CRACK PROPAGATION AND ARREST IN SHIP AND OTHER STEELS

SSC-219CRACK PROPAGATION AND ARREST INSHIP AND OTHERSTEELSThis document has been approvedfor public release and sale; itsdistribution is unlimited.SHIP STRUCTURE COMMITTEE1971

SHIP STRUCTURE COMMITTEEAN INTERAGENCY ADVISORYCOMMITTEE DEDICATED TO IMPROVINGTHE STRUCTURE OF SHIPSMEMBER AGENCIES:UNITED STATES COAST GUARDNAVALSHIP SYSTEMS COMMANDMILITARY SEALIFT COMMANDMARITIME ADMINISTRATIONAMERICAN BUREAU OF SHIPPINGADDRESSCORRESPONDENCE TO:SECRETARYSHIP STRUCTURE COMMITTEEU.S.COAST GUARD HEADQUARTERSWASHINGTON, D.C. 20591SR 1801971The Ship Structure Committee is sponsoring research in theapplication of modern experimental techniques to the brittlefracture of ship plates. This report describes experiments incrack initiation, propagation and arrest. Additional work inthis area is being undertaken. The possible development of acrack arrest criterion is indicated.Comments on this report are solicited.Rear Admiral, U. S. Coast GuardChairman, Ship Structure @remittee

SSC-119Final ReportonProject SR-180, “Fracture-Strain Program”to theShip Structure CommitteeCRACK PROPAGATION AND ARREST INSHIP AND OTHER STEELSbyG. T. Hahn, R. G. Hoagland, P. N. Mincer,A. R. Rosenfield, and M. SarrateBattelle Memorial InstituteunderDepartment of the NavyNaval Ship Engineering CenterContract No. NOO024-68-C-5073U. S. Coast Guard HeadquartersWashin ~7;, D.C.Y

ABSTRACTThis report describes a three–part investigation into the majorstages of fracture––initiation, propagation, and arrest. To study allaspects of the problem, a wedge–loaded double-cantilever–beam design wasused because of its crack arrest capability. Much of the experimentationwas done on Fe–3Si Steel where crack–tip yielding can be revealed by aspecial etching technique. Additionally, a number of experiments weredone on engineering steels, principally to study propagation resistance.The specimen and the plastic zones produced prior to crack initiationare first described and compared with analytical and experimentalresults in the literature, for purposes of calibration. The mechanism ofcleavage crack propagation was then investigated. It was found that thefast moving crack bypasses some of the grains as it grows, leaving behindunbroken ligaments. Rupture of these ligaments consumes a large amountof energy locally and this process can account for crack propagation re–sistance values estimated from these experiments.Upon increasing root radius of the initial notch,the crack mustbe overloaded to propagate, and a wide range of values of the crack drivingforce, G, can be obtained in a single experiment. This p~ovides anew method of measuring crack propagation resistance, R. Etching resultssuggest that R does not vary greatly as the crack grows. An energy balanceshows that R is the average value of G during propagation. By thismeans, Partial confirmation is given to the idea that R is equal to thevalue of GIC measured in an impact test. It is then shown that the rateand temperature dependence of KIC= (EGIC) 1/2 arises from the rate andtemperature dependence of the yield stress in the crack-tip plastic zone.These analyses and experiments provide a framework for develop–ing a practical arrest criterion for ship steels.ii

SHIP STRUCTURE COMMITTEEThe SHIP STRUCTURE COMMITTEE is constituted to prosecute a researchprogram to improve the hull structures of ships by an extension of knowledgepertaining to design, materials and methods of fabrication.RADM W. F, Rea, III, USCG, ChairmanChief, Office of Merchant Marine SafetyU. S, Coast Guard HeadquartersCapt. J. E. RasmussenNaval Ship Engineering CenterPrince Georges’Center BuildingCapt. T. J. Banvard, USNMaintenance and Repair OfficerMilitary Sealift CommandMr. E. S. DillonChiefOffice of Ship ConstructionMaritime AdministrationMr. K. h. Morland, Vice PreSidentAmerican Bureau of ShippingSHIP STRUCTURE SUBCOMMITTEEThe SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committeeon technical matters by providing technical coordination for the determinationof goals and objectives of the program, and by evaluating and interpreting theresults in terms of ship structural design, construction and operation.NAVAL SHIP ENGINEERING CENTERU. S. COAST GUARDMr. P. M. Palermo - Chairman LCDR C. S. Loosmore, USCG, SecretaryMr. J. B. O’Brien - Contract Administrator CDR C. R. Thom~son. USCG - MemberMr. G. Sorkin - MemberCDR J, W. Kime’,USCG - AlternateMr. H. S. Sayre - Alternate CDR.J. L. Coburn - AlternateMr. I. Fioriti - AlternateNATIONAL ACADEMY OF SCIENCESMARITIME ADMINISTRATIONMr. F. Dashnaw - MemberMr. A. Maillar - MemberMr. R. Falls - AlternateMr. Raymond F. Coombs - AlternateAMERICAN BUREAU OF SHIPPINGMr. S. G. Stiansen - MemberMr. F. J. Crum - MemberOFFICE OF NAVAL RESEARCHMr. R, W. Rumke, LiaisonProf. R. A. Yagle, LiaisonSOCIETY OF NAVAL ARCHITECTS & MARINEENGINEERSMr. T. M. Buermann, LiaisonMr. J. M. Crowley - MemberDr. W. G. Rauch - AlternateNAVAL SHIP RESEARCH & DEVELOPMENT CENTERMr. A. B. Stavovy - AlternateMILITARY SEALIFT COMMANDMr. R. R. Askren - MemberLT.JG. E. T. Powers, USNR - tknberBRITISH.NAVY STAFFDr. V. Flint, LiaisonCDR P. H. H. Ablett, RCNC, LiaisonWELDING RESEARCH COUNCILMr. K, H. Koopman, LiaisonMr. C. Larson, Liaisoniv

LIST OF ILLUSTRATIONSaINTRODUCTION1SCHEMATIC REPRESENTATION OF THE ENERGY CHANGES IN AMRGE PLATE UNDER UNIFORM TENSION FOLLOWING THEINITIATIoN OF A CRACK IN A “BAD” REGIoN Km ITS ARRESTBY THE BASE METAL SURROUNDING IT .. ., ., .. ... .2Section 11INFLUENCE OF THE RELATIVE STRESS INTENSITY LEVEL ONTHE PLASTIC ZONE SIZE OF DCB SPECIMENS .. ,. ., ... .52COMPARISON OF PLASTIC ZONES CALCULATED BY WILSON(5)WITH OUTLINE OF ZONE REVEALED BY ETCHING .. .. ... .53DOUBLE-CANTILEVER-BEAM SPECIMEN .. .. .. .. .. ... .645STRESS-STRAIN CHARACTERISTICS OF LOT P Fe-3Si STEELATIOO°C .. .. ,. .. .. .. .. .. ., ,. ..:w::~dbMEASURED COMPLIANCE VALUES WITH KANNINEN.. .. .. .. .,.,. ,.., . ... .. .676PLASTIC ZONE OF SPECIMEN 3P-,16LOADED TO K = 0.6 ~.Uy. .878PLASTIC ZONE OF SPECIMEN 3P-19 LOADED TO ~ = f3.7&,.‘YPLASTIC ZONES OF SPECIMEN 3P-23 .. ., .. .. .,. .. .9109PLASTIC ZONES DISPLAYED BY SERIES A SPECIMENS ON THEPLATE MH)SECTION .. .. .. .. .. .. .. .. ..,.10Section 21STRESS-STRAIN CHARACTERISTICS OF THE Fe-3Si STEEL ATO°CCOMPARED WITH IOOoC .. .. .. .. .. .. ... .172SCHEMATIC DRAWINGS OF THE PLASTIC ZONE PRODUCED BY:(a) Stationary Crack and (b) Growing Crack .. .. ... .173ARRANGEMENT USED IN WEDGE LOADING OF A DOUBLE-CANTI-LEVER-BEAM (DCB) SPECIMEN .. .. .. .. .. .. ... .1745PLASTIC ZONE FOR SPECIMEN 3P-17 FOR SLIT CUT IN UNDERLOAD CORRESPOi?U)INGTO —= K0.6.&i. .. .. .. .. ..ayPLASTIC ZONE OF SPECIMEN 3P-18 FOR SLIT CUT IN UNDER. .206LOAD CORRESPONDING TO K — =0.7G. .. .. .. .. ..UvPLASTIC DEFORMATION Associated WITH CLEAVAGE FRACTUREON THE SURFACE OF Fe-3Si SPECIMEN 3Q-16 .. .. .. ,.. .. .21227PLASTIC DEFORMATION ASSOCIATED WITH CLEAVAGE FRACTUREON THE PLATE MIDSECTION OF Fe-3Si SPECIMEN 3q-16. 150Xv. .23

EE?ESection 312345678910111213141516APPENDIX AA-1A-2TABLESection 112Section 21Section 3123THE DCBLIST OF ILLUSTRATIONS(Cont.)TEST SPECIMEN ““ ‘“ .“ -“ ‘“ ““ .- ‘- -“LOADING ARRANGEMENT:: .. “. .. .. .. .. .. ..A PLOT OF EQUATION (6) ILLUSTRATING THE DEPENDENCE OFK ON CRACK LENGTH FOR FIXED DISPLACEMENT, y .. .. .. ..COMPARISON OF CRACK PROPAGATION BEHAvIOR .. .. .. ..A COMPILATION OF THE TOUGHNESS DATA FOR THE FOUR STEELSSHOWING THE DEPENDENCE OF THE ARREST STRESS INTENSITY,Ka ON THE INITIATION LEVEL, KQ .. .. .. .. . .. ..FRACTURE SURFACE OF PROJECT STEEL E FRACTURED AT -196°C.REGION OF STABLE PROPAGATION .. .. .. .. .. .. ..CLEAVAGE FRACTURE PROFILES IN THE MILD STEEL ,. .. ..CRACK PROFILES IN Fe-3Si SPECIMEN TEsTED AT O“c .. .. ..INTERCONNECTIONS BETWEEN MICROCRACKS REVEALED BY PRO-GRESSIVESECTION .. .. .. .. .. ,. .. .. .. ..FRACTURE SURFACE OF A-517 TESTED AT -196°C .. .. .. ..CRACK PROFILE OF A-517 TESTED AT -196°C .. .. .. .. ..ARRESTED CRACK TIP IN QUENCHED 4340 AFTER UNSTABLEPROPAGATION AT-1960C .. .. .. .. .. .. .. .. ..DEVELOPMENT OF S’URFACEDEFORMATION WITH INCREASINGTEST TEMPERATURE IN Fe-3Si .. .. .. .. .. .. .. ..COMPARISON OF THE DEFORMATION AT THE SURFACE AND MID-THICKNESS OF A SPECIMEN TESTED AT 22°c .. .. .. .. ..REGION OF UNSTABLE CRACK PROPAGATION IN SPECIMEN SHOWNIN FIGURE14 .. .. .. .. .. .. .. .. -. .. ..SCHEMATIC REPRESENTATION OF THE ENERGY CHANGES ACCOMPANY-ING PROPAGATION AND ARREST IN A DCB sPEC1~EN .. .. ..CENTER-CIUiCKED SHEET LOADED BY POINT FORCES DISTRIBUTEDRANDOMLy OVER THE SLIT BOUNDARY .. .. .. .. .. ..THE RESULTS OF THE ANALYSIS FOR THE UNIFORMLY SPACED EQUALFORCE MODEL .. “. ““ .- .- “. .- “. “. .. ..LIST OF TABLESSUMMARY OF RESULTS .. .. .. .. .. .. .. .. ..ONSET OF THE CRACK-TO-BEAM-ZONE T~SITION .. .. .. ..SUMMARY OF RESULTS .. .. .. .. .. .. .. .. ..COMPOSITION AND YIELD STRENGTH PROPERTIES .. .. .. ..SUMMARY OF DCB TEST RESULTS .. .. .. .. .. .. ..TABULATION OF K K=, AND Rd VALUES FOR A-517 AT -196°C ..Q’viw283032353637383839404040424243465355812192834147

INTRODUCTIONWith the trend toward higher strength steels and more highly stressed shiphulls, more precautions must be taken to guard against fracture. Existing methodsalready make it possible to identify safe stress-level/flaw-size combinations, providedthe flaw is imbedded in material of standard quality. However, this LS notthe only source of failure. A more likely source is a crack located in an atypicalregion of low toughness (like the HAZ of a weld). Such a flaw will become unstableand begin to propagate at even lower stress levels. The question then is: will thecrack emerging from the “bad region be arrested when it reaches the “good (standardquality) material that surrounds it? The concept of designing for crack arrest isnot new. Pellini and his coworkers at NRL(l) have for some years advocated a “crackarrest” philosophy. What is needed now is a more precise description of steels’arrest capabilities--something like Pellini’s FAD (Fracture Analysis Diagram), butin terms of the length of running crack that can be arrested at different stresslevels by the base metal and by continuous weld-affected regions.This program was undertaken to explore the possibility of measuring andanalyzing crack propagation and arrest. These processes depend on a number offactors: (1) tliemechanics of the flawed structure (or test specimen), (2) theplastically deformed zone at the crack tip, (3] themetal’s resistance to plastiicflow and its race dependence, and (4) the processes of cleavage and ductile ruptureon the microstructural scale. The work sought numerical descriptions of the individualfactors with the aim of assembling these into a comprehensive, systems-typeanalysis of propagation and arrest.The studies employed the DCB (double-cantilever-beam) test specimen becausethis configuration offers the possibility of initiating, propagating, and arrestinga fast fracture, under controlled conditions, within the confines of a single specimen.Analyses of the stress fields of stationary cracks in DCB specimens are reportedin the literature. A flexible, one-dimensional analysis of a crack propagatingin a DCB specimen has recently been devised by M. F. Kanninen of Battelle-Columbus under separate sponsorship. Section 1 of this report deals with the plasticzones produced by stationary cracks in this type of specimen. This work, whichexploits the l?e-3Si etching technique, was undertaken to establish a base line forcomparisons with zones produced by moving cracks.Section 2 describes experiments which simulate slowly moving cracks.This work revealed that the deformed material, left behind by an advancing crack tiphas relatively little influence on tlm,stress field ahead of the crack, at leastunder plane strain conditions--a result which stiplifies the interpretation of propagatingcracks. The work described in Section 2 also demonstrates the advantagesof the DCB specimen for studies of fast fracture arrest. Under wedge loading, fastfractures travel in essentially a straight line into a continuously decreasingstress field and finally arrest. Metallographic sections of the arrested fracturesreveal that isolated, unbroken ligaments are left behind by the advancing crack front.The etching studies show clearly, for the first time, that the stretching of theseligaments behind the crack front is the main source of energy dissipation by plasticflow during propagation.

-2-With these results in hand, the research described in Section 3 turnedto quantitative studies of ~he relations between the stress intensity (K) levels atinitiation and arrest in a variety of steels. The method of estimating ~d, theaverage ~nergy absorption rate of a propagating fracturep from the stress fntensityvalues at initiation and arrest is discussed. Experiments in which the acuity” ofthe starting notch was varied show that K(arrest) decreases as the K(initiation) isincreased consistent with ~d-value close to the value of GIC. Accordingly, thearrest condition depends on the stress and flaw size at initiation, the geome~ry ofthe specimen, and %d, and is not an invariant. In the present experiments, theratio of K(initiation) to K(arrest) varied from-- 1 to +- 4. ~Detailed metallographicstudies show that the ligament mechanism of crack propagation occurs in all steelsstudied. By sectioning several samples, it was found that the ligaments are oflimited thickness and that they are isolated regions bypasse!lby the crack. Usingthis idea, a model of dynamic crack resistance is proposed,, in which the stressintensity at the crack tip is diminished by the effect of the ligaments which arebelieved to support a stress on the order of the yield stress.In overall terms, the study encourages the view that the crack propagationcharacteristics of steels can be measured, analyzed, and ultimately used to controlfracture arrest. This is illustrated in Figure 1 by an example, the case of a largeplate loaded in tension. The example presupposes that a crack in a “bad” region ofthe plate becomes unstable, propagates a short distance, and then is arrested by basemetal characterized by a relatively large value of the average energy absorption rate,Ed. Stress levels and the size of “bad” regions that can be tolerated can be estimatedin this way. Crack arrest may thus offer a more conservative approach tofracture safety, both from rhe viewpoints of design, inspection, and repair. However,both the experimental and analytical techniques need to be developed more extensively.In addition, the metallurgical factors governing arrest toughness need to be understoodfor the purposes of alloy development.Reference1.v,FractureAnalysisW. S. Pellini and F. P. Puzak,program Procedures for theFracture-Safe Engineering Design of Steel Structures”, NRL Report 5920, March 15,1963.; (basemetal)GA(31C(’bud” regi onR(“bed’’reglonHL /-v’Un$toble propagationCrackLength [o)Fig.1.SCHEMATIC REPRESENTATION OF THEENERGY CHANGES IN A LARGE PLATEUNDER UNIFORM TENSION FOLLOWINGTHE INITIATION OF A CRACK IN A“BAD” REGION AND ITS ARREST BYTHE BASE METAL SURROUNDING IT.HERE U REPRESENTS THE ELASTICSTRAIN ENERGY STORED IN THEPLATE.

-3-SECTION 1I?LASTIC ZONES IN Fe-3SiSTEEL DOUBLE~CANTILEVER-BEAM SPECIMENSbyG. T. Hahn, M.Sarrate, and A, R, RosenfieldABSTRACTPlastic zones generated in double-cantilever–beam specimens of anFe-3Si steel are revealed by etching. Zones ~orresponding to relativestress intensity levels in the range 0.4 =. < — < 0.8 =., beam height‘Yto length ratios # = 0.125 and 0.35, and conditions approaching~,13 (&a::strain are examined. The furthest extent of the zones, p z(Q ‘about. half that previously observed in pl~tes loaded in tension to comparableK-levels. The results are consistent with previous measurements byClark and lend support to Wilson’s calculations. At high stress levels,when the zone size to beam height ratio ~ ~ 0.09, the zone begins to tiltbackwards and undergoes a transition fro% a crack- to a beam-zone. Implicationsof this transition with respect to the minimum beam height require–ment are examined.

-4-PLASTIC ZONES IN l?e-3Si STEEL DOUBLE-CANTILEVER-BEAM SPECIMENS1. INTRODUCTIONIn view of the many applications for the DCB (double-cantilever-beam) testspecimen*, more complete characterizations of this configuration are desirable.(1~2)Such features as size limitations, thickness requirements, and plasticity correctionsare of interest, and these depend on the extent and distribution of the plasticdeformation generated by a crack in the specimen. A limited study of plastic zonesin DCB specimens has been conducted by Clark(s) using the l?e-3Si etching technique.His results are summarized in Figure 1 and indicate that the maximum extent of theDC13 zones is about half of that displayed by zones produced byfield intensity levels in plates under uniform tensile loading. ?~ya{~!~er~~~F~$receivessupport from Wilson(5) who has estimated enclave sizes and shapes from theelastic fields obtained by applying boundary collocation to the Williams stressfunction(6) for a number of specimen configurations. These calculations also showthat the infinite plate-uniaxial tension plastic zone is about twice as large as the DCBzone, at least at one stress level.;’

-5-yla0.15~~0 Present measurementsI ClarkP ❑A(~)’H/w=o.50/’10.06/-{\\WW=O.350.10L ụ5

-6-).370.2060r1.5C13.80—u~o.o Io.—IIIJ_1Fig.3.III I\I0.90 L\4‘Thread 6-40Depth 0.20 in.DOUBLE-CANTILEVER-BEAMSPECIMENo 2 4 6Fig.4. STRESS-STRAIN CHARACTERISTICS OF LOTP Fe-3Si STEEL AT 100°C.probably indistinguishable from those of a sharp crack. The zone size to thickness(7)ratios examined favor a close approach to plane strain conditions and this is discussedmore fully in the next section.The DCB specimens were fabricated from Fe-3Si Steel, annealed, aged, polished,and etched according to procedures described in detail in Reference 9. Series A specimenswere tested at room temperature and displayed a yield stress of 65,000 psi. Series1?specimens were tested at 100”C to facilitate comparisons with crack growth experimentsmade at this temperature to avoid cleavage. Lot P displayed a yield stress of53,500 psi at 100”C and some evidence ofstrain aging, but not enough to significantlyaffect the stress-strain curve (shown in Figure 4) during @e time the specimens wereunder load. The spectmens were stressed.in a horizontal loading device and both theload and the slit opening were monitored (the latter with a displacement gage). Loadswere applied and released relatively slowly, at about 5,000 Ibs. per minute. In onecase, a number of zones were produced in a single specimen by extending the slit aftereach load-unload cycle and then reloading to a different K-1evel. Compliance valuescalculated from the”Kanninen.(~”~ e~uation agree reasonably well with the actualmeasurements as shown in Figure 5. Plastic zones generated at various K-1evels wererevealed on the DCB surface and midsection by etching.

I-7-—1.4 1.6 1.8 2.0 2.2 2.4SlitLength, in.Fig.5.~A3d3,.~k2a2sinhkcCashAcc=~-1.sinAccosAc ~~~x3H3sinllz i.- Sinzkc[ ( )simhzAC+ sin2 AC * ~-i6ha( SiIlh2 Ac. sin2Xc)(Ac. siniccosAcsi!!h2 kc - Sinzkcsinhkc COSII(SeeTable1 torexplamticm ofsymbsls)(See Table 1, PageR, for explanation ofsymbols)COMPARISON OF MEASURED COMPLIANCE VALUES WITH KANNINEN EXPRESSION)1111. RESULTS AND DISCUSSIONExamples of the plastic zones observed on the surface and in the interioron the specimen midsection are presented in Figures 6-9. The general appearance%ofthe zones are in the main, similar tO Chose df.splayedby zones fn tensile loadedplates.(4) Values ofp, the furthest extent of the zone measured normal to the planeof the slit, are about 25% larger in the interior of the DCB specimens (on the platemidsection) than on the surface, a feature also displayed by the tensile loadedplates(41. Table 1 shows thar this is not a question of specimen alignment since agiven zone extends about the same amount on opposite surfaces of the same specimen.Values of /3, the specimen thickness co zone size index:

-8-(a) surface(b) midsection,,Fig.6, PLASTIC ZONE OF SPECIMEN 3P-16 LOADED TO K = 0.6 fir :‘Y(a) Specimen Surface and (b) MidsectionTABLE 1. SUMMARY OF RESULTSTABLE1. SUMMARYOi?~~SULTSlgtLOAD SLITLENGTH K~ ‘JY PLAsTICZONESIZE,p {in.)SPECLNXN (lb,) (in. ) ksi(~n.) (fin.) surface midsection oppositesurfaceA-3 628 3.30 ~,gttf 0.75 - 0.16A-4 535 2.50 33 0.5 0.0423P-16 2300 1.80 31 0.59 0.040 0.0433P-19 2720 1.80 37 0.69 0.058 0.0753P-23 1740 1.50 20 0.38

(a) Surface(b) Midsection(c) MidsectionFig.7.PLASTIC ZONE OF SPECIMEN 3P-19 LOADED TO ~= 0.7 fi.:‘v(a) Specimen Surface, (b) Midsection, and (c) Close-up Midsection

-1o-,, ,,.’,’ ,,,, ”,, ,,>,,,k!’ ,, ““, “’,”.: ,,~= 0.38 %. 0.57 0.70q(b) Midsection, ~= 0.8fi.‘YThe dashed line shows the approximateposition of the slit tip when the specimenwas loaded. The slit was subsequentlyextended from left to right.Fig.8. PLASTIC ZONES OF SPECIMEN 3P-23, A NUMBER OF ZONES WERE PRODUCED BY EXTEND-ING THE SLIT OUT OF RANGE OF THE ZONE BEFORE RELOADING TO A DIFFERENT STRESSINTENSITY LEVEL.(a)(b)[ = 0.5 Fiii. K (apparent) = 0.75 Y%.T Y ‘YFig.9, PLASTIC ZONES DISPLAYED BY SERIES A SPECIMENS ON THE PLATE MIDSECTION. THEDASHED LINE IN (a) SHOWS THE APPROXIMATE POSITION OF THE SLIT TIP WHEN THESPECIMEN WAS LOADED, THE SLIT WAS SUBSEQUENTLY EXTENDED FROM LEFT TO RIGHT.

-11-As shown in Figure 1, the p-values for the DCB specimens are consistentwith Clark’s findings and are about “112 as large at comparable K-levels as thevalues derived from edge and center notched plates loaded in tension. In the range0.4 En.

-12-backward tilt, and are in a comparable, early stage of the transition. The resultsfor these two specimens suggest a correlation between the onset of tilting (andattending deviations from calculated K-values) and ‘thezone size to beam height ratioP _% 0.09:HTABLE 2. ONSET OF THE CRACK-TO-BEAM-ZONE TRANSITIONSpecimen H, in.:$P. P $A-4 0.5 0.5 0.042 0.08531?-23 1.25 0.8 0.108 0.088This ratio can be transla&ed into a minimum specimen beam height requirement by wayof Equa~ion (1), where A = 0.13:(3)It would appear from this and the earlier discussion that the DCB specimen beam heightand thickness requirements for plane strain may be - e similar. This view fS con.sistent with the proportions recommended by Wessel( .f5’~or ~-~ype specimens, i.e.,H = 1.25t. However, it does raise a question about X-type specimens (H = 0.5this case, departures in the plane strain toughness observed with increasing ~ I/” :U,d[)arise from an inadequate beam height before the”limiting thickness is exceeded.y Inaddition, the difference between plastic zone size and shape in double-cantilever-beam— vs straight tension specimens is puzzling since measured Kc values on both specimens areconsistent. This suggests that the extent to which the plasttc zone reaches out may notbe a sensitive indic;~or of events at the crack tip. Th&e is a need to examine thispoint as well as for more expertients involving systematic variations of thickness andbeam height to establish minimum specimen size requirements.Iv.CONCLUSIONS1. At low stress intensity levels , plastic zones in DCB specimens have the same generalappearance as the zones in tensile loaded plates. The furthe~t ex’cen~of the DCBzones on the plate midsection is about half the values reportel for tensile loadedplates about 25% larger than on the surface.2. The DCB zones begin to til~ back and undergo a transition from a crack zone to”thezone of a partially yielded cantilever beam at high stress levels when the zonesize to beam height ratio~> 0.09. This transition probably invalidates calculatedK-values and places a low! ~imit on the specimen beam height which is tentativelyestimated as H> 1.5 Ki!ioq()

-13-V. REFERENCES1.2.3.4.5.6.7.8.9.10.R. G. Hoagland, “On the Use of the Double-Cantilever-Beam Specimen for Determiningthe Plane Strain Fracture Toughness of Metals”, Trans ASME, Vol. 89, p. 525, 1967.E. T. Wessel, “State of the Art of the WOL Specimen for I{IcFracture ToughnessTesting”, Eng. Fracture Mech., Vol. 1, p. 77, 1968.W. G. Clark, Jr., “Visual Observation of the Crack Tip Plastic Zone Developed ina 3 Fer Cent Si-Fe Alloys’f,Westin~house Scientific Paper, 66-1D6-BTLFR-P1,September 27, 1966.G. T. Hahn and A. R. Rosenfield, rrplasticFlow in the Locale on Notches andCracks in Fe-3Si Steel Under Conditions Approaching Plane Strain”, ship Structure,CommiLtee Report-191, Novmber, 1968.W. K. Wilson, ifGemetry and Loading Effects OJJ Elastic Stresses at Crack Tips”~Westin~house Research Report 67-ID7-BTLPV-R1 Proprietary Class 3, July 3, 1967.M. L. Williams, T(onthe stress Distribution at the Base of a Stationary crack~”Trans ASME, Vol. 79, p. 109, 1957.G. T. Hahn, A. R. Rosenfield, and M. Sarrate,rlob$ervations of yielding AccompanyingCrack Growth”, Inelastic Behavior of Solids, McGraw-Hill, New York, p. 673,1970.G. T. Hahn, M. Sarrate, and A. R. Rosenfield,‘rE~peri~entS on the Nature of theFatigue Crack Plastic Zone”, Proc. A.F. Conf. FatiEue and Fracture, Miami,December, 1969; also Al?YLTR-67-143 Part 111, January, 1970.G. T. Hahn, P. N. Mincer, and A. R. Rosenfield, “The Fe.3Si Steel EtchingTechnique For Local Strain Measurement” ~submitced to Experimental Mechanics)M. F. Kanninen, “An Augmented Double Cantilever Beam Model for InvestigatingUnstable Crack Propagation and Arrest” (to be published).

-14-Section 2OBSERVATIONS OF YIELDING ACCOMPANYING CRACK GROWTHbyG. T. Hahn, A.R. Rosenfield, and M. SarrateABSTRACTThis paper deals with direct observations of the effects of stablegrowth and unstable brittle crack propagation on the plastic zone of acrack. The experiments involved Mode I and plane strain conditions andutilized l?e-3Si Steel as the model material. Stable growth was simulatedby spark cutting s~its under load. Cleavage crack propagation and arrestwere obtained at O C by wedge–loading the specimen. Plastic zones on thesurface and in the interior were revealed by etching. The experiments showno striking differences between the monotonic and stable growth zones. Unlikeslow growth, the propagating cleavage crack generates virtually no deformationat its tip. Instead, the deformation is associated almost ex–elusively with unbroken sections or ligaments left behind by the main crackfront.

-15-OBSERVATIONS OF YIELDING ACCOMPANYING CRACK GROWTH1, INTRODUCTIONA quantitative description of the plastic zones at the tiis essential for under~tanding fracture. Progress ~s be~ng madet~- j, but a completeanalysis of the zone of the “classical” crack (stationary, vi!~~~ and crack monotonicallyloaded) is still not in hand, In the meantime, approximate solutionshave been derived from simplified models, such as those of McClintockt5J, Dugdale(b)and Bilby and coworkerscT~8). These are frequently inspired by experimental observationsand have proven extremely useful. Real fractures tend to have more complicatedhistories ~han the “classical” crack. They can involve stable growth duringloading, cyclic loads and fatigue growth, or uns~able propagation accompanied byextraordinary strain rates and dynamic effects. These problems are even more likelyto benefit from analytical shortcuts based on experiments.With this in mind, we have made direct observations of the zones attendingcracks in steel foil (plane stress) . It was found that the zones produced by astationary and slowly growin crack under monotonic loading are similar(9), but differfrom the cyclic growth zone (Ye) and the zone attending anuns’cable shear crack.(g,~l)The effect of crack growth was also studied in Fe-3Si Steel, where zones were revealedbyetchirig(12). There, crack growth was simulated in a controlled way by sparkcuttingslits in~o specimens under load (at constant stress intensity) , Under conditionsapproaching plane stress, the zone was wider than the zone produced by conventionalloading and unloading without crack :rowth. Experiments were not ruccessfu~under plane strain because cleavage cracks were initiated at room temperature duringthe spark-cutting operation.Accordingly, the i?e-3Si experiments have now been successfully repeatedat a slightly elevated temperature (1OO”C) which avoids cleavage. The work was alsoextended to cyclic loading, and to unstable cleavage crack propagation and arrestat O“C. This paper presents direct observations of the plastic zones attending thevarious kinds of crack growth, both on the surface and in the interior of the metaland compares the results with the stationary, monotonic zones reported in Section 1.11. EXPERIMENTAL PROCEDURESPlastic zones were observed on the surfaces and on the midsections ofl/2-in.-thick l?e-3Si9

-16-of cleavage initiation, unstable propagation and arrest. Tensile properties of thesteel at these two temperatures are shown in Figure 1. Since the l/2-in. thicknessof the DCB specimens exceeded the plastic zone size (the dimension P in Figure 2 bymore than a factor of six, the tests approximate plane strain conditions.The following procedures were devised LO simulate different types ofcracks under conditions that are comparable. The DCB specimens were mounted in asmall, horizontal testing machine, immersed in kerosene and positioned directly belowthe cutting head of a standard spark-machining unit. The spark unit was set upto cut slits* into the test specimens with 0.005 in.-dia. copper wire at the ratez 0.004 in. per minute. This arrangement permitted slits to be cut-in with thespecimen under load Ln kerosene+

80I-17-,; 60 –ao~:. 40–.G5 EGz 20–(a)0 0 2 4 6Elongation,percentFig.1. STRESS-STRAINCHARACTERISTICS OF THEFe-3Si STEEL AT O°CCOMPARED WITH 1000C(b)Fig,2. SCHEMATIC DRAWINGS OF THE PLASTICZONE PRODUCED BY: (a) STATIONARYCRACK AND (b) GROWING CRACK,——Fig.3. ARRANGEMENT USED IN WEDGELOADING OF A DOUBLE-CANTILEVER-BEAM (DCB)SPECIMEN

-18-111. RESULTSPlastic zones produced by the monotonic loading procedure* were shown inFigures 6 and 7 of Section 1. These are to be compared with the zones produced bycutting-in under load, the procedure simulating stable crack growth as shown inFigures 4 and 5. Here the etched sections reveal both the deformation left behindby the growing slit and the new deformation generated at the tip (as shown schematicallyin Figure 2) . Comparisons with the zones in Section 1, Figures 6 and 7, whichinvolve the same peak stress intensity levels, do not reveal any significant differencesbetween the monotonic and the stable growth zone: both the sizes of the zones(see Table 1) and the near tip strain distribution (c~pare Figure 5C with Section 1,Figure 7c) are virtually the same. The correspondence of both zone size and strafndistribution is in accord with simplified elastic-plastic analyses which predict adirect relation between zone size and the COD which, in turn, is closely relatedto the strain distribution.>’

TABLE 1.SUMMARY OF F,ESULTS.——.V&iLOAD SLIT LENGTH~t rPLASTIC ZONE SIZE, D (tn~SPECIMEN (lbs) (in) (Ksifi) (&) surface midsectionSimulation of Monotonic Loading (slit at 100°C~3P-16 23001.80 32 0,60.0400.0433P-19 27201.80 38 0.70.0580.075Simulation of Stable Growth(sli~ at 100*C)3P-17 2300-2220 1.80-1.90 32.2 0,6 0,035 0.0483P-18 2720-2640 1.80-1.88 38.0 0.7 0.055 0.074Cleavage Initiation, Propagation and Arres~ at O°C3Q-16~ ~(a)-2+5(b) ~o(a)-ll (b]. 0.73(a)-0.25(b) 0.080(a)/0.008(E)1/2 a- sli~ length (a) Corresponding with~K=P [ 3(a + a.)z + hz a_ - (0.6h) = 0.75 in cleavage initiationu13b(l ~h“- (height of arm) = 1.25 in (b) Corresponding with- V2) Ib- (Ehickness) = 0.5 incleavage arrestt$ UY(lOO c, Series P) = 54 Ksi v- (Poissons ratio) = 1/3P- (load)uy(OO C, Series Q = 68 KsiI- (moment of inertia) = bh3T

(b) midsectionFig.4. PLASTIC ZONE FOR SPECIMEN 3P-17 FOR SLIT CUT IN UNDER LOADCORRESPONDING To: — K = 0.6 ~.: (a) specimen surfaCe and(b) Midsection.‘Y

IIQuSurface(b) Midsection(c) Midsection, Close-Up of Slit TipFig.5. PLASTIC ZONE OF SPECIMEN 3P-18 FOR SLIT CUT IN UNDER LOAD CORRESPONDING TO ~= 0.7 m.

-22-Fig.6.(a)(b)(c)PLASTIC DEFORMATION ASSOCIATED WITHCLEAVAGE FRACTURE ON THE SURFACE OFFe-3Si SPECIMEN 3Q-16. The photographsof the specimen surface showportions of a cleavage crack that wasproduced by wedge-loading the specimenat OoC:near the slit tip where the crackinitiated:propagation region ~ 1.1 in. from slit:point of arrest w 1.5 in. from slit(a) initiation(b) propagation(c) arrest

_23-“.“.*a.,i, ,’,,”,’. ,,..,, ,,‘‘,B...“’,,< ’”!*.Fig.7.O*,,’ ,.c’” “%.,. ‘$.’ ‘,’.,“r,,. . *!,d *ffi:,!, ,’,- ‘_, , ,,. ... ... . . .PLASTIC DEFORMATION ASSOCIATED WITH CLEAVAGE FRACTURE ONTHE PLATE MIDSECTION OF Fe-3Sj SpECIMEIj3Q.IGm 150x‘v,.of fatigue cracks are larger than expected(lO~ , possibly because thd yield stress islower after a stress reversal (Bauschinger effect). With a reduced yield stress,more plastic deformation is produced during unloading and this may make it difficultto see the differences that existed before the load was removed. The ‘problemcouldbe overcome by aging the test specimens under load and cooling prior to unloading,a procedure that makes the unloading deformation transparent to the etchant.The present results are in accord with observations of steel foil underload(g-ll~, showing that crack growth proceeds with no major changes in the plasticzone, provided the crack speed is reasonably slow. However, Che zone size and pre.sumably the crack-tip displacement do depend on the fracture mechanism, the moststriking example being the marked difference between the zone artending cleavagecracking and those attending other fracture modes.These results are in conflict with a proposal of McClintock (14,15) thatthe plastic zone in front of a slowly growing crack differs noticeably from that infront of a static crack. McClintock’s proposal was offered as an explanation forstable crack growth and without this !Vhistoryeffectrfanother explanation is necessary.Previous experimen’cs in this laboratory have shown that stable crack growth insheets (--0.1in. thick) generally consists of crack advance at the midsection(tunneling) accompanied by plastic flow transverse to the sheet surface. In othersuch as hot-worked aluminum alloys, delamination occur parallel to the~u~~~~~~~~~ offering another possible mechanism. In either case, stable crack growthcan often be explained by the release of triaxial stresses and can be thought of asa transition from plane strain fracture towards plane stress fracture.

-24-The extremely limited amounts of plasticity left behind by the rapidlymoving cleavage crack arise from a number of sources none of which are operative inthe other specimens. In the first place the nature of the cleavage process plays arole . As suggested most recently by Dvorak, the progress of the crack trontwill be highly irregular; it will extend readily through grains favorably orientedfor cleavage leaving behind unbroken grains which are less favorably oriented.These unbroken grains will serve as links or Iigamenrs, tending to hold the metaltogether, until they eventually fail by tearing apart. This observation is reminiscentof a model suggested by Krafft.(lg) Ligament mechanism can be idealizedwith a modified Dugdale model consisting of a crack under load which is restrainedat its tip by a discrete array of evenly spaced pinching forces. We find that theligaments can account approximately for a factor of two reduction in the stressintensity factor, K. Another factor of two reduction in K can arise from the natureof the DCB specimen, since the stress intensity falls as the crack extends underwedge loading conditions. There is also a decrease due to dynamic effects. Measuredcrack speeds in steel ylates(20-2 2)are on the order of 1/3 C (C = sonic veloci~y).Broberg’s calculation 3, suggests that cracks moving at this speed are accompaniedby a stress intensity diminution which is again on the order of 1/2.Taken together, these three effects decrease the stress intensfty factorof a rapidly moving cleavage crack in a DCB specimen by almost an order of magnitude,compared to a stationary crack. Since the plastic zone size depends on (K/Y)2, itcould be thus reduced by a factor of 50-100. In fact, close examination at highmagnification away from the links of Figures 6 and 7 show that the zone extent isless than 1/200 of the static value. The remaining zone shrinkage can easily beaccounted for by the high strain rates at the crack tip, and the corresponding yieldstress elevation. Eftis and Krafft(24) estimate a crack tip strain ra~e of 107sec-1Unfortunately, reliable yield stress data exist only UP to 105se~1, for which strainrate the yield ‘stress of silicon iron is about 2-1/2 times its static value. (9) lnany event, yield stress elevation can contribute at least as much to zone shrinkage asany of the effects which decrease K. Furthermore, it is quite likely that thestress at the tip of a running cleavage crack is on the order of the theoreticalstrength of the lattice.Cleavage fracture also appears to be unique in that the zone associatedwith crack initiation is much larger than the zone associated with crack propagation.The reasons for this may arise from effects discussed by Griffiths and Oates .(25)They have suggested that the large energy ?or crack initiation represents the difficul~yin raising local values of the stress and strain to sufficient levels toinitiate cleavage in individual ferrite grains (these $deas are discussed further fnSection 4) . Based on this reasoning, one would conclude that crack extension bycleavage is a relatively inefficient process and that considerable amounts of energyare wasted in initiating cracking on the microscopic scale. Once microcrackingbegins, however, the energy requirements are substantially reduced and this makesit difficult to arrest a cleavage fracture.v* REFERENCES1. J. L. Swedlow, Inc. J. Fracture Mech., Vol. 5, p. 25, 1969.2. J. W. Hutchinson, J. Mech. Phys. Solids, Vol. 16, p. 13, 1968.3. J. R. Rice and G. F. Rosengren, J. Mech. Phys. Solids, Vol. 16, p. 1, 1968.4. J. R. Rice and M. A. Johnson, Inelastic Eehavior of Solids, M. F. Kanninen,et al, McGraw-Hill, New York, p. 641, 1970.

-25-5. J.A.H. I-Ioltand F. A. ‘McClintock, IX Int. Congress Appl. Mech. , Vol. 8, p. 51,1.956.6. D. S. Dugdale, J. Mcch. Fhys. Solids, Vol. 8, p. 100, 1960.7, E. A. Bil.by,A. H. Cottrell, and K. H. Swinden, Proc. Roy. Sot., Vol. A272, p.304, 1963.8. B. A. 13ilbyand K. H. Swinden, Proc. Roy. Sot., Vol. A285, p. 22, 1965.*9. G. T. Hahn, M, F. Kanninen, and.A. R. Rosenfield, Fracture 1969, P. L. Pratt,et al, cd., Chapman and Hall, London, p. 53, 1969.10. G. T. klahn,A. R. Rosenfielcl, and M. Sarrate, Technical Report AFML-TR-67-143,Wright-Patterson Air Force Base, Ohio, September 30, 1969.11. M. F. Kanninen, A. K. Mukherjee, A. R. Rosenfield, and G. T. Hahn, MechanicalBehavior of Materials under Dynamic Loads, U. S. Lindholm, cd., Springer-Verlag,New York, p. 96, 1968.12. G. T. Hahn and A. R. Rosenfield, Int. J. Fracture ‘Mech., Vol. 4, p. 79, 1968,13. G. T. Hahn and A. R. Rosenfield, Report SSC-I.91,Ship Structure Committee,Washin~ton. D. C.. 1968.Iz;* F. A. McClintock, J. Appl. MechO, Vol. 25, p. 581, 1958.15. l?.A. McClintock, Proc. Roy. Sot., Vol. A 285, p. 58, 1965.16. G. T. Hahn, A. K. Mukherjee, and ~. R. Rosenfield, Eng, Fracture Mech., inpress .17. R.E. Zinkham, Trans AIPIE,Vol. 245, p. 1919, 1969.18. J.P.Dvorak, Fracture 1969, P. L. Pratt, et al, eds., Chapman and Hall, London,3383 1969.19. J.20. A.21. H.22. J.23. K.24. J.M. Krafft, APP1. MatIs. Res., Vol. 3, p. 88, 1964.A. Wells and D. Post, Proc. Sot. Exptl. Stress Anal., VOI. 16, p. 69, 1958.C. van Elst, Trans AIME, Vol. 230, p. 460, 1964.M. cragil~, J. Mech. EnE. Sci., Vol. 5, p. 28, 1963.E. Broberg, Arkiv for Fysik, Vol. 18, p. 159, 1960.Eftis and J. M. Krafft, J. Basic En&., VO1. 87, p. 257, 1965.25. J. R. Griffiths and G. Oates, Fracture 1969, F’.L. PratL, et al, eds., Chapmanand Hallj London, p. 229, 1969.

-26-Section 3MECHANISMS OF FAST FRACTURE AND ARREST IN STEELSbyR. G. Hoagland, A. R. Rosenfield, and G. T. HahnABS!ITMCTThe initiation and arrest of cracks in four steels having widelydifferent yield strengths was studied as a means of characterizing the energyabsorption rate during rapid propagation. The fracture tests wereconducted on DCB specimens which were loaded by wedging, an arrangementwhich proved useful because of its inherent stiffness and because sidegrooves were unnecessary. Stable crack propagation in which the initia -tion stress intensity, K , and the arrest stress intensity, Ka, were near–ly equal, was observed t$ occur in each steel.was systematicallyvaried by changing the root radius of the starter ‘Q s OL. Generally smallincreases in K above the stable propagation level were found to producerelatively abrE/pt decreases in K to K /KQ ~0.4. This behavior could beexplained by appealing to a simp?e ene?gy balance which provided a rela–tion between K and K in terms of R , a velocity insensitivesorption rate.a An a8equate fit to *he I)CB test results for ‘;;;’Y f%steels could be obtained on the basis that R = 2/3 G Detailed meLallographicand fractographic examinations w~re made w %: ~ch establishedthat, at least during cleavage, the crack advances in a nonplanar fashiongenerating grain size unbroken regions or ligaments which remain unbrokenfor relatively large distances behind the crack front. From observationof deformation attending propagation in Fe–3Si, it was found that theseligaments deform and rupture during propagation, a process which canaccount for the overall energy of propagation. Deformation associatedwith the crack-tip during propagation could not be resolved. These resultstogether with an analytic model of a crack subject to tractions,suggest that the formation of unbroken regions is the principal source ofcrack propagation resistance in steel.

-27-MECHANISMS OF FAST FRACTURE AND ARREST IN STEULS1, INTRODUCTIONCrack propagation and arrest assume importance when a s~ructure containsisolated regions of low toughness. While such regions are likely sources of uns~ablecracks, they need not pose a threat to the structure. An unstable crackemerging from a “bad” region can still be arrested in the surroundin~ “good” (standardquality) material provided the “good” material has a sufficiently large resistance topropagation for the stress applied. The Charpy and drop weight impact tests offer ameasure of crack propagation resistance. Their usefulness as inputs to design arederived from intercomparison of test results or comparison against an empirically derivedscale. The Robertson~lj, ESSO{2J, and double tension test described by Yoshiki,et al(3j provides a combined measure of applied stress, crack length,.and Temperaturefor which arres~ is possible. From this data, the stress intensity at arrest can becalculated and Yoshiki, et al show that for equivalent specimen geometries, good agreementin conditions for arrest is obtained between propagation into a temperaturegradient and propagation through a uniform temperature distribution. The latter testis a “go or no-go” measurement as the tes’cdetermines whether or not propagation ispossible for a given set of stress and temperature conditions. A review of thesetechniques and che influence of the energy absorption rate of a running crack on theconditions for propagation and arrest has been written by Eluhm~4j .In several instances, crack propaga~ion test results have been interpretedto show that the energy absorption rate> R, for a rapidly running crack is less thanGIC , the crack resistance at the onset of propagation. For example, Itagaki, et al(5)obtained qualitative agreement between the ESSO and double tension test results and aprediction of energy absorption rates based on a dislocation model. For constants~ress and temperature, their model predicts that plastic work expended at the cracktip decreases with increasing crack speed. This result was also inferred by Hoagland(6~based on a comparison of initiation and arrest toughness values obtained for severalsteels and also for an aluminum and zirconium alloy. In these tests, a doublecantilever-beamspecimen was used in which initiation and arrest of crack propagationcould be accomplished several times in the same specimen. The stress intensity atarrest in these materials was always lower than the initiation value and in the caseof steels, arrest occurred as low as one-half the initiation level.Confusion concerning even the qualitative aspects of crack propagationresistance still exists as opposing interpretations have been proposed for similarsteels. One of the first direct measurements of the energy expended during rapidcrack propagation was made by Wells(7) in which he recorded the heat input to thecrack plane. His results indicate that R for a crack which is moving rapidly isgreater than at the onset of propagation, although there is some uncertainty in theGc data because of widespread yielding of his notched specimens prior to fracture.Using ver$ thin specimens and applying the same basic technique as Wells, Weichert andSchonert( ) found the opposite behavior for steel. It is possible, however, that thedifferences between these two sets of results could be attributed, in part, to differencesin thickness of the test specimens. Decreasing thickness will favor a transitionin fracture mode from flat fracture to through.the.thfckness shear and the dynamic Rfor these two fracture modes may respond differently to crack velocity.

-2$–TABLE 1. COMPOSITION AND YIELD STRENGTH PROPERTIESTABLF1. COMPOSITION ANDYIELDSTRENGTHPROPERTIESYieldTemperature StrengthMa~erial c M P s Si Ni Cr Mo (Oc) (ksi)4340 0.40 0.70 0.040. OLF 0.27 0.95 0.20 i22 240-196 310A-517 0.15 0.80 0.008 0.013 0.26 0.86 0.48 0.42 22 109-135 160-196 178NoFe-3Si 0,018 0.001 65 pm 3.5 100 552206265-75-19695130MildSteel 0.22 0.36 0,016 0.031 22 40-112 50-196 95—H+-@“’e... ../’-+Pin holes 0.531’’ dia.1-).32”tLI1—Sparkslit.machinedLength-HApproxknate Specimen DimensionsMaterial I L ] H I B 14340 I 8.5 11.501.5001A-517 q-~5 1.50 .37512’Specimenthickness❑aFig.1. THE DCB TEST SPECIMEN. THE SPARK MACHINED SLIT FACILITATES STARTINGTHE CRACK, THE SLIT WIDTH IS A VARIABLE IN THE STUDY, IN THECASE OF THE A-517 TWO SPECIMEN LENGTHS WERE EMPLOYED.

In a series of fracture toughness measurements of a mild steel in which bothtemperature anclloading rate were var

-30-Fig.2. LOADING ARRANGEMENT. The wedgeis forced between the hardenedsteel pins extending throughthe pin holes. The clip gagemounted on the specimen betweenthe two legs of the wedge monitorsdisplacement of the pinsa degree of uncertainty as to Lhe effect of side grooves on the propagation betlav~or.To circumvent the need for side grooves in this study, the specimens were tested byforcing a wedge between the loading pins. This loading arrangement is shown in Figure2* The force applied to the wedge by the tes’cingmachine produces a compressive stressin the specimen which reduces the tensile bending stress. As long as this longitudinalcompressive stress produced by the applied force acts parallel to the crack plan , itdoes not affect the crack-tip singularity and therefore does not affect the appliedstress intensity. For a given crack opening displacement, the stress intensity isindependent of applied load. If P is the opening force on the specimen, then the loadapplied to the wedge, Fa, isFa = 2P COSQ (~ cosO + sinO) (1)where 2~ is the wedge angle and # is the coefficient of friction between the pins andthe wedge. Suppression of the bending stress is controlled primarily by varying thewedge angle. Initially, an 11 degree wedge angle was used. For the approximate specimendimension given in Figure 1, this wedge angle was adequate for maintairiing straightforwardpropagation of cracks less than about 2 to 3 inches in length al~!nough longercracks turned to the side of the specimen. A 30 degree wedge angle was used later inthis study and was found to maintain the desired crack plane for cracks longer than 5to 6 inches. It should be pointed out that even though ~his loading method may encouragestraightforward advance of the crack at the initiation stage, several theoreticalinvestigations have shown that the crack-tip stress field undergoes reorientationwith increasing velocity to the extent that branching or at least curvature of thecrack path is favored. This effect can also be suppressed by increasing the wedgeangle but tht required wed.qe angle would depend on the maximum crack speed.

-31-lln important Eacet of this study involves the determination of the variationin the stress intens-ityat crack arrest with the stress intensity at ini~iation. In order to increase the initiation stress intensity above the minimumsharp crack value, l~lc, the specimans were provided with spark rnacl~inedslots ofVariOLISroot diameters, These starter slots were cut to depths of not less than H,the beam height.If the coefficient of frictfon is precfsely known, P can be cleterminsdfrom Fa via Equation (1). The applied stress intensity is given by Gross andSrawley(13) as(2)In practice, very little confidence can be given to a measurement of ~ since it islikely that ~ varies from test to !cestand also with applied load (clueto a slightpeenin~ of the ~wedgc at the point of contact with the pins). Alternatively, K maybe calculated from the pin displacement, y, and che crack length. If @ is the specimen

-32-0,40.3:\H= 1.5 inchesig.3. A PLOT OF EQUATION (6) ILLUS-TRATING THE DEPENDENCE OF K ONCRACK LENGTH FOR FIXED DISPLACE-MENT, yo I I I I I I I I0.8 I,2 1.6 z .0 2,4 2.8 3.2 3.6 4.0a/H4 plot of Equation (6) is shown in Figure 3. Clearly, for a constant pindisplacement, y, the applied K decreases rapidly with increasing crack length, acondition which favors crack arrest. However, truly fixed pin displacement as thecrack extends could be achieved only for an Infinitely stiff testing system. Relaxationof the loading system as the crack grows will produce an additional increasein y. lf we let b represent the total displacement of the system required to producea pin displacement of y then for de/da < 0, the specimen-load train system is inherentlyunstable since the stress intensity increases as the crack extends. In adetailed analysis of crack sta”biliry in varfous fracture mechanics specimens,Clausin~(18) includes the effect of the compliance of the loadfng system on the conditionfor crack instability. From Equations (18) and (19) in Reference 18, it canbe deduced that for a DCB specimen db]da must be positive for@L 1 on the basis of Equation (7). The UIOS’tmechanically compliantmember of the load train is the load cell, the wedge contributing only 8% to therotal compliance. The inherent stiffness of the wedge-loading technique is an ad-\ vantage since increased stiffness decreases the interaction between the testingmachine and the test specimen during rapid crack propagation.

-33-Room kcmperature ‘testswere conducted with the specimc;-,loaded verticallyas shown in Fi&ure 2 while the pin displacement was rEcorded continuously by memlsof the Lli]3~age. The gage used is similar to that described by Brown and Srawley, L19)Ilowcver, the sage is attached to the specimen by conical-pivot seats mounted on bothsides of the slot on the end-face of the specimen. This seaEing arrangement enableda positive ccjntactbetw~en the ~age and the gage blocks thereby mi.ntii.zingthe effectof the shock associatcilwith a rapiclpropagation evcnc. OEher arrangements provedunsatisfactory a.s Lhe ~a~c position relative to the speci~en chang’ed,or che ga~ewas completely clislo~edduring propagation. The gage calibration was repeatable toi 0.0002 in. and was checked at frequent intervals during this study. While the loadwas not used to determine K, the load-displacement record provided a convenient meansfor rioting the initiation and arrest conditions since a drop in the applied loadsignifies a propagation event. At test temperatures other than room temperature, thespecimen-displacement gage ass

-34-TABLE 2. SUMMARY OF DCB TEST RESULTS-—..... ... ~ . . ...K ksid%.TestETemperature slot RootMaterial (~c) Diameter (in.) Initiation Arrest (KQIY2)4340 22 sharp(a)AS quenched 0.0060.026-196 sharp0.006A-517 -135 sharp-196 sharp0.0070.0090.O250.061353382558132424369>11723.726.0< % 0.915.7< 29 7.45.931 11.918 6.912 6.316 2.5< 0.9Shoemaker andRolfe notchbend(z~) -196 sharp 35(static)Fe-3Si 100 sharp0.0266563- 63-600.40.422 sharpsharp0.0070.0422834(C)287526-827< 252.51.62.50.40 0.010 50 12 0.9-75 sharp0.017344033223.52.5ProjectSteel E -112 sharp 22 18 2.7-196 sharp 25 25 7’.20.007 19 23 13.10,O46 41 < 10 2.6‘a) Arrested crack tip.(b) Arrest values Iabelled with “4’ are computed assuming the crack arrested atthe limits of applicability of Equation (6). The crack turned tO the sideor ran to the end of the specimen and, therefore, the actual K at arrest isless than this.(c) An anomalously high initiation toughness believed to be caused by unbrokenregions atthe crack tip.

F’ig.4. COMPARISON OF CRACK PROPAGATION BEHAVIOR: (a) A-517 steelin which crack extension was stable, (b) mild steel specimenin which the crack propagated in an unstable fashionfrom the slot tip to the end of the specimen, and (c) unstablecrack in quenched 4340 which propagated from theslot tip to the side of the specimenIn the series of experiments on A-517, KQ was progressively increased byincreasing the slot width. For initiation from a sharp arrested crack, the propagationwas essentially stable and the KQ(KIC) and Ka are very nearly equal. Forhigher initiation thresholds, Ka decreases to approximately 1/2 the s~able propagationvalue. For comparative purpose, static and dynamic (fallinS weight) toughnessdata for identical material obtained by Shoemaker and Rolfe(20~ are included. Herethe increased loading rate results in a 20% decrease fn roughness.In the Fe-3Si and mild steel, slot widths great~r than 0.007 in. wererequired to elevate the initiation toughness and produce unstable propagation. However,even for a sharp crack, an anomalous increase in KQ as, for example, occurredin Fe-3Si at 22°C results in unstable propagation and a low arrest toughness. In thisparticular example, the increase in the toughness from 28 ksifi. to 34 ksi ~. isthe result of extensfve divisfon of the arrested crack tip as described in the followingsection. It is also interesting to note that sharp elevation of F@ by increasingthe temperature from 22°C to 100°C did not promote unstable propagation but resultedin very slow crack extension.

I.0-36-\ Legend0,8 -\4340 :A-517 FFe-3Si ❑-\Mild st~el~0.6 +\ERd ‘KIC——ERd ‘~K;C—-—-’\J\D-,5‘“4 -\\\‘-lp

-37-(a)(c)(d)Fig.6. FRACTURE SURFACE OFSTABLE PROPAGATION.(d) is the enlargedPROJECT STEEL E FRACTURED AT -196°C. REGION OF(b) is the enlarged center portion of (a).center portion of (c)

,.”m.. .‘m.:,,,!’.,’ ‘., ,...%.!.,,... *~.w 0.1 in. from final arrestfinal arrest.,, .,, ,,,,”,,,,: ’,, “, ,,, 6,” ,,,,!, ,’ .,.,1:‘v,..,,1’,~’,.”;Fig.7. CLEAVAGE FRACTURE PROFILES IN THE MILD STEEL. PHOTOGRAPHS OF THE MID-THICKNESS POSITION OF A SPECIMEN TESTED AT -196°C. CRACK EXTENSIONOCCURRED BY VERY SMALL JUMPSt?-,,,, “~. .(a) 0.5 in. from tip~~’ti~??

-39-.,..-’,,0.0012b“, “-. ,.“ *>..0.0026,,,,.,’.. .,.,P.,, ,REGION A OF FIG.8.0.0072.,. .ti~y-+,,!.’” .).,“,. ,“~J’0.0!“ $, “‘---.: .., * ,-0.0012. . >.”.‘*,, .’. .0.0043,-~+’”7-”-&,, ‘,,’)’, ;“ ,,., .,, -.”,,, ,,+ ‘,,’” ..-, .,. . .,- ..,” , “., ,,#,.“’” ~,.’0.00500.0072REGION B OF FIG.8.Fig.9.INTERCONNECTIONS BETWEEN MICROCRACKS REVEALED BY PROGRESSIVE SECTIONING.THE DEPTH OF EACH SECTION BELOW THE STARTING SECTION IS INDICATED

-4fJ-!!!,,,!’,::,:, ,’,),:“!(a) 0.030 from crack tipFIG.11. CRACK PROFILE OF A-517TESTED AT -196°C(b) crack tipFIG.12. ARRESTED CRACK TIP IN QUENCHED 4340 AFTER UNSTABLE PROPAGATION AT -196°C

-41-In Figure 7, it appears that several micro cracks are isola~ed and that the~igaments perhaps form a single multiply connected network. Sections revealing thecrack profile in the Fe-3Si also have the same appearance as shown in Figure S. Hereagain, apparen~ly isolaEed microcracks are common but become more numerous near Checrack tip. J3yprogressively sectioning in increments of about 0.002 in. (a total oftwelve sections were m~de) it was possible to obtain a three-dimensional concept ofthe crack shape and better judge the degree to which the microcracks were interconnected.From the sectioning, it was found that in no instance was a microcrackobserved to be completely isolated. Two examples in which apparently isolated micro-CraCICSwere observed to connecc Eo the main crack are ,sho~ in Figure 90 These resultssugg~st at least for the Fe-sSi that the ligaments correspond to islands ofunbroken material. The crack itcself forms a continuous surface and truly isolatedmicrocracks are rare. Because of Lhe close similarity in the fracture topographywith the Fe-3Si, this result should also apply co the mild sEeel although thismaterial was not progressively sectioned.In the A-517, which has a quenched and tempered microstructure, the crackpropagation mode was also primarily cleavage at -lg6°C. However, in contrast ‘cothemild steel and Fe-3Si, the cleavage facets shown in Figure 10 are smaller, moreirreeqlar, and generally not as well d~fined. Areas of ductile tearing were alsoevident. In profile, Figure 11, the crack was found to exhibit occasional discontirmitiesover most of its length. The crack shown in ~igure 11 propagated in arelatively stable manner by very small but rapid increases in length. The finalpropagation before the specimen was sectioned extended the crack approximately 0.10fnches . Near ‘&e crack tip, the crack path becomes quite discontinuous. Progressivesectioning in very small increments ( - 0.0004 in.) revealed Lhat the crack surfacein the A-517, like the Fe-3Si, is continuous and surrounds the unbroken ligaments.It would appear that in the case of A-517, these ligaments rupture at relativelysmall crack opening displacements since they are confined primarily ‘cothe crack-tipregion. Exactly the same behavior is evident in the Lk3ii0aS can be seen in Figure12. Here the crack propagated in a very unstable manner (at -lg6°C) for approximately2 in. before arresting with a microcrack array at the tip.Plastic Deformation During Propagation. EY giving the Fe-3Si spectmens alow temperature (1509C) anneal, dislocations are decorated With carbon and nitrogen.During subsequent etching, Lhe decorated dislocations are preferentially attackedwhich Ehereby permits observation of deformation zones. A detailed discussion ofthe specimen preparation, aging, and etching procedures for displaying deformationin Fe-3Si can be found in Reference 16. Here it is pointed out that this techniqueis sufficiently sensitive to reveal individual dislocations when the plastic strainsare small. As the plastic strain increases, the dislocations become so numerous chatthe area appears black. With further increases in plastic strain beyond 5 tO 10%,the material no longer etches due to insufficient carbon to adequately decorate thedislocations . Therefore, crack-tip plastic zones are delineated by two boundaries:an otlterone of essentially zero strain and an inner boundary within which theplastic strain exceeds 5 to 10%.In Figure 13, are shown a series of macrographs which illustrates the increasewith temperature of the extent of deformation on the surface of specimenstested at -75°C, O“C, and 100”C. The plastic zones extending on either side of thecrack are similar in size for both the O“C and -75°C test temperatures. At I009C,the plastic zone sfze is considerably larger cons

-42-(a) -75°C ,,,,,,,!!,,(b) 00C(c) 1000CFig.13. DEVELOPMENT OF SURFACE DEFORMATION WITH INCREASING TEST TEMPERATUREIN Fe-3Sic’!’$ ,.(b) MidthicknessFig.14. COMPARISON OF THE DEFORMATION AT THE SURFACE AND MIDTHICKNESS OF ASPECIMEN TESTED AT 22 C. THE INITIATION-ARREST LOCATIONS ARE IN-DICATED IN THE MIDTHICKNESS VIEW BY THE KAT WHICH PROPAGATIONOCCURRED

(a) 0.6 in. from crack tip0.25 in. from crack tip(c) arrested crack tip(d) crack tip(d) Enlargement of the tip regionof Fig.15(c) showing arrest at agrain boundary and subsequent deformationwithin the two adjacentgrainsFig.15. REGION OF UNSTABLE CRACK PROPAGATION IN SPECIMEN SHOWN IN Fig.14

744-Figure 14 shows a comparison of the surface deformatio]lwith the deformationat the rnidthicknezs position in a DCB specimen tested at 22°C. In thisspecimen, the crack propagated in short increments starting at 19 ksi fi. from the0.007 in.-wide SIOE and continued to propagate at a K I.evelin the range of 27 to32 ksi~n. Each of the loca’cionswhere arrest and reinitiation occurred is identifiablein the midthickness view by a plastic zone. Finally, at a K of 34 ksifi.at the crack length indicated in Figure 14, the propagation became very unstable andthe crack ran the remaining distance. In Figure 14, there is evidence of considerablecrack division resulting in fairly extensive unbroken regions just prior to the pointat which initiation occurred at the K of 34 ksifi. As unbroken ligaments may interferewith propagation, a point discussed in more detail later, their presence at thecrack Lip increases the initiation threshold. This is an effect equivalent to increasingthe root radius of the starter slot.On the surface where plane s~ress conditions predominate and stiallshearlips are tending to form, the relatively uniform deformation along the first portionof the path suggests that crack extension here is continuous. In the unstable portion,the plastic zone is much smaller and in some areas has completely disappeared. Nearthe tip, unbroken regions within which relatively intense plastic strains have occurredare indicated by the areas which have etched white. At the midthicknessposition, in Figures 15a, b, and C, plastic deformation is apparently confined to L“tiearrest-initiation locations and within and surrounding unbroken ligaments which occurat fairly random locations along the crack path. An excellent example of the crack tipdeformation which occurred after arrest, and which results from the residual load onthe specimen applied by the wedge, is shown in the magnified view in Figure 15d. Theseobservations are identical to those made on other Fe-BSi specimens tested at roomtemperature and below and addi~ional examples can be found in Figures 6 and 7 inSection 2 of this report.These results sugges~ that virtually no plastic deformation occurs at thecrack tip while it is moving. However, there is a small uncertainty in the extent ofplastic deformation introduced by the small amount of material removed from thecorners of the crack during etching. AS the etching should remove no more than 0.001in. from the crack, we may take this dimension as an upper limit to the plastic zonesize in the fast crack regions. In Section I, it was found that the plastic zone sizevaried as~=o.13:2in the DCB specimen. Therefore, during rapid propagation K/Y < 0.09 ~. at thecrack t~p. Near the arrested crack tip where the uncertainty in the extent of deformationdue to etching is small, K/y < 0.04 ~. The plastic zone at the arrested tipin Figure 15d provides the measure of the arrest stress intensity as 7.7 ksifi.taking the static yield strength to be 62.4 ksi. However, the unbroken regions spanningthe crack interface may support a portion of the applied load and, therefore,the applied stress intensity couldbe larger than this.+H—. --+ The arrested crack length in this specimen is outside the range of applicabilityof Equation (6).

45-Iv.DISCUSS1ONThe ratio Ka/K~ div%des the DCB test results into two regimes. Thr propertyof stable crack propagation has been attached to those results in which &/KQ is verynearly unftyo In all other tesCs, Ka/KQ was about 0.4 or less and here the term unstablepropagation was applied. Crack propagation behavior yieldiw lta/KQ values inthe range between these two extr~mes was not observed. From a macroscopic standpoint,crack propagation inscabili~y appears to develop very rapidly as ‘~, $

-46-4Legend—$!4 .— R@ is excess stroln energy,/ mnve.?ed t. kine,lc energyh-ShudedareaAfter P kinetic energy wedK“’22A Area @ = Area @ at orr@st7Fjg.16.SCHEMATIC REPRESENTATION OF THE ENERGYCHANGES ACCOMPANYING PROPAGATION ANDARREST IN A DCB SPECIMEN. The L#curve corresponds to crack growth underfixed-displacement. conditions, The R-curve is hypothetical.~+_-..-._--..x+Unstah:e propagoitcnI 1~—- - .J---L.Jherea. and af are the initial and “fillaIcrack ~cngths, respectively. In arri.vinSat Equatian (10), it is assumed that the system (the specimen and loadin~ mechanism)is conservative (isolated) except only for heat lost through the crack plane duringpropagation. This assumption essentially requires that all kinetic energy is dissipatedalong the crack plane. To proceed further requires knowledge of the dependenceof R upon crack velocity. When viewed on a macroscopic scale, the etchingresults show that the deformation is fairly uniform along the crack path. The deformationaccompanying crack propagation appears to show a dependence on crack velocityonly at the specimen surface when shear lips begin to form at the higher test temperatures. Therefore, as ~ reasonable first approximation, we can setR=‘Q=GQ ‘= o[1 ‘dV>o(11)where R dis constant. Equation (10) becomesaf1‘d=—dUaf-ao ! aoSubstituting Equation {5) and recalling that G = KL/E, integration of 12 givesr1[ 1.1 1/2 + ~ 1/4 ~ 1/4 + c 1./2 1/4 c 1/4‘d 3 .GQ Qa a ‘Q aor (13)It can be recognized from EquaEion (1.2) that Rd falls between G and Ga. values ofQRd calculated from Equation (13) and expressed in stress intenszty units for A-517steel.are given in the following table.

-47-TABLE 3.‘ABuLATION ‘F ‘Q’ ‘a’ ‘ND ‘d ‘ALUESFOR A-517 AT -196DC*VL ...—.———Diameter (in.) KQ (ksi~n.) Ka (kSi&) ~“ERd (ksiy~n)Sharp 32 (KIC) 31 310.007 42 18 280.009 43 12 240.0.25 69 16 36Compared to the range of Kq and I ,21{4,If this inequalityis not satisfied,continued propagation is energetically fa;ored.At high magnifications, the etching results also show that Rd

-48-along the cr~ck plane by a fini~e number of point forces. l?rom this analysis, thecrack-tip stress intensity is given bywhere I(A is the applied stress intensity, 1? is the average force exerted by eachligament, m is the number of unbroken ligaments and d is Che fraction of the cracklength (2a) over which Lhe ligaments remain unbroken (cf. Figure A: 1). The functionG(m,d) is plotted in Figure A-2 for a range of values of m and d.Measurements of the ligament spacing and diameters along unstable cracksin the Fe-3Si in sections near the midthickness, indicate Chat the spacing rangesfrom about 0.005 in. to about 0.060 in. with an average of 0.022 in. and that thediameters vary in Che range 0.002 to 0.020 in. averaging 0.007 in. Since the graindiameter in this steel is approximately 0.003 in. the ligaments involve roughly oneto ten grains, Furthermore, taking the ligaments to be roughly circular and equidistant,the areal fraction of unbroken IigamenCs is about 0.1. The distance backfrom the crack tip where unbroken ligaments could be found (a-~) averages 0.44 in.As the ligamen~ model is strictly two dimensional, it is necessary to rearrange theligament array on the surface into an equivalent pattern of unbroken strips extendingacross the specimen thickness. On this basis, the strip spacing would be me-halfthe observed ligament spacing and the area of each unbroken strip is, for a specimenthickness of 0.5 in., 5.5 x 10-4 in.~ . The ligaments are subject to considerablerestraint and high strain rates and,therefore,a reasonable estimate of the flowstress prior to rupture is 150 ksi. For a crack length of about 2 in., we find1?= 82.5 lbfd=O.22m=40G(m,d) ~ 160and2F G(m,d) ~z. -10 ksifi.As a “ballpark” estimate, this result is very significant as it implies that theligaments could successfully unload the crack tip. Furthermore, since this calculationis based upon measurements along the midthickness profile, it should underestimatethe actual reduction in crack-tip stress intensity since the ligaments nearthe surfaces are apparently larger and more closely spaced.The results of the above model serve to emphasize the importance of the unbrokenligaments on propagation behavior. If the ligaments act to produce a significantdifference between the applied K and the crack-tip K, then also the ligamentsmust provide an important sink for energy dissipation during propagation. Therefore,a major part of Rd can now be attributed to deformation and rupture of unbroken areasas the crack extends, clirect evidence for which was available only in the case of thtFe-3Si etching results.In summary, the etching results coupled with the energymodel analyses provide evidence that the source of the resistancegation is not in the crack-tip reg?on but rather unbroken regionsas the crack-grows . This conclusion seemsapplicable at least to-.balance and ligamentto rapid crack propawhichare bypassedthe steels and

-49-testing conditions employed in this study. The source of the ligaments is not yetclear although two possibilities exist: anomalously tough regions which are scatteredrandomly throughout the steel, or a region of one or more grains whose cleavage planesare poorly orien~eclwhile the surrounding grains are well oriented for propagation.The weclSe-loadedDC13 test used in this study provides a very use.Iulmeansof studying crack propagation as the entire spectrum of propagation stsbility can beexamined. Indeed, tl~~ability to achieve stable propagation is attribLltable to theinherent stiffness of the loading system. Furthermore, these tests indicated thston the basis of the arrest toughness, the apparent resistance to crack propagation isdependent upon the initiation conditions. Therefore, K:l is not, by its~lf, ~1testindependent fndicator of crack propagation resistance.Finally, there s.remany asp~cts of rapid crsck propagation which have notbeen considered here. In particular, elas~ic wave effects such as rtf~eCtiOIIS fromfree surfaces back to the crack tip may play an important r~le in propa~ati,on. blhilequasi-static analyses of crack propagation have been dev?lopcd, a fLl~~ydynamic treatmentof crack propagation would be enormously difficult. The evaluation uf sucheffects is more realistically attacked from the experimental standpui,nt.v. CONCLUSIONS1.The inherent stiffness of the wedge-loaded DC13 test affords a means of propa~atings crack in a relatively stable manner such that the stress intensity Jt initiation(KQ) and arrest (Ka} are very nearly equal. By increasing K throl-ghincreasingthe root radius of the st:lrL~rslut, Ka undergoes an abrupt fecre.;e to Ka/Kq at least in the Fe-3Si steel,is nearly ideally brittle with Rd(tip)/~-rc j 0.01. The deformation is confinedto the unbroken ligaments as the crack extends and the overall energ]- of propagationis primarily absorbed in their deformation and rqpture.An snalysis of point forces disEribLltedalong a crack SLlrfaCc~ms used to modelthe ligaments joinins the crack interfaces and thereby Eain an ~stima~r of Llleeffect of these ligaments on the crack-tip stress intensity. Based on measurementsof ligament size and spacing, this estimate indicates th~t tlhcactualcrack-tip stress intensity can be appreciably less than the applie~l stress in-‘censicydue to the load borne by the Llnbroken regions behind the crflcktip. T])isanalysis offers an independent check of the concl[lsion that the lig,amenLsuffordthe principal energy absorbing sink during propagation.

-50-VI .REFERENCES1. T. S, Robertson, J, Iron and Steel Inst. , p, 361, 1953.,. .,. . Y. hkita and K. Ikeda, TransporEaCion Tech. Research Inst., Report 56, Tokyo,December, 1962.3. pl.Yoshiki, T. Kanazawa, and S. Machida, Proc. Seventh Jap. Cong. Test. Mat.,p. 71, 1964.4. J. 1. Bluhm, Fracture, an Advanced Treatise, H. Liebowitz, cd., Academic Press?New York, p. 1, 1969.5. H. Itagaki, T. Kanazawa, and M. Yokhiki, Studies on Che Brittle Fracture Problemsin Japan, M. Yoshlkf and T. Kanazawa, eds., Sot. of Naval Architects of Japan, ~,1967, p. 72.6. R. G. Hoagland, Trans ASME, Series D, Vol. 89, p. 525, 1967.7. A. A. Wells, Welding Research, Vol. 7, p. 34, 1953.8. R. Weichert and K. Schonert, Inc. J. of Fracture Mech., VO1. j, p. 353, 196$1.9. J. Eftis and J. M. Krafft, Trans ASME, Series D, Vol. 87, p. 257, ~g64.10. 1?.P. Videon, 1?.W. Barton, and W. J. Halls SSC Report 148, 1963.11. K. E. Broberg, Arkin f~r Fysik, Vol. 18, p. 159, ~9b0.12. J. Dvorak, Fracture 1969, P. L. Pratt, et al, eds., Chapman and Hall, London,p. 338, 1969.13. P. B. Crosley and E. J. Ripling, Trans ASME, Series D, Vol. 91, p. 525, ~96go14. G. T. Hahn, W. S. Owen, B. L. Averbach, and M. Cohen, Welding J., September,1959.15. G. T. Hahn, B. L. Averbach, W. S. Owen , and M. Cohen$ Fracture, Proc. Swampscol:tConf., Wiley, New York, p. 91, 1959.16. G. T. Hahnp P. N. Mincer, and A. R. R@g,2afie~d, !,TheFe_3Si Stee~Etching Techniquefor Local Strain Measuranent”, s~bmitted to Experimental Mechanics —- (to be published) ,17. E. Gross and J. E. Srawley, NASA Technical Note, TN D-3295, Pebruary, 1966.18. D. P. Clausing, Int. J. I?rac.Mech., vol. .5, p. 211, 19bgG19. W. F. Brown and J. E. Srawley, Plane Strain Crack Toughness Testing of Hi#nStrenSth Metallic Materials, ils~ STP 41O, 1967.20. A. K. Shoemaker and S. T. Rolfe, Trans ASME, Series D, Vol. 91, p. 512, 1969.21. J. M. Krafft, NRL Progress Report, p. 4, November, 1963.220 G. C. Sib, Inelastic Behavior of Solids, McGraw-Hill, New York, p. 607, 1970.23. C. Atkinson and J. D. Eshelby, Int. J. of Fracture Mech., Vol. 4, p. 3, 1968.

-51.-ACKNOWLEDGMENTSThe authors are grateful to Ship Structure Commit~ee for Eheir support andLO Ac~visoryGroup 111 Of the Ship Research Committee (S. T. Rolfe, Coordinator) andto A. R. I.ytle and R. W. Rumke of the Academy for valuable advice and encouragemen~.They are also inde”btedto M. ~ightner of the U. S. Steel Corporation, who contributedthe heat of T-1 steel used in this study. Experimental results for 4340 steel arederived from studies for the Army Research Office (Durham). The authors also wish toacknowledge the experimental assistance of R. L. Stephenson, and fruitful discussionswith M. F. Kanninen. Valuable assistance in preparation of the manuscript was provi~eclbyMiss C. Pepper.

-52-APPF,NDIX ATHE EFFECT OF CRACK-LINE TRACTIONSON THE CRACK-TIP STRESS INTENSITYIF, as a crack grows, ft encircles and leaves behind islands of unbrokenmaterial or ligaments, the stress intensity describing the stresses in the crack-tipregion will become increasingly smaller than the applied stress intensity~ as the unbrokenligaments become more numerous. The effect of these ligaments may be adequatelytreated by appealing to a simple two-dimensional analogue consisting of alarge, center-cracked plate loaded along the crack plane by a series of point forceswhich simulate the ligaments-(Figure A-1). Following the complex variable method ofMuskhelishvili(~~, we define a function, @, in the complex z-plane such thato Xx+oYY= 2[$5’(2)-F@’(z)]We may consider the stress function @ as arising solely from the point force tractionsalong the crack plane. Then, if the plate is loaded in some fashion along its boundaryto produce an applied stress intensity, KA, the net stress intensity isK=KA~ ~im [@’(Z) +@’(z)]x~ay=ox>a(A-1)The conformal mappingtrafisformsthe unit circle in the ~-plane into a slit of length 2a in the z-plane.In the ~-plane, Muskhelishviliprovides a solution for a distributed force over anarc of the circle. By allowing the arc length to decrease to zero such that theresulting point force, F, is finite, Muskhelishvili’s solution reduces too(g) = -&An(o--g)where o is the point along the holea distribution of n point forces onboundary at which the force? F, is applied. Forthe crack plane except at the crack tips, x = ~ a,~~ The stress intensity based on the applied stress and crack length neglectingtractions along the crack surface.

-53-Fn‘n-1IYA-2(slit bwndory)r– 2(]––---”i[cl)F-nttttt+-1-—— 1“---—---++HH—--mm”p-l-8Fig.A-l. (a)(b)CENTER-CRACKED SHEET LOADED BY POINT FORCES DISTRIBUTED RANDOMLY OVER THESLIT BOUNDARY. THERE ARE N FORCES NUMBERED IN A CLOCKWISE FASHION.(b) SAME AS (a) EXCEPT THAT THE FORCES ARE EQUAL AND UNIFORMLY SPACED

-54-A-3Equation(D-1) becomessir@.3l-cose .J(A-2)where ej is defined by Xj = cos@; and Xj is the location of the jth force on thecrack plane. Let us now examine the particular case in Figure A.lb of equal magnitudeforces equally spaced a distance 6. The first force is positioned at xi = 4 and,making the subs~itution d = (a-A)/a, Equation (A-2) becomes~m’-[m(l-d)+(j-l)d]’or more compactlyK =KA-—$G(m,d) (A-3)where m = n/4. The function G(m,d) is plotted in Figure A-2. As m+ ‘, the forcedistribution becomes continuous and & G(m,d) approaches cos-l(l-d). Therefore, theterm due to the ligaments on the rigRt side of Equation (A-3) becomes, for large m(large number of ligaments)w~ich is precisely the result obtained by Dugdale(2~ for a continuous stress Y = F/6superposed along the crack surface near the crack tip.References1. N. 1. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity,Noordhoff, Holand, 1953.2. D. S. Dugdale, J. Mech. I’hys.Solids, Vol. 8, p. 100, 1960.

-55-moo=0.01A-h6@34002001-—/ 0.05,)0.1/ ,0+20.3~ ;~ 0.;~,1008060——$4; 0.9I.0—_40wmE’2077--v-10864,, ..+ — ——G’m’’=~~2..[m(,+,+(j.,)d]2II . .,+m—2Ii24 6810 20m40 60 80100 2004mFig. A-2.THE RESULTS OF THE ANALYSIS FOR THE UNIFORMLY SPACED EQUAL FORCE MODEL

NoneSe.cuntyClas51ficati0nDOCUMENT CONTROL DATA - R & D(.Sc,currty cJa.7, /lica~ron of tiflcr h,dy of ~h.trart ano index an+: ,mnorarion I>IU. ! be erztercd when the overall report is rla. xi fiecf),.1,”I OHl GlN4Tl NG AC TIVITV (Corporate author) 23. REPORT 5CCu RlTY CL A5SIF1 CATIONBattelle Memorial ~nstituteColumbus. Ohio3.REPORT TITLE2b. GROUPedCRACK PROPAGATION ANEIARREST IN SHIP AND OTHER STEELS4 DESCRIPTIVE NOTES (rype of reporf and inclusivt daies)5. PU THOR(S) (Fi,yt rwmc, middle initial, last name)G. T. Hahn, R. G. Hoagland, p. N, Mincer, A. R. Rosenfield, and M. Sarrate$. REPORT DATE 7a. TOTAL NO. OF PAGEs 7b. NO. OF REF5~ti. CONTF?4CTAugust, 1970OR GRANT NO.35ORIGINATORdS589a. REPORT NUM13ER(5)NOO024-68-C-5073ISSC-219b.PRO,ECT NO,SR-180c, 9b. OTHER REPORT NO(51 (AnY other number. fhat may be essignedthzs report)a,10. DISTR[@UT!Or.I STATEMENTDistribution of this document is unlimited.71 SUP PLEMENTAe VNOT E5 i>. SpONSORlhIC MILITARY 4CTIVITY13, ABSTRACTINaval Ship Engineering CenterI,This report describes a three-part investigation into the major stages offracture--initiation, propagation, and arrest. A wedge-loaded double-cantilever-beamdesign was used on Fe-3Si Steel where crack-tip yielding can be revealed by a specialetching technique. Additionally, a number of experiments were done on engineering steels, principally to study propagation resistance.It was found that the fast moving crack bypasses some of the grains as it grows, leavingbehind ligaments. Rupture of these ligaments consumes a large amount of energylocally and this process can account for crack propagation resistance values estimatedfrom these experiments. Upon increasing root radius of the initial notch, the crackmust be overloaded Lo propagate, and a wide range of values of the crack driving forceG, can be obtained in a single experiment. This provides a new method of measuringcrack propagation resistance, R. Etching results suggest that R does not vary greatlyas the crack grows. An energy balance shows that R is the average value of G duringpropagation. By this means, partial confirmation IS given to the idea that R is equalto the value of G Icmeasured in an impact test. It is then shown that the rate audtemperature dependence of KIC= (EGIC) 1/2 arises from the rate and t~mperature dependenceof the yield stress in the crack-tip plastic zone. These analyses and experimentsthus provide a framework for developing a practical arrest criterion for shipsteels.DD 1‘o’” NOV65 1473 (PAGEIJ.,- .-‘) wneSIN 0101-807-6801 \ SecurityClassification

ass~fication4KEYWORDSROLELINK A ““WTBWTROLELIF4KCWTFracture MechanicsFracture ToughnessCrack InitiationCrack PropagationCrack ArrestStructural SteelPlastic Zones of Crack TipsDouble-Cantilever-BeamSpecimenCleavage Fracture of SteelsElastic-PlasticAnalysisFracture, Rate, and Temperature Effects(PAGP2)NoneClassificationSecurityGPIY 917.317

SHIP RESEARCH COMMITTEEMaritime Transportation Research BoardNational Academy of Sciences-National Research CouncilThe Ship Research Committee has technical cwizance of the ShipStructure Committee’s Research Program. Thir entails recommending ‘Pesearchobjectives, preparing project prospectuses, evaluating proposals,providing liaison and technical guidance, reviewing project reports, andstimulating productive avenues of research.PROF. R. A. YAGLE, Chairman MR. D. FAULKNERP?ofessor of iVavalArehiteetzu%Resmx’ch Associat@Univasity of M{ekigan Massachusetts Institute of TechnologyDR. H. N. ABRAMSONDiFecto~, Dept. of Mechanical Sciences PROF. W. J. HALLSouthmst Reseamh Institute %ofesso~ of CiviZ EngineeringUnivmsity of IllinoisMR. W. H. BUCKLEYChief, Structural Criteria and Loads MR. J. E. HERZBell Aerosystems Co. Chief Structural Design EngineerSun Shipbuilding & Dry Dock Co.DR. D. P. CLAUSINGSenior ScientistMR. G. E. KAMPSCHAEFER, JR.U.S. Steel CorporationManager, Application Enginee~ingARMCO Steel CorporationMR. 1. E. COXSenior Progmm Manager PROF. B. R. NOTONNeoport Ne%s shipbuilding & DPy Dock Co. Prof. of Aerospace & Civil EngineeringWashington UniversityMR. J. F. DALZELLSenio~ Research Engineer MR. W. W. OFFNERStevens Institute of TechnologyConsulting Enginee?DR. W. D. DOTYCDR R. M. WHITE, USCGSenio~ Reseaxch ConsultantChief, Applied Engineering Section0,S, Steel Corporation U.S. Coast Gumd AcademyMR. F. D. DUFFEYManager of Welding & MathodsMaryland Shipbuilding & DPy Dock Co.MR. R. W. RUMKEExecutive SecretaTySkip Resea~ch CommitteeThis project was coordinated under the guidance of the followingAdvisory Group III, “Metallurgical Studies” membership:PROF. W. J. HALL, Chairman, P~of. of Civi2 Enginee~ing, Un-iversityof IllinoisDR. D. P. CLAUSING, Senior Scientist, U.S. Steel CorporationDR. W. D. DOTY, sen

SHIP s~R.uCTLIR,~C(lPliVITTTFFPUBL.JCATIONSSSC-206,SSC-207,SSC-208,SSC-209,SSC-21O,SSC-211,SSC-212,SSC--213,SSCY.214,Permissible Stresses and z7LeiP Limitations by J. J. Nibbering. 1970.AD 710520.,.,Effect of Flme and Hechanieal Stzw@htening on Material P~ope~ties ‘“of WeZ&ents by H. E. Pattee, R. P1. Evans, and R, E. Monroe. 1970. “ ‘ ,AD 710521.SZamming of Ships: A Critical ReviezJof the Current State ofKnoz+ledge by J. R. Henry and F. C. Bailey. 1970. AD 711267.f~om Full-Scale Measurements of Midship Bending Stresses owRewltgThree Dry Cargo Ships by 1. J. Walters and F. C. Bailey. 1970.AD 712183.Analysis of Sbnming Data from the ‘/S,S. WoZvetine State” by J. II.Wheaton, C. H. Kane, P. T. Diamant, and F. C. Bailey. 1970.AD 713196.Design & Installation of a Skip Response Instmentation SystemAboa~d the Container Vessel l’S.S. Boston” by R. A. Fain,J. Q. Cragin and B. H. Schofield. (To be published).Ship Response Instrumentation Abomd the Container Vessel l’S.S.Boston’r: Results fyom the 1st Opemtionul Season in North Atlantic$exvice by R,A.Fain, J. Q. Cragin, and B. H. Schofield. 1970.AD 712186’.A Gu2de.fo~ Ultrasonic Testi_ngwd Evaluation of JieldFlaus by R. A.Yous.haw. 1970,. AD 713202.Sh,ipResponse Instmentat20n Aboard the Conta