1、NASA TECHNICAL NOTEIZI-ZNASA TN D-8244PREDICTING FAILURE OF SPECIMENSWITH EITHER SURFACE CRACKSOR CORNER CRACKS AT HOLESj. c. Newman1, Jr.Lallgley Research CeJlterHampton, Va. 23665(-40LUT _ON _.t_76_19_NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. JUNE 1976Provided by IHSNot for R
2、esaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I. Report No. 2. Government Accession No.NASA TN D-8244“ 4. Title and SubtitlePREDICTING FAILURE OF SPECIMENS WITH EITHERSURFACE
3、 CRACKS OR CORNER CRACKS AT HOLES7. Author(s)J. C. Newman, Jr.9. Performing Organization Name and AddressNASA Langley Research CenterHampton, Va. 2366512. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D.C. 205463. Recipients Catalog No.5. Report DateJune
4、19766. Performing Organization Code8. Performing Orgamzation Report No.L- 1 O2O310. Work Unit No.505-02-31-0111. Contract or Grant No.13, Type of Report and Period CoveredTechnical Note14. Sponsoring Agency Code15. Supplementary Notes16. AbstractA previously developed fracture criterion was applied
5、to fracture data for surface-crackedspecimens subjected to remote tensile loading and for specimens with a corner crack (or cracks)emanating from a circular hole subjected to either remote tensile loading or pin loading in thehole. The failure stresses calculated from this criterion were consistent
6、with experimentalfailure stresses for both surface and corner cracks for a wide range of crack shapes and cracksizes in specimens of aluminum alloy, titanium alloy, and steel.Empirical equations for the elastic stress-intensity factors for a surface crack and for acorner crack (or cracks) emanating
7、from a circular hole in a finite-thickness and finite-widthspecimen were also developed.17. Key Words (Suggested by Author(s)CrackStress-intensity factorMaterials, metallicFracture strength19. Security Classif, (of this report)Unclassified18. Distribution StatementUnclassified - UnlimitedSubject Cat
8、egory 3920. Security Classif. (of this page) 21. No. of Pages 22. Price*Unclassified 37 $ 3.7 5For sale by the National Technical Information Service, Springfield, Virginia 22161Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for R
9、esaleNo reproduction or networking permitted without license from IHS-,-,-PREDICTING FAILURE OF SPECIMENS WITH EITHERSURFACE CRACKS OR CORNER CRACKS AT HOLESJ. C. Newman, Jr.Langley Research CenterSUMMARYA previously developed fracture criterion was applied to fracture data for surface-cracked speci
10、mens subjected to remote tensile loading and for specimens with a cornercrack (or cracks) emanating from a circular hole subjected to either remote tensile load-ing or pin loading in the hole. The failure stresses calculated from this criterion wereconsistent with experimental failure stresses for b
11、oth surface and corner cracks for awide range of crack shapes and crack sizes in specimens of aluminum alloy, titaniumalloy, and steel.Empirical equations for the elastic stress-intensity factors for a surface crack andfor a corner crack (or cracks) emanating from a circular hole in a finite-thickne
12、ss andfinite-width specimen were also developed.INTRODUCTIONFailures of many aircraft and aerospace vehicle components have been traced tosurface cracks. Such cracks initiate at structural discontinuities such as holes, materialdefects, or other abrupt changes in configuration and may propagate to f
13、ailure under oper-ating stress levels. In designing against these failures, the designer must be able to pre-dict the effects of crack size and shape on structural stren_h. Linear elastic fracturemechanics (LEFM), which utilizes the concept of elastic stress-intensity factors, has beenused to correl
14、ate fracture data and to predict failure for cracked plates and structuralcomponents when the crack-tip plastic deformations are constrained to small regions(plane-strain fracture (ref. 1). However, when plastic deformations near the crack tipare large, the elastic stress-intensity factor at failure
15、 KI, e varies with planar dimen-sions, such as crack size and specimen width. (See refs. 2to6.) To account for the vari-ation in KI, e with crack size and specimen width, the elastic-plastic-stress-strainbehavior at the crack tip must be considered.An equation which includes the effects of plastic d
16、eformation on fracture was derivedin references 4 and 5. This equation relates KI, e to the elastic nominal failure stressProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-and two material fracture parameters and is designated the two-parameter fractur
17、e cri-terion (TPFC). The TPFC was applied to surface-cracked and through-cracked sheet andplate specimens subjected to tensile loading in reference 4 and to compact and notch-bendfracture specimens in reference 5. Reference 6 has also shown that fracture data fromone specimen type and the TPFC can b
18、e used to predict failure of other specimen types.In the present paper the TPFC was applied to surface-crack specimens subjected toremote tensile loading and to corner-crack (surface crack or cracks emanating from acircular hole) specimens subjected to either remote tensile loading or pin loading (s
19、eefig. 1). Fracture data from the literature on several aluminum and titanium alloys andone steel (refs. 7 to 10) were analyzed.Previous solutions for the elastic stress-intensity factors for surface cracks andcorner cracks at holes either were restricted to limited ranges of crack shape and cracksi
20、ze or were presented in graphical form. To eliminate some of the restrictions and forease of computation, empirical equations which approximate the elastic stress-intensityfactors for a surface crack and for a corner crack (or cracks) in a finite-thickness andfinite-width specimen were developed. Th
21、ese equations :ire compared with other theoret-ical and experimental stress-intensity factors from the literature.SYMBOLSabCDFfbfwKFinitial depth of surface or corner crack, mnumber of cracks emanating from hole (1 _Jr 2)initial half-leng_th of surface crack or initial length of corner crack at hole
22、, minitial half-lengeth of through crack (see fi_. 13), mhole diameter, mcomplete boundary correction factor on stress intensityBowie correction factor on stress intensity for through crack (or cracks) atholefinite-width correction factor on stress intensityfracture toughness computed from equation
23、(1), N/m a/22Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-KI ModeI elastic stress-intensity factor, N/m3/2KI,bKI,eBowie stress-intensity factor (ModeI) for through crack emanating from hole,N/m3/2ModeI elastic stress-intensity factor at failure, N
24、/m3/2KI,hKI,sexperimental stress-intensity factor (ModeI) at intersection of crack andhole, N/m3/2experimental stress-intensity factor (ModeI) at intersection of crack andplate surface, N/m3/2KI,ppKI,ssstress-intensity factor (Mode I) for crack subjected to pair of wedge forceloads, N/m 3/2stress-in
25、tensity factor (Mode I) for crack subjected to uniform stress, N/m 3/2KI,spM estress-intensity factor (Mode I) for crack subjected to single wedge force loadand uniform stress, N/m 3/2combined front-face, back-face, and finite-width correction factor on stressintensity for surface or corner crackM1
26、front-face boundary correction factor on stress intensity for surface or cornercrackm fracture-toughness parameterP pin load at failure, NQ elastic surface-crack shape factorSSngross section stress at failure, Panominal (net section) stress at failure, PaSu nominal stress required to produce fully p
27、lastic region on net section, PaProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-T temperature, Kt specimenthickness, mWx(YUspecimen width, mdistance from center line of crack to location of wedge force load, mangle measured from plate surface to poin
28、t on surface-crack or corner-crackboundary (see insert in fig. 10)ultimate tensile strength, Paeys yield stress, PaTWO-PARAMETER FRACTURE CRITERIONThe two-pararneter fracture criterion (TPFC) developed and applied in references 4to 6 accounts for the effects of plastic deformation on fracture proper
29、ties and relates theelastic stress-intensity factor at failure Ki,e, the nominal (net section) failure stressSn, and two material fracture parameters KF and m. The equation isKF _ KI, e (Sn _ ays) (1)fS n 11 - m/-)Su jFor the surface-crack and corner-crack specimens, Su is equal to _u, the ultimatet
30、ensile strength. (For other specimen types, Su may be greater than _u (ref. 6).)The fracture parameters K F and m are assumed to be constant for a given combina-tion of material thickness, temperature, and rate of loading. To obtain fracture constantsthat are representative for a given material and
31、test temperature, the nominal failurestress must be less than _ys, and the fracture data should all be from the same specimenthickness and from tests that encompass a wide range of specimen widths or crack lengths.Reference 4 shows how the fracture parameters are determined from a given set of frac-
32、ture data.Equation (1) was derived for Sn _ Crys, but reference 4 has shown that equation (1)closely approximates the failure stresses for surface-cracked specimens even when Sn4Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-was greater than Crys. T
33、herefore, for the present study of surface cracks and cornercracks at holes, equation (1) was also applied for Sn _ys.ELASTIC STRESS-INTENSITYFACTORSThe form of the elastic stress distribution near a crack tip that containsthe stress-intensity factor KI andthe square-root singularity is well known(r
34、ef. 2). (The deter-ruination of KI is the basis for linear elastic fracture mechanics.) The stress-intensityfactor is a function of load, configuration (specimentype), andthe size, shape,and locationof the crack. In general, the stress-intensity factor canbe expressedasKI,e = Sn _ F (2)for any Mode
35、I crack configuration where Sn is the nominal (net section) stress, c isthe initial crack length (defined in fig. 1), and F is the boundary correction factor. Theboundary correction factor accounts for the influence of various boundaries and crackshapes on stress intensity.Previous solutions for the
36、 elastic stress-intensity factors or the boundary correc-tion factors for a surface crack (refs. 11 to 13) and a corner crack at a hole (refs. 8 to 10and 14) either were restricted to limited ranges of crack shape and crack size or werepresented in graphical form. To eliminate some of the restrictio
37、ns and for ease of con:-putation, empirical equations which approximate the elastic stress-intensity factors forthese crack configurations are developed in the appendix and are compared with other the-oretical and experimental stress-intensity factors from the literature. The following sec-tions giv
38、e the nominal stress equation and the boundary correction factor equation to beused in equation (2) for the surface-crack and corner-crack specimens.Surface-Crack SpecimenFor the surface-crack specimen with a semielliptical crack (fig. l(a), the elasticstress-intensity factor at failure is given by
39、equation (2) where the nominal (net section)stress expressed in terms of the gross stress isandS n -S1 _rac2tW (3)(4)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In equation(4), the term in parenthesesconverts the gross section stress to the net s
40、ectionstress; the square-root term adjusts the through-crack solution to treat the surface-crackconfiguration; and Me ksthe combinedfront-face, back-face, and finite-width correctionfactor (ref. 4). The elastic shapefactor Q was given in reference 11as the square ofthe elliptic integral of the secon
41、dkind. An expression was chosenin reference 4 to givea simple approximationand ks givenbyQ = I+ 1.47(-ac) 1“64c164q = 1 + 1.47(_ “(5)The expression for M eM e = IM1 +wherewas developed in reference 4 and is given by(6)p = 2+ 8(a) 3 (7)The term M 1 is the front-face correction, the a/t term is the ba
42、ck-face correction,and fw is the finite-width correction. The expression for M 1 is given byM 1 = 1.13 - 0.1a C)1o)j(8)and fw is given byCorner-Crack SpecimensUniform stress.- For the corner-crack specimen with a quarter-elliptical crack(fig. l(b), the elastic stress-intensity factor is also given b
43、y equation (2) where(9)6Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-S n = S (10)1 _D _bzra cW 4 tWandF= (1 - DW bra4t W) c_QMefb_/seczrD2w (11)These equations apply for either one (b = 1) or two symmetrical (b = 2) corner cracks. Illequation (11)
44、, the term in parentheses converts the gross section stress to net sectionstress; the square-root term containing Q adjusts the through-crack solution to treatthe surface-crack configuration; M e is the combined front-face, back-face, and finite-width correction factor; fb is the Bowie correction fa
45、ctor (ref. 15) for a through crack(b = 1) or two symmetrical through cracks emanating from a hole (b = 2); and the secantterm accounts for the effect of the finite width on stress concentration at the hole.The value of Q is computed from equation (5) and Me is given by equation (6).The expression fo
46、r M 1 in equation (6) is given byaMI= 1.2-0.1 _cM 1 = +0.1_(002 _ys“ For extremely smallcrack sizes, equation (19) predicts nominal failure stresses greater than Su, but in thesecases Sn is set equal to Su.Aluminum Alloy Specimens7075-T651.- Masters, Bixler, and Finger (ref. 7) conducted fracture te
47、sts on7075-T651 aluminum alloy surface-crack specimens for two specimen thicknesses (5and 13 ram) at room temperature. The tests included a wide variation in crack size(0.25 _ a/t a, the maximum stress-intensity factor is given byKI _ _ (A2)Irwin (ref. 11) also estimated the stress-intensity factor
48、for a semielliptical crack in afinite-thickness infinitely wide specimen. (See fig. l(a) for W c.) His equation wasrestricted to crack depths less than one-half the plate thickness.The boundary correction factors for a surface crack in an infinitely wide plate as afunction of a/t and a/c were obtained from the analytical results of references 12, 13,and 18. Smith and Alavi (ref. 12) obtained approximate solutions for a near penny-shapedcrack (a/c = 0.4 and 1.0) as a function of a/t. For shallow cracks, Rice and Levy(ref. 13) obtained approximate solutions for a/c = 0.1 and 0.2 as a
