VrHeatTreat are: Automated meshing of a gear. For example to mesh the gear shown in Figure 2, the user picks eight points in a GUI and specifies the desired number of elements in the mesh. Meshing requires about 5 minutes on an Intel Core 2 processor to generate very high quality curvilinear meshes, e.g., see Fig. 12. Furnace heating is modelled by specifying a time dependent convection boundary condition with furnace temperature and convection coefficient. A transient 3D thermal analysis computes the 3D temperature as a function of time for the complete heat treating process. Carburization is specified by a time dependent carbon potential. A transient 3D solute diffusion analysis computes the carbon concentration as a function of time. Parts can be masked to restrict carburization to certain areas. The carburized layer is often 1 to 2 mm thick. To resolve this layer, the size of elements in the surface layer is usually less than 10 microns. See Fig. 4 and Fig. 5 Quenching is is modelled by specifying a time dependent convection boundary condition with quench temperature and convection coefficient. The lowering of a part into a quench bath can be simulated by specifying the orientation and position of the part as a function of time as the part is lowered into the quench bath. The evolution of microstructure is simulated. Usually an initial ferrite-pearlite microstructure evolves to an austenite that is carburized. On quenching the austenite usually transforms to martensite and bainite. The variation of carbon concentration is included in the evolution of microstructure. See Fig. 6 and 9. During this entire heating, carburizing and quenching process, the 3D transient stress, strain and displacement are computed. All of these analyses are 3D non-linear, transient and coupled. The end result of the simulation is a prediction of the distortion, microstructure, hardness and residual stress in the part. VrHeatTreat software is designer driven which means that it is intended to be used by anyone in the design, development, manufacturing, operations and maintenance team. It is critical that distortion and residual stress on quenching be carefully controlled. Also the hardness and microstructure must be controlled carefully. The computing time on a single Intel Core 2 processor is about 24 hours for a gear meshed with 100K elements. More important, the user time to set up an analysis for heat treating a typical gear is usually less than one hour. To validate VrHeatTreat, the data reported by Zimmermann et al [1] for the test disk was used. They describe their experimental procedures and results that include measurements of the carbon profile, hardness profile and residual stress profile in the carburized layer. Their focus was on the differences between low pressure carburization and low pressure gas quenching and conventional atmosphere carburization (AC) plus oil quench. For atmosphere carburization they ran tests at three different carbon potentials; low AC 0.70% C, medium AC 0. 90 % C and high AC 1.1. % C. Their carburizing temperature 2
Figure 1: Carbon profiles of the samples measured using OES; the AC points are an average of two readings, LPC points are an average of three readings. From Zimmermann et al [1]. Figure 2: Microhardness profiles of AC and LPC cycles. From Zimmermann et al [1]. 3
Figure 3: Residual stress profiles for the low-carbon potential samples. From Zimmermann et al [1]. was 950 C for 3 hours followed by a 845 C hold for 20 minutes before quenching in 80.0 C oil. Parts were removed from the oil after 20 minutes. Samples were then tempered at 150 C for two hours. They ran three low pressure carburizing tests that matched the surface carbon potential of the atmosphere carburization. This was done using boost-diffuse steps. The quench was a 20 bar nitrogen quench. Samples were then tempered at 150 C for two hours. No attempt was made to model the experiments using the low pressure carburizing process. 3 VrHeatTreat Results The following figures summarize the results of the analysis using VrHeatTreat. 4
0.7 ts48-1 ts90-1 ts196-1 0.6 0.5 Carbon 0.4 0.3 0.2 0.1 0 2e-05 4e-05 6e-05 8e-05 0.0001 0.00012 0.00014 0.00016 Distance Figure 4: The carbon profiles from the surface to a depth of 0.16 mm are shown at time steps 48: 1501 s, 90: 12300.0 s and 196: 13900.0 s. Time step 48 is about one second into carburization. It shows the Dirichlet or prescribed carbon boundary condition that was used. The distance is in units of mm. The carburized layer thickness is less than 5 microns at this time. The carbon is in units of weight %. Time step 90 (12300 s) is about a half-hour into carburization. It shows the Dirichlet or prescribed carbon boundary condition was used. Time step 196 is the carbon profile at the end of the analysis. Note that the analysis does not run completely to the end of the BCs. This is still during the quench. During this period from time step 90/12300.0 s to time step 196/time 13900.0 s, the carbon flux was set to zero on the surface. This causes the peak carbon composition on the surface to decrease from 0.7 to 0.63 weight percent carbon and slightly increases the depth of carburization. 5
0.7 ts48-1 ts90-1 ts196-1 0.6 0.5 Carbon 0.4 0.3 0.2 0.1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 Distance Figure 5: The carbon profiles from the surface to a depth of 1.2 mm are shown at time steps 48: 1501 s, 90: 12300.0 s and 196: 13900.0 s. 4 Discussion The agreement between the data predicted by VrHeatTreat and the experimental data in published by Zimmermann et al [1] shown in all of these figures is strong evidence that VrHeatTreat model is valid. It is also worth noting that the carburized layer transforms to martensite after the interior has transformed to martensite. This is because the higher carbon region in the carburized layer has a lower Ms temperature. The interplay between thermal contraction on cooling and the volume expansion with the austenite to martensite transformation is an important factor in creating the compressive stress in the carburized layer. The simulation does not predict the spike in the stress in the thin layer of depth ranging from 0.0 to 0.05 mm shown in Figures 4-7 of reference [1]. The spike was strongest for specimens carburized by the low pressure carburization process and weaker in specimens carburized by atmospheric carburization. Zimmermann et al [1] suggest that depletion of manganese during vacuum heating might cause this affect. It is worth noting that our mesh size varies exponentially with depth from a 4.9 micron element size at the surface. 6
1 0.9 0.8 ts171-1 ts172-1 ts173-1 ts175-1 ts176-1 0.7 MartensitePhaseFrac 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.002 0.004 0.006 0.008 0.01 0.012 Distance Figure 6: The phase fraction of martensite along the axis of the disk is shown at time steps 171 to 176. Note that martensite first forms just inside the carburized layer in time step 171. At time step 172, this layer has thickened. In time step 173 the center is still austenite and martensite has not formed at the center. In time step 175 the phase fraction martensite has reached 90 % in the center. In time step 176, the carburized layer transforms to martensite. The increase in specific volume due to the increase in carbon is thought to be the main factor generating the compressive residual stress in the carburized layer. 7
850 800 ts171-1 ts172-1 ts173-1 ts175-1 ts176-1 750 700 Temperature3 650 600 550 500 450 400 0 0.002 0.004 0.006 0.008 0.01 0.012 Distance Figure 7: The temperature in degrees K along the axis of the disk is shown at time steps 171 to 176. Note that when martensite first forms just inside the carburized layer in time step 171, the Ms temperature is just above 600 K and the center of the disk is at 830 K. At time step 172, the temperature at the center of the disk has cooled to 760 K. In time step 173 the center is 660 K and is still austenite and martensite has not formed at the center. In time step 175 the temperature at the center reaches 550 K and the phase fraction martensite has reached 90 %. In time step 176, the carburized layer transforms to martensite with an Ms temperature near 450 K. As the center cools, it shrinks contributing to the compressive residual stress in the carburized layer but the volume expansion on transformation from austenite to martensite in the center reduces the compressive residual stress in the carburized layer. 8
4e+08 3e+08 2e+08 ts196-1 ts196-2 ts196-3 ts196-4 ts196-5 ts196-6 1e+08 StressNodal 0-1e+08-2e+08-3e+08-4e+08-5e+08 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 Distance Figure 8: The stress profile as a function of depth after quenching is complete is shown. Because the external traction is zero, only the two components of the stress tensor in the plane of the surface are not zero. These two components are approximately equal. This is consistent with a plane stress state on the surface as expected. The maximum magnitude of the compressive stress -348 MPa (-50 Ksi) agrees reasonably well with the values in the range of -345 to -413 MPa (-50 to -60 Ksi) reported in [1]. 9
900 ts190-1 850 800 750 700 Hardness 650 600 550 500 450 400 0 0.0005 0.001 0.0015 0.002 0.0025 Distance Figure 9: The VPN hardness profile is shown at 13900.0 seconds which is the end of quenching. The hardness varies primarily due to the dependence of hardness of the martensite on the carbon composition. 10
Figure 10: The carbon profile in a cross-section of the surface layer is shown. The mesh grading normal to the surface is such that the thickness of the first layer of elements is 4.9 microns. The element thickness increases exponentially with distance from the surface with exponent 1.2. 11
Figure 11: The hardness is shown on a cross-section after heat treating is complete. A surface layer about 1 mm thick has a maximum hardness of VPN 870. 12
This mesh is more than fine enough to completely resolve such a spike in the surface stress. We conclude that if a surface spike in stress exists it is due to a mechanism other than carburization. Any chemical reaction other than carburization ocurring during heat treatment including oxidation occurring as the disk is transferred from the carburizing furnace to the quench tank are possible causes of the spike. 5 References References [1] Craig Zimmermann, Jonathan Hall, Dan McCurdy and Ed Jamieson entitled Comparison of Residual Stresses from Atmosphere and Low Pressure Carburization, Heat Treating Progress, July 2007, 41-46. [2] See www.goldaktec.com for additional information on VrHeatTreat. 13
6 Appendix: A Bevel Gear Example. This appendix shows a few images of a similar heat treating and carburization analysis of a real gear. The bevel gear shown in this figure demonstrates VrHeatTreats capability to analyze the heat treatment and carburization of gears. The analysis computes the transient temperature when the part is placed in a furnace for several hours and then quenched. While in the furnace, the part is carburized forming a layer with peak carbon concentration of 0.7 % and a depth of about 1 mm. Regions of the surface that are not carburized are masked, e.g., by copper plating. The spatial resolution required to resolve this carburized layer is about 0.01 mm. This requires a very high quality mesh which we are able to create largely automatically. The microstructure evolves with heating and with changes in the carbon concentration. The stress, strain and displacement change with temperature, phase changes and concentration changes. If quenching involves lowering into a quench liquid, this too can be simulated. VrHeatTreat software predicts all of these changes including the surface hardness required for wear resistance, the residual stress needed for adequate fatigue life and the distortion which must be controlled to meet geometric tolerances. The time for a designer to prepare the data is about 30 minutes. The computing time to solve is about 20 hours and the time to post process the results is less than 10 minutes. The high quality mesh that is generated almost automatically is particularly noteworthy. 14
Figure 12: This figure shows the mesh of a bevel gear made with 69,300 8-node brick elements. 15
Figure 13: The distortion due to heat treating the gear is shown zoomed into a crosssection. The mesh shows the original shape of the gear. The color shows the deformed or distorted gear with deformation magnified 5x. The maximum distortion was 1.63 mm. 16
Figure 14: The distortion due to heat treating the gear is shown in a full cross-section. The mesh shows the original shape of the gear. The color shows the deformed or distorted gear with deformation magnified 5x. The maximum distortion was 1.63 mm. 17
Figure 15: The first principal residual stress is shown. 18