Canale L.C.F., Mesquita R.A., Totten G.E. Failure Analysis of Heat Treated Steel Components

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full use of compressive residual stresses in dyna-

mically loaded parts can be made in this way.

Figure 52 shows a cylindrical workpiece or

sample with initial diameter D

and initial height

. Its purpose is to show the process of residual

stresses after induction surface treating in the

central part of the workpiece (Ref 15, 27). With

energy input to the thin surface layer, the initial

diameter increases to the value of D

. Change of

diameter is associated with thermal expansion of

the material and is due to ferrite and/or pearlite

transformed into austenite.

After quenching, a thin surface layer with a

martensite microstructure is obtained that has a

different speciﬁc volume than the initial micro-

structure. The hardened surface layer is ready to

receive a greater diameter (D

), which is resis-

ted by the initial microstructure. Of interest are

the residual stresses in the radial and axial

directions. Residual stresses are compressive in

the hardened layer, then they change into tensile.

Residual stresses in the axial direction are

compressive in the middle part of the hardened

layer and turn into tensile below the hardened

layer. In this way, very high tensile residual

stresses are achieved at the bottom of the

hardened layer. Compressive residual stresses

prevail in the remaining part of the nonhardened

surface layer. A residual-stress proﬁle is un-

favorable in the transition zone between the

hardened layer and the rest of the nonhardened

part of the workpiece.

The transition from tensile to compressive

residual stresses presents a serious danger for

catastrophic failure. From the aforementioned

it can be understood that the workpiece must

be slowly heated and also quenched with the

correct cooling rate. The actual cooling rate is

very important throughout the martensitic trans-

formation and must be as close as possible to the

critical cooling rate. The quenching process

must be carried out very carefully in the mar-

tensitic transformation temperature range to

ensure internal stresses lower than the yield

point.

Figure 53 presents a crankshaft formed by hot

forging, and Fig. 54 shows the manufacturing

procedure from blank to crankshaft (Ref 15, 36).

The procedure of forming should be carefully

prescribed, including the initial and ﬁnal tem-

peratures of forging and the uniform plastic

deformation rate for the entire volume.

Fig. 51 Microhardness and residual-s tress proﬁles at various heating times, t

–t

. Source: Ref 15, 54

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This will ensure a ﬁne-grained, banded

microstructure contributing to a favorable rela-

tionship between strength and toughness of the

product. The forging procedure is followed by

annealing to remove the residual stresses in-

curred by the reﬁnement procedure applied to

forgings. Deformation of the crankshaft occurs

after heat treatment, as early as in the phase of

heating to the austenitization temperature. Due

to stress relief as well as the effects of nonuni-

form cooling of the product, it is necessary for

the forgings to be subjected to straightening

prior to mechanical treatment. If necessary ad-

ditional annealing can be prescribed to remove

internal stresses induced by straightening. This

is followed by turning and rough grinding to

approach the ﬁnal dimensions of the product.

The technology of manufacturing the crankshaft

involves careful selection of the conditions of

turning and subsequent rough grinding to avoid

the occurrence of internal stresses that would

remain in the material even after induction sur-

face hardening and grinding, thus reducing the

fatigue strength of the material. Induction hard-

ening may be preceded by stress annealing if the

depth of the surface hardening is smaller than the

depth of the damaged layer, since, in this way, it

is possible to change the unfavorable stress state

in the surface layer induced by machining. In

this case, the depth of the induction surface

hardening was greater than the depth of the

damaged surface layer; therefore, machining

could immediately be followed by induction

surface hardening. After induction surface

hardening, the size and distribution of residual

stresses contribute to toughness and fatigue

strength of the material. In these tests, induction

surface hardening was followed by ﬁnish grind-

ing and nondestructive magnetic inspection of

the surface to reveal the possible existence

of cracks on the product surface.

Crankshafts were taken from production after

induction surface hardening with the heat treat-

ment and machining conditions as speciﬁed in

the technology sheet. The residual stresses on

the main crankshaft bearings were measured on

the bearing location in the middle (sample A in

Fig. 53), on the extreme left side (sample C) and

on the extreme right side (sample G).

Fig. 52

Radial and axial residual-stress proﬁles after induction hardening the surface layer in the central part of a cylinder steel rod.

Source: Ref 15, 27

Fig. 53

Schematic presentation of a crankshaft with marked

main bearing locations. Source: Ref 15, 36

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Figure 55 shows residual-stress distribution

after induction surface hardening in the central

bearing location (sample A) and on the extreme

left side (sample C) (Ref 15, 20, 44). For both

locations, residual stresses were measured on

two samples. The distribution of residual stres-

ses on location A is very similar on both sam-

ples, as expected, with the highest compressive

stress ranging between 1020 and 1060 N/mm

a depth of approximately 250 mm and then

slowly dropping to a depth of 3.5 mm.

The residual-stress distribution after induc-

tion surface hardening on bearing location C is

very similar to that in the central bearing loca-

tion A, except that its absolute values are slightly

lower, and a distinct decrease in the residual

stresses can be noted as early as a depth of ap-

proximately 3 mm, reaching its minimum value

at a depth of approximately 5.0 mm.

The residual-stress distribution is just as

favorable as in the central location, except that

its absolute values are slightly lower. The dif-

ference in the residual-stress distribution can

be related to the period of overheating in the

austenitization temperature, which resulted in a

thinner layer in austenitization and also a thinner

hardened surface layer.

Figure 56 shows a zone of the measured

values of residual stresses at four bearing loca-

tions of the knee shaft (Ref 54). The arithmetic

mean value for characteristic depths of the har-

dened layer was determined, and the highest and

lowest values of residual stresses at the given

depth were established, respectively.

The upper and lower values of the residual

stress with the individual depths of the hardened

layer were deﬁned by the range of scatter of

residual-stress values. The upper and lower con-

ﬁdence limits were deﬁned using a statistical

data analysis of the measured values of the resi-

dual stresses through the hardened-layer depth.

Figure 57 shows a zone of the scattered values

of residual stresses, the calculated variation of

mean values in the individual depths, and the

zone determined by the upper and lower

conﬁdence limits for the hardened-layer depth,

to a depth of 5.5 mm (Ref 54).

The zone between the upper and lower con-

ﬁdence limits is important and requires a very

deﬁnite gradient of residual stresses. Where the

limit, that is, the depth, should be set and where

the gradient should be controlled depends on the

chosen induction-heating conditions. The heat-

ing conditions applied in the study indicated that

the speciﬁed gradient of residual stresses should

be ensured at a depth ranging between 3.0 and

5.0 mm.

A practical application showed that the stress

gradient between the surface and a depth of

Fig. 54 Machining and heat treatment procedure from blank to crankshaft. Source: Ref 15, 36

Fig. 55

Residual-stress proﬁle after induction surface hard-

ening on sample A of the mean bearing location in

the middle of the crankshaft and on sample C on the extreme left

side. Source: Ref 15, 20, 44

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3.0 mm was not problematic, since the values

obtained lay in this range in all cases. Difﬁcul-

ties may be encountered in induction heating

and induction hardening, respectively, if the

residual-stress value obtained at the surface lies

at the lower limit of the scattered results. This

means that the measured compressive residual

stresses are at the lower limit as well, which

may result in a steeper gradient to the depth of

3.0 mm. Consequently, the required residual-

stress variation cannot be achieved through the

entire hardened layer.

The cylindrical specimen was surface induc-

tion heated to a temperature of 980



C and

then quenched in saltwater. Figure 58 shows

the calculated distribution of individual

microstructural phases from the surface to the

center of the cylindrical specimen at the end of

cooling (Ref 20, 47).

The initial microstructure was preserved to a

radius, r, of 5.5 mm. In the radii between 5.5 and

6.6 mm, the pearlitic-ferritic microstructure and

low-carbon martensite appeared. With the radii

exceeding 6.6 mm, a ﬁne martensitic micro-

structure with approximately 6.0% residual

austenite was obtained due to intensive cooling.

With the selected conditions of induction heat-

ing and fast cooling of the specimen, no homo-

geneous martensite was formed in the surface-

hardened layer. Figure 59 shows the calculated

and measured variations of individual com-

ponents of residual stresses (Ref 20, 47). The

Fig. 56 Residual-stress proﬁles for six measurements on four bearing locations after induction hardening. Source: Ref 54

Fig. 57

Determination of upper and lower conﬁdence limit and arithmetic mean values of residual stresses through the hardened

depth. Source: Ref 54

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calculated variations of residual stresses repre-

sent high compressive stresses at the surface,

that is, the axial component of residual stresses,

, equals 803 N/mm

, and the tangential one,

,is588 N/mm

. On the contrary, the tensile

residual stresses were calculated after hardening

in the core, with the preserved pearlitic-ferritic

microstructure. Thus, the axial component of

residual, stresses, s

, calculated for the core

equalled to +370 N/mm

and the tangential

one, s

, was +62 N/mm

. The diagram in

Fig. 59 indicates that the maximum tensile

stresses were attained in the transition zone

between the hardened layer and the unhardened

one (Ref 47). At a greater depth, very low stress

gradients occurred, and in the opposite direction,

that is, in the thin surface layer to a depth of

2.5 mm, very high gradients of residual stresses

occurred. The variations of residual stresses

were determined experimentally by the x-ray

diffraction method. The large gradient changes

of the measured residual stresses in the

thin surface layer can also be conﬁrmed by

measurement. The results of the measured and

calculated variation of residual stresses in the

surface-hardened layer sufﬁciently agree with

small local deviations. To determine the local

deviations of the variation and of residual

stresses, numerous calculations were made with

varying physical parameters of the material as

well as different process parameters.

A particular problem with steels having

ferritic-pearlitic and pearlitic-ferritic micro-

structures, respectively, is that heating of short

duration does not ensure complete homo-

genization of austenite.

Figure 60 shows the inﬂuence of inhomo-

geneity of austenite on the level of residual

stresses, which is particularly noticeable in the

martensite zone (Ref 20, 47). The initial inho-

mogeneous austenitic microstructure resulted

in the appearance of a martensitic transfor-

mation with a small fraction of residual auste-

nite. With regard to the volume fraction of

martensite and residual austenite, plastiﬁcation

of the material occurred, which produced in-

ternal stresses and the variation of residual

stresses, particularly in the thin surface-

hardened layer.

Figure 61 shows the calculated distribution of

residual stresses due to heating of the specimen

with heating rates of 200 and 800



C/s to a

temperature of 1050



C, followed by cooling

with a cooling rate of 1500



C/s (Ref 20, 47).

With the high heating rate, 800



C/s, a very steep

transition of residual stresses from the com-

pressive to the tensile zone was obtained, which

resulted in a decrease in fatigue strength. With

the considerably lower heating rate, 200



C/s,

the variation of residual stresses in the thin

surface layer was essentially more favorable than

that with the high heating rate. The variation of

Fig. 58

Calculated distribution of microstructures along

the cylinder radius at the end of cooling. Source:

Ref 20, 47

Fig. 59

Calculated and measured residual-stress proﬁles

after induction surface hardening. Source: Ref 20, 47

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the tangential and axial components of residual

stresses permits the following observations:

 With the lower heating rate, the residual

stresses at the surface are lower by 100 to

200 N/mm

 The stress gradient for the tangential and

axial components, s

and s

, is very small in

the subsurface, from a depth of 0.7 to

4.5 mm.

 The transition from compressive to tensile

residual stresses does not occur before a

depth of 2.6 mm due to a small stress

gradient.

The radial component of residual stresses is

0 at the surface. In the subsurface, it is of the

tensile character. Thus, it equals approximately

50 N/mm

with the higher heating rate, 800



s, and is 400 N/mm

with the lower rate,

200



C/s.

Figure 62 shows simulation of the variation of

residual stresses with a favorable rate of surface

induction heating, 200



C/s, which gives the

Fig. 60

Residual-stress proﬁles after induction surface hardening for heterogeneous and homogeneous austenite at austenitizing

temperature. Source: Ref 20, 47

Fig. 61

Simulated residual-stress proﬁles at maximum surface temperature (T

max

= 1050



C) with various heating rates

= 200



C/s and V

= 800



C/s) and at a given cooling rate, V

, of 1500



C/s. Source: Ref 20, 47

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maximum temperature obtained at the surface,

that is, 1050



C (Ref 20, 47). This was followed

by quenching with two cooling rates, 1500 and

300



C/s.

The variation of the tangential and axial

components of residual stresses permits the

following observations:

 With the higher cooling rate, compressive

residual stresses are obtained at the surface,

that is, the axial component of 800 N/mm

and the tangential component of 1050

N/mm

 With a low gradient, the axial and tangential

components of the stresses vary; they change

their sign to the tensile zone only at a depth

between 2.6 and 2.8 mm.

 With the lower cooling rate, considerably

lower compressive residual stresses are

obtained at the surface, that is, an axial

component of 275 N/mm

and a tangen-

tial component of 390 N/mm

 A comparison of the axial and tangential

components of residual stresses indicates

that because of the considerably reduced

cooling rate, the latter is lower in the thin

surface layer by a factor of 3.

 The gradients of residual stresses with a

higher or lower cooling rate are favorable,

since a slow decrease of compressive to

tensile residual stresses results in a minor

susceptibility of a machine part to fatigue

under dynamic loads.

Residual stresses due to surface induction

hardening of the gear wheels were calculated

along the tooth surface during the heating pro-

cess as well the quenching process.

The series of images in Fig. 63(a) show dis-

tributions of internal stresses during the heating

process after 20, 60, 100, and 187 s (Ref 52).

The proﬁle variation of internal stresses indi-

cates that:

 In the initial heating phase, the internal

stresses in the tooth root are of the com-

pressive character and reach up to 700 N/

; with further heating, they change into

tensile internal stresses ranging from +200

to +300 N/mm

 They are considerably lower in the zone

reaching from the root to the pitch circle.

Up to a heating time of 60 s, they are of

the tensile character and reach up to 700

N/mm

. With further heating, they gradually

change to compressive stresses attaining

100 N/mm

 They are obviously very low and insigni-

ﬁcant in the upper part of the gear-wheel

tooth, from the pitch-circle diameter to the

tip of the tooth, therefore, they are not plot-

ted. For this reason, deformations are the

greatest at the tip of the gear-wheel tooth.

The series of images in Fig. 63 show changes

of internal stresses during the heating pro-

cess (Fig. 63a) and the cooling or quenching

Fig. 62

Simulated residual-stress proﬁles at maximum surface temperature (T

max

= 1050



C) with heating rate, V

, of 200



C/s and at

a various cooling rates (V

= 1500



C/s and V

= 300



C/s). Source: Ref 20, 47

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process (Fig. 63b) (Ref 20, 52). It is charac-

teristic of the quenching process that con-

siderably higher internal stresses occur and are

more important in the tooth root. The ﬁgures

show the magnitude and variation of internal

stresses after the cooling times of 0.1, 1, 10, and

300 s, when the gear wheel is ﬁnally cool. The

series of graphic representations of the internal

stresses at the tooth surface indicate that:

 In the initial quenching phase, at 0.1 and 1 s,

the internal stresses are of the tensile char-

acter along the entire tooth height. They are

the highest in the tooth root and gradually

decrease toward the tip of the tooth.

 Between the quenching times of 1 and 10 s,

the sign of the internal stresses changes,

becoming gradually of the compressive

character and ranging between 100 and

150 N/mm

in the upper part of the tooth and

up to 600 N/mm

in the tooth root.

 At the end of quenching, after the cooling

time of 300 s, the internal stresses change

considerably only in the tooth root and at-

tain up to 1500 N/mm

The magnitude of residual stresses was also

measured with the x-ray diffraction method and

strain gages. Figure 64 shows the results of stress

measurements in the pitch circle, that is, at the

middle of the tooth surface for both teeth and in

the tooth root where critical residual stresses

occur (Ref 20, 52). By means of the x-ray dif-

fraction method, it was found that:

 The highest residual stresses occur in the

root. At the surface they equal approximately

540 N/mm

, then increase to 750 N/

at a depth of 30 mm to reach 870 N/

at a depth of 60 mm.

 The residual stresses are a bit lower in the

middle of the tooth surface, that is, at the

pitch circle. At the surface, they equal ap-

proximately 90 N/mm

, then gradually in-

crease with a greater depth to reach 400 N/

at a depth of 60 mm.

A general conclusion can be drawn that the

experimental as well as theoretical results agree

very well and provide useful information,

especially to a technologist in the manufacture

of gear wheels.

Figure 65 shows a part of a gear in cross

section, with residual stress distribution in the

surface-hardened layer of the gear tooth (Ref 15,

20). Also in this case, a residual-stress distri-

bution typical of induction hardening is ob-

tained, that is, compressive residual stresses in

the hardened layer with a martensite micro-

structure, followed by tensile residual stresses,

and, at greater depth, compressive residual

stresses once again. The size and distribution of

residual stresses can be inﬂuenced by power

density.

(b)

(a)

050

Stress σ

0.1 s 1 s 10 s 300 s

20 s 60 s 100 s 187 s

daN/mm

Fig. 63

Principal stress during (a) induction surface

heating process and (b) quenching process. Source:

Ref 20, 52

Fig. 64

Residual-stress measurements on the root below the

tooth surface. Source: Ref 20, 52

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A number of authors have done research into

the effects of power density or energy input used

in heating, with the purpose of determining op-

timal induction-hardening conditions that lead

to good mechanical properties of gears. Lower

power density at the same current frequency

requires longer heating times at the same depth

of the hardened layer and results in higher com-

pressive residual stresses with a moderate tran-

sition of residual stresses from the compressive

into the tensile region.

In induction hardening of gears, it is necessary

to ensure the most uniform depth of the hardened

layer to achieve a symmetric distribution of

residual stresses in the gear tooth cross section.

Workpiece Distortion in Induction

Surface Hardening

Dimensional changes of the workpiece are

closely related to the internal stresses occurring

in heating and cooling. During heat treatment,

when internal stresses in the workpiece are

higher than the yield point, distortion of the

workpiece takes place. When the workpiece has

an axisymmetric shape, it is very important to

place the induction coil so that symmetric

heating and quenching is achieved, resulting in

uniform thickness of the hardened layer with a

martensitic microstructure.

Figure 66 shows induction surface hardening

of a cylindrical rod and tube. When the gap

between the coil and the workpiece varied from

the maximum gap, r

, to the minimum gap, r

that is, r

, the hardened layer thickness

varied also (Ref 15, 27). This means that the side

of the workpiece with a thicker hardened layer

will suffer greater changes in volume than the

side with the thin layer. A changing thickness of

the hardened layer will result in distortion or

curvature of the cylindrical rod in the direction

of the thinner induction-hardened layer.

Figure 66(a) shows a cylindrical tube with an

induction-hardened inner surface. Asymme-

trical placement of the coil inside the tube (hole,

bore) causes differences in the gap between the

coil and the bore surface inside the workpiece.

The conditions of heating are very similar to

those mentioned earlier, and the cylindrical rod

bends in the direction of the thicker hardened

layer.

Similar distortion happens on prismatic bod-

ies where the specimen dimensions are a · h · l.

Distortion of workpieces subsequent to induc-

tion surface hardening on rectangular cross-

sectional rods, strips, plates, and similar forms is

deﬁned or estimated with respect to the size of

the object and thickness of the hardened surface

layer (Ref 27).

In unilateral surface hardening of prismatic

bodies, the distortion will be greater with a

smaller height (h) and greater length (l). Dis-

tortion also grows with the depth of the hardened

surface layer. Figure 67 shows distortion or,

more precisely, bending of a steel rod with a

rectangular cross section, where the rod has the

same cross section a · h and the same length, l

(Ref 15). Figure 67(a) presents specimens of

equal size and shape that have been induction

hardened to different depths. For an ideal com-

parison, choose heat treatment conditions that

will compare easily, that is, equal power (P) and

frequency (f ), and change the time of heating.

Changing the induction heating time allows the

identiﬁcation of different depths of the hardened

layer and very similar microhardness or micro-

structure in the transition zone. Figure 67(b)

shows the conditions in induction surface heat-

ing when the temperature transformation is not

exceeded, T

. This means that on the comple-

tion of quenching, the hardened layer has not

Fig. 65

Residual-stress distribution in the induction surface-

hardened layer of the gear tooth. Source: Ref 15, 20

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Fig. 66

Inﬂuence of nonuniform thickness of surface-hardened layer on distortion for cylindrical steel rod and tube. Source:

Ref 15, 27

Fig. 67

Bending of a steel rod of rectangular cross section as a function of the thickness and location of the hardened layer. Source:

Ref 15

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