a fatigue life model for 5percent chrome work roll steel.pdf

7/27/2019 A fatigue life model for 5percent chrome work roll steel.PDF

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International Journal of Fatigue 26 (2004) 683689www.elsevier.com/locate/ijfatigue

A fatigue life model for 5% chrome work roll steelunder multiaxial loading

K.S. Kim , K.M. Nam, G.J. Kwak, S.M. Hwang

Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang 790-784, South Korea

Received 5 August 2003; received in revised form 18 September 2003; accepted 20 November 2003

Abstract

The fatigue behavior of 5% chrome steel heat-treated for wear resistance has been investigated under axialtorsional loading.This material exhibits brittle fracture under monotonic and cyclic loading. The preferred site for crack initiation appears to becarbide clusters on or near the surface. Crack propagation initially progressed in a transgranular mode followed by a mixedtransgranularintergranular mode at a later stage. A parameter given in terms of the maximum normal stress range and thehydrostatic stress range is found to correlate fatigue lives reasonably well. This parameter correctly predicts the experimentaltrend that in-phase loading is more damaging than out-of-phase loading under a given ratio of axial/shear stress amplitudes.Models for tensile and compressive mean stress effects have also been proposed based on the uniaxial test results.# 2003 Elsevier Ltd. All rights reserved.

Keywords: Multiaxial fatigue; Normal fracture; Mean stress effect; 5% Chrome steel; Work roll

1. Introduction

Heat-treated 5% chrome steel is widely used forwork rolls in cold rolling operations. Work rolls aresubjected to surface damage of various types. Among

these are normal wear, bruising and spalling.Micro-cracks are commonly observed in ultrasonic

and eddy current testing during periodic dressing of theroll surface. Cracks may be initiated by thermal shocks

[13] from frictional skidding between the roll andwork piece, or from excessive local deformation due to

pinching and cobbling of the incoming strip. The local

heat buildup may result in material softening and crackinitiation upon sudden cooling. Once initiated, crackscan propagate under repeated contact loads, and acci-

dental spalling of the roll surface may entail.Another type of surface damage of a work roll

is fatigue damage due to repeated contact loads. Thematerial in the contact zone is subjected to complex,

multiaxial, compressive stresses, which can initiate fatigue

cracks and cause surface damage. Contact fatiguemodels have been reviewed by Tallian [4], Alfredssonand Olsson [5] recently. The immediate area outsidethe contact zone in the roll undergoes tension, whichmay become large enough for fatigue considerationsin adverse circumstances, such as the presence ofsharp corners at the contact edge or material defects.Salehizadeh and Sakas analysis [6] shows that thematrix material around hard inclusions in the contactzone experiences tensile stresses if the contact load ishigh enough to produce plastic strain in the matrix.The material under investigation can be deformed

plastically under highly concentrated contact loads.The material is found to be much weaker in tensionthan in compression. Therefore, studies on tensilefatigue fracture, as well as compressive fatigue resist-ance under contact load, would be of considerablepractical interest.

The purpose of this paper is to investigate the fatiguebehavior of heat-treated, 5% chrome steel under uniax-ial, torsional and combined axialtorsional loading con-ditions that lead to tensile fatigue fracture. A fatiguemodel will be proposed suitable for the material underthe loading conditions employed. Some uniaxial tests

Corresponding author. Tel.: +82-54-279-2182; fax: +82-54-279-5899.

E-mail address: [email protected] (K.S. Kim).

0142-1123/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijfatigue.2003.11.005


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will also be conducted in the presence of mean stress,and a model will be proposed for the mean stress effect.The results obtained in this work will be useful forstudying the multiaxial fatigue behavior of other similarhard steels such as tool steels and high-speed steels.

2. Material and specimen

The chemical composition of 5% chrome steel underconsideration is given in Table 1. Specimens used inthis study are solid specimens with a round cross-

section. The gage section had a diameter of 6 mm anda length of 20 mm. The specimens were machined fromforged material that has undergone electrical remeltingand spheroidizing. Prior to heat treatment initialmachining was done such that the diameters at thegage section and at the grip area were 0.5 mm largerthan the final dimension. The specimen was then auste-nized at 980

v

C for 20 min and oil quenched at 60v

C.Then, the specimen was tempered for 3 h at 130

v

Cand cooled in air. The gage section of the heat-treatedspecimen was ground at a very slow rate to the finalsize to ensure that heat generated in the grinding pro-cess would not affect hardness. Finally, the gage sectionwas polished with alumina powder. After this step, thespecimen had hardness in the range of Rc 6465. Themicrostructure of the material is primarily temperedmartensite matrix with carbides (Fe,Cr)7C3 [7,8] dis-persed in the matrix and on the prior austenite grainboundary, as shown in Fig. 1. Most of the grains were

observed in the size range of 1015 lm. The averagecarbide diameter was 0.52 lm, with some having dia-meters as large as 2 lm.

The monotonic stressstrain curve of this material isasymmetric in tension and compression. The com-pression test was conducted in a nonstandard wayusing a fatigue specimen, and terminated before failureoccurred for safety reasons. It was found that thismaterial is much stronger in compression than in ten-sion (see Fig. 2). The mechanical properties obtainedfrom these tests are: Youngs modulus 197 GPa; 0.2%tensile yield strength 900 MPa; tensile strength 1400

MPa; elongation 1.3%; 0.2% compressive yield strength2000 MPa; compressive strength >2500 MPa.

3. Experiment

Fatigue tests were carried out with an axialtorsionalservo-hydraulic Instron machine at room temperature.The waveform utilized was triangular, and frequencyvaried from 0.5 to 5 Hz, with higher frequenciesapplied to lower amplitude tests. Failure was defined as

a complete separation of the specimen. All tests were

carried out under load control. It was unnecessary tomeasure strain because the loaddisplacement response

Table 1Chemical composition of 5% chrome steel

Element C Si Mn P S Ni Cr Mo Cu

wt% 0.88 0.33 0.35 0.009 0.001 0.11 4.97 0.41 0.33

Fig. 1. Microstructure of test material. Fig. 2. Monotonic stressstrain curve in tension and compression.

684 K.S. Kim et al. / International Journal of Fatigue 26 (2004) 683689


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was approximately linear for all test conditions. Load-ing conditions for uniaxial tests and torsional tests aregiven in Table 2. The combined axialtorsional testsare summarized in Table 3. All tests in Table 3 arefully reversed tests. Three phase angles between theaxial and shear stresses were investigated under a given

ratio of stress amplitudes. It is noted that the phaseangles were found somewhat shifted from the intendedvalues of 0

v

, 45v

and 90v

(see Table 3), where suffices1, 2, and 3 in the specimen numbers are in the order of

increasing phase angles. The phase angle, nevertheless,stayed steady during each test.

4. Fatigue life prediction

The fatigue parameter to be used in this study isgiven in terms of the maximum normal stress range

and the hydrostatic stress range. This parameter hasbeen constructed based on the fact that fracture of abrittle material is dictated by the maximum tensilestress, and on the fact that the parameter must be ableto describe the relative experimental trends for differentloading conditions. The fatigue criterion is given by:

Pn Drn k1Drh r0f2Nf

b; 1

where Pn is the normal parameter, Drn is the maximumnormal stress range, Drh is the hydrostatic stress range,

Nf is the number of cycles to failure, k1, b and r0f are

material constants to be determined from uniaxial andtorsional fatigue test data.

The plasticity effect has not been included in thisfatigue criterion since the cyclic stressstrain responseof the material was elastic for all test conditions. Thehydrostatic stress term in the parameter was introducedto model the differences in fatigue lives between uniax-ial and torsional loading with identical maximum nor-mal stress ranges. The hydrostatic stress was entered invarious fatigue criteria in different ways. Haigh [9] and

Sines [10] considered the mean hydrostatic stress as ameasure of the mean stress effect in multiaxial fatigue.Fatigue properties were set to vary with hydrostaticstress in the fatigue criteria by Libertiny [11], Davisand Connelly [12], Manson and Halford [13], andKalluri and Bonacuse [14]. Kakuno and Kawada [15]proposed a criterion given in terms of equivalent stressrange, hydrostatic stress range and mean hydrostaticstress. Dang-Van [16] used shear stress and hydrostaticstress ranges in the parameter for high cycle fatiguelife prediction. It does not appear, however, that thehydrostatic stress range has been used with normal

stress criteria for brittle materials.The computation of fatigue life was carried out using

a computer program written for this study. It wasassumed that the crack initiates and propagates on thecritical plane where the maximum normal stress rangeoccurs. The critical plane was determined using anincrement of 1

v

in the angle of orientation of the planethat varied from 0

v

to 180v

from the specimen axis.The fatigue parameter and life were then evaluated onthe critical plane.

It is worth noting that a shear fatigue criterion givenby Ds sDrn s

0f2Nf

b, where Ds is the maximum

Table 2

Uniaxial and torsional fatigue test conditions and observed livesLoadingtype

Stress amplitude(MPa)

Mean stress(MPa)

Life(cycles)

Uniaxial 950 0 290850 0 1658800 0 4516700 0 24,434650 0 102,032600 0 128,175

Uniaxial 600 300 3479500 300 65,657400 300 519,592350 300 2,388,905

Uniaxial 900 100 3422

850 100 2320800 100 112,038750 100 308,211720 100 81,438

Uniaxial 900 300 8486850 300 192,110820 300 45,819800 300 2,615,767

Torsional 1000 0 8595900 0 18,454850 0 13,096800 0 95,313700 0 367,012650 0 1,017,325

Table 3Loading conditions for combined axialtorsional fatigue tests

Specimen no. Axial stress(MPa)

Shear stress(MPa)

Phase angle (v

)

A1 747 432 14A2 748 433 58A3 735 432 94B1 589 598 14B2 589 605 58B3 594 597 101C1 423 747 7C2 434 751 50C3 430 745 101D1 674 390 14D2 690 394 72D3 680 390 108E1 551 548 14E3-1 550 549 101E3-2 549 543 94F3 642 791 79G1 396 499 14

K.S. Kim et al. / International Journal of Fatigue 26 (2004) 683689 685


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shear stress range, Drn the normal stress range on theDs plane, s0f, s, b are fatigue properties, was also inves-tigated for the possibility of shear fracture in the veryearly phase, which is difficult to verify because of theextremely small crack sizes involved. A similar attemptcan also be found in an early study by Sines [10] on

cast iron. For type 304 stainless steels, which show nor-mal fracture under most loading conditions, a shearfracture parameter of this type, but given in strain,provides a reasonable correlation of life data [1719]. Itwas found, however, that this parameter does notprovide the experimental trend for the current materialthat in-phase loading is more damaging than out-of-phase loading. The effort was then abandoned.

5. Results and discussion

The orientation of fracture planes in uniaxial and

torsional tests resembled that of a typical brittlematerial; 90

v

for uniaxial loading and 45v

for torsionalloading as shown in Fig. 3. A low magnification SEM

micrograph of the fracture surface (Fig. 4(a)) was

taken on a specimen subjected to uniaxial loading of

Dr 350 MPa, Rr 0:125. The crack appears to have

initiated in the area marked by A and propagated

approximately 0.4 mm deep in thumbnail shape before

the onset of unstable fracture occurred. SEM micrographsof higher magnification revealed that crack initiation

might have taken place at a cluster of subsurface car-

Fig. 3. Fractured specimens in fatigue tests: (a) uniaxial, (b) tor-sional.

Fig. 4. SEM micrographs of fracture surface: (a) overall view, (b) site A, (c) site B, (d) site C.



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bide particles (Fig. 4(b)). A similar observation canbe found in Mueling et al. [7] for similar steels. Thecrack propagated in a transgranular mode initially(Fig. 4(c)) which was followed by mixed transgra-nular and intergranular fracture at a later phase(Fig. 4(d)). The development of intergranular fracture

is attributable to the carbide particles on the grainboundary, which reduce the grain boundary strength.The stressstrain hysteretic response obtained in all

of the tests in Tables 2 and 3 was essentially elastic,even if the stress amplitude was considerably largerthan the monotonic tensile yield stress. No significantchanges of the hysteresis loop were observed during thetest. An example is given for the axialtorsional test onspecimen A1 in Fig. 5. The linear behavior duringunloading and reloading is expected to span over the

range of tensile yield stress plus compressive yieldstress in view of the Baushinger effect in elasticplasticmaterials. It is expected for this material that this rangewill be extended due to the substantially larger linearresponse on the compression side.

The fatigue parameter versus life curve was determ-ined from the results of uniaxial and torsional fatiguetests shown in Table 2. The fatigue curve is given inFig. 6 (solid symbols), and fatigue properties are foundto be: r0f 4100 MPa, b 0:079, k1 0:77.

The fatigue criterion in the presence of mean stresswas not possible to be described with a single equation.The following two equations are proposed for tensileand compressive mean stress effects, respectively:

Drn k1Drh r0f 1k2

rmn

r0f

2Nf

b for rmn ! 0; 2

Drn k1Drh r0f 1k3

rmn

Drn

2Nf

b for rmn 0; 3

where rmn is the mean normal stress on the plane ofmaximum normal stress range, k2 and k3 are materialconstants.

For tensile mean stresses, the parameter versus liferelation had the same slope as the no mean stress case.It is noted that Eq. (2) is in the same form as Morrowsmean stress model [20] other than the presence of aconstant k2. The compressive mean stress data yieldedchanging slopes in the fatigue curve. Instead of definingthe exponent b as a function of Nf, the fatigue strengthcoefficient was set to be dependent not only on themean stress but also on the normal stress range. This

was deduced from the assumption that the tension-

Fig. 5. Stressstrain hysteresis loops in axialtorsional loading test(A1).

Fig. 6. Fatigue parameter versus life relations with and withoutmean stress.



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undergoing portion in a stress cycle, which can beexpressed in terms of the total stress amplitude andmean stress, is responsible for the major fatigue dam-age. The separation of the carbidematrix interface isconsidered to be the controlling damage mechanism,and it is most likely to occur under tensile interface

stresses. The correlation results are also shown inFig. 6. The proposed model provides the general trendof mean stress effects. The constants k2 and k3 werefound to be 3.49 and 2.49, respectively. It is apparentin Fig. 6 that compressive mean stress is more ben-eficial at high cycles than at low cycles, while tensilemean stress results in the same degree of detrimentaleffects at both low and high cycles. The considerablescatter found in life data would be related to the stat-istical nature of carbide size and distribution. Morescatter is found with compressive mean stress data, forwhich the slope of the fatigue curve is small.

The results of life prediction are summarized inTable 4 along with the experimental lives. It is foundthat the angles of fracture surface, measured from theplane normal to the specimen axis, agree reasonablywell between predictions and measurements. The scat-ter in the data considerably obscures the phase-angledependence of life. However, it seems certain that life isshorter for test conditions closer to in-phase loading(suffix 1) than for tests under more out-of-phase load-ing (suffices 2 and 3). The proposed fatigue parametermodels this trend correctly. Under strain control testson ductile metals, it is usually found in the low cycle

fatigue regime that out-of-phase loading is more dam-aging than in-phase loading. This may be attributed tohigher stress amplitudes due to additional hardeningunder nonproportional loading. The stress control

employed in this study does not differ from strain con-

trol since the material response is linear and there is no

cycle-dependent change. Thus, the life trend between

in-phase and out-of-phase loading is reversed for the

present material from that of ductile materials under

strain control in the low cycle regime.

An interesting comparison of the present results withavailable data can be seen in high-cycle in-phase and

out-of-phase fatigue, where deformation is basically

elastic as in the current study. Such data can be found

in Refs. [21,22]. The determination of whether in-phase

or out-of-phase loading is more damaging at high

cycles is dependent on the material. Nishihara and

Kawamoto [21] reported that mild steel, hard steel and

cast iron exhibited more damage under in-phase load-

ing than out-of-phase loading at 107 cycles under com-

bined bending and torsion. The results of this study are

consistent with their results. However, duralumin tes-ted by the same authors [21] did not show phase-angle

dependency at 107 cycles, and the high strength steel

42CrMo4V tested by Lempp [22] showed that out-

of-phase loading is more damaging at 2 106 cycles in

bending-torsion tests.The predicted lives were compared with experimental

lives in Fig. 7. It is observed that the parameter corre-

lates the data but with some conservatism. The dotted

line represents a band of life factor 3. Most of the data

points fall within or very close to this band. It is also

noted that there is more scatter in life data than usuallyobserved in ductile metals. This is believed to be an

inherent character of materials whose life is controlled

by defects [7,23].

Table 4Summary of test results and predictions

Specimenno.

Life (cycles) Fracture angle (v

)

Experimental Predicted Experimental Predicted

A1 3044 1252 25 24A2 46,794 5709 10 12A3 45,385 9579 172 174

B1 5147 1450 31 32B2 6040 14,276 25 38B3 20,609 45,150 143 140C1 2139 1383 41 37C2 13,727 6281 40 41C3 6890 20,514 135 137D1 12,130 3878 21 24D2 45,731 36,950 10 9D3 13,842 19,832 170 168E1 20,174 3315 39 31E3-1 279,968 89,102 32 39E3-2 110,207 87,984 35 39F3 8889 3069 40 42G1 124,234 53,996 31 34 Fig. 7. Comparison of predicted and experimental fatigue lives

under axialtorsional loading.



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6. Conclusions

A series of axialtorsional fatigue tests were conduc-ted on 5% chrome steel heat-treated for wear resist-ance. This material is widely used for work rolls instrip milling operations. The following conclusions canbe drawn:

1. The test material fails in a brittle manner with insig-nificant plasticity being developed under fatigueloading. Fracture occurs on the maximum tensilestress plane.

2. The crack tends to initiate at a cluster of carbideparticles on or near the surface. The crack propa-gates in a transgranular mode initially followed by amixed transgranularintergranular mode at a laterstage.

3. A multiaxial fatigue parameter has been developedin terms of the maximum normal stress range and

hydrostatic stress range. This parameter correlatesexperimental lives with most data points in a bandof factor 3.

4. Under axialtorsional fatigue loading with a givenratio of stress amplitudes, in-phase loading producesgreater damage than out-of-phase loading for thetest material.

5. Compressive mean stresses are more beneficial athigh cycles than at low cycles, while tensile meanstresses are detrimental to the same extent at lowand high cycles. Separate models have been pro-posed for tensile and compressive mean stresseffects.

Acknowledgements

This study was supported partly by the BrainKorean 21 Project, and partly by Posco Company. Theauthors are grateful for the support. The authors alsothank Y.C. Park of R&D Center, Doosan HeavyIndustries and Construction Company, for his help inpreparing the specimens used in the study.

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