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Induction Case Hardening of Axle Shafts

\bla\Gregory A. Fett, Dana Corporation

\a\Introduction

Axle shafts are ideally suited to case hardening, or surface hardening by induction.

Although induction heating has the capability to through harden shafts, it is case

hardening or surface hardening that is addressed in this article. Axle shafts are certainly

one of the most common induction-hardened components found throughout the world.

There are several reasons for this:

\bl\

The round, elongated geometry permits them to be rotated and scanned with

relatively simple induction coils and equipment.

Axle shafts normally transmit torque, so the stress is highest at the surface, which

is exactly where induction hardening increases the hardness and strength.

Likewise, axle shafts sometimes transmit bending loads, and the stress for this

type of loading is also greatest at the surface.

Induction hardening leaves the surface with a residual compressive stress that

greatly enhances fatigue life and the long-term durability of the shaft.

Induction hardening permits the use of low-cost plain carbon steels, which keeps

the manufacturing costs to a minimum.

The process is relatively quick, environmentally friendly, and does not require a

great amount of floor space.

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Induction-hardened axle shafts grew in popularity in the United States during the

1960s. Prior to that, many axle shafts were still heat treated by through hardening or

quenching and tempering. With this method, the entire shaft cross section is hardened in a

furnace. A typical through-hardened shaft was made from an alloy steel, such as SAE

4140 or 4145 with a quenched and tempered hardness of 45 to 52 HRC. Reportedly,

fatigue failures in the field were not uncommon with through-hardened axle shafts in this

era. With the advent of induction hardening of axle shafts, fatigue failures all but

disappeared, due to the vastly superior fatigue life.

Some through-hardened shafts were also made from plain carbon steel, such as SAE1046. Even though a quench-and-temper process was used to harden the shaft, a case was

created due to the limited hardenability of the steel. The outer surface achieved a higher

hardness than the core, similar to an induction-hardened component. Reportedly, this was

able to overcome some of the fatigue-life concerns due to the formation of a residual

compressive stress layer near the surface, similar to that created by the induction

hardening process.

\a\Axle Shafts

\c\Types of Axle Shafts.\ce\ Axle shafts are used in automobiles, trucks, off-

highway vehicles, and other machinery and equipment, primarily to transmit torque. The

ends of the shaft are commonly connected to the components the torque is being

transmitted from and to by splines, joints, or flanges. Axle shafts can typically range in

diameter from 20 mm (0.8 in.) to well over 100 mm (4.0 in.). Some of the more common

types of automotive and truck axle shafts are shown in Fig. 1.

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The full-float axle shaft shown at the top of Fig. 1 is designed to transmit torque

only and is typically found on medium- to heavy-duty trucks with a rigid beam-style axle

assembly. The shaft connects the center section of the axle to the hub located on the

wheel end. The shaft is connected to the side gear, in the center section, using a spline,

while the outboard end is connected to the wheel hub by a flange and fasteners. The

diameter of the shaft is typically relatively uniform over the entire length. The weight of

the vehicle is transmitted from the wheel and hub through inner and outer wheel bearings

to the spindle and into the axle housing, thereby bypassing the axle shaft. The induction-

hardened pattern on this type of axle shaft normally extends the full length of the shaftuntil the diameter increases sufficiently in the flange radius so that induction hardening is

no longer needed. The case depth required is usually constant for the entire length.

The semifloat axle shaft, which is shown in the middle and bottom of Fig. 1, is

designed to transmit both torque and bending loads. This type of axle shaft is typically

found on passenger cars and some light-duty trucks with rigid beam-style axle

assemblies. The diameter of the semifloat axle shaft typically increases as it moves

outboard from the spline toward the flange, to accommodate the bending load. With the

semifloat shaft, the wheel is attached directly to the flange of the shaft so the bending

load is transmitted through the shaft into the wheel bearing and into the axle housing.

There are two types of semifloat shafts: one that employs a tapered unit bearing, which

has an inner and outer race; and the other that uses an on-shaft roller bearing, which uses

the axle shaft as the inner race. On the latter type, the shaft hardness must be sufficiently

high in order to also function as the inner race to the bearing. This is accomplished by

using a higher-carbon steel. Again, the induction-hardened pattern of both types of shafts

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typically extends nearly the full length of the part and ends in the flange area when the

diameter increases to the point that induction hardening is no longer required. The case

depth may be constant over the entire length, or it may decrease toward the flange. The

torsional stress is greatest near the spline because of the small diameter, while the

bending stress is greatest toward the flange due to the design.

The last type of axle shaft, shown in Fig. 2, is a jointed shaft assembly that is

designed to primarily transmit torque. A minor bending component may also be present

due to the reaction of the joint. This type of shaft may be found on a rigid beam front-

steer axle in a light truck or sport utility vehicle (SUV). It may also be found on a front orrear independent axle assembly, where the vehicle weight is not supported by the axle

assembly. The ends of the shaft-and-joint assembly are connected to the mating

components using splines. The particular shaft-and-joint assembly shown here uses a

cardan or universal-type joint that is attached to the shafts via yoke ears. Other types of

shaft-and-joint assemblies may employ constant-velocity joints. The induction-hardened

pattern extends full length on both shafts and typically ends in the yoke ear radius.

\c\ Steels Used for Induction-Hardened Shafts.\ce\ Many induction-hardened

shafts use plain carbon steels. It is primarily the surface hardness, case depth, and core

hardness that determine shaft performance in torsion. The choice of material is

determined by the hardenability needed. The grade of steel is chosen to provide sufficient

hardenability to be able to achieve the required case depth. The steel must have enough

hardenability, at the low end of its specification, to be able to always obtain the required

case depth. Automotive, light truck, and SUV shafts are normally about 20 to 40 mm (0.8

to 1.6 in.) in diameter. Typical steels are SAE 1038, 1040, 1045, 1050Mod (manganese

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0.80 to 1.10), 1541, 1137, 10B38, or their international equivalents. With plain carbon

steels, residual alloying elements such as chromium can be very critical to hardenability

and may need to be specified. Normally with electric arc furnace steel, this is not a

problem. However, basic oxygen furnace steels will typically have very low levels of

residual alloying elements, which tend to limit hardenability. Alloy steels such as SAE

5140 and 4140 or their international equivalents are also sometimes used.

Medium- and heavy-duty truck axle shafts are normally about 40 to 55 mm (1.6 to

2.2 in.) in diameter. Plain carbon steels are still often used, but the hardenability is

normally maintained at a higher level than the aforementioned grades. Typical steels areSAE 1541Mod (ideal diameter controlled) and 15B41. Again, alloy steels such as SAE

5140 and 4140 or their international equivalents are also sometimes used.

Off-highway and industrial shafts are normally 40 to 100 mm (1.6 to 4 in.) in

diameter. Due to the large diameter and deeper case depth requirements, alloy steels such

as SAE 5140 or 4140 are typically used, although plain carbon steels may still be used if

the case depth requirements are not demanding.

Resulfurized steels are also sometimes used for axle shafts. Typical grades are

SAE 1137 or 1141. This is for improved machinability. The manganese sulfide inclusions

found in these steels seem to have little effect on shaft performance in torsion and in

bending. However, they will usually guarantee that the shaft will fail in the longitudinal

direction when being tested in torsion. The fracture will typically initiate and propagate

longitudinally for a distance and then fail at a 45 angle from one or both ends. This is

also sometimes true with plain carbon or alloy steels.

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\c\Manufacturing of Axle Shafts.\ce\ Axle shafts are typically manufactured

from forgings, unless the diameter is relatively constant for the entire length, in which

case bar stock is used. Shafts with flanges or yokes on the end are normally hot forged.

Shafts with splines on both ends and with changes in diameter can either be hot forged or

cold formed. The normal process is to forge, machine, induction harden, and then to

finish machine. Sometimes, the forging may also be normalized or quenched and

tempered prior to machining.

Semifloat axle shafts are typically hot upset forged on the flange end and then

cold extruded on the spline end. Starting with a moderate-diameter hot rolled bar stockallows a relatively large-diameter flange to be forged. The cold extrusion process then

reduces the diameter on the spline end and lengthens the shaft. This keeps the bearing

diameter, near the flange, large to accommodate the bending loads and reduces the spline

diameter to that necessary to handle the torsional loads. The hot rolled bar stock used to

make the forging will typically have some decarburization at the surface. This

decarburization will remain in those areas of the shaft that are left unmachined, which

will affect the surface hardness. Normally, direct surface is not measured in these areas

but rather only in areas of the shaft that are fully machined. In the areas with

decarburization, the surface hardness is normally measured at some depth below the

surface, such as 1.25 mm (0.05 in.).

Full-float axle shafts are hot upset forged at the flange end and also sometimes at

the flange end if the spline diameter is larger than the shaft body. It is typical to leave the

shaft body as hot rolled bar stock. Like the previous example, this means the surface

hardness may be lower due to decarburization. It is possible for this to have some effect

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on shaft performance, such as fatigue life. If necessary, the shaft may be made from a

larger-diameter bar and machined full length, or made from turned-and-polished bar

stock.

\c\Equipment Used to Induction Harden Axle Shafts.\ce\ Most axle shafts are

induction hardened by the scanning method. The relatively simple shape and length

makes them ideally suited to this method. As long as the shaft diameter does not change

significantly, a single induction coil can be used to harden many different parts with

various lengths and shapes.

The induction scanners may be vertical- or horizontal-type units. Depending on production volumes, these scanners may be single-station units, two-station units, or

multiple-station units. With multiple-station units, more set-up time will be required to

ensure that all parts meet specifications, because the results on each station can be

different. The induction frequency range used for most axle shafts is 1 to 10 kHz. The

lower frequencies provide a greater depth of heating. Typically, the smaller-diameter

automotive and light-truck shafts will use 4 to 10 kHz. This will depend on the case depth

required. For deeper case depths, lower frequencies are better suited. For medium- to

heavy-duty truck axle shafts, 3 kHz is common. For larger-diameter industrial-type

shafts, 1 kHz is more common.

Axle shafts are sometimes hardened by the single-shot method. Here, the coil is

stationary, and the entire part length is hardened at the same time. Typically, the coil

follows the contour of the part. One advantage of the single-shot method is that shafts

with an irregular geometry can be hardened without soft areas due to deflection of the

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spray quench. Another advantage can be a shorter cycle time. However, a disadvantage is

that a given coil will typically only harden one part with a fixed geometry.

\a\Properties of Induction-Hardened Axle Shafts

\c\Effect of Case Depth on Torsional Strength.\ce\ Induction hardening

increases the hardness near the surface of the shaft, where it is needed most, and leaves

the surface in compression, which improves fatigue life (Ref 1). It is the case depth that is

primarily responsible for the torsional strength and performance of the shaft.

Case depth can be measured in different ways. In this article, case depth is defined

by two points: one called effective case depth and one called total case depth. Effective

case depth is measured to 40 HRC, while total case depth is measured to 20 HRC.

Sometimes only effective case depth is used, and sometimes the hardness level of the

effective case depth may change depending on the carbon content of the steel. The

advantage to using effective and total case depths is that this will offer relatively constant

performance with any grade of steel. Using effective case depth may be sufficient as long

as the carbon content and the hardenability of the steel do not change. If the level of

hardness for the effective case depth is changed, this will also change the strength level

that is being designed to. On the other hand, 40 HRC is a value that can be used with any

steel from 0.20% C and up, without changing the strength level.

Figure 3 is a plot of torsional strength and torsional stress in the cross section of a

shaft. Torsional yield strength and applied stress are shown on the vertical axis on the left

side, while the radial position of the shaft in terms of percent of the bar diameter is shown

on the horizontal axis on the bottom. The surface of the bar is on the left at 0%, while the

centerline is toward the right at 50%. To determine torsional strength, hardness was

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converted to strength, as shown in the upper right portion of the figure. Rockwell C was

first converted to Brinell, which was then converted to ultimate tensile strength using

SAE J413. SAE J413 defines the correlation between hardness and strength for steel. If

the hardness of a steel is known, the ultimate tensile strength can be accurately estimated.

From there, the yield strength was estimated and then converted to torsional yield by

multiplying by a conversion factor of 0.6. Torsional yield strength is shown on the

vertical axis.

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 linearlyfrom the center to the surface. This is shown as the applied stress line in Fig. 3. As the

torsional load is increased on a shaft, this line gradually increases from zero until it meets

the strength curve of the induction-hardened case. Thus, only the surface must be

hardened to a depth to adequately exceed the applied stress.

When the surface layer is hardened, martensitic transformation takes place, which

causes it to expand. This leaves the surface in compression, as opposed to through

hardening where the core also expands, leaving the surface in tension. This residual

compressive stress is extremely beneficial to torsional fatigue life.

The depth to which a shaft must be hardened can be determined theoretically.

Figure 3 shows two different induction case depths, A and B. Case depth B is the deeper

case on the right, while A is the shallower case on the left. Both of these cases have a

surface hardness of 52 HRC and a core of 12 HRC.

Obviously, case depth A will fail first at the case-core interface. This is because

the applied stress curve exceeds the strength curve at the case-core interface. However,

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case depth 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 at

the same time. Thus, it may fail at the surface or at the case-core interface. Hardening

deeper than case depth B in this situation will do no good, because it will fail from the

surface even if the strength curve is shifted further to the right. This is what is called the

optimum case depth. It is the best that can be done; it is the strongest shaft that can be

made. Hardening deeper will not increase the strength. In fact, if an attempt is made to

harden too deep, the residual surface compressive stress may be reduced, causing a

reduction in fatigue life.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% of the bar diameter. Case depth

B has an effective depth of 23% of the bar diameter and a total depth of 31% of the bar

diameter. 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

exceedingly 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 shaft torsional performance to case depth,

609.6 mm (24 in.) long test shafts splined at both ends were induction hardened to

varying case depths. These test shafts had a diameter of 28.58 mm (1.125 in.) and 38.86

mm (1.530 in.) in the center and a slightly larger spline on both ends, which caused the

failure to occur in the middle. The 28.58 mm (1.125 in.) test shaft is shown in Fig. 4.

Different hardenability steels were used to look at the relationship of effective and total

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case depth. The effect of core hardness was also looked at by using shafts made from hot

rolled steel, cold-drawn steel, and quenched and tempered steel.

Results of the static torsional testing are shown in Table 1. Also included are

some data from production axle shafts made from SAE 1038 and 1040 steel. It should be

noted that the yield strength was determined by the Johnson elastic limit (JEL) method,

which is defined by a 50% change in slope.

Table 1 shows the steel grade in column two. Column three shows the diameter of

the test shaft. Again, the length of all the shafts was 609.6 mm (24 in.). The fourth

column shows the effective case depth, which was the depth below the surface measuredto 40 HRC. This is also shown in parentheses as a percent of the bar diameter. The next

column to the right shows the total case depth, which was the depth below the surface

measured to 20 HRC. In the event the core was 20 HRC or greater, the total case depth

reported was the total visual case. Total case is also shown in parentheses as a percent of

the bar diameter. The next column shows the core hardness, followed by the surface

hardness. The final two columns show the torsional yield strength and the torsional

ultimate strength.

The first material shown is SAE 1040 cold-drawn steel. The core hardness of this

material was approximately 17 HRC. The range of case depths tested was from 0%

effective to approximately 25% effective. The surface hardness for this steel was

approximately 55 HRC. It should be noted that all parts in Table 1 were tempered

between 170 and 205 C (340 and 400 F) after induction hardening. The second material

shown is SAE 1541 steel, which was quenched and tempered prior to induction

hardening. The core hardness of this material was approximately 21 HRC, and only two

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case depths were tested: 11.5 and 13% effective. Since they were relatively close, no

significant difference in strength was found. Next is SAE 1541 hot rolled steel. The core

hardness of this material was approximately 19 HRC, which is only marginally lower

than the quenched and tempered product above it. Obviously, there was not a significant

gain in core strength by performing the quench-and-temper treatment. Again, only two

case depths were tested: 18 and 23% effective. The next material shown is SAE 1050

modified steel. The modification here is simply an increase in manganese to 0.80 to

1.10% to increase the hardenability. This material is typically used for automotive axle

shafts that also serve as an inner bearing. These shafts require a surface hardness of 58HRC minimum to provide adequate rolling contact fatigue resistance. The core hardness

of this steel was approximately 15 to 18 HRC. The next material shown is SAE 4140 hot

rolled steel. The range of case depths for this material is from 0% effective to

approximately 27% effective. The core hardness is approximately 10 HRC. The last two

groups of shafts were production shafts made from SAE 1038 and 1040 steel. The core

hardness for the SAE 1038 steel was approximately 6 HRC, while the SAE 1040 steel

was approximately 12 HRC.

The test results are graphically shown in Fig. 5 as effective case versus torsional

strength. In this figure, it can be seen that both the torsional yield strength (on the bottom)

and torsional ultimate strength (on the top) increase with case depth to a point, and then

the curve levels off, as expected. Again, the point where the curve levels off is the

optimum case depth. As one may recall from the theoretical calculation, this point should

have been approximately 23% of the bar diameter as effective case. This is exactly the

point where the curve levels off, so here theory and reality agree, which is not always the

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case. The bottom line of each curve represents the minimum strength versus case depth

values for the steels listed. There is some scatter or variation to the data, but there is a

relatively good correlation between effective case depth and torsional strength. 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 approximately 1379 MPa (200,000 psi). In Fig. 5, it can be seen

that SAE 4140 provides a lower torsional strength for any given case depth compared to

the rest of the steels, except at the far right portion of the curve. This is because 4140 has

higher hardenability than the other steels and hence a lower total case depth for the sameeffective case. This indicates that effective case depth is not the only factor in

determining torsional strength, and that total case depth must also be considered. At the

far right of the curve, all of the steels are approximately equal, indicating that only

effective case is important in this area of the curve.

Figure 6 shows the results for total case depth versus torsional strength. This

curve is very similar to the previous curve except the 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. As

one may recall, this is exactly where the theoretical prediction was. Again, it can be seen

that there is a difference in the minimum strength depending on the grade of steel. This

time, SAE 1541 and 4140 provided a higher torsional strength for any given case depth

compared to the other steels, especially in the portion of the curve at the right. This is

because the higher-hardenability steels have a deeper effective case depth for any given

total case depth compared to the rest of the steels. Also, SAE 1541 has a quenched and

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tempered core with a greater hardness. The higher core hardness is similar to a deeper

total case depth. This indicates that both effective case and total case are important in

determining torsional strength, but between the two, effective case seems to be a more

accurate predictor.

Figure 7 shows a graphical representation of torsional strength versus applied

stress for four steels that provided the same torsional strength. Each one of the four case

depths provided a minimum torsional yield of 621 MPa (90,000 psi). The lower-

hardenability steel SAE 1040 did so with a shallower effective case and a deeper total

case compared to the higher-hardenability steels. The effective case is 15% of the bardiameter, and the total case is 25%. The highest-hardenability steel, which was 4140,

required an effective case of approximately 18% and a total case of 22% to achieve the

same strength. The position of the applied stress line indicates the torsional strength

should be slightly lower for the 4140 material compared to the 1040 material, but in

reality, they were approximately the same. The 1541 with its quenched and tempered

core only required an effective case of 13% and a total case of 18% to achieve the same

strength. This is because the effect of increasing the core hardness is the same as

increasing the total case depth. It basically allows the applied stress line to reach a higher

level before it intersects the case-core portion of the strength curve. Moving this portion

of the strength curve to the right or upward should increase the strength. The 1050

modified steel had an effective case of 18% and a total case of 25%, similar to the 1040

steel. In examining the figure, it appears that the only two things that should matter in

determining torsional strength are the surface hardness and the total case. The effective

case is well above the applied stress line and does not appear to be a factor. However, the

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effective case seems to be the better predictor of torsional strength, but both the effective

and total case depths must be considered. In theory, the 1050 modified steel with its

higher surface hardness should be able to provide a higher torsional strength if the case

depth is deep enough. However, additional work has shown that this is not always the

case. The important information to learn from Fig. 7 is that there are various ways to

achieve the same torsional strength, and that both effective and total case as well as core

hardness must be considered.

\c\Effect of Case Depth on Torsional Fatigue.\ce\ Figure 8 shows the fatigue

characteristics of the SAE 1040, 1541, and 4140 test shafts. Only these three groups ofsteels were fatigue tested. All shafts were run in fully reversed torsional fatigue at a stress

of 407 MPa (59,000 psi). The data show that there is a correlation between fatigue life

and torsional yield strength, which is not unexpected. However, considerable scatter or

variation is present, which is normal in most fatigue testing. Below approximately

200,000 cycles, the variation from high to low life appears to be approximately 10:1 for

any given strength level. At the right, as the knee of the curve is approached, the variation

from high to low increases to over 20:1. This is not unusual for induction-hardened shaft

testing in torsional fatigue.

Runout or suspension at 1 million cycles on the right side of the curve occurred at

a torsional yield that was approximately double the applied stress. This equates to a

fatigue limit of 50% of the torsional yield. On the left side of the curve, as the torsional

yield approaches the applied stress, it appears the life is only a few thousand cycles. From

Fig. 8 it also appears the plain-carbon-grade1040 reached suspension at 1,000,000 cycles

before the other two grades.

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The results displayed in Fig. 7 provide a potential explanation for this. The four

case depths shown have an equal static strength of 621 MPa (90,000 psi) minimum.

However, if one looks 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 seems to indicate that total case depth may be more critical for

fatigue life.

Figure 9 shows the fatigue life versus total case depth. The data demonstrate that

fatigue life does increase with increasing total case depth. The runout or maximum

fatigue life appears to occur at approximately 31% total case depth. In this figure, SAE1541 steel appears to provide higher fatigue life for the same total case depth compared

to the other two materials. The reason for this is the higher hardness of the quenched and

tempered core, which essentially acts the same as a deeper total case depth. This allows

the applied stress line to reach a higher level before intersecting the strength curve. SAE

1040 and 4140 have the same fatigue life, even though these two steels are on the

opposite ends of the hardenability spectrum. This reinforces the idea that total case depth

is most important for fatigue. As long as the total case depth is the same, the fatigue life

is the same with a constant core hardness.

A good example of the importance of total case depth can be seen in Fig. 10. A

production axle shaft made from SAE 1038 steel was not providing the desired fatigue

life, so a more premium grade, SAE 4140, was substituted. The thought was that this

would increase the fatigue life, but only effective case depth was considered. 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

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increased. The reason can be explained by looking at Fig. 10, which shows torsional

fatigue life versus effective case depth. At 15% effective case, 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 to 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 depth along with it. In the end, 4140 did not really provide any benefit in

fatigue over the current production parts.

Validation of axle shaft performance is commonly done by running torsionalultimate and torsional fatigue tests. Torsional strength is important for all axle shafts that

transmit torque. Torsional fatigue may also be important, but to determine this, one must

know how the shafts fail in actual service. With through-hardened shafts, where the life is

lower, fatigue testing is certainly important. However, with induction-hardened shafts,

where the fatigue life is much greater, fatigue testing may not be as critical if this is an

uncommon failure mode. An axle shaft is much different than a ring-and-pinion gear that

sees millions of cycles as it travels down the road. An axle shaft may only see one

torsional cycle as a vehicle accelerates and enters a highway and travels for many miles.

As demonstrated earlier, torsional fatigue life has some dependence on torsional

strength. However, its dependence is just as great on the residual-stress profile that is

created by the specific coil and quench system that is performing the induction hardening.

In other words, a stronger shaft does not always translate into higher fatigue life. This can

be seen when comparing through-hardened shafts to induction-hardened shafts. The

torsional strength of both may be identical, but the torsional fatigue life of the through-

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hardened shaft is typically a fraction of the induction-hardened shaft. Table 2 shows the

torsional strength and fatigue life of three through-hardened shafts versus three induction-

hardened shafts. The through-hardened shafts are 4140 and 4340 quenched and tempered

to 45 to 52 HRC. Also shown is a 4140 shaft that has been austempered to 40 HRC. The

induction-hardened shafts are a 1040 shaft with a light case depth, a 1541 shaft with a

moderate case depth, and a 1541 shaft with a deep case depth. Shown are the static

torsional properties for each shaft and the torsional fatigue life. The torsional fatigue life

is shown as the Weibull B10, B50, and B90 life. Also shown is the fully reversed

torsional stress at which each shaft was run. Even though the stress levels are not all thesame, it is evident as to the comparison of torsional fatigue life of the different shafts.

The through-hardened shafts can achieve torsional strength levels similar to induction-

hardened shafts; however, the torsional fatigue life is much lower.

Figures 11 and 12 show long-term torsional fatigue data for two full-float axle

shafts that are dimensionally the same. Figure 11 is a shaft made from SAE 1038 steel

with a shallow case depth. The torsional strength and case depth data are also given in the

caption. The figure is a plot of torsional fatigue life versus applied stress. The life is

shown from 10,000 to 1,000,000 cycles. The life is dependent on stress to some degree,

but the curve is relatively flat. What is most notable is the wide amount of scatter in life

at the same stress level. At a given stress level, the life can vary by 100:1. This is not

atypical for induction-hardened shafts. Part of the reason is that induction case depths are

not able to be controlled as tightly as carburized case depths. Another part of the reason is

the different residual-stress profiles created by different induction equipment, as well as

different lots of steel. However, in these data, it does not hold true that the higher-

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strength shafts are always the ones with the greater fatigue life. Figure 12 is a shaft made

from SAE 1541 steel with a deeper case depth. The torsional strength data in the caption

show that the shaft is indeed stronger than the SAE 1038 shaft. It can be seen that the

average fatigue life is better than the SAE 1038 shaft, but the minimum life is

approximately the same. Higher torsional strength does not always mean greater fatigue

life; in fact, it could actually be lower. This may or may not be critical to the actual

application and must be determined by the user.

\c\Effect of Shaft Length on Torsional Properties.\ce\ The length of an

induction-hardened shaft affects the torsional strength and fatigue life. Table 3 showsdata generated from 28.6 mm (1.13 in.) diameter SAE 1038 test shafts. The shafts had

splines at both ends and a reduced-diameter gage length in the middle. The gage length of

the 609.6 mm (24 in.) shafts was 457.2 mm (18 in.), and the gage length of the 203.2 mm

(8.0 in.) shafts was 50.8 mm (2.0 in.). The shafts were made from the same lot of steel

and were induction hardened to the same case depth at the same time to provide a

moderate strength level. The torsional ultimate strength was the same for both shaft

lengths. However, the torsional yield strength, or JEL, is greater for the shorter shaft. The

ductility or degrees of twist is also much lower for the shorter shaft. The average ratio of

JEL to ultimate strength for the longer shaft is 0.60, while the ratio for the shorter shaft is

0.74.

The bottom of the table shows the fatigue data for both shafts. All of the shafts

were run at the same stress under fully reversed fatigue. The B10, B50, and B90 Weibull

data show a considerable difference in life. The B50 life (the life one can expect 50% of

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the samples to fail) of the shorter shaft with the higher JEL is approximately eight times

the life of the longer shaft.

It is the effective length of the shaft that is important, rather than the absolute

length. The effective length is the length of the smallest diameter or the portion of the

shaft that is expected to fail. A shaft can be relatively long with a large diameter for most

of the length and a small diameter for only a short length, and it will act like a short shaft.

\c\Effect of Changes in Diameter on Torsional Shaft Performance.\ce\ Many

induction-hardened shafts have changes in diameter along their length. This is typically

done to accommodate bearings, seals, and attachment points. In the case of semifloat axleshafts, the diameter is increased at the bearing area to satisfy the bending stress. As the

shaft diameter increases, the torsional stress decreases, as shown in Fig. 13. As the stress

decreases, the induction case depth can be decreased. The case depth requirement of a

shaft is calculated at the smallest diameter. As the shaft diameter increases, any decrease

in case depth is calculated based on the initial calculation at the smallest diameter.

Eventually, the shaft diameter will reach a point where induction hardening is no longer

required.

Figure 14 is an example of an induction pattern that begins at a radius. The outline

of the effective and total case depth is shown. As one moves from right to left along the

shaft length, the torsional stress for any given torque decreases as one moves through the

radius and then into the shoulder. It is helpful to consider the torsional stress plane by

plane as one moves along the length. Typically, in torsion the radius itself is not a stress

concentrator and has little or no effect on the strength. A shaft with a flange and radius

will have the same strength and fatigue life in torsion as a straight shaft with no radius. If

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the diameter of the shoulder is large enough, the torsional stress may be reduced to the

point that induction hardening is no longer required. The torsional strength of the

unhardened area can be estimated by multiplying the tensile strength by 0.6 to make this

determination.

If the shoulder is large enough to discontinue hardening, typically all that is

required of the pattern is to extend around the radius, as shown.

It is also important to consider the pattern depth at the beginning of the radius,

where it blends into the shaft. Shown are the 45 and 0 points of the radius. At 0, it is

critical that the induction-hardened case be at full depth for both effective and total casedepths. If it is not, it will be expected to fail here, because the torsional stress is the same

for this plane as it is for any other plane farther to the right. If the induction-hardened

case is lower in any given diameter where the torsional stress is constant, that will be the

area to fail under extreme loading. Because induction case depths are not uniform in

depth along the entire length of a shaft, this is something that must always be considered.

\c\Designing Shafts for Torsional Applications.\ce\ Table 4 shows an example

of how an engineer may design a series of different-diameter shafts to provide three

different torsional strength levels and consistent fatigue life. The low-strength series of

shafts on the left provide a minimum torsional yield strength of 483 MPa (70,000 psi).

The minimum torsional ultimate strength is 933 MPa (135,000 psi). Keep in mind that the

typical values will be somewhat higher. These values are also shown in the table. The

middle column is intended to provide a minimum torsional yield strength of 621 MPa

(90,000 psi). The minimum torsional ultimate strength is 1138 MPa (165,000 psi). The

column at the right is the optimum case depth or the strongest shaft that can be produced.

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It provides a minimum torsional yield strength of 793 MPa (115,000 psi). The minimum

torsional ultimate strength is 1379 MPa (200,000 psi). Also shown for each series of

shafts is the typical torsional yield and ultimate strengths that are expected. The required

case depth is shown for each series of shafts from a diameter of 19 to 51 mm (0.75 to 2.0

in.). The case depth for any sized shaft can be calculated by simply using a fixed percent

of the bar diameter as effective and total case depths. For the low-strength series of

shafts, the case depth is 11% effective and 20% total. For the middle series of shafts, the

case depth is 15% effective and 25% total. For the optimum case depth, the values are

23% effective and 31% total. Again, keep in mind that these case depths are designed to provide both minimum torsional strength and consistent fatigue life. If torsional strength

is the only consideration, then the case depth can be directly determined from the

effective and total case curves in Fig. 5 and 6. The data show that a plain carbon steel,

such as 1040, requires an effective case of 15% of the diameter and a total case of 25% to

achieve a minimum torsional yield of 621 MPa (90,000 psi). These percentages also work

for other steels, although the strength may actually be greater for a higher-hardenability

steel such as 4140. To achieve the same strength, the 4140 steel only requires 18%

effective and 22% total case depth. The minimum 621 MPa (90,000 psi) static yield

strength could also be obtained with a quenched and tempered core of approximately 21

HRC by using an effective case of 13% and a total case of 18%. However, the quench-

and-temper operation also adds a fair amount of cost to the part.

Case depth plays a very important part in determining the static and fatigue

properties of shafts. From the data thus far, torsional strength increases with case depth,

but only to a point, after which deeper hardening does no good. Both effective and total

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case depths must be considered to optimize shaft performance. Effective case depth

appears to be the best predictor of torsional strength, while total case depth is the best

predictor of fatigue life. The relationship between case depth and torsional strength is

certain, but there is a 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. Fatigue life correlates to shaft strength to some degree; however, there is

considerable scatter or variation.

\c\Effect of Case Depth on Bending Strength.\ce\ Induction-hardened casedepth affects bending strength in a similar manner to torsional strength. In bending, the

calculated strength and stress values will be much higher than in torsion. The other major

difference is that torsional strength is not affected much by radii, or stress concentrations,

while bending strength is. In torsion, an induction-hardened shaft typically does not fail

at the radius; however, in bending it does. Figure 15 is an example of an induction-

hardened test shaft with different radii loaded in bending. The steel used for the shaft was

SAE 1038, and different case depths were evaluated. It can be seen that the bending

strength increases with case depth. However, the amount of increase is dependent on the

radius, or stress concentration. If the stress concentration is low, the increase in bending

strength with case depth is high. If the stress concentration is high, the effectiveness of

increasing the case depth is limited.

\c\Effect of Carbon Content on Torsional Strength.\ce\ Most induction-

hardened shafts are made from steels with nominal carbon levels ranging from 0.35 to

0.50%. Figure 16 shows test data from test shafts made from various alloy steels with

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nominal carbon content of 0.20, 0.30, 0.40, 0.50, and 0.60%. The shafts were splined at

both ends with a total length of 609.8 mm (24.0 in.) and a reduced diameter in the middle

of 28.58 mm (1.13 in.). All of the shafts were made from hot rolled steel. The starting

microstructure was pearlite and ferrite. The data show that the torsional yield strength and

ultimate strength increase with carbon content up to approximately 0.40% C. Above this

level, the ultimate strength begins to decrease. Eventually, the yield and ultimate

strengths become the same, and there is no plastic deformation prior to failure.

A similar study performed on small-diameter quenched and tempered shafts

yielded much different results (Ref 2). These test shafts were 16 mm (0.63 in.) indiameter and made from plain carbon-manganese steel and chrome alloy steel. The

carbon content ranged from approximately 0.40 to 0.65%. Figure 17 shows that shafts

made from higher-carbon steel exhibited higher torsional strength. This work also

showed that deeper case depths, up to and including through hardening, produced the

greatest torsional strength. This is contrary to much of the previous data that have been

shown. This indicates that the prior microstructure can potentially have a significant

effect on the final properties of an induction-hardened shaft. General rules of thumb or

relationships should not be assumed to automatically apply to all situations. It is best to

always verify performance by testing.

\c\Effect of Prior Microstructure.\ce\ As has been shown, quenching and

tempering or cold drawing prior to induction hardening can increase the torsional strength

of a shaft for any given case depth or allow a lighter case depth to be used to achieve the

same strength level. Another effect of prior quenching and tempering is that it becomes

easier to austenitize and transform the microstructure to martensite during induction

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hardening. This can result in a deeper case depth for any given hardening parameters or

can provide the potential to lower the parameters. It can also result in a more completely

martensitic microstructure. The negative of altering the microstructure prior to induction

hardening is the cost. Many years ago, it was more common to either normalize or

quench and temper prior to induction hardening. However, today (2013) many shafts are

induction hardened in the as-forged or as-hot-rolled condition. Typically, the same

properties can be achieved, but the case depth is slightly greater.

Prior microstructure can also have some effect on shaft defects, such as internal

cracking after induction hardening. For example, large grain size has been associatedwith an increased risk of transverse internal cracking.

\c\Effect of Splines on Induction-Hardened Shaft Performance.\ce\ Splines are

normally used to connect the axle shaft to the differential side gear. Shaft splines are

typically hobbed or rolled. The geometry of the spline has an effect on the performance

of the shaft. For most calculations, it is assumed that the spline is equal to a smooth shaft

that is the same diameter as the minor diameter of the spline. This is somewhat

conservative, because the spline will transmit some torque even if the entire center of the

shaft below the minor diameter is machined away. However, it is a safe approach.

Figure 18 shows torsional strength data for splined test shafts versus smooth test

shafts. The test shafts were made from steels with different carbon levels. In this case, the

minor diameter of the spline was approximately 10% smaller than the diameter of the

smooth shaft, so the splined shaft is expected to be weaker. The splined test shaft is

shown in Fig. 19. From the data, it is evident that the relationship between the splined

shafts and smooth shafts is very dependent on the carbon content of the steel. At the

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lower carbon levels, the splined shaft is actually as strong as the smooth shaft. However,

at the higher carbon levels, the splined shaft is significantly weaker than the smooth shaft,

as expected.

\c\Hollow Axle Shafts.\ce\ Because in torsion, and in bending, the stress is

greatest at the surface of a shaft and it is zero in the center, it is possible to eliminate the

center of the shaft without significantly affecting the strength. Obviously, this will

depend on how much of the center is removed and the thickness of the remaining wall

section. The driving force for doing this is weight reduction. The largest disadvantage is

the reduction in fatigue life associated with doing this. The outstanding fatigue life foundin induction-hardened shafts is a result of the compressive residual stress generated by

the hardening process. To generate the residual compressive stress at the surface, there

must be an equal, and offsetting, residual tensile stress in the core. If the core is

eliminated, this will not happen. Hollow induction-hardened axle shafts are used today

(2013); however, in each case it must be determined whether the fatigue life is adequate

for the particular application.

\a\Operations after Induction Hardening

\c\Straightening of Induction-Hardened Axle Shafts.\ce\ Axle shafts are

typically mechanically straightened after induction hardening. This is done by first

measuring the runout on the shaft, either on centers or on rollers, and then supporting the

shaft at both ends while applying a load in the center to do the straightening. To

accomplish this, the yield strength must be exceeded and the ultimate strength must not.

One problem associated with this is the potential to either break or crack the shaft. If the

shaft is cracked and placed in service, a failure normally results. Shafts can be inspected

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after straightening by magnetic particle inspection or ultrasonic inspection, if the crack is

deep enough. Typically, the cracks will be through the entire effective case, due to the

high hardness level. Acoustic emission crack-detection devices may also be used in

conjunction with the straightening process to pick up the crack in real-time.

Axle shafts are also usually straightened in the soft condition prior to induction

hardening. This is done before or during machining. The reason is that the straighter the

shaft prior to induction hardening, the straighter the shaft after induction hardening. If the

shaft has significant runout prior to induction hardening, one portion of the shaft will be

closer to the coil, so the heating may be uneven. Nonuniform residual stress in the steel bar has also been associated with excess runout after induction hardening. For example, a

steel bar that has been coiled and straightened may have uneven residual stresses.

It is also possible for the residual stresses created by straightening after induction

hardening to be relieved in service. Depending on the operating temperatures and

operating stresses, this can cause shaft runout to partially return to where it was prior to

straightening.

Straightening after induction hardening has been eliminated in some operations by

employing a chuck to clamp the flange during hardening. The chuck clamps the flange on

the inboard face and rotates with the shaft during the scanning operation. It is believed

that this helps keep the shaft centered in the coil throughout the entire process.

\c\Tempering of Induction-Hardened Axle Shafts.\ce\ Tempering can also have

an effect on the straightening of axle shafts. The common belief is that tempering will

always make an induction-hardened part more ductile. This is not always the case. In

bending, tempering can increase the yield strength, thereby requiring a higher load to

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straighten. Also, the yield strength becomes closer to the ultimate strength, making the

shaft more prone to cracking because straightening requires the yield strength to be

exceeded but not the ultimate strength. Because of this, some shafts are straightened prior

to tempering. However, this should not be done on shafts that may tend to crack if not

tempered relatively soon after induction hardening. This includes higher-carbon and

higher-hardenability shafts as well as those with radii.

Axle shafts are typically tempered anywhere from 140 to 260 C (280 to 500 F).

In general, tempering tends to reduce the residual compressive stress created by induction

hardening and lowers the fatigue life. This is especially true at the higher end of thistemperature range. However, on some shafts made from 1038 steel, tempering has been

documented to improve the fatigue life. The important lesson is that one cannot assume

that tempering has the same effect on all shafts regardless of material and prior

microstructure. The benefit of tempering should be established by mechanical testing. In

some cases, tempering may not be necessary. Some shafts made from SAE 1035 and

1038 steel have been induction hardened without tempering for many years.

\c\Quality Control of Induction-Hardened Axle Shafts.\ce\ Axle shafts are

most commonly inspected by destructively sectioning and checking hardness, case depth,

and microstructure. The most effective technique is to section each shaft from each

station or coil to make certain everything is acceptable. Then, if anything changes that

may affect the process, the shafts are again sectioned. Sometimes, this may be

supplemented or replaced by ultrasonic inspection for case depth. Determining where to

section or check the shaft is very critical. Initially, it is recommended to section the shaft

lengthwise to locate the critical locations with the shallow case depth. With induction

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hardening, the case depth is usually not uniform along the entire shaft length due to

changes in diameter, scan speed, or power. Again, if the setup significantly changes, this

process may have to be repeated. As new heat codes of steel are introduced, the

inspection is normally repeated to account for any differences in hardenability.

It is also important to verify the case microstructure. Even though a shaft may

meet the hardness and case depth requirements, the microstructure can be partially

nonmartensitic. This may be a result of incomplete austenitization, or it may be the result

of a slow or interrupted quench. This can have an effect on the performance of the shaft.

\e\REFERENCES

1. G. Fett, Importance of Induction Hardened Case Depth in Torsional Applications,

Heat Treat. Prog., Oct 2009, p 15 19

2. T. Ochi and Y. Koyasu, Strengthening of Surface Induction Hardened Parts for

Automotive Shafts Subject to Torsional Load, SAE Paper 940786, Feb 28

March 3, 1994

[Figure Captions]

Fig. 1 Common types of automotive and truck axle shafts

Fig. 2 Shaft-and-joint assembly

Fig. 3 Case depth versus torsional strength and stress. UTS, ultimate tensile strength

Fig. 4 Smooth test shaft

Fig. 5 Effective case depth versus torsional strength. CD, cold drawn; Q&T, quenched

and tempered; HR, hot rolled

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Fig. 6 Total case depth versus torsional strength. CD, cold drawn; Q&T, quenched and

tempered; HR, hot rolled

Fig. 7 Case depth providing 620 MPa (90,000 psi) minimum torsional yield strength.

UTS, ultimate tensile strength; Q&T, quenched and tempered

Fig. 8 Fatigue life versus torsional yield strength. CD, cold drawn; Q&T, quenched and

tempered; HR, hot rolled

Fig. 9 Torsional fatigue life versus total case depth (at 407 MPa, or 59 ksi). Q&T,

quenched and tempered

Fig. 10 Torsional fatigue life versus effective case depth (at 407 MPa, or 59 ksi). Q&T,quenched and tempered

Fig. 11 Full-float torsional fatigue of 1038 steel with ultimate torsion strength of 1359

MPa (1214 1566) and torsional yield strength (by Johnson elastic limit method) of 710

MPa (676 800). Effective case depth was 14% (11 28), with total case depth of 25%

(16 33) and core hardness of 9 HRC (3 17). Primary failure mode was midshaft,

secondary was spline.

Fig. 12 Full-float torsional fatigue of 1541 steel with ultimate torsion strength of 1497

MPa (1207 1862) and torsional yield strength (by Johnson elastic limit method) of 966

MPa (710 1269). Effective case depth was 22% (15 33), with total case depth of 33%

(17 50) and core hardness of 19 HRC (5 31). Primary failure mode was midshaft,

secondary was spline.

Fig. 13 Increase in shaft diameter versus reduction in torsional stress

Fig. 14 Induction-hardened pattern that begins at a radius

Fig. 15 Bending strength of SAE 1038 induction-hardened test bars

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Fig. 16 Torsional strength versus carbon content for induction-hardened test shafts made

from hot rolled steel. Smooth test shafts with heavy case depth (9.53 mm, or 0.375 in.,

total)

Fig. 17 Torsional strength versus case depth versus carbon content for small-diameter

quenched and tempered test shafts. t /r , thickness/radius. Source: Ref 2

Fig. 18 Smooth test shafts versus splined test shafts

Fig. 19 Splined test shaft

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