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Abstract—the article presents the results of an

experimental–analytical study of the cyclic fracture process in a

locally austempered ductile iron (LADI). A heat treatment is

realized in such a way as to form three layers with different

microstructure, mechanical properties and resistance to cyclic

loading. The fracture criterion, the stress intensity factor K,

dependent on stresses of cyclic loading and induced residual

stresses, was chosen as a criterion for analyzing the process of

cyclic fracturing. The limiting values of threshold stress intensity

factor range ΔKth were determined for the compact tension (CT)

specimens after application of loading and they were found to be

different. It was determined that residual stresses increase the

ΔKth factor when the crack propagation rate is less than 10-11

m/cycle.

Index Terms—cracking threshold, residual stresses.

I. INTRODUCTION

Austempered ductile iron (ADI) is a specially heat-treated

cast iron with spheroid graphite. It has good properties of

strength, plasticity, fracture toughness, fatigue and resistance

to wear, and is therefore widely used in engineering practice

to produce the engineering elements in various fields of

industry, e.g., transportation and the mineral mining

industries, for the manufacturing of gears, shafts, etc. [1], [2].

The process of heat treatment involves three stages, the

duration of which depends on the shape and size of the

element to be produced. For large gears and supports, needed

when producing mining equipment in the mineral industry,

austempering with induction heating of a localized zone is

applied. This technique replaces the conventional

heat-treating process and provides the desired ADI

microstructure in the required zone and depth [3]-[5]. The

locally austempered ductile iron (LADI) is obtained by using

high frequency induction heating or by applying direct

electric current [6]. Application of the LADI makes it

possible to obtain almost the same properties as conventional

ADI [7]. However, due to the different micro structural

transformations in heat- affected and unaffected zones,

residual stresses are induced. These zones significantly

influence the fatigue, i.e., the fracturing indicators [8]-[10].

The conventional method in this experimental and analytical

investigation is replaced by another one, aiming to evaluate

several factors of the separate layers, namely the static and

cyclic properties of the material, its microstructure, in

homogeneity and other factors.

II. SPECIMENS

SG cast iron was chosen as the basic material for

producing the layered cast iron specimens. The mechanical

properties of SG cast iron are presented in Table 1.

Table 1. Cast iron mechanical properties

Cast iron R0.2, MPa Rm, MPa Z, %

SG 630-634 863-933 3.7-6.7

The threshold stress intensity factor ranges of ΔKth =

7.9-9.1 MPa·m1/2

were determined for the compact tension

(CT) specimens by applying the known techniques [11].

Eight work-pieces of larger bars for preparing the CT

specimens (dimensions: 65 mm 62.5 mm 25 mm) were

produced for performing the cyclic tests. The work-pieces for

the austenitizing were placed in an induction heating furnace

and heated up to the temperature required for austenitizing

(900 oC). Then the work-pieces were placed in an isothermal

transformation chamber where they were kept for the

conventional duration for the austempering. The heat

treatment was applied in such a way as to form three different

layers in the specimen. Cuts were made in the CT specimens

to ensure that the fatigue crack started in the hard layer

(heat-treated layer), further propagating through the

subsequent perpendicular to the intermediate and mild layers

of the crack front (Fig. 1). The arrangement of layers was

determined by the measurements of etching and hardness.

The mechanical properties of the separate layers were quite

different. The properties of the mild layer during heat

treatment changed insignificantly. Table 2 shows that the

plasticity of the hard layer slightly increased. The properties

of the intermediate layer were conditional. It was difficult to

establish them precisely enough. The heat treatment process

is hard to control, and therefore the size and the location of

the intermediate layer in the investigated CT specimens are

different. The thicknesses of the layers are shown in Table 2.

The thickness of the hard layer Lh varies within the bounds of

27.5 mm and 36.5 mm when analyzing all the specimens,

while that of the intermediate layer varies within the bounds

of 1 mm and 4 mm. The remaining CT specimens can be

described as the mild (thermally unaffected) layer. The

different locations and thicknesses of the layers described

above result in different impacts on the cyclic fracturing

indicators.

Fatigue Crack Propagation in Locally

Heat-Treated Ductile Iron Mindaugas Leonavičius, Algimantas Krenevičius, Gediminas Petraitis, Arnoldas Norkus

Vilnius Gediminas Technical University, Saulėtekio al. 11, 10223, Vilnius, Lithuania

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Hard layer (temperad layer)

Intermediate layer

Mild layer

LmLh15

a

W

1.2

W

Li Fig. 1 Arrangement of layers in CT specimens

Table 2. Thicknesses of layers in CT specimens after

austempering

Specimen

Hard layer

size Lh,

mm

Intermediate

layer size Li,

mm

Mild layer

size Lm,

mm

1 32.3 1.0 16.7

2 27.5 2.5 20.0

3 27.7 3.0 19.3

4 31.0 3.0 16.0

5 31.8 1.0 17.2

6 31.5 2.0 16.5

7 36.5 4.0 9.5

8 33.5 1.0 15.5

The microstructure and the hardness were investigated for

specimen 5: the thickness of the hard layer is Lh = 31.8 mm,

that of the intermediate layer is 1 mm and that of the mild

layer is 17.0 mm. The properties were determined at five

points, namely at 5 mm, 17 mm, 33 mm, 47 mm, and 59 mm

from the side of the cut, as shown in Fig. 2.

Fig. 2 Microstructure and hardness measurement points

Cylindrical specimens (Fig. 3) for identifying the

mechanical properties were produced from the CT

specimens. Then tension tests were performed with the

specimens. Analysis of the determined mechanical properties

shows that the microstructure, hardness and mechanical

properties of the heat-treated parts differ significantly from

the properties of the basic cast iron and those of the

non-heat-treated part.

Fig. 3 Cutting scheme and dimensions of tension specimens

The determined mechanical properties are presented in

Table 3.

Table 3. Mechanical properties

Layer Rpr,

MPa

R0.2,

MPa

Rm,

MPa

E,

GPa

Z,

%

mild 492 607 869 165 3.3

mild 490 602 864 164 2.9

intermediate 490 603 864 163 2.8

intermediate 494 608 874 163 3.2

hard 748 957 1261 162 3.6

hard 756 963 1254 159 4.1

The microstructures are shown in Fig. 4. An initial

microstructure of the SG cast irons is shown in Fig. 4a. It

consists of pearlite with slight inclusions of ferrite and

spherical graphite. The microstructure of the heat-treated part

is shown in Figs. 4b, 4c, 4d, and 4e. A coarse-needle

martensite, spheroid graphite, several cementite inclusions

and a residual austenite are resident for the microstructure.

The microstructure at the level of 59 mm, corresponding to

the heat-unaffected part of the specimen, is shown in Fig. 4f.

It consists of pearlite, ferrite and graphite. The microstructure

of the intermediate layer (thickness 1 mm) consists of trostite,

ferrite, and pearlite and spheroid graphite. The microstructure

of the heat-treated part is characteristic of that of austempered

ductile iron. The heat-unaffected part corresponds to that of

normalized iron. The microstructure of the other specimens is

common. The microstructure of the non-treated layers is the

same for all specimens except for specimen 3, where more

ferrite was detected compared with the other specimens. The

coarse-needle martensite in the heat-treated part was detected

only for specimens 4 and 7. The martensite of specimen 6 is

medium-sized. Fine-needle martensite was identified for

specimen 1. Residual cementite was found in specimens 4, 5,

6 and 7 but was missing in specimens 1, 3 and 6. The

intermediate layer usually consists of trostite, ferrite

(specimens 3, 4, 5, 8), in some cases with inserts of cementite

(specimens 1, 2, 6, 7) and fine plate pearlite (specimen 4).

The hardness was determined at the same locations where the

microstructure was determined, as mentioned above (Fig. 2).

At the distances of 5 mm, 17 mm, and 33 mm (hard layer) it

was 388 BHN, 401 BHN, and 401 BHN, at 47 mm

(intermediate layer) it was 302 BHN, and at 59 mm (mild

layer) it was 285 BHN. The hardness of the other specimens

was similar. The large magnitude of hardness is conditioned

by the martensite.

5 3 1

4 2 6

5

31

14

12

M1

0

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(a) (b)

(c) (d)

(e) (f)

Fig. 4 Structures of layers: initial (a), heat treated layer at 5 mm (b), 17 mm (c), 33 mm (d), 47 mm (e),

Non-heat-treated layer at 59 mm (f)

III. EXPERIMENTS

Cyclic loading tests were performed to determine the

threshold stress intensity factor range ΔKth in different parts

of the specimens. CT specimens made from heat-treated

work-pieces were tested. The test procedures conform to the

standard ASTM E647 [11], but introducing a modification to

determine the threshold crack propagation rates,

corresponding to their lower magnitudes (identified during

the exploitation of real structures) and their durability

(serviceability) exceeding 25 years. The determined

thresholds correspond to the cases of crack propagation rates

being less than 10-11

m/cycle. The procedure for determining

the threshold involves an initial pre-cracking with a

subsequent gradual decreasing of the load magnitude until

the crack stabilizes for the fixed number of cycles. The

procedure is repeated several times for the tested specimens,

i.e., to determine the various thresholds corresponding to the

different crack sizes. Such an approach makes it possible to

identify the crack propagation through the separate layers

under investigation. The relationships of crack propagation

rates vs. the stress intensity factor range were developed by

processing the test data of eight CT specimens (Fig. 5).

Referring to ASTM E647 to calculate the stress intensity

factor K, the following formula was employed:

,minmax KKK

.6.572.14

32.1364.4866.01/2)(

,/

,/

43

22/3

2/1

f

Wa

fBWFK

(1)

where K is the stress intensity factor, F is the tension force,

B = 25 mm is the specimen width, W = 50 mm is the specimen

base length, f() is the geometrical function, and a is the

crack size (depth) (Fig. 1).

100 μm 100 μm

100 μm

100 μm 100 μm

100 μm

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(a)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

19,0

27,5

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

□ – 19.0

○ – 27.5

(b)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

19,0

27,5

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

◊ – 17.0

Δ – 18,9

(c)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

15.6

18.0

22.9

34.1 mild

37.4 mild

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 15.6

□ – 18.0

◊ – 22.9

▲ – 34.1

27.5ggfd

fdfghdfg

h34dfgh

dfgh34,1 (d)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

15.1

20.3

24.1

27.5

30.4

44.7 mild

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 15.1

□ – 20.3

◊ – 24.1

Δ – 27.5

+ – 30.4

(e)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

15.4

23.9

26.6

27.4

33.9 mild

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 15.4

□ – 23.9

◊ – 26.6

Δ – 27.4

● – 33.9

(f)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

15.3

18.3

28.8

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 15.3

□ – 18.3

◊ – 28.8

(g)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crack size a, mm

17.6

24.3

32.6

36.1

40.1 mild

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 17.6

□ – 24.3

◊ – 32.6

Δ – 36.1

● – 40.1

(h)

1e-12

1e-11

1e-10

1e-9

1e-8

1e-7

5 10 15 20 25 30

crak size a, mm

17.5

21.2

25.0

31.8

38.3 mild

39.6 mild

5 10 15 20 25 30

ΔKth (MPa∙√m)

10-8

10-10

10-12

da

/dN

(m

/cy

cle)

a, mm

○ – 17.5

□ – 21.2

◊ – 25.0

Δ – 31.8

● – 38.3

Fig. 5 Relationships for crack propagation rates (da/dN) vs. stress intensity factor range (ΔKth) of specimens: (a) specimen 1, (b)

specimen 2, (c) specimen 3, (d) specimen 4, (e) specimen 5, (f) specimen 6, (g) specimen 7, (h) specimen 8.

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The thresholds of all the specimens depending on crack

size and corresponding to a rate of less than 10-11

m/cycle

were determined for different layers. These were different:

for the hard layer ΔKth = 7.72-16.72 MPa m , for the

intermediate layer ΔKth = 10.1 MPa m , for the mild layer

ΔKth = 9.5-14.62 MPa m . The significant difference in the

determined magnitudes of the thresholds shows the influence

of the residual stresses and microstructure. The stresses in the

hard layer change when the notches in the CT specimens are

made. At an initial stage of cyclic loading, when the crack

size is 15.6-20 mm, the ΔKth for the layer and the base

material are similar. When the crack exceeds 20 mm, the ΔKth

increases to 16.72 MPa m , as the compressed mild layer

constrains the opening of the crack. When the crack passes

the intermediate layer, the ΔKth quickly declines until the

magnitude of 9.5 MPa m .

IV. DISCUSSION

The residual stresses have a great influence on fatigue

fracturing and its indicators, and one can find many

techniques for determining these stresses [12]-[14]. The

relationships (Fig. 6) of the thresholds vs. crack size were

developed on the basis of the performed experimental data to

evaluate the influence of the residual stresses.

a)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

notch crack

b)

10 20 30 40 a (mm)

20

16

12

8

Δ

Kth

(M

Pa√

m)

c)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

d)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

e)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

f)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

g)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

h)

10 20 30 40 a (mm)

20

16

12

8

ΔK

th (

MP

a√m

)

Fig. 6 Relationships of threshold stress intensity factor range (ΔKth) vs. crack size (a) for specimens : (a) specimen 1, (b)

specimen 2, (c) specimen 3, (d) specimen 4, (e) specimen 5, (f) specimen 6, (g) specimen 7, (h) specimen 8; ○ – crack tip before

intermediate layer; ● – crack tip beyond intermediate layer

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Fig. 7 shows the generalized relationship (obtained via

processing the experimental data of all specimens, given in

Fig. 5) of the threshold vs. crack size.

Fig. 7 Generalized relationship for specimens 3, 5, 7 and 8 of

threshold stress intensity factor range (ΔKth) vs. crack

size (a): ○ – hard layer; ● – mild layer

Analysis of the relationships of the thresholds vs. crack

sizes shows that the threshold increases when the crack

approaches the intermediate and mild layers, and reduces

when it enters the mild layer. The maximum magnitude of

ΔKth is reached just prior to the intermediate layer (Figs. 6b,

6g, 6h). The processed experimental data resulted in the

following relations:

mean: ,503.1423.0th aK (2)

upper limit: ,734.343.0th aK (3)

lower limit: .032.143.0th aK (4)

The images of the fractures in specimens 3 and 5 are

presented in Fig. 8. It can be seen that at the first stages

of cyclic loading many focuses of cracks appear in the

vicinity of the notch. Further, when increasing the number of

loading cycles and when the crack size reaches approx. 2-3

mm from the top, the main crack is formed. One can also

identify the separate layers of different structure in the

fractures.

(a)

(b)

Fig. 8 Fractures of CT specimens 3 (a) and 5 (b)

The images of the separate zones, obtained by scanning

electronic microscopy (SEM), are presented in Fig. 9. It can

be seen that the microstructures (presented in Fig. 4) of the

different layers have a great influence on the fracturing

process.

(a) (b) (c)

Fig. 9 SEM fracture images of 5th specimen at hard (a), intermediate (b) and mild layers (c)

Fig. 10 shows the crack propagation model with regard to

the influence of residual stresses. When residual stresses σr

do not develop (Fig. 10a), the characteristic pre-cracking

zone forms in the material and the crack opening gradually

increases through the specimen. In the presence of residual

compressive stresses (Fig. 10b), the pre-cracking zone and

the crack opening are smaller as residual stresses reduce the

effective stress intensity factor at the crack tip. As a result, the

threshold stress intensity factor increases, i.e., the fracture

process slows down. The tension stresses must be increased

up to σ', as shown in Fig. 10c, to continue the cracking

process.

Hard (40.2mm)

Mild (19.3mm)

Intermediate (3.0 mm)

Intermediate (1.0 mm)

Hard (46.8 mm) Mild

(17.3 mm)

a (mm)

ΔK

th (

MP

a·√

m)

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(a)

σ

σpre-crack

a

pre-fracture

zone

(b)

σ

σ

pre-fracture

zone

transitional

layer

σr

σr

mild layer

hard

layer

(c)

σ'

σ'

pre-fracture

zone

σr

σr

a

Fig. 10. Crack growth model: (a) – at stresses σ, without

residual stresses; (b) – at stresses σ, with residual stress, crack is

closed (does not spread); (c) – for crack propagation the stresses

σ‘ =σ + σr are necessary

The threshold stress intensity range decreases when the

crack crosses the heat-affected layer.

V. CONCLUSIONS

1. During the localized austempering three layers with

different microstructures, hardnesses and mechanical

properties are formed comparing with a basic cast iron. The

developed residual stresses, which distribute unevenly along

the crack propagation direction, influence the loading cycle

and affect the process of cyclic fracturing.

2. For evaluation of the influences of cyclic loading, micro

structural changes and residual stresses on fracturing process

the stress intensity factor K was chosen. For the obtaining the

dependency ΔK-da/dN the experimental research methodizes

had involved the crack size and layers arrangement.

3. The thresholds determined for separate layers vary

within the wide range of 7.72 and 16.72 MPa·m1/2

in the case

when crack propagation rate is less the 10-11

m/cycle and it

rapidly decreases having passed the intermediate layer.

4. The test results yield the variation of ΔKth = 7.72-10.55

MPa·m1/2

related to the crack depth variation of 15.6-20 mm.

The increment of crack enlarges the ΔKth. This means that the

microstructure and the residual stresses change stress strain

state at crack tip so reducing the crack propagation.

VI. ACKNOWLEDGMENT

The equipment and infrastructure of the Civil Engineering

Scientific Research Center of Vilnius Gediminas Technical

University was employed for investigations.

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2003.

[4] E. S. Davenport, and E. C. Bain, ―Transformation of austenite

at constant subcritical temperatures,‖ Trans Am Inst Min

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[5] E. Dorazil, ―High strength austempered ductile cast iron,‖

Prague, Ellis Horwood, p. 244, 1991.

[6] S. Tada, T. Abe, T. Takahashi, and H. Nemoto, ―Local

Austempering Treatment by Electric Current Zone Heating,‖

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[7] C. Bixler, K. Hayrynen, J. Keough, G. Pfaffmann, et al.

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Paper 2010-01-0652, doi: 10.4271/2010-01-0652, 2010.

[8] D. H. Herring, ―A Discussion of Retained Austenite,‖

Industrial Heating, vol. 72(3), pp. 14-16, 2005.

[9] T. J. Marrow, H. Centinel, S. H. Macdonald, A. Venslovas, and

M. Leonavičius, ‖X–ray Tomography of Short Fatigue Cracks

in Ductile Iron,‖ In: Proceedings of the 14th Biennial

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Handbook, vol. 4, pp. 682-692, 1991.

[11] ASTM E 647-00. ―Standard Test Method for Measurement of

Fatigue Crack Growth Rates‖.

[12] K. Xu, J. He, and H. Zhou, ―Effect of residual stress on fatigue

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[13] M. Benedetti, V. Fontanari, B. R. Hohn, P. Oster, and T. Tobie,

―Influence of Shot Peening on Bending Tooth Fatigue Limit of

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intermediate

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evolution around a crack-tip during tensile loading and

unloading cycle,‖ Scripta Materialia, vol. 53, pp. 971-975,

2005.

AUHTOR’S PROFILE

Prof. Mindaugas Leonavičius. Professor of Dept.

of Strength of Materials of Vilnius Gediminas Technical University. Research interests: strength of materials, experimental mechanics, fracture

mechanics.

Prof. Algimantas Krenevičius. Professor of Dept.

of Strength of Metarials of Vilnius Gediminas Technical University.

Research interests: fatigue of structures, fracture mechanics.

Assoc. Prof. Gediminas Petraitis. In 2002 graduated Vilnius Gediminas Technical university. Since 2006 head of

Research Laboratory of Strength Mechanics of Vilnius Gediminas Technical

University. Research interests: high cycle fatigue, fracture mechanics.

Prof. Arnoldas Norkus. Professor at Vilnius Gediminas Technical University, Dept. of Geotechnical Engineering. Since

2007 Head of Dept. Research interests: soil mechanics, modeling of mechanical properties of materials, mechanics of structures