1972 r.h. heyer and d.e. mccabe - plane-stress fracture toughness testing using a crack-line-loaded...

8/12/2019 1972 R.H. Heyer and D.E. Mccabe - Plane-stress Fracture Toughness Testing Using a Crack-line-loaded Specimen

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PLANE STRESS FRACTURE TOUGHNESS TESTINGUSING A CRACK LINE LOADED SPEClMENt

R. H. HEYER and D. E. MCCABEArmco Steel Corporation, Research and Technology, Middletown, Ohio, U.S.A.Akhret-A crack-line-loaded specimen of modified WOL design was adapted for ioughness tesiing of highstrength sheet materials. A wedge-opening device was used to load the specimen and propagate the crack.because of the specimen configuration and loading system. the crack never becomes unstabie. and fullcrack growth resistance. R curves, can be developed for many materials.When it can be shown that these R curves are characteristic of a material, and independent of specimenconfiguration. they will be useful to predict instability conditions for other specimen types.CRACK-fine-loaded specimens have proved useful for determining the plane-strain stressintensity factors &, and k;,. These specimens are compact, require relatively lowloads, and are amenable to self-contained loading devices for environmental testing.Clausing [ 1) has shown by analysis that crack growth in crack-line-loaded specimensis stable over the entire range of crack extension provided a stiff displacement con-trolled loading system is used.The compact tension specimen, CTS, now used in KI, testing and having H/W =06. is also a crack-line-loaded (CLL) specimen and was derived from the Westingucrasewedge-opening-loaded (WOL) specimen. The term double-cantilever beam (DCB) hasalso been used to designate this family of specimens, including Riplings[2 taperedversion which can be designed for constant ii; independent of crack length.

Novak and Rolfe[31 reported using a compliance calibration of a self-loaded modi-fied WOL-IT specimen to determine the applied load from the measured crack openingdisplacement, COD. This technique was used with further modification of the specimenin the present investigation to determine crack growth resistance. I?, curves for highstrength sheet materials.

A crack growth resistance concept was suggested by Irwin and Kies [4] in 1954, andmodified in 1960 [5.6] to show increasing resistance with crack extension. Krafft et ui.171 demonstrated that crack growth ins~bility, G,, could be predicted for various speci-men sizes from the R curve for the material. Characteristics of R curves were exten-sively treated by Srawley and Brown[8]. Experimental determinations of R for alum-inum alloys, using center cracked tension specimens, were reported by Carman et al,r91

SPECIMENS, ~XTURES. PROCEDUREThe specimen configuration chosen was based on the Westinghouse WOL-T type

[lo] with specimen height to width ratio. H/W = O-486. The specimen sizesare shownin Fig. I. Sheet thicknesses varied between 0,026 and 0.066 in. The small specimendesignated 2T is dimensioned. except for thickness, according to the WestinghouseWOL-2T specimen for K,, dete~inations on 2-in-thick plate. The 4T specimen issimifarly related to the 4-in.-thick K,, specimen, WOL-4T. To measure COD, diamondindentation marks spaced at O-750 in. are impressed in the specimens 0.06 in. from the+Presented at the National Symposium on Fracture Mechanics at Lehigh University, Augusr 25. 1969.

393

EFM. Vol. 4. No. 3-A


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394 R. H. HEYER and D. E. MCCABE

Ii j WOL-ZT WOL-47--I n 2.48 4.961 W 5.1 IO.2

L 6.46 I I.562f-l s I-50 3.0jj

Fig. 1. Modified WOL-T specimens for plane stress toughness tests.

front edge. These points are l-3 in. from the specimen load line for both specimen sizes.?Specimens are machined in packs up to 1.5 in. thick. The hole for the loading deviceis precision bored with respect to the front edge. The g-in. slot is saw cut. Individual

specimens are then notched using a &-in-thick cut-off wheel. The end of the notch issharpened with a very light cut using a hack-saw blade ground to a 40 vee tooth con-tour.

The specimens are precracked about &in. by cyclic tension loading in the apparatusshown in Fig. 2. Backup plates &-in. thick are used to prevent buckling.

Figure 3 shows the die and wedge opening device used for the 2T specimens, withthe top cover plate removed. Lubricated Teflon sheets are placed on either side of thespecimen to reduce friction from the hold-down loads. The upper cover plate is boltedon to the lower die with firm, but not heavy pressure. The wedge is hardened steel,chromium plated and lubricated, with a total taper angle of 3, or about 20 : 1 taper. Thewedge drives hardened steel dies contoured to fit the l*%n.-dia. hole in the specimen.These dies operate in a slot cut into the bottom plate normal to the crack direction. Thewedge is forced downward through the die opening using a Universal testing machineor a simple hydrauiic press. Crack propagation is observed during loading, and thewedge is stopped at various increments of crack extension. The COD and crack lengthare measured to the nearest +OWO2 in. with a stage micrometer, see Fig. 4. The di eshown in this figure and in Fig. 5 is for the 4T specimen. An auxiliary clamp provideshold-down pressure over the central portion of the specimen. The view in Fig. 5 showsthe window through which the crack is observed.

CALIBRATIONCrack length and COD measurements are used to obtain the effective load through a

relationship established by a compliance calibration:ERV,P =f(a/W)E = modulus of elasticity, ksi

PFor caicuiation purposes the COD measurement for she WOL-4T specimen is linearly extr pol ted fromthe plastic zone corrected crack front to a position 2.6 in. forward of the specimen load line. This preservesgeometric similarity between the two specimen sizes.


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Fig. 2. Fatigue cracking machine.

Fig. 3. Die for 2T specimen top piate removed).

[Facing page 3941


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Fig. 4. Loading of4T specimen.

Fig. 5. Crack in 4T specimen.


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Plane-stress fracture toughness testingB = thickness, inchesV = COD at the gage location. inchesP = effective load, kipsa = effective crack length, inches

W = width, inchesK = stress intensity factor, Ksi-irYR = crack growth resistance factor. Ksi-in.

395

(1)

Two PH 14-8Mo specimens of the 2T size, 0.049 in. thick, were tension oaded with-in the elastic range between f-in-thick support plates. A NASA type clip gage mountedbetween knife edges spaced at O-4 in. was used to measure COD. From COD-loadrecords, V/P ratios were obtained at 4 in. increments of crack length. The cracks wereabout 0.020 in. wide produced by jeweiers saw cuts. Test data in Fig. 6 include those

Fig. 6. Compliance calibration for WOLspecimen, H W = 0486.

of Novak and Rolfe[31. obtained from l-in-thick modified WOL-1T maraging steelspecimens. The polynomial obtained by least squares curve fit to the Armco data is:EBVIP = 59.79-594.77 (a/W) +28& .51 (@f)

-5208.8 (~/W)~+3803.85 (u/W)~=~$ (2)CalcuIation of the stress intensity factor K is based on dispiacement at the load line,V,, obtained by linear interpolation

V,=lVa+ I.3 (3)


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396 R. H. HEYER and D. E. MCCABEUsing V, in equation ( 1)&,(alW) = 177*23- 1629.0 (a/W) +5838*0 (a/W)*-89252 (~fW)~+5390.4 (a/W)K is obtained from (4)

(5)

K = & [-814.5 (a/W) + 5838.0 (a/W)* - 13387.8 (t~/W)~i- 10780.8 (a/W)*]*. (6)Within the range of the calibration this agrees closely with Wilsons relationship ofRef. [ 101, Fig. 7, obtained analytically. Wilsons equation is:

K =A r30.95 (a/W)--1956 (alW)+73@6 (c~jW)~-1186.3 (a/W)-t7546(a/W)7 (7)

=&*fL (a/W).For stable cracks, the driving force K and the crack growth resistance R are equal

at the crack tip. In calculating R from wedge loading test data, equations (2) and (7)are combined, relating R to I/ and a.

R = z .fL(atW herea f(ulW) (8)

u am-i-r,& = measured crack length

(9)

YS = 0.2 per cent offset yield strength in uniaxial tension. An iteration procedure ona is used to solve for R,

A method of interpolating the load line displacement reported by Roberts [ 111 givesslightly higher values of V, than obtained by the Iinear interpolation of equation (3).The Irwin plastic zone correction, rP, is subject to verification for use in this applica-tion where the magnitude of the correction on high toughness materials can be largeconsidering measured crack growth and specimen dimensions.The plastic zone has been the subject of intensive study by many investigators, andalternate plastic zone estimates have been suggested[ 12-161. However, the Irwinconcept was selected as the sting point in this investigation.

TEST DATATypical crack growth resistance curve data are shown in Figs. 7 and 8. Coincidence

of the curves for 4T and 2T specimens, having starting crack lengths of approximately


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Plane-stress fracture toughness testing 397

PH l4-BMo, onrmelt8*0.049 Ill

L, WOL 4T0 woi-2r

1 I I 1 t0 o-5 I.0 I.5 2.0Cmck extetwon, in.

Fig. 7. Crack growth tesistance curves for wedge ioaded WOL-T specimens.

PH 14-SMo, vacuum melt0*OG46

_l WOL-4f (00 WOL -4T (2): WOL -2f f2)

55 C :5 23Cmk txtens10n. I

Fig. 8. Crack growth resistance curves for wedge loaded WOL-T specimens.3-f and 1*6 in.. demonstrates that R is independent of initial crack length. This is alsoshown in Fig. 9, where the crack was started twice in the same 4T specimen fromstarting lengths of 3.15 and 4.41 in.

Extremes in crack growth resistance curve characteristics are shown in Figs. 10 and


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400

300

~$ 2oo100 j d

G/+--PH 14- 8Mo. SRH950, WOL-4TYS = 208.5 ksi bOQ49 mStortmg truck length, 4.41 m

. 0 Starting Crack bngth, 3.15 in

Crack extension, I.Fig.9. Crack growth resistance curves for WOL-4T specimen with two starting crack lengths.

-4T+L.._ 2f

Aa,,,= measuredcrock extensionI;.E

_c*--.IP 100 -

;/-.._.&

u //CI/

:Aa = effectwecrock extensbn Al alloy 2024-T3

3OJ- / YS a46.0 kl /9*0.066I .4

. WOL -4T (2)0 WOL-PT (2)

I.0 I.5 2.0Crock extension. I.

Fig. 10. Crack growth resistance curves for wedge loaded WOL-T specimens.11 for aluminum alloys 2024-T3 and 7075-T%, and in Figs. 12 and 13 for stainlesssteels 414 Ti and PH 157Mo. In Figs. 10 and 12 the difference between the curve formeasured crack length, a,, and for the plastic zone corrected crack length indicates avery large plastic zone correction, compared to Figs. 11 and 13.


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h - -3#---$0 00

-4TK e -__2T

Btalloy 7O?S-T6YS.75.6 ksi B-0066

. WOL-4T 2)0 WOL-2T 4)

, ,I O .f 2.0

Crack extenston, in

Fig. 11. Crack growth resistance curve for wedge loaded WOL-T specimens.

500t

-4tKc--,2T

Stainless steel type 4f4 TiYS=lO45 ksi B-@O38 hr.WOL- 4-f 2)

o WOL-2T 2)

Crock exteniion. in.Fig. 12. Crack growth resistance curve for wedge loaded WOL-T specimens.

The low toughness materials of Figs. 11 and 13 exhibit sudden bursts of crack exten-sion at high loads, and replication is inferior to that for tougher materials.

It becomes increasingly apparent that toughness of sheet materials cannot be ex-pressed as a single Kc value. independent of specimen size and geometry. Crack growthresistance curves offer the possibility of determining a Kr value for specific specimens


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PH I +7M0, RH1050YS = 212.0 ks i B= 0.050

.WL-4Tf210 WOL-2T 21

0 0.2 0.4 0+3 0.8 I.0

Crack exknston. tn.Fig. 13. Crack growth resistance curve for wedge loaded WOL-T specimens.

or structural elements, where Kc is the point of tangency of the crack driving force (K)curve and the crack growth resistance (R) curve. Experimental proof of this conceptis difficult when strain rate effects are present and when the crack length at instabilitycannot be accurately measured. These difficulties are not encountered in determining astatic crack growth resistance curve by the method reported here.When the K and R curves are expressed in numeric terms. the tangent intercept canbe computed by simultaneous solution of the expressions for slopes of the curves. Bothcurves can be expressed as polynomial functions of a/W, and this procedure wasfollowed in this report for Kc calculations.A procedure which may prove more satisfactory was suggested by Irwin in a privatecommu~cation. Irwin proposes that R be expressed in terms of ptastic zone size. crackextension, and the plateau K value, K,.

Aa = (u, try) a 0a, = actual crack length [= a, of equation (911rl , = 7r(K/YS)a@ initial crack lengtha = parameter determined by measurementF-m ~~(~~iYS~~.

110)

The function,& may be tanh (X), whereX = Aalar,,,.


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Plane-stress fracture toughness testing 401Applying this model to several materials of this investigation, data fit was excellentproviding an adjustment, Co, was added to correct the fit near the origin of the R curve.

x = halffr;, + c,The two methods of data fitting are compared in the following table on the basis ofpredicted instability.

Table 1. Load control Kc predictions for WOL specimens

Material7075-T6

WOL Kc- ksi din.specimen

size Polynomial Tanh21 66 68PH 14-8Mo CH900 2T 122 123PH14-8Mo SRH950 2T 205 206PH14-SMoSRH1050

PHl4-3MoSRH~lOOPH 14-8Mo SRH950Vacuum MeltTi-6AI-4V

2T 233 2334T 310 30214T 349 3432T 148 146

The tanh method is desirable in that material properties are used to define the Rcurve. However, the K, value could not be developed in some of the high toughnessmaterials even using the 4T specimen.The third order polynomial curve fitting procedure was applied only to data in theregion of the expected instability K value. in order to obtain an accurate fit in thiscritical area. The tanh curve fitting procedure, on the other hand, includes all the dataexcept for values of R close to the origin.

METHODS OF LOADING WOL PLANE-STRESS SPECIMENSWedge loading provides displacement control of crack extension. wherein K and P

decrease with crack growth, as shown in Fig. 14(a). When displacement is increased tmoderate rate from A to B, the K vs. a/W relationship departs from the static R curve,then time dependent crack growth at constant displacement from B to C establishespoint C on the curve. As the plateau region of the R curve is approached, time depen-dent crack growth after each increment of displacement increases. While 5 or 10 min issu%icient to attain a practical equilibrium condition in early stages of time dependentcrack growth. measurable crack extension may be observed after an hour or more inthe plateau region.

Loading the specimen in a tension testing machine having load control capability, Kand V increase with crack extension at constant load, as shown in Fig. 14(b). Whenload is increased incrementally, as from D to E, time dependent crack growth at theattained load will follow a load controlled crack extension force curve such as EF tothe point F on the static R curve. With load control. specimen instability occurs at thepoint of tangency between the K and R curve. When operating at very slow crossheadmovement the instability is observed as a definite fall-off of load with crack extension.This limits the extent of the R curve which can be determined by the load controlmethod, whereas using displacement control and a su~ciently large specimen, the Rcurve can be determined to a plateau value.


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K curves for400 - constant displacemmt

300 -

cc 200 -y

IOO-F

I I I /0 01 o-2 03 04 OS O-6

O/W

Fig. 14(a). Crack driving force K curves for WOL-4T specimen related to R curv e for PH14-8M0, SRH 950, vacuum melt. Displacement control test.

400

300

K curves forconstant load

0 0. I 0.2 03 0.4 O-5o/W

Fig. 14(b). Crack driving force K curves for WOL-4T specimen related to R curve for PH14-8M0, SRH 950. vacuum melt. Load control test.


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Plane-stress fracture toughness testing 403An example of data obtained by both displacement and load control is given inFig. 15. Kc by termination of the R curve in the load control tests coincided with Kc

predicted from the R curve obtained with displacement control. The Instron load waspredicted within reasonable limits from displacement and the plastic zone correctedcrack length. using equation (2). This supports the accuracy of the plastic zone correc-tion as applied to this material, which had r, = 0.33 in. and u, = 2.00 in. at the Kc n-stability.

In the case of load controlled tests of 2024-T3, the Instron loads were considerablyhigher than loads predicted from displacement and the plastic zone correct.ed cracklength. Furthermore, the Instron load and displacements give smaller effective cracklengths. by equation (21, than those of Fig. 10 for displacement controlled tests. Usingthese calculated crack lengths and the Instron loads. the values ofR from equation (7)yielded a curve only slightly to the right of the curve in Fig. 10 for measured crackextension, a,. This R curve would result in Kc nstability values higher than would beobtained from the curve for wedge loading.

These results indicate that the caiculated plaaGc zone correction does not give thecorrect effective crack length for 2024-T3. This subject is treated further m a latersection.

Data from load controlled tests of 2024-T3 resulted in an R curve coincident withone from wedge tests when R was calculated from displacement and r, corrected cracklength. This curve terminated at the Kc predicted from the wedge loaded test, in themanner of Fig. 15 for stainless steel.

Experimentally the sustained tension loading procedure is more difficult to carryout than the wedge loading, displacement controlled procedure. The problems are inmaintaining alignment in the testing machine, in reducing holddown friction to obtainaccurate load readings, and in a less convenient setup for measuring crack length and

400

y3oo ./??Tzzz

IAT zoo

P PH l4-9th. SRH It00YS =180.0 ksl 8=0,049 tn.o. WOL -2T load control

i / 10 05 I.0 15 2.0Cmck extenston, I.

Fig. 15. Crack growth resistance curves for displacement and load control.


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404 R. H. HEYER and D. E. MCCABEdisplacement. Two operators are needed, whereas the wedge loading procedure is read-ily performed by a single operator.

Load controlled tension instability stress intensity, Kc, can be calculated using theR curve and the load control K curve for the specimen. The Kc values for 2T and 4Tspecimens in Figs. 7-13 were calculated from the solution for the point of tangency ofthe crack driving force, K, and crack growth resistance, R, curves, using the Wilsonvalues forf; (a/W). Note that Kc for the 4T specimen is always slightly higher than forthe corresponding 2T specimen.

Assuming that an R curve developed with WOL specimens is characteristic of amaterial, it should be possible to predict the appropriate Kc instability stress intensityfor other specimen types. Such predictions have not been adequately verified, andremain a major objective of this investigation. Some hypothetical examples showing theinfluence of fracture toughness, specimen width, and starting crack length on Kc ofcenter cracked tension specimens are shown in Figs. 16-19, where the K curves for thecenter-cracked tension specimens were calculated using Isidas [ 171 equation:

PdaK = m Y, where (11)Y= 1.77+0~227 2aiW) -0310 (2~f~)*i-27 (2& q3.

In Fig. 16, a 20.4-in.-wide center cracked tension specimen (CCT) has a predictedKc. nearly equal to that of the WOL-47 specimen, with starting crack length a/W =O-3 in both cases.

CCT

21-20.4

Fig. 16. Load controlled crack driving force K curves for WOL-4T and CCT specimens relatedto R curve for PH 148Mo. SRH 950, vacuum melt.


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PH 14 - SMo, SRH 950. vacuum meli

I

YS 9208.8 B -0.0458

I , I IO-I 0.2 03 o 4 0:s 0

O/WFig. 18.Effect of width of CCT specimens on predicted K,.

Table 2. Characteristics of center cracked tension specimens cal-culated from crack growth resistance curves. Specimen widthvariable. Starting crack length constant at a/W = 0.3

Width2.w

PH 14-8Mo PHi4-8MoSRH950 SRH950Air melt Vat. meltFig. 17 Fig. 18 2024T3

oys. ksiCT,,,,ksi

P,,,, ksi

Kc. k&in*

a,. in.

ha, in.

51.020.410.251.020.410.2

208.5 208.8 46.063.4 99.8 34.097-o 147.2 46-6130.2 187.4 59.4105.2 148.3 67.360-9 806 34.438.3 48.2 19.2

51.0 23320.4 22810.2 21851.0 8-5720.4 3.7910.2 2-1051 0 o-92 1.63 2.5520.4 0.73 1.16 1.59IO.2 0.57 0.76 I-14

371349314

9.284.222.30

123.7110498-7IO.201.6.5267

PLASTIC ZONE CORRECTION TO CRACK LENGTHIn plane stress testing the calculated contribution of local plastic deformation to the

effective crack length can be very large, as shown in Figs. 10 and 12. We have made


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5::rzbi

0 01 02 03 04 0.5 0O/W

Fig. 19. Effect of starting crack length of CCT specimens on predicted K,.Table 3. Characteristics of center cracked ten-sion specimens calculated from crack growthresistance curve. Starting crack length variable.Width constant at 20.4 in.

Starting al WPH14-8Mo SRH950Vacuum melt - Fig. I9

0.15 0.30 0.45uy.


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Strom patterns mwedge loadiigof2024-T3, WOL-4T

a, -startmg crack length

Dtstance from loadhe. m.

,

3

Fig. 20. Strain at seven pbsitions on the crack-line of a WOL-4T specimen of 2024-T3. wedgeloaded.

strain of 0.63 per cent. In subsequent tests crack length vs. strain readings up to andabove the uniaxial yield strain were obtained. The measured crack length, a,, coinci-dent with development of this strain was used to obtain a measure of the length of theplastic zone in advance of the crack. These values are compared to r, = 3m Ki YS)* inTable 4. They range from 101 to 117 per cent of r,, for the stainless steels and from 80to 102 per cent of r, for 2024-T3.

Additional tests are being made using 90 rosette type gages to obtain both x and ystrains at a given gage location. These strains are used to obtain the actual y directionstresses. The von Mises yield criterion is then used to obtain the elastic-plastic border.On this basis the strain level for yielding is lowered, and the apparent plastic zone sizeis increased beyond that indicated in Table 4. Thus the approximate agreement betweenthe plastic zone size based on y direction strains only and the Irwin r, value may befortuitous.

After the strain gage tests had been run a is in. wide slot was progressively milledalong the crack line to remove the deformed metal of the plastic zone so that the CODwould be restored to the before-test value. While the original measurement of O-750 in.was not attained, Fig. 2 1 shows that the great& portion of the recovery had occurredwhen the slot length was equal to r, = h K/YS).

Another means of determining plastic zone size was by measurements under sus-tained loads in an Ins&on testing machine, calculating the effective total crack lengthfrom the compliance relationship, equation (2). Subtracting the measured crack length,


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Plane-stress fracture toughness testing 409Table 4. Length of plastic zone based on strain gage measurementsalong the crackline

Material

Strain gageindication based onuniaxial yield strength r, = f?r Strain

strain (KIYS ) gage/r,(1, PH15-7MoRHIlOO

0.104 in 0.072 in. 144(2) PH14-8Mo 0.207 0.201 1.03SRH950 0.209 0.201 1G4(3) Ti-6A1-4V

(4) PH 14-8MoSRH I 050(5) PH 14-8MoSRH 1 OG

(6) PH 14-8MoVacuum meltSRH1050(7) 2024~T30.03 15 in.(8) 2024-T3O-03 5 in.

(9) 2024-T30.066 in.(10) Type414Ti

0.2150.2400.310

0.430.490.48064

0.710.650.750.760.76 1.18 0.641.08 2.10 0.511.24 2.73 0.45

0.220 0.980.263 0.910.265 1.17

0.40 I.070.49 I.000.53 0.910.59 I.08

0.68 1.04O-69 0.940.79 o-950.95 0.80

the effective plastic zone was determined. Table 5 compares r, values so obtained tothose predicted by r, = +7r(K/YV. Except at low R values the agreement obtained inthe steel specimens is good, considering the sensitivity of the compliance technique toelastic modulus variations and errors in load measurement. In the case of the aluminumspecimen there is definite disagreement between the two methods. At first. it wasthought that friction of the retainer plates might account for the unexpected high ten-sion loads. but this was disproved in a special friction test. in which 2024-T3 developedless frictional resistance than the stainless steels. The fit of aluminum to the compliancecalibration curve, obtained with steel specimens, was also suspect, but this also wasdisproved by a calibration test of 2024-T3.

Recapping, plastic zone size for 2024T3 is about 80-100 per cent of r, = trr (K/YWwhen determined by the strain gage technique (Table 41, and under 28 per cent of r ,by the load-compliance calculation, (Table 5). .4 possible explanation of this anomalylies in the relatively high work-hardening in the plastically deformed metal ahead of thecrack in 2024-T3 compared with the higher strength materials. Strengthening in theplastic zone could partially offset the expected relaxation. so that the effective cracktip is moved towards the actual crack tip.


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40.75i t AI0 0.5 I .o I.5

Slot length/rFig. 2 1. Recovery of displacement by removing deformed metal from the plastic zone.

Table 5. Effective length of plastix zone based on indicated load and dis-placement (equation 2) compared to r, = +v(K/YS)~Load, lb

Plastic zone: Length, rp, in.Material R, ksiqin. Indicated Calc.* 47r(K/YS)**PH 14-8Mo 110 2475 2556 0.118 0.045SRH950 200 4275 4247 0.128 0.146226 4475 4462 0.181 0.188PH14-8Mo 112 2505 2582 0.124 0.061SRHllOO 238 5005 5049 0,299 0.278303 5605 5658 0.475 0.452

2024-T3 42 1102 923 0.054 0.16163 1452 1182 0.050 0.35474 1602 1269 0.111 o-419a4 1702 1282 0.148 0.525

*Equation (8).?Equation (2).*By iteration using equations (8) and (9).

DISCUSSIONMajor areas for future investigation are: (1) verification of predictions of load con-

trol instability Kc for various specimen types and structural elements using WOLgenerated R curves; (2) determination of minimum specimen size limitations: (3)


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Plane-stress fracture toughness testing 411determination of proper plastic zone size correction for the tougher materials. A solu-tion is presently available in compliance determination of effective crack length by theload control technique.

It is anticipated that the stress patterns now being determined by strain gaugesahead of the crack will be useful in defining the plastic zone. and hopefully the effectivecrack length.Other likely areas for future work include variation of test temperature. strain rate,environment, and specimen thickness.

We are presently developing correlations of center-notched wide panel test resultsto the WOL developed R curves. Preliminary results have been quite favorable. Diffi-culty is expected however, in the low strength, high toughness materials.

RESULTS AND CONCLUSIONS(I) Crack growth resistance (R) curves for sheet metals were determined using a

modified WOL type crack-line-loaded specimen.(2) Expe~men~l compliance calibration tests confo~ed to analytical and experi-mentai determinations reported in the literature for WOL type specimens.

(3) Stiff, displacement controlled loading was attained using a tapered wedge. Stablecracks were maintained throughout the test, from which complete R curves were devel-oped for several materials.

(4) Using sustained tension controlled loading. stable R curves were produced onlyup to the load instability stress intensity. Kc. This value was in agreement with Kccalculated as the point of tangency of the K driving force and the stable R curve ob-tained by wedge loading.(5) The wedge loading procedure involves measurement of visible crack length andcrack opening displacement by microscope at spaced increments of crack extension. Ris then calculated using the compliance relationship and an iterative procedure to correctthe crack length for the term &T(KlYS) .

(6) Loads calculated by the above procedure were consistent with testing machineindicated loads within limits of experimental error in the case of load controlled tests ofstainless steels. Inconsistently high measured loads were obtained in load controlledtests of 2024-T3, indicating plastic zone sizes much smaller than those obtained by othermeans. High work-hardening in the plastic zone may reduce the effective crack lengthin this material.

(7) Plastic zones defined by uniaxial 4 direction strain measurements along thecrack line were approximately equal to Irwins r, = ip(K/YS)?.(8) Progressive removal of plastically deformed metal along the crack line of testedspecimens tended to return the crack opening displacement to the unstressed value.These results were consistent with the plastic zone size determinations by strain gages.

(9) The WOL-2T specimen yields a sufficiently complete R curve in most of thematerials tested so that instability Kc can be predicted for a wide range of specimentypes. Corresponding curves for WOL-4T specimens are coincident over the range ofthe WOL-2T curves. but extend to higher crack lengths and R values. This suggeststhat the 2T specimen size yields valid results within its limits of calibration. However,further proof is needed that these R curves represent material properties. independentof specimen shape and size.

Correlations between WOL type and center cracked tension tests of wide panels,


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412 R. H. HEYER and D. E. MCCABEnow in progress, are expected to yield information on validity ofR curves for the crack-line loaded specimens.~cknowfedge~~n~s-The authors are deeply appreciative of the many suggestions and comments frommembers of the ASTM Committee E-24 during the course of this investigation, of the able assistance ofMr. D. M. Hammonds in the mechanical tests and Mr. R. A. Brown in test fixture and specimen oremuation,and of the support of this work by Armco Steel Corporation.

ltw%RJmcEsIll D. P. Clausing, Crack stability in linear etastic fracture mechanics. lnt. 1. Fr ucture Me& ., 2 I 1 1969).121 S. Mostovoy, P. B. Crosley and E. J. Rip@, Use of crack-tine-loaded specimens for measuring plane-strain fracture toughness. 1. Muter 2,66 t (1967).[3] S. R. Novak and S. T. Rolfe, Modified WOL specimen for Kl,cc environmental testing. Tech. Rep.,Project No. 89.018-026, May 3 1,1968. to be published.141 G. R. Irwin and J. A. Kies, Critical energy rate analysis of fracture strength, Welding Res. Suppl. 19,193 1954).@I G. R. Irwin, Fracture testing of hip-spend sheet materials under conditions appropriate for stressanalysis. Naval Res. Lab. Rep. No. 5486 ( 1960).[6] Report of a Special ASTM Committee, Fracture testing of high strength sheet materials. ASTM Bull.29(1969).[7] J. M. Krafft, A. M. Sullivan and R. W. Boyle, Effect of dimensions on fast fracture instability of notchedsheets. Froc. Crack Propagation Symp., Vol. 1, p. 8. College of Aeronautics, Cranfield, England ( 196 1).[8] J. E. Srawiey and W. F. Brown, Jr., Fracture toughness testing methods. ASTM STP No. 410, 133f 1966).[9J C. M. Carman, D. F. Armiento and H. Markus, Crack resistance properties of high strength a~u~nurnalloys, Int. Co&. Fructcrre, Sendai, Japan. (1965).[ 101 W. K. Wilson, Review of analysis and development of the WGL specimen. Westinghouse Res. Rep.67-707.BTLPV-RI (1967).[11] Ernest Roberts, Jr., Elastic crack-edge displacements for the compact tension specimen. Mat. Res.Stats 9,27 (I 969).[i2] G. T. Hahn, A. R. Rosenfieid, L. E. Hulbert and M. F. Kanninen, Elastic-plastic fracture mechanics.Tech. Rep. AFML-TR-67- 143, Part II. Battelle Memoriai Inst. Columbo, Ohio ( I9681.[ 131 D. S. Dugdate. Yiekiing of steel sheet containing slits. J. Me&. Phys. Solids 8,100 ( 1960).[ 141 A. S. Kobayashi, W. L. Engstrom and B. R. Simon, Crack-opening displacements and normal strains incentrally notched plates. Expi M ech. 9,163 ( 1969).[IS] J. C. Newman, Jr., Fracture of cracked plates under plane stress, Engng Fructure M ech. 1, 137 1968

[ 61 Royce G. Forman, Experimental program to determine effect of crack buckling and specimen dimensionson fracture toughness of thin sheet materials. AFFDL-TR-65-146 (1965).[ 171 W. F. Brown, Jr. and J. E. Srawley, Plane strain crack toughness testing of high strength, metatlic mater-i&s. ASTM STP4 10. p. I I ( 1966).(Received 5 November 197 1)

1972 r.h. heyer and d.e. mccabe - plane-stress fracture toughness testing using a crack-line-loaded...

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