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Experimental measurements and numerical simulation of stress and microstructure in carburized 5120 steel disks
Materials Science and Engineering A298 (2001) 158 – 165 www.elsevier.com/locate/msea
Experimental measurements and numerical simulation of stress and microstructure in carburized 5120 steel disks P. Rangaswamy *, C.P. Scherer, M.A.M. Bourke Material Science and Technology, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 22 February 2000; received in revised form 3 July 2000
Abstract A combined experimental and numerical study of residual stress and microstructure was performed on a carburized disk of 5120 steel. The disk-shaped specimen was carburized and quenched in agitated oil at 71°C. X-ray diffraction combined with electropolishing layer removal was used to determine stresses through the case of the disk, within 1 mm of the surface. Both martensite and retained austenite volume fractions were determined through one flat surface. Rietveld analysis was used to determine the lattice parameters of the constituents at sequential depths. Microstructure and residual stress profiles were compared to predictions. The numerical predictions were from ABAQUS; a finite element code coupled with a user-defined material subroutine (UMAT), that accounted for microstructure evolution. Measured retained austenite values varied from 25 vol.% at the surface to a maximum of 30% at 100 mm, then decreased to 4% at a depth of 600 mm. The numerical simulation predicted a maximum of 25 vol.% at the surface that monotonically decreased to 7% at a depth of 600 mm, and reached a minimum of 4% at 1.0 mm. The maximum measured compressive stress was 380 MPa at 550 mm, compared to the predicted value of 450 MPa at 330 mm. In addition, the carbon profile predicted from the numerical simulation was comparable to the profile obtained from the combustion burnout technique. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Microstructure and residual stress; Carburized disk; Predictions
1. Introduction Carburizing, a surface treatment applied to a part to ensure beneficial surface compressive stresses and increased hardness, improves wear and fatigue resistance. The development of compressive residual stresses inevitably is accompanied by distortion [1 – 4]. Although distortion and residual stresses have been widely studied, accurate predictions for a diversity of geometries remain elusive. With the continuous increase in computing power and decline in computational costs, there is currently much emphasis on modeling and simulation of heat treatment processes [5 – 8]. Accurate measurements of residual stress and microstructure remain a challenge for validating predictions of computer simulations.
* Corresponding author. E-mail address: [email protected] (P. Rangaswamy).
Our objective was to compare experimental results with numerical simulations using the ABAQUS [9] code coupled with TRAST [10], (a commercial material model that predicts phase composition). The comparison was performed on a carburized 5120 steel disk. In the experimental study, depth profiles of residual stress and microstructure were recorded through the case, the carburized layer, using conventional electropolishing and X-ray diffraction techniques [11,12]. Rietveld analysis of the X-ray diffraction data was used to determine the depth dependence of the lattice parameters of the austenite and martensite at each depth, which varied due to the combined effect of carbon content and stress [1–5,13,14]. Using the lattice parameters in conjunction with the stress measurements, the carbon content was also identified [1,14]. These measurements were compared with the carbon combustion burnout technique. The efficacy of the model and its assumptions were gauged by comparing predictions of the microstructure, residual stress profile, and carbon profile with experimental results.
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 0 ) 0 1 2 9 2 - 2
P. Rangaswamy et al. / Materials Science and Engineering A298 (2001) 158–165
159
Table 1 Chemical analysis of 5120 bar stock prior to carburization Element
C
Mn
P
S
Si
Ni
Cr
Mo
Cu
Al
N
O
Wt.%
0.23
0.83
0.012
0.03
0.22
0.15
0.8
0.04
0.15
0.031
0.008
0.003
3. Experimental procedures
3.1. X-ray diffraction
Fig. 1. Schematic of the disk, showing the directions for X-ray measurements.
2. Sample preparation Multiple cylindrical disks (30 mm diameter and 10 mm thick) as shown in Fig. 1 were cut from 5120 bar stock. The vendor-provided chemical analysis is shown in Table 1. The carburization schedule was at a carbon potential of 0.85% at 900°C for 3.25 h, followed by 840°C for 0.75 h. This was followed by an agitated oil quench at 71°C and a temper at 177°C for 1.5 h. Fig. 2 is a metallographic cross section of the carburized disk, with the surface at the top of the photo. The first 30–40 mm, below the surface shows evidence of decarburization. The martensite core is readily identified.
X-ray measurements were performed using a standard methodology as outlined in SAE-J784A [15] with a Phillips vertical diffractometer operating at 40 kV and 20 mA. Incident slits masked the beam, to illuminate approximately a 2 mm square on the surface. One flat surface of the disk was polished and all X-ray profiles were obtained through this surface. A schematic of the disk showing the measurement region is shown in Fig. 1. A circular region 6 mm in diameter in the center of the disk was electropolished at 54°C using a mixture of phosphoric and sulfuric acids and distilled water, volume ratio 2:1:1. The current was controlled at approximately 4.2 mA mm − 2 to minimize surface pitting. All measurements were performed using chromium radiation (wavelength : 2.289 A, ) for which the martensitic (211) reflection occurs at :156° (2u) and the austenite (220) reflection at : 128° (2u). Measured intensities were corrected for absorption at different c tilts, and normalized with respect to the Lorentz polarization factors. Background corrections were applied before calculating peak positions using the conventional parabolic technique.
Fig. 2. Photomicrograph of a cross-section of disk, from surface (top) down, showing evidence of de-carburization at surface.
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3.3. Retained austenite determination (con6entional X-ray and Riet6eld) Following progressive polishing at each depth, 2u scans from 40° to 161° were recorded at c= 0 for both conventional [16] (single-peak) and Rietveld structure refinements using ‘Generalized Crystal Structural Analysis’ (GSAS) [17]. In the refinement, a body centered tetragonal structure (I4/mmm) was assumed for the martensite, and a face centered cubic structure (Fm3m) for the retained austenite. The diffraction pattern was treated in its entirety, so peaks for individual hkl reflections need not be resolved [13,17]. By comparing the observed diffraction patterns to a pattern calculated from a model, the parameters were refined to fit the observations [18,19]. Refined variables include microstructural parameters (lattice constants, atomic positions and occupancies), peak shape parameters (strain and particle size), sample absorption, extinction, and Debye-Waller factors. Austenite volume fractions were also determined using the conventional technique of comparing intensities of the austenite (220) and martensite (200) reflections.
3.4. Carbon determination Fig. 3. Intensity versus angle, for Rietveld refinements of X-ray data, (a) showing both austenite and martensite reflections at the surface, and (b) showing only martensite 1 mm below the surface.
3.2. Stress measurements The penetration for chromium radiation in steel is approximately 3– 5 mm. Surface residual stress profiles in both the martensite and austenite were obtained using the classical ‘d versus sin2 c’ analysis of the diffraction data [11,12], Eq. (1) (dfc − d0)/d0 = [(1+ n)/E]sf sin2 c −(n/E)(s11 +s22) (1) where dfc and d0 are the lattice spacing in the measured direction (f) and tilt (c) of the scattering vector and the unstressed lattice spacing respectively for any given set of hkl planes. y and E are Poisson’s ratio and elastic modulus respectively, (0.3 and 205 GPa are representative of the bulk material). sf is the direction of the stress measured on the surface. Stresses in both the martensite and austenite were calculated (using a X-ray elastic constant of 6.3 ×10 − 6 MPa − 1) in two orthogonal directions at the center of the disk to a maximum depth of 1.2 mm, as shown in Fig. 1. A total of ten c tilts, five positive and five negative, were recorded.
An extra facet of the Rietveld method is that it offers an estimate of the carbon content by virtue of its effects on the c/a ratio. The relationship between the c/a ratio and the carbon content was independently determined on quenched samples of 5120, 5140, 5160, and 5180 steel, that have nominal carbon contents of 0.2, 0.4, 0.6, and 0.8 wt.%, respectively [19]. Using this as a calibration, the carbon profile of the 5120 disk was determined. Two other techniques, combustion burnout and microhardness profiling were also used to infer the carbon content. Combustion burnout has wide applicability for determining carbon content, and offers a resolution of approximately 50 mm in depth [20].
4. Experimental results
4.1. General obser6ations on X-ray data Generally, the X-ray diffraction peaks were broad (\ 10°, 2u) at higher angles (\ 120°) of 2u (Fig. 3). At the surface, the martensitic reflection was 14° wide, with 85% of the intensity coming from a width of 4° (2u). Peak splitting was not observed. There was no evidence of preferred orientation. Rietveld refinements for the surface and for a 1 mm depth are presented in Fig. 3. The tick marks indicate the positions of the peaks (including Ka1 and Ka2), and the difference between predicted and observed intensities is shown as the lower line in each plot. At a depth of 1 mm, the
P. Rangaswamy et al. / Materials Science and Engineering A298 (2001) 158–165
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austenite reflections were absent, while the martensite reflections were sharper, indicating the presence of martensite only.
4.2. Residual stress From the X-ray diffraction data, residual stress profiles along one direction for both martensite and austenite were determined and plotted, see Fig. 4a. Similar stress profiles were measured in both orthogonal direc-
Fig. 5. 2-D axisymmetric model of the carburized disk used for finite element calculations. Thermal and carbon concentration boundary conditions were defined at the top and outer surfaces of the disk; the bottom surface is a symmetry plane.
tions [19]. The profiles presented in Fig. 4a were corrected for layer removal using the Moore & Evans technique [12]. From the surface to a depth of 150 mm, there was scatter in the residual stress measurements for both martensite and austenite. At depths greater than 150 mm, the martensite and austenite exhibited similar trends. The maximum compressive stress of 380 MPa was at 600 mm, and the crossover from compressive to tensile occurred at approximately 1150 mm.
4.3. Retained austenite Fig. 4b shows the retained austenite profiles determined from both conventional and Rietveld analysis of the X-ray diffraction data. Near the surface, there was approximately 30 vol.% retained austenite dropping to near 2–4% at a depth of 800 mm. Constituent determination using conventional techniques compares well with the Rietveld determined data.
4.4. Carbon Fig. 4c shows the carbon profiles determined from X-ray, and combustion burnout techniques, along with microhardness data. Below 350 mm, there was good agreement in the carbon profiles determined from X-ray data and combustion burnout techniques. However, the variation in carbon from the surface to 350 mm for these two techniques was significant. Combustion burnout showed a maximum of 0.76 wt.% carbon from 50 to 150 mm depth from the surface; and the carbon determined from the X-ray data had a maximum of 0.67 wt.% at 100 mm depth.
5. Finite element analysis Fig. 4. (a) Residual stress profiles in the martensite and austenite; (b) retained austenite volume fractions versus depth (conventional and Rietveld analysis of X-ray data); and (c) carbon (from X-ray and combustion) along with hardness profiles from Vicker’s micro-indentation technique.
5.1. Procedure For the numerical analysis, a 2-D axisymmetric finite element model that represented the disk, along with the meshing scheme, is shown in Fig. 5. Over the first 1 mm
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of thickness from the top surface, the mesh was graded in layers of 60 mm, while a coarser mesh of 120 mm was used for the interior. This meshing scheme reflects the steep stress gradients in the carburized layer (or case region) and the resulting microstructural variations. Material properties for Swedish 2511 steel were used, since these properties were not available for 5120 steel in a form accessible to the numerical model. The 2511 steel is chemically, thermally, and mechanically similar to 5120. To represent the heat transfer during quenching, film coefficients for agitated oil were applied to the top and outside boundaries of the disk, in the ratio of two to one [6]. Simulation of carburization and quenching was achieved using the commercial package TRAST, which was coupled to ABAQUS as a User Defined Material Subroutine (UMAT) [9,10,21]. TRAST predicts and describes the material behavior of the various possible steel constituents formed during quenching. The simulation was carried out in three steps. First, the carbon distribution was predicted using the mass diffusion material model in ABAQUS. Secondly, the temperature profile and constituent compositions were determined using the thermal/ metallurgical model in ABAQUS/TRAST (incorporating the results from the first step). Finally, stresses were calculated using the mechanical model in ABAQUS/TRAST (incorporating the results from steps one and two).
5.2. Finite element analysis predictions Contour plots of hoop stresses, retained austenite volume fraction, and carbon concentration, from the numerical analysis are presented in Fig. 6. A contour plot of the hoop stresses is shown in Fig. 6a. The predicted hoop stresses (and radial stresses) were compressive with a maximum of 420 MPa at the top surface, and becoming tensile (ranging from 60 to 150 MPa) at the interior of the disk (Fig. 6a). Fig. 6b shows the predicted volume fraction of retained austenite. The outside surfaces were at a maximum of 25 vol.%. The retained austenite montonically decreased across the case. The interior of the disk shows a uniform austenite volume fraction of 2 vol.%. The balance of the predicted microstructure was martensite; no other microstructures (pearlite, bainite, or ferrite) were numerically predicted (or experimentally observed). Fig. 6c shows the carbon distribution after the completion of the carburizing cycle. The carbon content decreases montonically from 0.85 wt.% at the outer surfaces of the disk to 0.2 wt.% within the interior of the disk.
6. Comparison of numerical and experimental data The numerical predictions are compared with the experimental results in Fig. 7, for (a) stress, (b) retained austenite, and (c) carbon content.
6.1. Residual stress A comparison of the predicted and measured stresses is presented in Fig. 7a. At depths greater than 500 mm below the surface, the agreement for the properties investigated was reasonable. However, closer to the surface, in the case region, the prediction overestimates the measured values in some locations by more than 100%. Moreover, the predicted depth of maximum compressive stress was shallower in the model than measured on the disk. Because of the scatter in data for the measured stresses, within the first 100 mm of the surface, the possibility of a local maximum or minimum is ill defined. Note, however, that the near surface region where the stress was over-estimated, is similar to the region where the model under-estimates the retained austenite fraction!
6.2. Retained austenite The retained austenite prediction shows less variation with depth than the experimental data (Fig. 7b). The model predicts variation from 25 to 2 vol.%, whereas the experimental measurements suggest that the true maximum values may exceed 30 vol.%. Like the stress predictions, the region of biggest disparity between experimental data and the model predictions are within 400 mm of the surface. Notably, the predicted values show no evidence of a local maximum or minimum near the surface. The measured values differ by as much as 3–5 vol.% depending on whether the analysis was performed by Rietveld or conventional analysis. Although we have not quantified the errors, we are inclined to give more credence to the Rietveld data, since it uses three peaks per phase instead of just one in analyzing the data.
6.3. Carbon Prediction of the carbon content was performed in ABAQUS using the mass diffusion material model. Fig. 7c shows a plot of the carbon as predicted from the model, and experimentally by both a combustion burnout technique and from c/a ratio data taken from the Rietveld analysis of the X-ray data. The predicted values, showed as expected, a monotonic decrease in carbon from a maximum surface value of 0.85–0.32 wt.% at a depth of 1.0 mm, and continuing to decrease to 0.2% at 1.3 mm. Agreement between the model and the combustion burnout measurements was excel-
P. Rangaswamy et al. / Materials Science and Engineering A298 (2001) 158–165
lent over the complete range profiled. However, there was a noticeable plateau at 0.76 wt.% C in the combustion data, from the surface to about 200 mm. Consider-
163
ing this disparity, the agreement between the model and the combustion data was good. There was significant disparity between the model and Rietveld estimate of
Fig. 6. Contour plots from numerical analysis simulations showing (a) hoop stress (MPa) in the disk after material removal on the top surface; (b) retained austenite (volume fraction); and (c) carbon variation (wt.%) at end of carburizing cycle.
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6.4. O6erall comparison Table 2 summarizes the salient features from the predictions and measured values. The model used in this work incorporates a description of the microstructure phase evolution (TRAST) with a conventional finite element solution for the mechanical and thermal history of a carburized steel. Despite the fact that neither the boundary conditions (e.g. heat transfer coefficients) nor the material properties (TRAST predictions used Swedish 2511 steel properties) were optimal, comparison with experimental validation measurements was encouraging. The most notable disparity between model and experiments came in the near surface region (0–400 mm), which may be associated with decarburization (this is qualitatively supported by the microhardness data). Other reasons for disparity may derive from tempering effects, which are notoriously hard to model, and are not included in TRAST.
7. Conclusions Comparison of the ABAQUS numerical predictions of residual stress, retained austenite, and carbon showed reasonable agreement with experimental measurements at depths greater than 400 mm from the Table 2 Comparison of experimental data with numerical predictions
a) Stress Maximum stress Depth of maximum stress Depth of comp.tens. (cross over) Fig. 7. Comparison of numerical simulations with experimental data for (a) residual stress; (b) retained austenite profiles; and (c) carbon profiles.
b) Austenite Maximum austenite Depth of max. austenite At 1.0 mm depth c) Carbon (wt.%): Maximum carbon (wt.%)
carbon, (derived from the c/a ratio) over the region from 0 to 400 mm; (the same region where the model faired poorly in predicting the retained austenite and residual stress distributions). Also shown in Fig. 7c are Vicker’s hardness measurements, which qualitatively track the carbon content variation. The Vicker’s hardness measurements are included for comparative purposes only, since they are not calibrated for carbon content.
Depth of max. carbon (wt. %)
At 1.0 mm depth
Experimental
Numerical simulation
−380 Mpa 550 mm
−450 Mpa 330 mm
1.2 mm
1.3 mm
30 vol.% 100 mm
25 vol.% Surface
2–4 vol.% 0.67 wt.% (XRD-c/a ratio) 0.76 wt.% (combustion) 100 mm (XRD-c/a ratio) 50–150 mm (combustion) 0.38 wt.% (XRD-c/a ratio) 0.37 wt.% (Combustion)
4 vol.% 0.80 wt.%
Surface
0.32 wt.%
P. Rangaswamy et al. / Materials Science and Engineering A298 (2001) 158–165
surface. However, from the surface to a depth of 400 mm significant disparities were observed. In the near surface region (B400 mm) the predicted stresses exceeded the measurements by as much as 200 MPa. Moreover, the depth of maximum compressive stress was displaced to a shallower depth than what was measured. Although the predicted retained austenite profile showed better agreement with the experimental data it also differed from the measurement by as much as 10%. For the carbon prediction there was relatively good agreement with the combustion measurements but less good agreement between the three experimental techniques. Although the lower value of the X-ray measurements might be consistent with decarburization, the disparity with the combustion measurements is not immediately explicable. However, the use of X-rays to profile carbon content is a relatively new approach and the technique may need further work to improve our understanding of the sensitivity of lattice parameters to alloy composition It is clear that the model, although adequate below 400 mm, is at best qualitative in its predictions from the surface to a depth of 400 mm. However, the model, as applied includes several approximations; the microstructure was modeled for a different steel, heat transfer coefficients as well as the inelastic (temperature dependent) mechanical properties were estimated, and the tempering process was ignored. In the past, attempts to model residual stress and distortion have met with mixed success. The phase changes have been mimicked either by incorporation of a temperature dependent yield strength or by large changes in thermal expansion coefficient [22,23]. In those approaches, microplasticity and microscopic deviatoric strains are not accounted for and the predictions showed large discrepancies from the measured stresses [24–26]. Correctly accounting for the thermal, mechanical and microstructural mechanisms is likely to improve the models but, as we have shown in this uncoupled-serial analysis, achieving a good agreement with experiment is not easy. Nevertheless we consider that further attempts to refine microstucture-thermomechanical hybrid models are worthwhile.
References [1] [2] [3] [4] [5]
[6]
[7]
[8]
[9] [10]
[11]
[12] [13] [14] [15]
[16]
[17]
[18]
[19]
[20] [21]
Acknowledgements
[22]
We gratefully acknowledge Maurice Howes and Gerry Koller from IITRI for heat treating the specimens. We appreciate the assistance of Peggy Goldman (Los Alamos National Laboratory) in implementation and use of TRAST and Charles A. Anderson (Los Alamos National Laboratory) for valuable discussions. .
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[23] [24] [25] [26]
D.P. Koistinen, Trans. ASM 50 (1958) 227. L.J. Ebert, Metallurgical Trans. A 9A (1978) 1537. R.C. Fischer, Metallurgical Trans. A 9A (1978) 1553. G. Krauss, Metallurgical Trans. A 9A (1978) 1527. W. Dowling, T. Pattock, B.L. Ferguson, D. Shick, Y. Helen Gu, M. Howes, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 350, ASM International, Materials Park, OH, 1996. D. Shick, D. Chenoweth, N. Palle, W.T. Lee, W. Elliot, H. Walton, M. Howes, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 357, ASM International, Materials Park, OH, 1996. D. Bammann, V. Prantil, A. Kumar, J. Lathrop, D. Mosher, M. Callabresi, H.J. Jou, M. Lusk, G. Krauss, B. Elliot Jr., G. Ludtka, T. Lowe, B. Dowling, D. Shick, D. Nikkel, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 367, ASM International, Materials Park, OH, 1996. C. Anderson, P. Goldman, P. Rangaswamy, G. Petrus, B.L. Ferguson, J. Lathrop, D. Nikkel Jr., 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 377, ASM International, Materials Park, OH, 1996. HKS Inc, ABAQUS Users Manual, Providence, RI, USA, 1993. N. Jarvstrat, S. Sjostrom, Current Status of TRAST: a Material Model Subroutine System for the Calculation of Quench Stresses in Steel, Linkoping University, ABAQUS Users’ Conference Proceedings, 1993, pp. 273 – 287. I.C. Noyan, J.B. Cohen (Eds.), Residual Stress, Measurement by Diffraction and Interpretation, Springer-Verlag, New York, 1987, pp. 117 – 130. M.G. Moore, W.P. Evans, SAE Trans. 66 (1958) 341. R.B. Von Dreele, J.D. Jorgensen, C.G. Windsor, J. Appl. Crystallogr. 15 (1982) 581. C.S. Robert, Trans. AIME, J. Met. Feb (1953) 203–204. M.E. Hilley (Ed.), Residual Stress Measurement by X-ray Diffraction, SAE Information Report J784a, Society of Automotive Engineers, New York, 1971, pp. 12 – 25. B.D. Cullity (Ed.), Elements of X-ray Diffraction, second ed., Addison-Wesley Publishing Co, Inc, New York, 1978, pp. 411– 415. A.C. Lawson, R.B. Von Dreele, Generalized Crystal Structural Analysis System (GSAS), Los Alamos National Laboratory, LAUR 86-748, 1966. A.C. Lawson, A. Williams, J.A. Goldstone, D.T. Eash, R.J. Martinez, J.I. Archuleta, D.J. Martinez, B. Cort, M.F. Stevens, J. Less-Common Met. 167 (1991) 353 – 363. P. Rangaswamy, M.A.M. Bourke, A.C. Lawson, J. O’Rourke, J.A. Goldstone, in: J.V. Gilfrich, et al. (Eds.), Advances in X-ray Diffraction Analysis, vol. 39, Plenum Press, New York, 1997, pp. 319 – 329. Metals Handbook — Desk Edition — Published by ASM, Metals Park, Ohio, 1998, pp. 28 – 44. N. Jarvstrat, Two Dimensional Calculation of Quench Stresses in Steel, Thesis No. 45, Linkoping, Sweden, 1990. J.A. Goldak, in: S.A. David, M. Vitek (Eds.), Recent Trends in Welding Science and Technology, ASM International, Gatlinburg, TN, 1985, pp. 71 – 82. S. Sjostrom, Mater. Sci. Technol. 1 (1985) 823 – 829. A.S. Oddy, J.A. Goldak, J.M.J. McDill, J. Press. Vessel Technol. 114 (1992) 33 – 38. B.L. Josefson, C.T. Karlsson, J. Press. Vessel Technol. 114 (1992) 376 – 378. A.S. Oddy, J.A. Goldak, J.M.J. McDill, Eur. J. Mech. A-Solids 9 (1990) 253 – 263.
Experimental measurements and numerical simulation of stress and microstructure in carburized 5120 steel disks P. Rangaswamy *, C.P. Scherer, M.A.M. Bourke Material Science and Technology, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 22 February 2000; received in revised form 3 July 2000
Abstract A combined experimental and numerical study of residual stress and microstructure was performed on a carburized disk of 5120 steel. The disk-shaped specimen was carburized and quenched in agitated oil at 71°C. X-ray diffraction combined with electropolishing layer removal was used to determine stresses through the case of the disk, within 1 mm of the surface. Both martensite and retained austenite volume fractions were determined through one flat surface. Rietveld analysis was used to determine the lattice parameters of the constituents at sequential depths. Microstructure and residual stress profiles were compared to predictions. The numerical predictions were from ABAQUS; a finite element code coupled with a user-defined material subroutine (UMAT), that accounted for microstructure evolution. Measured retained austenite values varied from 25 vol.% at the surface to a maximum of 30% at 100 mm, then decreased to 4% at a depth of 600 mm. The numerical simulation predicted a maximum of 25 vol.% at the surface that monotonically decreased to 7% at a depth of 600 mm, and reached a minimum of 4% at 1.0 mm. The maximum measured compressive stress was 380 MPa at 550 mm, compared to the predicted value of 450 MPa at 330 mm. In addition, the carbon profile predicted from the numerical simulation was comparable to the profile obtained from the combustion burnout technique. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Microstructure and residual stress; Carburized disk; Predictions
1. Introduction Carburizing, a surface treatment applied to a part to ensure beneficial surface compressive stresses and increased hardness, improves wear and fatigue resistance. The development of compressive residual stresses inevitably is accompanied by distortion [1 – 4]. Although distortion and residual stresses have been widely studied, accurate predictions for a diversity of geometries remain elusive. With the continuous increase in computing power and decline in computational costs, there is currently much emphasis on modeling and simulation of heat treatment processes [5 – 8]. Accurate measurements of residual stress and microstructure remain a challenge for validating predictions of computer simulations.
* Corresponding author. E-mail address: [email protected] (P. Rangaswamy).
Our objective was to compare experimental results with numerical simulations using the ABAQUS [9] code coupled with TRAST [10], (a commercial material model that predicts phase composition). The comparison was performed on a carburized 5120 steel disk. In the experimental study, depth profiles of residual stress and microstructure were recorded through the case, the carburized layer, using conventional electropolishing and X-ray diffraction techniques [11,12]. Rietveld analysis of the X-ray diffraction data was used to determine the depth dependence of the lattice parameters of the austenite and martensite at each depth, which varied due to the combined effect of carbon content and stress [1–5,13,14]. Using the lattice parameters in conjunction with the stress measurements, the carbon content was also identified [1,14]. These measurements were compared with the carbon combustion burnout technique. The efficacy of the model and its assumptions were gauged by comparing predictions of the microstructure, residual stress profile, and carbon profile with experimental results.
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 0 ) 0 1 2 9 2 - 2
P. Rangaswamy et al. / Materials Science and Engineering A298 (2001) 158–165
159
Table 1 Chemical analysis of 5120 bar stock prior to carburization Element
C
Mn
P
S
Si
Ni
Cr
Mo
Cu
Al
N
O
Wt.%
0.23
0.83
0.012
0.03
0.22
0.15
0.8
0.04
0.15
0.031
0.008
0.003
3. Experimental procedures
3.1. X-ray diffraction
Fig. 1. Schematic of the disk, showing the directions for X-ray measurements.
2. Sample preparation Multiple cylindrical disks (30 mm diameter and 10 mm thick) as shown in Fig. 1 were cut from 5120 bar stock. The vendor-provided chemical analysis is shown in Table 1. The carburization schedule was at a carbon potential of 0.85% at 900°C for 3.25 h, followed by 840°C for 0.75 h. This was followed by an agitated oil quench at 71°C and a temper at 177°C for 1.5 h. Fig. 2 is a metallographic cross section of the carburized disk, with the surface at the top of the photo. The first 30–40 mm, below the surface shows evidence of decarburization. The martensite core is readily identified.
X-ray measurements were performed using a standard methodology as outlined in SAE-J784A [15] with a Phillips vertical diffractometer operating at 40 kV and 20 mA. Incident slits masked the beam, to illuminate approximately a 2 mm square on the surface. One flat surface of the disk was polished and all X-ray profiles were obtained through this surface. A schematic of the disk showing the measurement region is shown in Fig. 1. A circular region 6 mm in diameter in the center of the disk was electropolished at 54°C using a mixture of phosphoric and sulfuric acids and distilled water, volume ratio 2:1:1. The current was controlled at approximately 4.2 mA mm − 2 to minimize surface pitting. All measurements were performed using chromium radiation (wavelength : 2.289 A, ) for which the martensitic (211) reflection occurs at :156° (2u) and the austenite (220) reflection at : 128° (2u). Measured intensities were corrected for absorption at different c tilts, and normalized with respect to the Lorentz polarization factors. Background corrections were applied before calculating peak positions using the conventional parabolic technique.
Fig. 2. Photomicrograph of a cross-section of disk, from surface (top) down, showing evidence of de-carburization at surface.
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3.3. Retained austenite determination (con6entional X-ray and Riet6eld) Following progressive polishing at each depth, 2u scans from 40° to 161° were recorded at c= 0 for both conventional [16] (single-peak) and Rietveld structure refinements using ‘Generalized Crystal Structural Analysis’ (GSAS) [17]. In the refinement, a body centered tetragonal structure (I4/mmm) was assumed for the martensite, and a face centered cubic structure (Fm3m) for the retained austenite. The diffraction pattern was treated in its entirety, so peaks for individual hkl reflections need not be resolved [13,17]. By comparing the observed diffraction patterns to a pattern calculated from a model, the parameters were refined to fit the observations [18,19]. Refined variables include microstructural parameters (lattice constants, atomic positions and occupancies), peak shape parameters (strain and particle size), sample absorption, extinction, and Debye-Waller factors. Austenite volume fractions were also determined using the conventional technique of comparing intensities of the austenite (220) and martensite (200) reflections.
3.4. Carbon determination Fig. 3. Intensity versus angle, for Rietveld refinements of X-ray data, (a) showing both austenite and martensite reflections at the surface, and (b) showing only martensite 1 mm below the surface.
3.2. Stress measurements The penetration for chromium radiation in steel is approximately 3– 5 mm. Surface residual stress profiles in both the martensite and austenite were obtained using the classical ‘d versus sin2 c’ analysis of the diffraction data [11,12], Eq. (1) (dfc − d0)/d0 = [(1+ n)/E]sf sin2 c −(n/E)(s11 +s22) (1) where dfc and d0 are the lattice spacing in the measured direction (f) and tilt (c) of the scattering vector and the unstressed lattice spacing respectively for any given set of hkl planes. y and E are Poisson’s ratio and elastic modulus respectively, (0.3 and 205 GPa are representative of the bulk material). sf is the direction of the stress measured on the surface. Stresses in both the martensite and austenite were calculated (using a X-ray elastic constant of 6.3 ×10 − 6 MPa − 1) in two orthogonal directions at the center of the disk to a maximum depth of 1.2 mm, as shown in Fig. 1. A total of ten c tilts, five positive and five negative, were recorded.
An extra facet of the Rietveld method is that it offers an estimate of the carbon content by virtue of its effects on the c/a ratio. The relationship between the c/a ratio and the carbon content was independently determined on quenched samples of 5120, 5140, 5160, and 5180 steel, that have nominal carbon contents of 0.2, 0.4, 0.6, and 0.8 wt.%, respectively [19]. Using this as a calibration, the carbon profile of the 5120 disk was determined. Two other techniques, combustion burnout and microhardness profiling were also used to infer the carbon content. Combustion burnout has wide applicability for determining carbon content, and offers a resolution of approximately 50 mm in depth [20].
4. Experimental results
4.1. General obser6ations on X-ray data Generally, the X-ray diffraction peaks were broad (\ 10°, 2u) at higher angles (\ 120°) of 2u (Fig. 3). At the surface, the martensitic reflection was 14° wide, with 85% of the intensity coming from a width of 4° (2u). Peak splitting was not observed. There was no evidence of preferred orientation. Rietveld refinements for the surface and for a 1 mm depth are presented in Fig. 3. The tick marks indicate the positions of the peaks (including Ka1 and Ka2), and the difference between predicted and observed intensities is shown as the lower line in each plot. At a depth of 1 mm, the
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austenite reflections were absent, while the martensite reflections were sharper, indicating the presence of martensite only.
4.2. Residual stress From the X-ray diffraction data, residual stress profiles along one direction for both martensite and austenite were determined and plotted, see Fig. 4a. Similar stress profiles were measured in both orthogonal direc-
Fig. 5. 2-D axisymmetric model of the carburized disk used for finite element calculations. Thermal and carbon concentration boundary conditions were defined at the top and outer surfaces of the disk; the bottom surface is a symmetry plane.
tions [19]. The profiles presented in Fig. 4a were corrected for layer removal using the Moore & Evans technique [12]. From the surface to a depth of 150 mm, there was scatter in the residual stress measurements for both martensite and austenite. At depths greater than 150 mm, the martensite and austenite exhibited similar trends. The maximum compressive stress of 380 MPa was at 600 mm, and the crossover from compressive to tensile occurred at approximately 1150 mm.
4.3. Retained austenite Fig. 4b shows the retained austenite profiles determined from both conventional and Rietveld analysis of the X-ray diffraction data. Near the surface, there was approximately 30 vol.% retained austenite dropping to near 2–4% at a depth of 800 mm. Constituent determination using conventional techniques compares well with the Rietveld determined data.
4.4. Carbon Fig. 4c shows the carbon profiles determined from X-ray, and combustion burnout techniques, along with microhardness data. Below 350 mm, there was good agreement in the carbon profiles determined from X-ray data and combustion burnout techniques. However, the variation in carbon from the surface to 350 mm for these two techniques was significant. Combustion burnout showed a maximum of 0.76 wt.% carbon from 50 to 150 mm depth from the surface; and the carbon determined from the X-ray data had a maximum of 0.67 wt.% at 100 mm depth.
5. Finite element analysis Fig. 4. (a) Residual stress profiles in the martensite and austenite; (b) retained austenite volume fractions versus depth (conventional and Rietveld analysis of X-ray data); and (c) carbon (from X-ray and combustion) along with hardness profiles from Vicker’s micro-indentation technique.
5.1. Procedure For the numerical analysis, a 2-D axisymmetric finite element model that represented the disk, along with the meshing scheme, is shown in Fig. 5. Over the first 1 mm
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of thickness from the top surface, the mesh was graded in layers of 60 mm, while a coarser mesh of 120 mm was used for the interior. This meshing scheme reflects the steep stress gradients in the carburized layer (or case region) and the resulting microstructural variations. Material properties for Swedish 2511 steel were used, since these properties were not available for 5120 steel in a form accessible to the numerical model. The 2511 steel is chemically, thermally, and mechanically similar to 5120. To represent the heat transfer during quenching, film coefficients for agitated oil were applied to the top and outside boundaries of the disk, in the ratio of two to one [6]. Simulation of carburization and quenching was achieved using the commercial package TRAST, which was coupled to ABAQUS as a User Defined Material Subroutine (UMAT) [9,10,21]. TRAST predicts and describes the material behavior of the various possible steel constituents formed during quenching. The simulation was carried out in three steps. First, the carbon distribution was predicted using the mass diffusion material model in ABAQUS. Secondly, the temperature profile and constituent compositions were determined using the thermal/ metallurgical model in ABAQUS/TRAST (incorporating the results from the first step). Finally, stresses were calculated using the mechanical model in ABAQUS/TRAST (incorporating the results from steps one and two).
5.2. Finite element analysis predictions Contour plots of hoop stresses, retained austenite volume fraction, and carbon concentration, from the numerical analysis are presented in Fig. 6. A contour plot of the hoop stresses is shown in Fig. 6a. The predicted hoop stresses (and radial stresses) were compressive with a maximum of 420 MPa at the top surface, and becoming tensile (ranging from 60 to 150 MPa) at the interior of the disk (Fig. 6a). Fig. 6b shows the predicted volume fraction of retained austenite. The outside surfaces were at a maximum of 25 vol.%. The retained austenite montonically decreased across the case. The interior of the disk shows a uniform austenite volume fraction of 2 vol.%. The balance of the predicted microstructure was martensite; no other microstructures (pearlite, bainite, or ferrite) were numerically predicted (or experimentally observed). Fig. 6c shows the carbon distribution after the completion of the carburizing cycle. The carbon content decreases montonically from 0.85 wt.% at the outer surfaces of the disk to 0.2 wt.% within the interior of the disk.
6. Comparison of numerical and experimental data The numerical predictions are compared with the experimental results in Fig. 7, for (a) stress, (b) retained austenite, and (c) carbon content.
6.1. Residual stress A comparison of the predicted and measured stresses is presented in Fig. 7a. At depths greater than 500 mm below the surface, the agreement for the properties investigated was reasonable. However, closer to the surface, in the case region, the prediction overestimates the measured values in some locations by more than 100%. Moreover, the predicted depth of maximum compressive stress was shallower in the model than measured on the disk. Because of the scatter in data for the measured stresses, within the first 100 mm of the surface, the possibility of a local maximum or minimum is ill defined. Note, however, that the near surface region where the stress was over-estimated, is similar to the region where the model under-estimates the retained austenite fraction!
6.2. Retained austenite The retained austenite prediction shows less variation with depth than the experimental data (Fig. 7b). The model predicts variation from 25 to 2 vol.%, whereas the experimental measurements suggest that the true maximum values may exceed 30 vol.%. Like the stress predictions, the region of biggest disparity between experimental data and the model predictions are within 400 mm of the surface. Notably, the predicted values show no evidence of a local maximum or minimum near the surface. The measured values differ by as much as 3–5 vol.% depending on whether the analysis was performed by Rietveld or conventional analysis. Although we have not quantified the errors, we are inclined to give more credence to the Rietveld data, since it uses three peaks per phase instead of just one in analyzing the data.
6.3. Carbon Prediction of the carbon content was performed in ABAQUS using the mass diffusion material model. Fig. 7c shows a plot of the carbon as predicted from the model, and experimentally by both a combustion burnout technique and from c/a ratio data taken from the Rietveld analysis of the X-ray data. The predicted values, showed as expected, a monotonic decrease in carbon from a maximum surface value of 0.85–0.32 wt.% at a depth of 1.0 mm, and continuing to decrease to 0.2% at 1.3 mm. Agreement between the model and the combustion burnout measurements was excel-
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lent over the complete range profiled. However, there was a noticeable plateau at 0.76 wt.% C in the combustion data, from the surface to about 200 mm. Consider-
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ing this disparity, the agreement between the model and the combustion data was good. There was significant disparity between the model and Rietveld estimate of
Fig. 6. Contour plots from numerical analysis simulations showing (a) hoop stress (MPa) in the disk after material removal on the top surface; (b) retained austenite (volume fraction); and (c) carbon variation (wt.%) at end of carburizing cycle.
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6.4. O6erall comparison Table 2 summarizes the salient features from the predictions and measured values. The model used in this work incorporates a description of the microstructure phase evolution (TRAST) with a conventional finite element solution for the mechanical and thermal history of a carburized steel. Despite the fact that neither the boundary conditions (e.g. heat transfer coefficients) nor the material properties (TRAST predictions used Swedish 2511 steel properties) were optimal, comparison with experimental validation measurements was encouraging. The most notable disparity between model and experiments came in the near surface region (0–400 mm), which may be associated with decarburization (this is qualitatively supported by the microhardness data). Other reasons for disparity may derive from tempering effects, which are notoriously hard to model, and are not included in TRAST.
7. Conclusions Comparison of the ABAQUS numerical predictions of residual stress, retained austenite, and carbon showed reasonable agreement with experimental measurements at depths greater than 400 mm from the Table 2 Comparison of experimental data with numerical predictions
a) Stress Maximum stress Depth of maximum stress Depth of comp.tens. (cross over) Fig. 7. Comparison of numerical simulations with experimental data for (a) residual stress; (b) retained austenite profiles; and (c) carbon profiles.
b) Austenite Maximum austenite Depth of max. austenite At 1.0 mm depth c) Carbon (wt.%): Maximum carbon (wt.%)
carbon, (derived from the c/a ratio) over the region from 0 to 400 mm; (the same region where the model faired poorly in predicting the retained austenite and residual stress distributions). Also shown in Fig. 7c are Vicker’s hardness measurements, which qualitatively track the carbon content variation. The Vicker’s hardness measurements are included for comparative purposes only, since they are not calibrated for carbon content.
Depth of max. carbon (wt. %)
At 1.0 mm depth
Experimental
Numerical simulation
−380 Mpa 550 mm
−450 Mpa 330 mm
1.2 mm
1.3 mm
30 vol.% 100 mm
25 vol.% Surface
2–4 vol.% 0.67 wt.% (XRD-c/a ratio) 0.76 wt.% (combustion) 100 mm (XRD-c/a ratio) 50–150 mm (combustion) 0.38 wt.% (XRD-c/a ratio) 0.37 wt.% (Combustion)
4 vol.% 0.80 wt.%
Surface
0.32 wt.%
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surface. However, from the surface to a depth of 400 mm significant disparities were observed. In the near surface region (B400 mm) the predicted stresses exceeded the measurements by as much as 200 MPa. Moreover, the depth of maximum compressive stress was displaced to a shallower depth than what was measured. Although the predicted retained austenite profile showed better agreement with the experimental data it also differed from the measurement by as much as 10%. For the carbon prediction there was relatively good agreement with the combustion measurements but less good agreement between the three experimental techniques. Although the lower value of the X-ray measurements might be consistent with decarburization, the disparity with the combustion measurements is not immediately explicable. However, the use of X-rays to profile carbon content is a relatively new approach and the technique may need further work to improve our understanding of the sensitivity of lattice parameters to alloy composition It is clear that the model, although adequate below 400 mm, is at best qualitative in its predictions from the surface to a depth of 400 mm. However, the model, as applied includes several approximations; the microstructure was modeled for a different steel, heat transfer coefficients as well as the inelastic (temperature dependent) mechanical properties were estimated, and the tempering process was ignored. In the past, attempts to model residual stress and distortion have met with mixed success. The phase changes have been mimicked either by incorporation of a temperature dependent yield strength or by large changes in thermal expansion coefficient [22,23]. In those approaches, microplasticity and microscopic deviatoric strains are not accounted for and the predictions showed large discrepancies from the measured stresses [24–26]. Correctly accounting for the thermal, mechanical and microstructural mechanisms is likely to improve the models but, as we have shown in this uncoupled-serial analysis, achieving a good agreement with experiment is not easy. Nevertheless we consider that further attempts to refine microstucture-thermomechanical hybrid models are worthwhile.
References [1] [2] [3] [4] [5]
[6]
[7]
[8]
[9] [10]
[11]
[12] [13] [14] [15]
[16]
[17]
[18]
[19]
[20] [21]
Acknowledgements
[22]
We gratefully acknowledge Maurice Howes and Gerry Koller from IITRI for heat treating the specimens. We appreciate the assistance of Peggy Goldman (Los Alamos National Laboratory) in implementation and use of TRAST and Charles A. Anderson (Los Alamos National Laboratory) for valuable discussions. .
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[23] [24] [25] [26]
D.P. Koistinen, Trans. ASM 50 (1958) 227. L.J. Ebert, Metallurgical Trans. A 9A (1978) 1537. R.C. Fischer, Metallurgical Trans. A 9A (1978) 1553. G. Krauss, Metallurgical Trans. A 9A (1978) 1527. W. Dowling, T. Pattock, B.L. Ferguson, D. Shick, Y. Helen Gu, M. Howes, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 350, ASM International, Materials Park, OH, 1996. D. Shick, D. Chenoweth, N. Palle, W.T. Lee, W. Elliot, H. Walton, M. Howes, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 357, ASM International, Materials Park, OH, 1996. D. Bammann, V. Prantil, A. Kumar, J. Lathrop, D. Mosher, M. Callabresi, H.J. Jou, M. Lusk, G. Krauss, B. Elliot Jr., G. Ludtka, T. Lowe, B. Dowling, D. Shick, D. Nikkel, 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 367, ASM International, Materials Park, OH, 1996. C. Anderson, P. Goldman, P. Rangaswamy, G. Petrus, B.L. Ferguson, J. Lathrop, D. Nikkel Jr., 2nd International Conference on Quenching and the Control of Distortion. Proceedings, p. 377, ASM International, Materials Park, OH, 1996. HKS Inc, ABAQUS Users Manual, Providence, RI, USA, 1993. N. Jarvstrat, S. Sjostrom, Current Status of TRAST: a Material Model Subroutine System for the Calculation of Quench Stresses in Steel, Linkoping University, ABAQUS Users’ Conference Proceedings, 1993, pp. 273 – 287. I.C. Noyan, J.B. Cohen (Eds.), Residual Stress, Measurement by Diffraction and Interpretation, Springer-Verlag, New York, 1987, pp. 117 – 130. M.G. Moore, W.P. Evans, SAE Trans. 66 (1958) 341. R.B. Von Dreele, J.D. Jorgensen, C.G. Windsor, J. Appl. Crystallogr. 15 (1982) 581. C.S. Robert, Trans. AIME, J. Met. Feb (1953) 203–204. M.E. Hilley (Ed.), Residual Stress Measurement by X-ray Diffraction, SAE Information Report J784a, Society of Automotive Engineers, New York, 1971, pp. 12 – 25. B.D. Cullity (Ed.), Elements of X-ray Diffraction, second ed., Addison-Wesley Publishing Co, Inc, New York, 1978, pp. 411– 415. A.C. Lawson, R.B. Von Dreele, Generalized Crystal Structural Analysis System (GSAS), Los Alamos National Laboratory, LAUR 86-748, 1966. A.C. Lawson, A. Williams, J.A. Goldstone, D.T. Eash, R.J. Martinez, J.I. Archuleta, D.J. Martinez, B. Cort, M.F. Stevens, J. Less-Common Met. 167 (1991) 353 – 363. P. Rangaswamy, M.A.M. Bourke, A.C. Lawson, J. O’Rourke, J.A. Goldstone, in: J.V. Gilfrich, et al. (Eds.), Advances in X-ray Diffraction Analysis, vol. 39, Plenum Press, New York, 1997, pp. 319 – 329. Metals Handbook — Desk Edition — Published by ASM, Metals Park, Ohio, 1998, pp. 28 – 44. N. Jarvstrat, Two Dimensional Calculation of Quench Stresses in Steel, Thesis No. 45, Linkoping, Sweden, 1990. J.A. Goldak, in: S.A. David, M. Vitek (Eds.), Recent Trends in Welding Science and Technology, ASM International, Gatlinburg, TN, 1985, pp. 71 – 82. S. Sjostrom, Mater. Sci. Technol. 1 (1985) 823 – 829. A.S. Oddy, J.A. Goldak, J.M.J. McDill, J. Press. Vessel Technol. 114 (1992) 33 – 38. B.L. Josefson, C.T. Karlsson, J. Press. Vessel Technol. 114 (1992) 376 – 378. A.S. Oddy, J.A. Goldak, J.M.J. McDill, Eur. J. Mech. A-Solids 9 (1990) 253 – 263.