1、.*fNATIONALADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTE 4394THE RATE OF FATIGUE-CRACK PROPAGATION INTWO ALUMINUM ALLOYSBy Arthur J. McEvily, Jr., and Wslter IllgLangley Aeronautical LaboratoryLangley Field, Va.WashingtonSeptember 1958i.-= ,.,Provided by IHSNot for ResaleNo reproduction or network
2、ing permitted without license from IHS-,-,-TECH LIBRARY KAFB,NMNATIONAL ADVISORY cowm FOR mKINAums Ilulllllllrlu!lll!ilulluIluhmiTECHNICAL NOTE 4394THERATEOF FATIGUE-CRACK PROPAGATION INTWO Aumm ALLOYSBy Arthur J. McEvily, Jr.,A general method has been developedand Walter Illgfor the determination o
3、ffatigue-crack propagation rates. In order to provide a check on thetheoretical predictions and to evaluate certain empirical constantsappearing in the expression for the rate of fatigue-crack propagation,an extensive series of tests has been conducted. Sheet specimens,2 inches and 12 inches wide, o
4、f 2024-T3 and 7075-T6 aluminm alloyswere tested in repeated tension with constant-smplitude loading.Stresse6 ranged up to 50 ksi, based on the initial area. Good agree-ment between the results and predictions was found.INTRODUCTIONThe rate of propagation of fatigue cracks is a subject not only ofaca
5、demic but also of practical interest as applied to fail-safe design.Some theoretical and experimental work has already been done in thisfield, but as yet no generally applicable method for the quantitativeprediction of the rate of fatigue-crack propagation is available. Theaim of the present investi
6、gation is to present such a method and applyit to the aluminm alloys 2024-T3 and 7075-T6.SYMBOLSacsemhlajor sxis of ellipse, in.half-width of plate, in.material constant, ksic-N“constant of integration, cyclesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from I
7、HS-,-,-2f fl fzKEKHKN%nNmrRsesnetsoxa7PPP=aafYrate-determining functionstheoretical stress-concentrationtheoretical stress-concentrationtheoretical stress-concentrationeffecttheoretical stress-concentrationexponentnumber of cyclesincremental number of cyclesNACA TN 4394.factor for ellipsefactor for
8、circular holefactor modified for sizefactorrate of fatigue-crack propagation, in./cyclesratio of minimum stressendurance limit (or themaximum load divided bymaximum load divided byto maximum stressstress at 108 cycles), ksi *renining net sectional area, ksi iiinitial netone-half of total length of c
9、entralsectional area, ksi .symmetrical crack, in.1I-stress-dependentproportionality constant, in. 2 cyclenumber of cycles from beginning of work-hardening stageradius of curvature, in.Neuber material-constant, in.effective radius of curvature at tip of fatigue crack,in.local stress, ksifracture stre
10、ngth of critical region, ksiyield strenh of critical region, ksi-d.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 4394 3THEORETICAL CONSIDERATIONSBackground InformationAn excellent review of the state of knowledge on the gr-h offatigue cracks
11、 has recently been given by Schivje (ref. 1) smd will notbe repeated in detail herein. However, the work of Head (ref. 2) andWeibu.11(refs. 3, 4, and 5) is of particular interest and will bebriefly described.Head developed a physical model of the process of fatigue-crackpropagation based upon Orowan
12、s concept of fatigue (ref. 6), which con-siders that localized fracture occurs as the result of an increase instress due to an accumulation of work-hardening in the vicinity of astress raiser. Head visualized the process of fatigue-crack propagationin the following manner: At the tip of an existing
13、crack or flaw, thelocal strengthwould be exceeded in accordance with the Orowan mechanism.The crack would then advance an incremental amount into a region whichhad not yet been fully work-hsrdened. The region at the tip of theextended”crackwould then be hardened, and the process would be repeatedove
14、r and over at an ever increasing rate since the stress-concentration* factor at the crack tip would increase as thetcrack grew in length. Theexpression for the rate of fatigue-crack propagation developed from thismodel is of the following type:.(1)From integration of equation (1) the crack length as
15、 a function of Nisx-; =a(C -N)where a is a factor depending on stress, Cisaone-half the crack length, and N is the nmnber oftions sxe limited by a rnnnberof assumptions, amonglinear law of work-hardening applies, that the mean(2)constant, x iscycles. These equa-which are: that astress is zero, andth
16、at the medium is of infinite extent. Thermnber of arbitrary constantsinvolved in the determination of the constant u precludes the generalquantitative use of equations (1) and (2). Head ccxnpsredthe trend pre-dicted by equation (2) with experimental results obtained for steeltested in rotating bendi
17、ng and, although the tests were not in keepingwith all of his assumptions, found fairly good agreement over most ofthe range. Schive did not find as good agreement frcm comparison ofbequation (2) with test results for axially loaded aluminm-alloy specimensat R=O.*Provided by IHSNot for ResaleNo repr
18、oduction or networking permitted without license from IHS-,-,-IllvX m 4394dWeibull (ref. 3) has presented data on fatigue-crackpropagationfor a series of constant-loadfatigue tests-at R= C) for sheet spec- _ -mens of 2024T-3 and clad 7075-T6 aluminun alloys. He also developedsemiempirical expression
19、s for the rate of fatigue-crackpropagation inthese alloys. In deriving these expressions he assumed that the peakstress at the tip of the fatigue crack is he principal factor whichdetermines the rate of fatigue-crack propagation. The resultant expression was of the formdx = kSnetn_m (3)where the con
20、stants k and n are to be determined empirically anddepend upon the original specimen dimensios, the material, and possibly also the stress distribution. (Althoh WeJbull was cognizant of the- fact that the stress-concentrationfactor increasedwith crack length,no attempt was made to incorporate this f
21、a.c.tinto eq. (3).) Weibull checked the validity of equation (3) with test results and found goo during the second st%e the crack is Propa-gated an incremental smount into material which has not been work-hardened. Then the first stage is repeated, and so forth.The extent of crack growth during the
22、second stage will dependinversely upon the smount of plastic deformation required to advancethe fracture front. Hence, it would be expected that in relativelybrittle materials the extent of this advance would be greater than inmore ductile materials.In order to clarify the role of the work-hardening
23、 stage, sane ofthe main points of Orowans theory (ref. 6) are briefw reviewed.According to this theory, in any metal object there exist certain weaksites which will deform plastically while the remainder of the bodyremains elastic, provided the yield stress ay of the sites is exceeded.During cyclic
24、loading the local stress at these sites increasesbecauseof the cmmlative effects of work-hsrdenfig and when the 10CSJ.stressProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA TN 4394is raised to the local fracture strength, a fatigue crack is nuc
25、leated.(Unfortunately,the local fracture strength is a quantity which has not . -yet been quantitativelydefined.)Although the material at the critical sites may be thought of ashsrdening to the fracture strength, the work of Wood and Segall (ref. 7)has shown that there is a limit to the amount of ov
26、erall hardening whichcan be developed through cyclic loading in a ecimen for a givenplastic-strain smplitude. In their experiments, this limiting valuevsries approximately as the square root of the plastic-strain qmplitude.Once this limit has been reached, the specimen cam be cycled indefinitelywith
27、out a further change in the yield level OT the material. The factthat the material yield strength leveled off instead of rising indefi-nitely was attributed to a process of stress relaxation.In the present investigation,the first-stageprocess of work-hardening at the tip of the fatigue crack is thes
28、e values are 0.003 and 0.002 inch for 2024-T3 and7075-T6, respectively.Once the values of Pe have been established, KN (eq. (13) canbe evaluated for various crack lengths. In figure 7 a plot of KNagainst crack length covering the range of the present tests is presentedfor each material and specimen
29、width. With KN known, theKNSnet can be obtained at any stage during the propagationcrack.In figures 8 to 1.1,plots of Knet against the rateproductof a fatieof fatigue-crack propagation are presented. The data for different widths anddifferent materials have been plotted separately for clarity. In ea
30、chfigure the rate is essentially a single-valuedfunction of the psmmeterN%et a71From equation (12), the rate is seen to depend upon KNSnet and theendurance limit Se. An equation which fits the test data and incorpo-rates these quantities in addition to satisfying the boundary conditionthat the rate
31、should go to zero as Nsnet approaches the endurancelimit isloglo r =This equation has beeno.WQXmt - 5.472 - 34net -34plotted as the dashed line in figures(15)8to=andis see to agree well with all the data, irrespective OF material orspecimenwidth. Although agreement for a particular material irrespec
32、-tive of width was anticipated, it was not ected that a single curvewould fit the data for both materials.The principal discrepancy between the data and the general curveoccurs for 2024-T3 specimens tested at an initial maximum net sectionstress of 50-ksi. A possible explanation of this discrepancy
33、is thatthe net section stress for the material is above the elastic limit, andtherefore a modification of the work-hardening process and, consequently,of the rate of fatigue-crack propagation might be expected.Although the parameter Knet in these tests takes on values upto 600 ksi, the work of Wood
34、and Segall (ref. 7) tends to show that theactual stress in the region at the tip of the crack would never attainsuch a high value but would level off at some lower value. Just whatvalues sre develuped is not lamwn, but the present results indicate thatProvided by IHSNot for ResaleNo reproduction or
35、networking permitted without license from IHS-,-,-14the levelregion atattained is a functionthe tip of the crack.NACA TN 4394Hf Iagainst N should fall along straight lines. Since the type of testutilized herein is not in accord with several of Headls assumptions,good agreement would be rather surpri
36、sing. Nevertheless, the data dofall on approximately straight lines as seen in figure 15. Since thisis the case, a possibility for a simple method for integration of therate equation (lj)presents itsti.The several unknown constants in Heads theory can be combined intoa single stress-dependent consta
37、nt which determines the slopes of theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 NACA TN 4394straight lines in figure 15. This constant a, which appears in therate expression developedby Head (eq. (l), isdx=dNIn the present derivation theexpre
38、ssionrate is given by the more complexdx = logo (1 0.00509KNet - 5.472 - 34dN ) (16)Nsnet -34Since both expressions appesx to give reasonablythe rate of fatigue-crackpropagation, the right-handbe equated and solved for the unknown a: xgood results forsides of each can1Lx=-x -: -1mlo (O.OONSnet - 5.4
39、72 - 342 ) (17)KNSnet - 34Since m is supposed to be a constant for a given stress level, itfollows that the product on the right-hand side must also be a constantfor that stress level. In order to check on this conclusion, a hasbeen evaluated for the present data and the re”sultssre given in table I
40、V.The results indicate that CL is approximately constant, at least forshort cracks although a general increasewith crack length is noted. Thevariation of a with crack length is seen to be much less than the vari-ation of a with the stress level So. The namely, 0.002 inch, ascompsred with the value f
41、or 2024-T3 of 0.003 inch.Through a ccznbinationof the present theory and the theory of Head,=an approximation has been made which enshles the rate expression to be.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 NACA TN 4394easily integrated in or
42、der to obtain crack lengths as a function of thenumber of load cycles. .In conclusion, it should be pointed out that the present investiga-tion has been concerned only with shple specimens tested at an Rvalue of approximately zero, where R is the ratio of minimum stressto maximum stress. Information
43、 is needed on other R vslues of inter-est and also on the effect of variable-amplitudeloading on fatigue-crack propagation, so that in combinationwith aircraft-load statisticsa rational fail-safe progrsm of periodic inspectionmight be set up.Langley Aeronautical Laboratory,National Advisory Committe
44、e for Aeronautics,Langley Field, Vs., July 14, 1958.4.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4394 19AFPENDIKCNCU2WION OF KNThe method of calculation of KN, the stress-concentrationfactorcorrected for size effect, is presented in this
45、 appendix. This methodwas developed in,reference 8, and is given in greater detail therein.For the case of a sheet containing a central, symmetrical crack,such as in the present investigation, the stress-concentrationfactor fora circular hole KH of diameter equal to the total length of the crackis d
46、etermined from Howlands curve (ref. 11) shown in figure 16. Thecrack is then considered to be an ellipse of major axis equal to thetotal length of the crack, and the stress-concentrationfactor fw sucha configuration is assumed to be related to that for a hole as follows:)8201,8201,WI1,ED3l,Wl,all,m1
47、,E!CX3535030.2#21M5 KLlmimadlcy11L1i1d2222L220.50.L5.W.UJ5.14-Gmckdid notlb. l,aw 2 13A-W =, , m 3k- 41,6C0 50,3W 60,s03 % *,WJ :=m 1,230 2 5,%0 lo,?m ti,m u,em 23?600 27,630 2,100 54,203 35,532 !30,3WX,cwa 1,220 2 2,g,tm,ko m 2 %3 530 1,0s8 l,l.69;8:o148.4689.0599.34210.2210.Thx1.2791.2571.26!51.1$)41.1601.1791.1281.1371.U)81.0811+.4318.3618.M19.6522.63373:7415.04i3.3544.3619.0622.9X 10-52.9907.7u372x 10-5 58.2060.9563.1966.78x 10-571.43-E.*77.3683.X2:%lcQ.6lu.o127.5162.22.8242.4- . -5.0555.0525.1315.1075.2105:7575ilL95.2%5.4005.CA95.8791.7761.7321.6921.5741.5401.4991.4851.4641.379-.-
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