a study of complex defects failing by fatigue, …

International ConferenceNuclear Energy in Central Europe 2001Hoteli Bernardin, Portorož, Slovenia, September 10-13, 2001www: http://www.drustvo-js.si/port2001/ e-mail:[email protected].:+ 386 1 588 5247, + 386 1 588 5311 fax:+ 386 1 561 2335Nuclear Society of Slovenia, PORT2001, Jamova 39, SI-1000 Ljubljana, Slovenia

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A STUDY OF COMPLEX DEFECTS FAILING BYFATIGUE, DUCTILE TEARING AND CLEAVAGE

Bostjan Bezensek, Zoran RenUniversity of Maribor

Faculty of Mechanical EngineeringSmetanova 17, SI-2000 Maribor, Slovenia

[email protected], [email protected]

John W. HancockUniversity of Glasgow

Mechanical Engineering DepartmentGlasgow G12 8QQ, Scotland, UK

[email protected]

ABSTRACT

Defect assessment procedures ensure the structural integrity of plant, which maycontain complex defects. The present work addresses complex defects with re-entrant sectors,which develop from the interaction of two co-planar surface breaking defects in fatigue.Experimental studies show rapid fatigue growth and amplified crack driving forces in there-entrant sector. This leads to the rapid evolution of the complex crack into a bounding semi-elliptical defect.

Experiments involving ductile tearing of cracks with a re-entrant sector show thattearing initiates in the re-entrant sector and that the defect evolves into a bounding semi-elliptical defect. Cleavage failures of defects with re-entrant sectors indicate there-characterisation procedure is only conservative after invoking constraint arguments.

The study confirms the conservatism inherent in the re-characterisation rules ofassessment procedures, such as BS 7910 [1] and ASME Section XI [2] for complex defectsextending by fatigue or ductile tearing. A potentially non-conservative situation exists fordefects with re-entrant sectors failing by cleavage at small fractions of the limit load.

1 INTRODUCTION

Fracture mechanics tests are routinely performed on standard geometries with straightcrack fronts. Parameters such as the critical stress intensity factor characterise the materialresistance to crack propagation. Structural integrity is demonstrated by assessing fracturemechanics parameters around the perimeter of a real or idealised defect in comparison withthe critical value obtained from the standard test geometry. Defect assessment procedures,such as BS 7910 [1] and ASME Section XI [2] give guidelines for assessing individual andmultiple defects. In order to simplify the analysis procedures complex defects are usually

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Proceedings of the International Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001

re-characterised with a simpler, but more detrimental defect. Significant work has beendevoted in refining flaw combination criteria and this has led to revised set ofre-characterisation rules implemented in BS 7910, and discussed by Wiesner [3]. In BS 7910co-planar interacting defects are re-characterised when the adjacent crack tips touch.

The present study considers the conservatism of the re-characterisation procedure asapplied to defects with complex shapes, failing by fatigue, ductile tearing and cleavage.

1.1 Defect re-characterisation

The defect re-characterisation procedure for a co-planar defect is approached in twostages, as shown schematically in Figure 1. First a characterised defect is generated byenclosing the real defect in a box, with dimensions equalling those of the real defect.Secondly, a re-characterised defect is generated by inscribing a semi-elliptical or an ellipticaldefect in a box for surface breaking and subsurface cracks. One axis of the semi-ellipse isparallel to the free surface, while the other axis is in the through-thickness direction. Thesame procedure is applied to multiple adjacent defects. The defects are re-characterised, whenthe flaw combination criteria are met. The criteria specified in codes are derived fromengineering estimations of defect interaction effects. The criteria are usually applied to flawsextending by fatigue, but may be applied to brittle and ductile monotonic failures.

2 GEOMETRY AND TEST PROCEDURE

The work investigated the interaction of two surface breaking cracks, originating fromtwo co-planar notches by fatigue under three point bending. The experimental work wasperformed on a plain C-Mn grade 50D steel (BS 4360). Specimens were manufactured to thegeometry shown in Figure 2. Two co-planar starter notches were cut with a slitting wheel of70 mm in diameter and 0.15 mm thick. The notches had a nominal depth of 2 mm, surfacelength of 25 mm and a part circular cross section. The initial separation of adjacent notch tipswas 25 mm, which is the same as the free surface length of the notch.

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All tests were performed on a servo hydraulic testing machine in three point bending.Fatigue tests were performed at a frequency of 4 Hz and a stress ratio of 0.1. The appliedstress intensity factor was kept within the range of valid LEFM, by shedding the maximumload during the test. The evolving fatigue cracks were monitored with a “beach mark”technique, which produces distinct striations on the surface by altering the load ratios for apredefined blocks of loading cycles. Cleavage and ductile tearing tests were conducted underquasi-static conditions, at a cross-head velocity of 0.5 mm/min. Two cleavage test conditionswere examined: firstly on the lower shelf and then in the ductile-to-brittle transition, toaddress lower shelf operation or low toughness arising from environmental effects. The testtemperature was controlled with liquid nitrogen and was maintained at –196 oC for lowershelf failures, while tests in the ductile-to-brittle transition regime were performed at a testtemperature of –100 oC. Consideration was also given to the upper shelf failure by testingrepresentative configurations at 20 oC, where crack extension occurred by ductile tearing.

3 EXPERIMENTAL RESULTS

3.1 Fatigue

The beach marks on a typical fractograph, such as Figure 3, show that crack growthinitiated from the premachined notch and grew towards formation of a semi-elliptical crack.In all fatigue tests the crack deviated from the initial co-planar plane near the free surface, inaccord with experiments reported by Leek and Howard [4]. Non-coplanar growth affected thecoalescence of adjacent defects and formation of the re-entrant sector. Coalescence was foundto occur near the surface, when the crack deviated to the same side of the plane containing thenotches resulting in a pronounced re-entrant sector. Otherwise coalescence occurred sub-surface and resulted in a modest re-entrant sector. Further details of these features aredescribed by Bezensek [5]. Here it suffices to note that in the majority a sub-surfacecoalescence was observed and resulted in a limited number of configurations withpronounced re-entrant sector, which are of most interest in cleavage failure.

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Figure 3a: Fractograph of evolving cracks in fatigue

Figure 3b: Detail of the re-entrant sector

nal Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300

Loading cycles [x 1000]

Cra

ck d

epth

[mm

]

Defect 1 - B

Defect 2 - B

Re-entrant - A

Figure 4: Crack depth in the re-entrant sector (A)and the deeper segments (B) during coalescence

in fatigue

at

D2 D1

A B Coalescence

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Crack growth in the through-thickness direction, shown in Figure 4, was measured fromthe spacing of consecutive beach marks and combined with a fatigue crack growth law toextract the stress intensity factors, shown in Figure 5 for the re-entrant and deepest position ofre-entrant geometries. As the adjacent crack tips coalesced and formed a re-entrant sector, thefatigue crack growth rate increased dramatically in the re-entrant sector, as shown both by thebeach marks in Figures 3 and 4, and by the amplified values of the stress intensity factor inFigure 5. During this process the remainder of the crack front showed a minor retardation inthe fatigue growth rate. Coalescence was completed within 11 per cent of test life, indicatingthe speed of the coalescence process. Following coalescence, a bounding semi-elliptical crackwas formed, as shown in the fractograph of Figure 3 and by the merger of the stress intensityfactors for positions A and B in Figure 5.

3.2 Cleavage fa

The fatigue studof complex cracks. Tperformed on geombounding semi-elliptiand –196 oC, as descrtested on lower shelfnumerically for the re-entrant sector occuthe lower shelf (-196 difference between thbrittle regime (-100 o

compared to the bouload. Test geometrieconstraint effects werSince these effects ar

nal Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001

ilure

y demonstrated amplified stress intensity factors in the re-entrant sectorhese are particularly relevant to cleavage failures. Cleavage tests wereetries with pronounced re-entrant sectors, shown in Figure 6, andcal geometries, shown in Figure 3a. Tests were performed at –100 oCibed in Section 2 and results are summarised in Table 1. Configurations failed at a small fraction of the global limit load, which was evaluatedspecific geometry and test temperature. Failure of a real defect withrred at an 18 per cent lower load to that of a re-characterised defect onoC). The failure loads show statistical scatter, which may arise from thee profiles of the re-entrant sectors. In contrast failures in the ductile-to-C) show an increased failure resistance of the real complex geometrynding geometry. In this case failure occurred close to the global limits were analysed numerically by Bezensek [6,7] where the in-planee found to elevate the toughness of the pronounced re-entrant sectors.e load dependant, they become significant at failure loads close to the

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

S2 - B

S3 - B

S4 - B

S5 - B

S6 - B

S13 - B

S2 - A

S4 - A

S5 - A

S13 - A

Figure 5: Stress intensity factor in the re-entrant sectorand at the deepest positions from a set of specimens

(denoted S2, S3, S4, S5, S6 and S13) tested by fatigue

Db aKπσ∆

∆

ta

at

D2 D1

A B

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global limit load. At small fractions of the global limit load constraint effects are notsignificant and failure is governed by the applied crack driving force term alone.

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Tof dispFigure7b. Thfatiguedepthsload in

Efollowblack remainof crac

ngs

D

eslac

7ae in stu in ea

xted headerk a

Figure 6: Fractograph of cleavage failure of a defect with pronouncedre-entrant sector

of the International Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001

uctile tearing

ts to examine defect interaction by ductile tearing were performed for large amountsement controlled tearing for a configuration with two separate defects, shown in, followed by a coalesced defect with moderate re-entrant sector, shown in Figuredividual cracks prior to ductile tearing were produced by fatigue, as described in thedy. The test configurations are presented schematically in Table 2, where the crack

the re-entrant sector and at the deepest segments are given with the tearing initiationch stage of the experiment.

ensive plasticity was observed in the re-entrant sector for both test configurations,by a stable ductile tear which was confined to the re-entrant sector, as indicated by at tint mark and a dark grey tear in Figure 7, followed by brittle fracture. The of the crack front underwent crack tip blunting and exhibited only minor amountsdvance.

Table 1: Failure and limit loads for cleaved geometries with re-entrant sector and re-characterised geometries

Lower shelf test DTB test

Failure load Globallimit load Failure load Global

limit loadGeometry[kN] [kN] [kN] [kN]

7585

256251

210 197

90

98

229

22593 108

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Figure 7: Fractographs of ductile torn configurations at room temperaturea) Configuration with separate defects andb) Defect with a moderate re-entrant sector

a)

b)

f the Inte
rnational Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001
Table 2: Ductile tearing of geometries with interacting and coalesced defects. Initiation load in each stage is given together with crack depths in the re-entrant sector and at deepest crack tips at the end of stage.

Stage 1 Stage 2Pinit aA aB Pinit aA aB

[kN] [mm] [mm] [kN] [mm] [mm]

Configuration with separate defects

141 6.4 12.3 224 10.8 13.0

Defect with a moderate re-entrant sector

128 9.0 12.4 191 11.8 12.8

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4 DISCUSSION

In fatigue neighbouring defects develop largely independently of one another until theiradjacent crack tips meet and coalesce. Coalescence is a rapid local process affecting the localregion, where crack tips meet and generate a complex crack with a re-entrant sector. Theapplication of re-characterisation procedures to interacting defects extending by fatigue isconservative, since the crack evolves within a finite number of cycles into the re-characterisedshape. A re-characterisation procedure which neglects interaction effects is conservative, butmay reduce the operational life. Allowing for a limited amount of defect interaction, butprecluding coalescence, as proposed in the revised British Standard document BS 7910,rationalises the assessment of such defects, while maintaining the conservatism of theassessment procedure.

The interaction and development of the re-entrant sectors in ductile tearing is similar tothat observed in fatigue. Tearing is initially confined to the re-entrant sector, which developstowards the bounding shape. Both experimental studies show strong similarity in the initialstages of coalescence of co-planar defects in bending between the two distinctly differentmechanisms, ductile tearing and fatigue. Re-characterising complex defects extending byductile tearing is conservative, since crack again develops from the re-entrant sector towardthe re-characterised shape.

The conservatism of the re-characterisation procedure applied to complex defectsfailing by cleavage relies on constraint effects. For failures at small fractions of the globallimit load, constraint effects are not sufficient to compensate for the amplified crack drivingforces in the re-entrant sector. This is exemplified by the lower shelf failures in the presentwork, where failure originated from the re-entrant sector (Bezensek [6]). In contrast, cleavagefailures close to the global limit load in the ductile-to-brittle transition benefit from theconstraint enhanced toughness, which counterbalance the amplified crack driving forces in there-entrant sector and favour failure of the re-characterised geometry.

5 CONCLUSIONS

The re-characterisation rules of BS 7910 simplify defect assessment while maintainingthe necessary conservatism for defects extending by fatigue and ductile tearing. In the cases ofcleavage failure the conservatism becomes load dependant through constraint effects. Forcleavage failure at a small fraction of limit load the re-characterisation rules are notconservative.

6 ACKNOWLEDGEMENTS

Authors are pleased to acknowledge support of British Energy Generation Limited andhelpful discussion with Dr. R. A. Ainsworth. The support of the Institution of Materials(IoM) and Faculty of Mechanical Engineering, University of Maribor, Slovenia, throughtravel grants is gratefully acknowledged.

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7 REFERENCES

[1] BS 7910, “Guide on methods for assessing the acceptability of flaws in metallicstructures”, British Standard Institution, London, 1999

[2] ASME, 1992, Boiler and pressure vessel design code, Section XI , American Society ofMechanical Engineers, Philadelphia, Pa.

[3] Wiesner, C.S., Maddox, S.J., Webster, G.A., Burdekin, F.M., Andrews, and R.M.,Harrison, J.D., “Engineering critical analyses to BS7910 – the UK guide on methods forassessing the acceptability of flaws in metallic structures”, Int. J. Press. Vess. Pip., 77,2000, pp:883-893

[4] Leek, T.H. and Howard, I.C., “An examination of methods of assessing interactingsurface cracks by comparison with experimental data”, Int. J. Press. Vess. Pip , 68,1996, pp: 181-201

[5] Bezensek, B. and Hancock, J.W., “The non-coplanar coalescence of interacting defectsin fatigue”, Proc. Int. Conf. SAE Brasil Fatigue 2001, Sao Paulo, Br., Dec 12-14, 2001

[6] Bezensek, B. and Hancock, J.W., “Failure of complex defects with re-entrant sectors byfatigue, ductile tearing and cleavage”, To be published, 2001

[7] Bezensek, B. and Hancock, J.W., “Brittle failure from interacting surface breakingdefects”, Proc. Int. Conf. 2001 ASME Pressure Vessels and Piping, Atlanta, Ga, USA,July 22-26, 2001, PVP-Vol. 423, p.25

a study of complex defects failing by fatigue, …

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