troshchenko2000 - threshold fatigue and fretting fatigue of metals

7/28/2019 Troshchenko2000 - Threshold Fatigue and Fretting Fatigue of Metals

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Strength of Materials, Vol. 32, No. 5, 2000

THRESHOLD FATIGUE AND FRETTING FATIGUE OF METALS

V. T. Troshchenko UDC 539.4

General regularities in the variation of threshold stress intensity factors of metals are considered taking

into account the influence of various factors. Justification is offered of the possibility of predictingfatigue limits for smooth specimens and specimens under conditions of fretting from the known

characteristics of threshold stress intensity factors.

Keywords: threshold stress intensity factor, fatigue limit, fretting fatigue.

Introduction. The criteria of fracture mechanics (mechanics of cracks) are used both for describing the

regularities in the propagation of macroscopic fatigue cracks and for constructing models, which are based on

consideration of structural and service defects accumulated in materials and make it possible to describe general laws of

their fatigue failure. The latter approach appears to be particularly efficient for structurally inhomogeneous materials,

e.g., titanium alloys, wherein we can generally detect structural elements acting as structural stress concentrators, and

also for the cases of loading (e.g., fretting conditions) where microcracks appear at the earliest stages of cyclic loading

and the entire subsequent process of fatigue is the process of propagation of those cracks.

The main characteristic that governs the onset of crack propagation and therefore defines the value of the fatigue

limit is the threshold stress intensity factor Kth .

1. Experimental Procedure. This paper presents a generalization of the results of a wide range of investigations

into the characteristics of fatigue and crack-growth resistance of various metallic materials.

Since it is impossible within the scope of this paper to consider in detail the experimental procedures used, we

shall give only references to the works where they are described.

Thus, in [1] one can find the description of the procedures for the investigation of fatigue and crack growth

resistance of alloys in bending, in [2, 3] methods for studying fatigue and crack-growth resistance of alloys in

tensioncompression and methods for the investigation of crack growth resistance in pure shear, and in [24] methods

for studying fretting behavior.

Fretting fatigue was studied under conditions of axial loading with fretting initiated by pressing bridge-shaped

fretting pads against specimen surfaces with the help of elastic rings. The results of those investigations were used to plot

fatigue curves on the coordinates stress vs logarithm of the number of cycles to fracture lg N for a test duration of107 cycles.

The investigation of crack growth resistance involved construction of diagrams in the coordinates crack

propagation rate da dN / vs the range (K) or the maximum value (Kmax ) of the stress intensity factor. The tests wereperformed at frequencies in the range from 20 to 100 Hz.

The stress intensity factor range was taken to be equal to Kmax at R 0 and to K Kmax min at R 0, whereR K K= min max/ is the load ratio. The quantity K Kth thmax ( ) , which is the threshold stress intensity factor, was takenas the maximum value of the stress intensity factor at which a crack does not grow during a specified number of load

cycles [1].

In the literature, an effective value of the stress intensity factor Keff is used, which is determined from theformula

K K Keff op= max ,

where Kop is the stress intensity factor that corresponds to the crack opening displacement.

00392316/2000/32050427$25.00 Copyright 2001 Plenum Publishing Corporation 427

Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from

Problemy Prochnosti, No. 5, pp. 34 43, September October, 2000. Original article submitted June 26, 2000.


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A typical relation between the magnitudes of the threshold stress intensity factors K Kth thmax , , and Kth eff forvarious cycle asymmetries is shown in Fig. 1 using steel 15Kh2MFA as an example [5].

2. Correlation between Parameter of the Kth and Other Mechanical Characteristics of Materials. Acomparative analysis of the magnitudes of the threshold stress intensity factors, Kth , and of corresponding values of theoffset yield stress, 0 2. , ultimate strength, u , and fatigue limits in bending, 1, for a large group of chromium andheat-resistant steels and titanium and nickel alloys in symmetrical bending was made in [6].

The results of this comparative analysis revealed that there is no clear-cut correlation between the values of

Kth and 0 2. , u , and 1. The absence of a correlation between the values of Kth and 1, which are bothcharacteristics of fracture resistance under cyclic loading, is attributed to the dependence of the fatigue limit not only on

the magnitude of the threshold stress intensity factor, but also on structural features of the alloy under study. We shall

illustrate this by the relationships following from the linear elastic fracture mechanics.

In the general form, the stress intensity factor is equal to

K Y a aI = + 0 , (1)

where is the stress, a is the crack size, a0 is the size of a structural defect, and Y is a geometrical factor.For K KthI = , = 1, and a = 0, we have

K Y ath = 1 0 and ( ) . =10

pthK

Y a

(2)

If we take the effective value of the threshold stress intensity factor to be the governing one, we obtain

K Y atheff = 1 0 and ( ) .* =10

p theffK

Y a

(3)

The justification of the possibility of using formulas (2) and (3) to describe the relationship between 1 andKth and Ktheff for titanium alloy VT3-1 after various regimes of thermomechanical treatment will be given below.

3. The Influence of Various Factors on the Value of Kth. The magnitude of the threshold stress intensityfactor of metals Kth depends on the stress ratio in a cycle, temperature, test medium, overload, and other factors.

The investigations of carbon and chromium steels and titanium, aluminium, and nickel alloys showed that the

value of Kth decreases as the stress ratio in a load cycle increases. An appreciable scatter in the results is observed [1].

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Fig. 1. The dependence of K thmax (1), Kth (2), and Ktheff (3) on the stress ratioin a cycle for steel 15Kh2MFA.

K thmax , MPa m K Kth th eff , , MPa m


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Earlier in [6] it was shown that for chromium steels and for titanium and nickel alloys a considerable reduction

(down to 50%) in the threshold stress intensity factors is observed with a rise in temperature.

The authors of [2, 7] present the results of an investigation of the influence of the vapors of a sea-salt solution on

the value of Kth for chromium steels and titanium alloys under fully-reversed load cycles. They found that in this casethe decrease in the value of Kth reached 40% and higher. An appreciable difference is observed in the degrees of thereduction of K

thfor titanium alloys of different chemical compositions and thermal treatments.

Overloads were found to have a significant effect on crack propagation. Upon overloading, deceleration of crack

growth is observed, which is attributed to both crack blunting and the formation of a residual compressive stress zone at

the crack tip [1]. Overloads also lead to an increase in the threshold stress intensity factors.

The influence of overloads on the magnitude of the threshold stress intensity factor for high-temperature steels

and titanium and nickel alloys at room and high temperatures was studied earlier in [1]. A reduction in the intensity of

the increase of the value of Kth after overloading with a rise in the test temperature was shown.4. Interrelation between Fatigue Limits and Threshold Stress Intensity Factors. The investigations were

performed on titanium alloy VT3-1, which was subjected to various thermomechanical treatments (Table 1), to obtain

different structures and mechanical properties [8]. A typical microstructure of the investigated alloys is a combination of

two phases in the form of -globules, -plates, and ( + )-matrix. We denote the size of -globules by d and thethickness of secondary -plates by b; their values for VT3-1 alloy are listed in Table 1.

It is universally accepted that the level of cyclic strength of two-phase titanium alloys is defined by the

properties of a component of lower strength, and for VT3-1 alloy this is the -phase.Fatigue limits and threshold stress intensity factors were determined in bending in one plane [8]. As follows

from the data listed in Table 1, there is a clear-cut relation between the size of -globules and the value of the fatiguelimit.

Using relation (2), which defines the value of the fatigue limit, and substituting the values of Kth and a d0 =into it, we get the calculated values of the fatigue limit ( ) 1 p listed in Table 1. As is seen, the calculated values of thefatigue limits exceed appreciably the experimental ones. Fatigue limits were also calculated by formula (3), wherein the

effective values of the threshold stress intensity factors were used, which were calculated according to the

recommendations of [9] by the formula

K Etheff = 16 10 5. ,

where E is the modulus of elasticity of the material.

The magnitudes of the fatigue limits ( ) 1 p obtained in this way and presented in Table 1 in the last column

are in close agreement with those obtained by experiment.

5. Fretting Fatigue. Fretting takes place when contacting surfaces move (slide) a small distance

( . .1 0 10 2 5 106 1 mm) relative to each other. This results in fracturing of one of the contacting surfaces and in the

formation of local cracks. The further process of fatigue fracture consists in the propagation of those cracks and can be

described using the approaches of fracture mechanics [2, 1012].

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TABLE 1. Regimes of Thermomechanical Treatment of Alloy VT3-1, Corresponding Sizes

of Structural Elements, and Mechanical Properties

Alloy Treatment regime 0 2. ,

MPa

u ,

MPa

d,

m

b,

m

1,

MPa

Kth,

MPa m

( )1 p *,

MPa

( )1 p **,

MPa

I As received 1065 1114 2.0 0.1 700 4.74 1740 725

II Quenched for 0.5 h at 1323 K,

rolled at 1073 K and annealed

for 5 h at 1073 K

1009 1069 3.0 0.7 600 5.06 1445 591

III The same but rolled at 1123 K 1027 1084 1.8 1.5 650 4.60 1460 648

IV The same but rolled at 1173 K 1011 1070 1.8 750 5.06 1930 764

V The same but rolled at 1223 K 1100 1210 4.0 4.0 500 4.11 1060 512

VI The regime used in industry 998 1026 10.0 320 5.06 820 324

* Calculated by formula (2); ** calculated by formula (3).


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5.1. Main Regularities of Fretting Fatigue. The investigated materials, testing conditions, and fatigue limits in

the presence of fretting are given in Table 2.

Except for specially indicated cases, the tests were performed under axial loading with a fully-reversed cycle.

The degree of decrease in the fatigue limit under fretting is characterized by the value of Kf, which is equal to the ratio

between the fatigue limits of specimens without fretting and of those with fretting.

Figure 2 shows the dependence of the value of Kf on the number of cycles to fracture for various cycle

asymmetries for aluminium and titanium alloys [4]. The results presented show that for the alloys investigated the

presence of fretting reduces fatigue limits appreciably. The degree of influence of fretting increases with increasing

number of cycles to fracture, and fully-reversed load cycles are the most dangerous in this respect.

The data form the literature show that under conditions of fretting the fatigue limit decreases as the contact

pressure increases to a certain level [4].

Fatigue cracks are initiated at an early stage of loading (5 to 10% of the total lifetime) in a surface layer under

the action of surface forces in the zone of fretting.

A scheme of the forces acting in the fretting zone is shown in Fig. 3, where F is a variable external force, Fpis the pressure force, and F FQ p= is the friction force, where is the coefficient of friction.

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TABLE 2. Investigated Materials, Testing Conditions, and Fretting Fatigue Limits

Material 0 2. ,

MPa

b ,

MPa

, % Material of a

counterbody

Pressure in the

contact zone,

MPa

Fatigue limit for test

duration 107 cycles, MPa

Kf

without fretting in the presence

of fretting

Steels

15kp

20kp

08GSYuT

22G2TYu

15G2AFV

230

403

410

380

390

540

600

532

27

27

30

16

32

Steel 45 120

120

120

120

120

180

195

250

290

250

130

175

125

150

120

1.40

1.12

2.00

1.93

2.10

Aluminium alloys

AMg6

AMg6N

AMg6N

D16AT

157

343

343

322

360

430

430

424

19

7

7

10

Alloy AMg6

Steel 30KhGSA

Alloy AMg6N

Alloy D16AT

50

50

100

50

190 (R = 0)

112

120 (R = 0)

56

70

55

1.58

2.04

Titanium alloys

VT9

VT14

1030

980

1140

1040

7

6

Alloy VT10

Alloy VT14

80

50

485

140

300

1.62

Fig. 2. Kf vs number of cycles to fracture for aluminium D16AT (1, 2, 3) and AMg6 (4) and

titanium VT-14 (5) alloys at R = 1 (1), R = 0 (2, 4, 5), and R = 0.5 (3).

Kf

N, cycles


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The stress intensity factors KI and KII induced by the stresses P and Q (Fig. 4) can be found from the

following formulas [13]:

KP

aPI = + + +

( )( . . . . .1 0 824 0 06 0 84 15 41 53 38 52 2 3 4 9 74 21 82

1 1 2949 0 0044 0 128

5 6

2

. . ) ,

( )( . . .

= + +KQ

aQI 1 10 89 22 14 10 96

1 1 294

2 3 4 5

2

+ +

=

. . . ) ,

( )( .KP

aPII 1184 5 442 28 14 41 8 22 38

2 3 4 5. . . . . ) , + + +

= K KQ

PQ PII I .

(4)

In the presence of fretting, a fatigue crack is generally initiated at an angle to the surface, which is close to 45o,

and then moves on into the plane perpendicular to the latter.

Figure 5 presents some results of investigation of the kinetics of fatigue-crack angle variation for aluminiumAMg6 and titanium VT9 alloys as the crack grows deep into the material [2].

5.2. A Model of Fatigue Crack Propagation under Fretting. Earlier the authors of [12] proposed a model for

fatigue crack propagation under fretting that takes into account regularities in the growth of such cracks observed in an

experiment (Fig. 6). The propagation of a crack at the initial stage is assumed to be defined by the shear stress intensity

factor K [14]:

K K K

= + 1

2 23 1cos [ sin ( cos )],I II (5)

where KI and KII are the stress intensity factors from all the stress components acting in the surface layer. It is

suggested that at stage I the crack propagates at an angle that corresponds to the maximum values of K .

At stage II, the crack growth is governed by the normal stress intensity factor [14]:

K K K

=

cos cos sin .

2 2

3

2

2I II (6)

The condition for the transition of a crack from stage I to stage II (Fig. 6) that occurs at stresses above the

fatigue limit (curve 1 in Fig. 6) can be written in the following form:

K K K Kth th , .

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Fig. 3 Fig. 4 Fig. 5

Fig. 3. A loading scheme for a fretting fatigue specimen.

Fig. 4. A scheme of crack loading.

Fig. 5. Fatigue crack slope vs its depth for aluminium AMg6 (1, 2) and titanium VT9 (35) alloys:

(1) a = 90 MPa; (2) a = 75 MPa; (3, 4) a = 210 MPa; (5) a =160 MPa.


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The condition of nonpropagation of a crack that corresponds to the stresses below the fatigue limit has the form

(curve 2 in Fig. 6)

K K th < .

In the above relationships Kth and K th are the threshold stress intensity factors in tension and in shear,

respectively.

The values of Kth and K th for some of the alloys studied are listed in Table 3.

With the magnitudes of Kth and K th determined for the alloy investigated and plotting the stress intensity

factors K and K vs crack size a, as follows from Fig. 6, we can estimate the magnitude of the fatigue limit under

conditions of fretting.For stresses above the fatigue limit with the given da dN / vs K diagrams for the corresponding loading

schemes, the stress intensity factors for fretting cracks considering the components from , P, and Q, the direction ofcrack propagation, the tribotechnical characteristics of the contacting pairs, and the characteristics of the material cyclic

plasticity, we can calculate, as was shown earlier in [12], the number of cycles required for the crack to reach a given

size.

Figure 7 illustrates the results of this calculation for steel 15kp made on the assumption that the initial crack size

is 0.01 mm and the critical size is 3.0 mm [12]. A fairly good agreement between the calculated and experimental results

is observed.

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TABLE 3. Threshold Values of the Stress Intensity Factors in Cyclic Tests

Material R Kth, MPa m K th , MPa m K Kth th/

Steels:

15kp

08GSYuT

22G2TYu

0

1

0

1

0

1

7.86

5.07

5.54

4.18

4.72

3.05

5.00

2.95

3.48

2.46

3.10

1.83

1.54

1.72

1.60

1.70

1.52

1.67

Titanium alloy VT-9 0

1

2.70

1.65

1.86

1.08

1.45

1.53

Aluminium alloy

AMg6N

0

1

4.30

3.82

2.94

3.70

1.46

1.42

, MPa

N, cycles

Fig. 6 Fig. 7

Fig. 6. A model for the propagation of fretting-fatigue cracks.

Fig. 7. Experimental (points) and calculated (lines) fatigue curves for steel 15kp:

without fretting (1) and with fretting (2).


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Conclusions. General regularities in the influence of the load ratio, temperature, medium, and overloading on

the threshold stress intensity factors are considered. The possibility of predicting fatigue limits for a titanium alloy

subjected to various thermomechanical treatments with the use of effective values of the threshold stress intensity factors

and the size of structural elements has been established. The model for crack propagation under conditions of fretting has

been justified, and the essential role of the threshold stress intensity factors in the prediction of fatigue limits under

fretting conditions is shown.

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troshchenko2000 - threshold fatigue and fretting fatigue of metals

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