IMPORTANCE OF INDUCTION HARDENED CASE DEPTH IN TORSIONAL APPLICATIONS Induction hardened case depth plays a very important part in determining the static and fatigue properties of shafts. Both effective and total case must be considered to optimize shaft performance. Gregory A. Fett* Dana Corp. Maumee, Ohio
*Member of ASM International and member, ASM Heat Treating Society
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his article updates work originally published in February 1985 Metal Progress, which examines the relationship between induction hardened case depth and torsional strength and fatigue life. This relationship is especially important when designing shafts to transmit torque, such as automotive and truck axle shafts. The recent work also examines the effect of both different steel grades and prior microstructures on the relationship. Induction hardened shafts lend themselves very well to most torsional applications because induction hardening increases the hardness near the surface where it is most needed and it leaves the surface in compression, which improves fatigue life. When a shaft is loaded torsionally, the shear stress is highest at the surface and zero at the center. In the absence of a stress concentration factor, stress increases linearly from the center to the surface. Thus, only the surface needs to be hardened to a depth to adequately exceed the applied stress. When the surface layer is hardened, martensitic
1,200 Case depth A Case depth B
Torsional strength and stress, MPa
1,000
800
HRC 52 50 40 30 20 10 0
HB 514 481 371 286 226 187 150
ULT 1793 1690 1276 966 759 655 517
Tensile Yield 1614 1524 1152 941 614 503 366
Torsional Yield 966 917 690 503 366 303 221
From SAE J413 (units are MPa)
600
Case depth B
Case depth A 400
200 Applied stress 0 0
10
20
30 40 Percent of bar diameter
Fig. 1 — Case depth versus torsional strength and stress.
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50
60
transformation causes it to expand leaving the surface in compression, as opposed to through hardening where the core also expends leaving the surface in tension. The depth to which a shaft must be hardened can be determined theoretically. Figure 1 shows two different induction case depths (A and B) with a surface hardness of 52 HRC and a core of 12 HRC. The applied stress is shown as a straight line from zero at the center to a maximum at 52 HRC at the surface with no stress concentration factor. Also shown are the corresponding torsional yield strength values which were derived by converting hardness to tensile and yield and then using a factor of 0.6 to convert yield to torsional yield. Clearly, case depth A will fail first at the case-core interface. The applied stress curve exceeds the strength curve at the case-core interface. However, case B is able to take full advantage of the 52 HRC surface hardness. The applied stress curve just touches the strength curve at the surface and at the case core interface. Thus, it may fail at the surface or at the case-core interface. Hardening deeper than case B in this situation will do no good because it will fail from the surface even if the strength curve is shifted farther to the right. This is the optimum case depth. In addition, by hardening too deep, the residual surface compressive stress may be reduced. Case depth A has an effective depth measured to 40 HRC equal to 15% of the bar diameter and a total case depth to 20 HRC equal to 25%. Case depth B has an effective depth of 23% and a total depth of 31%. Although case depth B (the optimum case depth) takes full advantage of the situation, case depth A may be sufficient in many applications where the stress is not excessively high. Case depth A could also be improved if necessary by increasing the core hardness possibly through a quench and temper operation. To examine the correlation of actual 15
shaft torsional performance to case depth, test shafts splined at both ends were induction hardened to varying case depths. The shafts had diameters of 28.58 and 38.86 mm (1.125 and 1.530 in.) in the center and a slightly larger spline on both ends, which caused the
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failure to occur in the middle. Different hardenability steels were used to look at the relationship of effective and total case depth. The effect of core hardness also was studied by using shafts made of hot-rolled (HR), cold-drawn (CD), and quench and tempered (Q&T) steels.
HEAT TREATING PROGRESS • OCTOBER 2009
1,800 Ultimate
1040 CD ultimate 1040 CD yield 1541 Q&T ultimate 1541 Q&T yield 1541 HR ultimate 1541 HR yield 1050M HR ultimate 1050M HR yield 4140 HR ultimate 4140 HR yield 1038 HR ultimate 1038 HR yield 1040 HR ultimate 1040 HR yield
1,600
Torsional strength, MPa
1,400 1,200 Yield
1,000 800 600 4140 steel
400 All others
200 0
0
5
10 15 20 Effective case depth, % of bar diameter
25
30
Fig. 2 — Effective case versus torsional strength. 1,800 Ultimate
1,600
1040 CD ultimate 1040 CD yield 1541 Q&T ultimate 1541 Q&T yield 1541 HR ultimate 1541 HR yield 1050M HR ultimate 1050M HR yield 4140 HR ultimate 4140 HR yield 1038 HR ultimate 1038 HR yield 1040 HR ultimate 1040 HR yield
Torsional strength, MPa
1,400 1,200 Yield
1,000 800 600 400
1541, 1541 Q&T, 4140
200 All others 0 0
10
20 30 40 Total case depth, % of bar diameter
50
60
Fig. 3 — Total case depth versus torsional strength. 1,400 1040 steel 1541 steel 1050M steel 4140 steel
1,200 Torsional strength and stress, MPa
Static Torsional Test Results Table 1 lists results of static torsional tests, which also includes data from production axle shafts made of SAE 1038 and 1040 steel. It should be noted that the yield strength was determined by the JEL (Johnson elastic limit) method, which is defined by a 50% change in slope. Also, total case was defined as 20 HRC, or the total visual case if the core was 20 HRC or greater. Effective case versus torsional strength (Fig. 2). The torsional yield and torsional ultimate strengths increase with case depth up to a certain point, and level off at the optimum case depth. The bottom line of each curve represents the minimum strength versus case depth values for the steels listed. The minimum yield for the optimum effective case depth of 23% of the bar diameter is approximately 795 MPa (115,000 psi). The minimum ultimate strength for the same 23% effective case depth is about 1,379 MPa (200,000 psi). SAE 4140 provides a lower torsional strength for any given case depth compared with the rest of the steels, except at the far right portion of the curve. This is because 4140 has higher hardenability, and, hence, a lower total case depth for the same effective case, indicating that total case depth is also a factor in determining torsional strength. At the far right of the curve, all of the steels are about equal, indicating that only effective case is important in this area of the curve. Total case depth versus torsional strength (Fig. 3). This curve is similar to that in Fig. 2, except case depth values for any given strength are greater (as expected) and there appears to be more variation in the data. The optimum case depth where the yield strength levels off is at 31% of the bar diameter. Again, there is a difference in the minimum strength depending on the grade of steel. In these tests, SAE 1541 and 4140 provided a higher torsional strength for any given case depth compared with the other steels, especially in the right hand portion of the curve. This is because the higher hardenability steels have a deeper effective case depth for any given total case depth compared with the rest of the steels. Also, SAE 1541 has a quench and tempered core with a greater hardness. The higher core hardness is similar to a deeper total case depth. Both effective case and total case are important in determining torsional strength, but effective case seems to be a more
1,000 1050M 4140
800 1040 steel
HRC 52 50 40 30 20 10 0
HB 514 481 371 286 226 187 150
ULT 1793 1690 1276 966 759 655 517
Tensile Yield 1614 1524 1152 941 614 503 366
Torsional Yield 966 917 690 503 366 303 221
From SAE J413 (units are MPa)
600 400 1541 Q&T 200
Applied stress 0 0
10
20
30 40 Percent of bar diameter
50
60
Fig. 4 — Case depth providing 621 MPa minimum torsional yield strength.
accurate predictor. Torsional strength versus applied stress (Fig. 4). Case depth for each of the four steel grades tested provided a minimum torsional yield of 621 MPa (90,000
HEAT TREATING PROGRESS • OCTOBER 2009
psi). The lower hardenability steels did so with a shallower effective case and a deeper total case compared with the higher hardenability steels. The 1541 with its quench and tempered core did 17
so with a shallower effective and shallower total case. This demonstrates that both effective and total case depths are important in determining torsional strength, and there are various ways to achieve the same strength. In theory, Fig. 4 indicates that the only two things that should matter in keeping the strength curve above the stress curve are total case depth and surface hardness. However, in reality, both effective and total case make a difference, and the higher hardness of the 1050M material did not provide a higher strength even at greater case depths. 1,200 SAE 1040 CD 1541 Q&T 4140 HR
Cycles at ±407 MPa, ×103
1,000
800
600
400
200
0 1
100
200
300 400 500 600 700 Average torsional yield strength, MPa
800
900
1,000
Fig. 5 — Fatigue life versus torsional yield strength.
Fatigue Characteristics Figure 5 shows the fatigue characteristics of the SAE 1040, 1541, and 4140 test shafts. All shafts were run in fully reversed torsional fatigue at a stress of 407 MPa (59,000 psi). The data show the correlation between fatigue life and torsional yield strength. Considerable scatter, or variation, is present, which is normal in fatigue testing. It appears that the plain carbon-steel grade 1040 reached suspension at 1,000,000 cycles before the other two grades. A plausible explanation for this is shown in Fig. 4, where all the case depths have an equal static strength of 621 MPa (90,000 psi) minimum. However, if we look at the applied stress shown at various levels, the 1040 has a deeper total case depth, and the applied stress is somewhat higher where it intersects the case-core interface. This would seem to indicate that total case depth may be more critical for fatigue life. Fatigue life versus total case depth is shown in Fig. 6. The data demonstrate that fatigue life increases with increasing total case depth. SAE 1541 steel appears to provide higher fatigue life for the same total case depth compared with the other two materials. The reason for this is the higher hardness of the quench and tempered core, which essentially acts the same as a deeper total case depth. SAE 1040 and 4140 have the same fatigue life even
Table 2 — Required case depth versus torsional strength Minimum torsional strength Ultimate, MPa
966
1,138
1,379
Yield, MPa
483
621
793
1,172
1,310
1,517
621
758
862
Typical torsional strength Ultimate, MPa Yield, MPa Diameter, mm
Case depth required (effective/total), mm
19.05
2.11/3.81
2.87/4.78
4.39/5.92
22.23
2.44/4.45
3.33/5.56
5.11/6.88
25.40
2.79/5.08
3.81/6.35
5.84/7.87
28.58
3.15/5.72
4.29/7.14
6.58/8.86
31.75
3.51/6.35
4.78/7.95
7.32/9.86
34.93
3.84/6.99
5.23/8.74
8.03/10.82
38.10
4.19/7.62
5.72/9.53
8.76/11.81
41.28
4.55/8.26
6.20/10.31
9.50/12.80
44.45
4.90/8.89
6.68/11.13
10.24/13.79
47.63
5.23/9.53
7.14/11.91
10.95/14.76
50.80 Any diameter
5.59/10.16
7.62/12.70
11.68/15.75
0.11(diam)/0.20(diam)
0.15(diam)/0.25(diam)
0.23(diam)/0.31(diam)
Note: torsional yield strength is valid for longer shafts with length/critical diameter ratio of 6 and greater. The critical diameter is the smallest diameter of the shaft where most of the deflection and failure occurs. As shaft length decreases, the ratio of yield/ultimate increases. Torsional ultimate strength does not depend on length, and is valid for any length shaft.
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HEAT TREATING PROGRESS • OCTOBER 2009
Applying the Knowledge Table 2 illustrates how the results of this study can be used, where an engineer is trying to design a series of shafts to be good for three different torsional strength levels. The middle column is intended to provide a minimum torsional yield of 621 MPa (90,000 psi). From the data in Figs. 2 and 3, we found that for a plain-carbon steel such as 1040, this would require an effective case of 15% of the diameter and a total case of 25%. These percentages would also work for other steels, although the strength may actually be greater. A higher hardenability steel, such as 4140, would require a 17% effective and 23% total case. The 621 MPa (90,000 psi) static yield strength could also be obtained with a quench and tempered core of approximately 20 HRC by using an effective case of 15% and a total case of 19%. However, the quench and temper operation would also add a fair amount of cost to the part. A couple of other examples we could look at would be minimum torsional yield strength of 485 MPa (70,000 psi) minimum and the highest strength shaft of 795 MPa (115,000 psi) minimum. Figs. 2 and 3 show that the 485 MPa (70,000 psi) shaft would re-
1,200,000
1040 steel 1541 steel 4140 steel
1,000,000
Cycle life, ×103
800,000
600,000
1541 Q&T 1040 and 4140 400,000
200,000
0
0
10
20 30 40 Total case depth, % of bar diameter
50
60
25
30
Fig. 6 — Torsional fatigue life versus total case depth at ±59,000 psi (±407 MPa). 1,200,000
1040 steel 1541 steel 4140 steel
1,000,000
800,000
Cycle life, ×103
though these two steels are on the opposite ends of the hardenability spectrum. As long as the total case depth is the same, the fatigue life is the same. A situation encountered several years ago serves to illustrate this. A production axle shaft made of SAE 1038 steel was not providing the desired fatigue life, so a more premium grade (SAE 4140) was substituted. The manufacturing plant induction hardened the 4140 to the same effective case depth as the production parts and discovered that the fatigue life actually decreased rather than increased. The torsional fatigue life versus effective case depth shown in Fig. 7 indicates the reason for this. A 15% effective case with 1040 steel provides a fatigue life in excess of 200,000 cycles, while the same case depth with 4140 provides a life of less than half of that. The reason is that 4140 has a lower total case depth compared with 1040 due to the difference in hardenability. To increase the fatigue life of 4140, it was necessary to increase the total case depth. This also means increasing the effective case along with it. In the end, 4140 did not really provide any benefit in fatigue over the current production parts.
600,000
1040 and 1541 Q&T
4140
400,000
200,000
0
0
5
10 15 20 Total case depth, % of bar diameter
Fig. 7 — Torsional fatigue life versus effective case depth at ±59,000 psi (±407 MPa).
quire 11% effective case and 20% total, while the 795 MPa (115,000 psi) shaft would need 23% effective and 31% total. These numbers could be applied to any diameter shaft, but as the size increases, the hardenability of the steel would also have to increase to be able to obtain these case depths. Conclusions Induction case depth plays a very important part in determining the static and fatigue properties of shafts. Torsional strength does increase with case depth, but only to a point, then hardening deeper does no good. Both effective and total case must be considered to optimize shaft performance. Effective case appears to be the best predictor of torsional strength, while total case is the best predictor of fatigue life. The relationship between case depth and torsional strength is certain, but there is a
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considerable amount of scatter or variation. It is easy to see that if the range of case depths observed was not wide enough, the relationship could be missed. Core hardness must also be considered because it has the same effect as changing the total case depth. While fatigue life does correlate to shaft strength to some degree, there is even more scatter or variation then with the case depth versus strength data. Below 200,000 cycles, the scatter from high-tolow life can be up to 10:1. Above that, as we approach the fatigue limit, the HTP scatter can be in excess of 20:1. Bibliography Fett, G., Induction Case Depths for Torsional Applications, Metal Progress, p 4952, Feb., 1985. For more information: Gregory Fett, Dana Corp., Maumee, Ohio; tel: 419-887-3296; email:
[email protected]; www.dana.com.
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