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J. Mater. Sci. Technol.  2020, Vol. 49 Issue (0): 157-165    DOI: 10.1016/j.jmst.2019.10.044
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Multi-length scale modeling of carburization, martensitic microstructure evolution and fatigue properties of steel gears
Edward Charles Henry Crawford O’ Brien, Hemantha Kumar Yeddu*()
School of Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
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Multi-length scale modeling is performed to (i) predict the carburized case depth of SAE8620 steel gears by solving the Fick’s second law of diffusion, (ii) model the martensitic microstructure evolution in a grain inside the carburized case as well as to study the effect of stress cycling on retained austenite (RA) and martensite using a 3D phase-field model, (iii) simulate the effect of carburization and different RA contents on macroscale fatigue behavior of SAE8620 steel spur gear using the finite element method. The diffusion model predicts that the case depth increases with increasing heat treatment time and temperature. The phase-field simulations show that RA can transform to martensite during fatigue loading, where the extent of the transformation will depend on the type of stresses applied, i.e. stresses in a high stress regime or low stress regime of fatigue loading. Reverse transformation of martensite to austenite is also observed in low RA sample under high stress regime. The macroscale simulations show that the carburized case with high RA gives rise to better fatigue life compared to that with low RA.

Key words:  Phase-field model      Martensitic transformation      Microstructure      Gear steel      Carburization     
Received:  04 May 2019     
Corresponding Authors:  Hemantha Kumar Yeddu     E-mail:  hemanth.

Cite this article: 

Edward Charles Henry Crawford O’ Brien, Hemantha Kumar Yeddu. Multi-length scale modeling of carburization, martensitic microstructure evolution and fatigue properties of steel gears. J. Mater. Sci. Technol., 2020, 49(0): 157-165.

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Fig. 1.  Diffusion of carbon in SAE 8620 steel after carburizing for (a) 2 h and (b) 5 h.
Fig. 2.  (a) Phase-field stress cycling simulations. Evolution of martensite volume fraction and mean von Mises equivalent stress in (b) high RA sample and (c) low RA sample. (d) Variation in the mean equivalent plastic strain with martensite volume fraction.
Fig. 3.  Simulated microstructures of an austenite grain with high RA content (50 % RA) subjected to stress cycling. Microstructure (a) before the stress cycling (as-quenched), (b) after completion of loading part of stress cycle-1 in the low stress regime, (c) after completion of stress cycling in the low stress regime, (d) after completion of stress cycling in the high stress regime. Martensite variants 1, 2 and 3 are shown in red, blue and green, respectively. Areas of martensite reversion are shown by ellipses (white).
Fig. 4.  Simulated microstructures of an austenite grain with low RA content (14 % RA) subjected to stress cycling. Microstructure (a) before the stress cycling (as-quenched), (b) after completion of stress cycling in the low stress regime, (c) after completion of stress cycling in the high stress regime.
Fig. 5.  Spur gear (inset) designed using Inventor and the gear tooth considered for fatigue analysis (ellipse). Carburized case can be clearly seen in the single gear tooth (left). Arrow indicates the loading direction and location.
Uncarburized Carburized
S Nf S Nf
425 11818 850 1 ×106
396 17150 900 3.5 ×105
365 46349 1000 7.5 ×104
327 129619 1100 1.9 ×104
300 294496 1100 8.7 ×104
279 449772 1200 4.8 ×103
262 733053 1300 1.5 ×103
Table 1  Experimental data of stress (S) (in MPa) and the number of cycles to failure (Nf) used in fatigue analysis of uncarburized [43] and carburized [25] gear with 0.9 mm case depth using Ansys.
Low RA High RA
S Navg S Navg
1750 9 ×103 2100 1.5 ×104
1500 1.95 ×104 1950 2.17 ×104
1250 7.33 ×104 1650 2.2 ×104
1100 1.5 ×105 1350 5.93 ×104
950 2.38 ×105 1100 8.7 ×104
900 7 ×105 900 5.13 ×105
800 2.75 ×106 800 3.39 ×106
NA NA 750 6.41 ×106
NA NA 700 6.73 ×106
NA NA 650 107
Table 2  Experimental data of stress (S) (in MPa) and average number of cycles to failure (Navg) used in fatigue analysis of gears with different RA content using Ansys [3].
Fig. 6.  ANSYS results of fatigue life of (a) uncarburized and (b) carburized gear tooth with case depth of 0.9 mm under a force of 50 kN at 45o with X-axis, (c) corresponding equivalent alternating stress of gear tooth shown in (b).
Fig. 7.  ANSYS results of (a) equivalent alternating stress and (b) von Mises equivalent stress in gear tooth with a carburized case containing high RA content under 10 kN force at 45o with X-axis.
Fig. 8.  ANSYS results of effect of RA on fatigue life. (a) Low RA and (b) high RA gear tooth under a force of 100 kN at 45o with X-axis.
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