The Effect of Dents on the Stable Crack Growth in 2024-T3 Bare SheetAluminum Alloy under Constant Amplitude Loading.

Bert L. Smith1, Praveen Shivalli2

Wichita State University, Wichita, Kansas 67260-0044

Brijesh Kumar3

Boeing Integrated Defense system, Wichita, Kansas 67277-7730

1Professor, Department of Aerospace Engineering. Senior Member AIAA2Graduate Research Assistant, Department of Mechanical Engineering

3Research Engineer, Boeing Integrated Defense Systems

Abstract

The purpose of this study was to determine the effect of dents on the stable crackgrowth in 0.04 inch thick 2024-T3 bare aluminum sheet. The test specimens were eitherpristine dented or reworked. The edge-cracked pin-loaded specimens of 8 inches inwidth were tested at constant amplitude loading with a stress ratio of 0.2 producing stablecrack growth of close to 4 inches completely through two dents on the crack line. Dentswere produced with a drop tower having a one inch spherical hardened steel indenterhead. Dent depths ranged from 0.03 inch to 0.0325 inch measured on the convex side ofthe specimen. A starter notch of 0.3 inch was produced at the edge of the specimen witha jewelers saw blade. The specimen was fatigue loaded under constant amplitude loadingto produce an initial crack length of 0.37 inch at which time readings of crack length vs.cycles began. The same constant amplitude cyclic loading used to produce the initialcrack length was used during the testing. The crack lengths were measured with anoptical microscope at 160X magnification. Nine specimens were tested including threereplications for each of the three conditions. Crack growth data is given in both tabularand graphical form for all specimens. Crack growth rate data is also presented ingraphical form. The overall crack growth in the dented specimens was significantlygreater than in the pristine specimens. It was also, on the average, faster in the reworkedspecimens; reworking, in general, did not recapture the life displayed by the pristinespecimens.

List of Symbols

a = crack lengthW = width of the speciment = thickness of specimenN = number of cyclesKImax = stress intensity factor at σmax

KImin = stress intensity factor at σmin

da/dN = crack growth rate∆KI = KImax - KImin = (1-R)KImax

R = σmin/σmax

6th AIAA Aviation Technology, Integration and Operations Conference (ATIO)25 - 27 September 2006, Wichita, Kansas

AIAA 2006-7728

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

σmax = maximum stress in a cycleσmin = minimum stress in a cycleβ = geometric correction for stress intensity factor.ai = current crack lengthai+4 = crack length 4 data points after ai

ai-4 = crack length 4 data points before ai

Ni = cycle count at ai crack lengthNi+4 = cycle count 4 data points after Ni

Ni-4 = cycle count 4 data points before Ni

Introduction

The primary choice of material for the surface (skin) of aircraft structure duringthe past 40 years has been 2024-T3 aluminum alloy, and is still the alloy of choice formost airframes today. Continued cyclic loading will cause cracks to initiate and to growin a stable manner until a critical crack length is reached, after which unstable crackextension will occur which may produce catastrophic results. There are many physicalparameters that may adversely affect the propagation of cracks. For example, one suchparameter is dents, which may be caused by a number of things such as flying runwaygravel, accidental tool drop, and hail. The designer must take into account any negativeaffects of these physical parameters to avoid unexpected catastrophic results.

The purpose of this project is to determine the effect of dents on the stable crackpropagation of 2024-T3 bare sheet material under constant amplitude cyclic loading.This is addressed by comparing the crack growth in specimens that have dents with thecrack growth in pristine specimens and in specimens with dents that have been reworked.

Although there is much data in the literature on physical and mechanicalproperties of metallic alloys that are used for airframe construction, little data is availableon the effect of dents. There are numerous parameters that influence dent resistance (1).The most important among these are the boundary conditions, the curvature and size ofthe panel, the location of the dent in the panel, and the source of the dent. Theparameters in the study presented herein were limited to a single configuration. An edge-cracked panel with two dents aligned on the crack line was selected so that the crackwould undergo stable crack extension while passing through both dents before becomingunstable. A single indenter diameter along with a single indenter mass, drop height andboundary condition were used to produce the dents. The objective was to determinewhether dents accelerated or retarded stable cracking and whether dents influenced thedirection of cracking, and also weather reworking of dents produced favorable results interms of crack growth rate.

Previous research (2) conducted on small edge-cracked specimens with singledents showed that overall crack growth was accelerated; however, in this study the stablecrack extension barely went through a single dent before unstable crack extensionoccurred. Reworking of the dents recaptured some of the life, but not necessarily to thelevel of the undamaged (pristine) specimens, and also the results from reworkedspecimens were not consistent. Three materials were used in the previous study (2):2024-T3, 7475-T7351 and 7050-T7451. The reworked specimens of 2024-T3 and 7475-T7351 showed little to no decrease in crack growth rate when compared with dented

specimens. However, the 7050-T7451 reworked specimens showed a noticeable decreasein the crack growth rate when compared with the dented specimens. In general, theresults from the 2024-T3 material are in good agreement with the results obtained fromthe work described herein. The results herein also left doubt about the helpfulness of thereworking process in recapturing the same characteristics as the pristine specimens.

Another study (3) concluded that there is also a considerable reduction in fatiguelife for the un-cracked dented specimens of 2024-T3 alclad aluminum alloy comparedwith the pristine specimens. However the static mechanical properties were notsignificantly different between the pristine, dented and reworked specimens. The resultsfrom static testing concluded that the dented and reworked specimens show a minorincrease in yield strength and ultimate tensile strength and a minor reduction in percentelongation. The interesting aspect of reduction in percent elongation was that thisproperty is considered a representation of the ductility of the material. Thus, a loss insome of the ductility of the material may represent a reduction in toughness or the abilityto resist crack growth after it has initiated.

The research described herein includes stable crack growth testing of 2024-T3bare aluminum alloy specimens having three different conditions: pristine, dented, andreworked. The edge cracked pin loaded specimens of 8 inches in width were tested atconstant amplitude loading so as to produce stable crack growth of close to 4 inchescompletely through two dents on the crack line before critical conditions were reached.The study clearly shows that the overall propagation of stable cracking in the dentedspecimens was significantly faster than in the pristine specimens. It was also faster, onthe average, in the reworked specimens; however, the crack propagation of the reworkedspecimens was not as consistent as it was for the pristine and dented specimens. Thecrack growth in the dented specimens was accelerated in comparison with the pristinespecimens until the crack tip came close to a dent, after which the propagation wasretarded until the tip of the crack grew completely through the dent, where the growthagain became accelerated. This may be due to cold working, geometric changes, and/orresidual stresses, but it is not clear which of these have the greatest effect. Previous work(3) has shown that residual tensile stresses will be induced due to the process of denting.Analysis of the results of the testing herein also show that the crack life of the dentedspecimens is about the same as the crack life of the pristine specimens if the amplitude ofthe cyclic loading on the pristine specimens is increased by about eight percent.However, this only applies to the specimen geometry and dent metrics used in this studyand may be different for other configurations.

Test Matrix

Fatigue crack growth tests were conducted with 2024-T3 bare aluminum alloyspecimens having three different conditions: pristine, dented, and reworked. The edgecracked pin loaded specimens were 8 inches wide and tested at constant amplitudeloading so as to produce stable crack growth of close to 4 inches before criticalconditions were reached. The pristine specimens had no dents. Each of the dentedspecimens had two dents produced with a drop tower. These dents were located alongthe crack line so that stable crack growth completely through both dents could berecorded before unstable cracking occurred. Details of the specimen geometry, the

denting procedure, and the procedure for reworking are provided later. The specimenswere bolted at their extremities to fixtures that were designed for pin loading, and theassembly was placed in the MTS servo-hydraulic testing machine for constant amplitudetesting.

The test matrix, which consists of three specimens for each condition (pristine,dented, and reworked) is shown in Table 1. The ratio of the minimum stress to themaximum stress of the constant amplitude cyclic loading was 0.2 (R = 0.2), and testingwas done at a frequency of 10 Hz.

Table 1: Test Matrix

Condition Material (thickness, in.) Form No. of Specimens

Pristine 2024-T3 (0.04) bare sheet 3Dented 2024-T3(0.04) bare plate 3

Reworked 2024-T3 (0.04) bare plate 3

Test Specimen

The material used for each specimen was 2024-T3 bare sheet with a thickness of0.04 inches. The specimens were machined to the dimension of 8" by 20" and were T-Lspecimens (fracture mechanics nomenclature), which means that the grain direction wasperpendicular to the load. Each specimen has two rows of fastener holes (15 holes).Each end of the specimen was sandwiched between two identical test fixtures (double lapsplice). A test specimen and the end fixtures are shown in Figure 1. The end fixtureswere machined from 0.25 inch thick aluminum plate. The specimen geometry is shownin Figure 2.

To avoid failure of the test specimens at the fastener holes, tabs were bonded toeach side of each specimen at both ends. The tabs were 3" by 8" with a thickness of 0.09inches. A starter crack (notch) of approximately 0.3 inches was produced at the edge ofeach specimen. The notch was produced by hand sawing with a jeweler's saw blade.

Figure 1. Specimen mounted to the end fixtures.

Figure 2. Specimen geometry and location of dents.

Crack Position of dents

Grain direction

1.25" 1"

8"

1/4" diameter holes, 1" pitch, both ends

8"

1/2"

3/4"

3/4"

Dents were produced with a drop tower consisting of a base with a fixture to holdthe specimen, guide shafts, a sled mounted to the guide shafts, and an indenter assemblyattached to the sled. Dents were created with a 1" diameter hardened steel indenter byclamping the specimen in the test fixture and dropping the sled and indenter assemblyfrom a predetermined height. This height was previously determined by using a dummyspecimen of the same material and varying the drop height until a dent of the desireddepth was produced. The edge crack was predicted to undergo stable crack growth untilit reached a length of approximately 4 inches. The two dents were spaced on thepredicted crack line within the four inch length so that the crack would undergo stablecrack extension completely through both dents. The dent depths ranged from 0.03 to0.0325 inches measured on the convex side of the specimen. The dents were producedwith a one inch diameter harden steel indenter. The specimen was clamped between twothick aluminum plates with a 2" by 2" window. The first dent was placed at 1.25" fromthe edge of the specimen, and the second dent was placed at 1" from the first dent (2.5"from the edge of the specimen). After the first dent was produced, the specimen wasshifted between the two clamped plates and rotated at 45 degrees so that the second dentcould be produced while the first dent was still within the 2" by 2" window.

Dent depths were measured on the convex surface of the dent with a digital depthgage. The specimen was placed on a granite table with a smooth hard surface. Equal 20lb weights (cylindrical in shape with 6" diameter) were placed on both sides of the dent toeliminate the slight curvature in the specimen from denting. The plunger of a digitaldepth gage was placed at the edge of the specimen nearest to the dents and the gage wasset to zero. The plunger was then placed at the crest of the dent and another reading wastaken and used as the dent depth. Dent depths measured with this method were veryconsistent, and the range of the dent depth for all the specimens was between 0.03” to0.0325”.

The objective of reworking was to attempt to return the condition of the dentedspecimen as closely as possible to the condition of the pristine specimen in a manner thatwould simulate the kind of working condition found in a repair depot. Reworking wasdone by striking the convex side of the dent with a carpenter's hammer. Several malletswith different striking materials were tried including dense rubber and plastic. However,these materials had no affect toward flattening the dent. Also, ball peen hammer headsseemed to do more damage than good since they produced more dimples because of thesmall radius of the striking head. The carpenter's hammer is made of steel, which provedto be far superior to rubber and plastic, and the striking surface of the carpenter's hammeris only slightly convex, which kept from making further severe dimples when the targetwas not exactly hit.

The specimen was placed on a solid granite table top and struck several timeswith a carpenter's hammer until the dent was sufficiently removed and no further changesin dent geometry were noticed. A plastic film was placed between the table and thespecimen to prevent scratching. A thin padded vinyl barrier was placed on top of thespecimen to prevent scratching from the hammer head. All denting was performed by thesame person for consistency.

Experimental Set-up and Testing

A 5-kip servo-hydraulic MTS testing machine was used for the crack growthtesting of the specimens. The hydraulic actuator was controlled with the MTS FlextestGT system. MTS Multi-Purpose Testware™ software was used for providing therequired loads for the specimens and for recording the data. A Hirox optical microscope(BH-1000 BGA) was used to monitor and record the crack growth data. The microscopehas a capability of 20X to 160X magnification and with a field of view of 15.4 ~ 2.0 mm.The setup of the specimen with the microscope is shown in Figure 3.

Figure 3. A specimen with optical microscope mounted in the testing machine.

The microscope was mounted on a mechanical traverse and wired to a videomonitor for viewing the crack tip. The scale on the mechanical traverse was used tomeasure and record crack length. Crack length was measured by aligning the tip of thecrack with the hairline mounted vertically at the center of the monitor and measuring theposition of the traverse. The highest magnification of the microscope (160X) was used toobtain the crack growth data.

Before mounting the specimen in the testing machine, one face of the specimenwas polished with Mother’s Aluminum Polish around the expected crack growth path.Polishing was done to remove the oxide layer on the specimen and make the crack moreclearly visible in the TV screen connected to the optical microscope. Both of the tabbedends of the specimen were then fastened to the end fixtures with nuts and bolts as shownin Figure 1. The specimen with the end fixtures was then mounted in the testing machine.

Fatigue testing of all the specimens was carried out at a cyclic frequency of 10Hz with a maximum load of 2000 lb (6,250 psi) and a minimum load of 400 lb (1,250psi). Crack growth data was recorded approximately every 0.04" increment in the cracklength and the corresponding value of the cycle count was recorded. The same cyclicloading that was used during the testing was used to pre-crack the specimen from theinitial saw cut notch length of 0.3" to the length of 0.37". The purpose of pre-cracking isto ensure that the crack growth data taken during the test corresponds to an actual crackrather than a man-made notch that would have different conditions at its tip (4). Thevalue of 6,250 psi for the maximum stress in the constant amplitude cyclic loading andthe 8-inch width for the test specimen were chosen so that the crack would grow in astable manner to about 4 inches before becoming unstable. This length would be longenough for the crack to grow completely through two dents. The dent spacing of one inchwas considered to be a reasonable minimum spacing for dents in aircraft skin.

Tabular Results

Tables 2, 3, and 4 provide the optical crack growth data for each of the threepristine, dented and reworked specimens respectively.

Table 2: Crack Growth Data for the Pristine SpecimensPristine Specimens: Cycles vs. Crack Length

Specimen #1 Specimen #2 Specimen #3Cycles (inch) (mm) Cycles (inch) (mm) Cycles (inch) (mm)

0 0.3701 9.4 0 0.3701 9.4 0 0.3701 9.443821 0.4331 11 9109 0.3898 9.9 24290 0.3976 10.172915 0.4724 12 46405 0.4252 10.8 49993 0.4331 1189848 0.4961 12.6 78268 0.4606 11.7 64956 0.4528 11.599158 0.5079 12.9 103604 0.4843 12.3 80038 0.4724 12128534 0.5551 14.1 125365 0.5197 13.2 108554 0.5118 13145143 0.5906 15 150308 0.5591 14.2 124321 0.5394 13.7164989 0.6299 16 172563 0.5984 15.2 187165 0.6614 16.8179220 0.6654 16.9 190338 0.6378 16.2 201549 0.7047 17.9196395 0.7087 18 203517 0.6732 17.1 213357 0.7362 18.7211480 0.7480 19 216116 0.7087 18 227813 0.7795 19.8225032 0.7874 20 220868 0.7205 18.3 237589 0.8071 20.5235845 0.8268 21 232115 0.7480 19 246422 0.8268 21245026 0.8661 22 243839 0.7874 20 258809 0.8661 22254430 0.9055 23 255820 0.8268 21 267801 0.9055 23264071 0.9449 24 264690 0.8622 21.9 277206 0.9449 24271736 0.9843 25 272323 0.8976 22.8 286035 0.9843 25279259 1.0236 26 285792 0.9449 24 293358 1.0236 26286482 1.0630 27 292577 0.9803 24.9 301223 1.0630 27

294389 1.1024 28 299767 1.0157 25.8 308596 1.1024 28302264 1.1417 29 305975 1.0472 26.6 314891 1.1417 29310923 1.1890 30.2 315013 1.1024 28 323232 1.1890 30.2316864 1.2205 31 321390 1.1417 29 328480 1.2205 31323297 1.2598 32 327130 1.1811 30 334522 1.2598 32328385 1.2992 33 332590 1.2244 31.1 341478 1.2992 33333610 1.3386 34 337661 1.2598 32 346989 1.3386 34339857 1.3780 35 342505 1.2992 33 350019 1.3701 34.8344154 1.4173 36 346986 1.3386 34 358953 1.4370 36.5349279 1.4567 37 351286 1.3740 34.9 362983 1.4646 37.2353206 1.4961 38 355604 1.4173 36 367524 1.5039 38.2356697 1.5354 39 359649 1.4567 37 371132 1.5433 39.2360865 1.5748 40 363282 1.4961 38 374746 1.5827 40.2364245 1.6181 41.1 367268 1.5354 39 380486 1.6614 42.2367005 1.6535 42 370742 1.5748 40 385493 1.7244 43.8370097 1.6929 43 374288 1.6142 41 389290 1.7795 45.2373037 1.7323 44 376301 1.6457 41.8 391169 1.8465 46.9375530 1.7717 45 380234 1.6929 43 394173 1.9094 48.5378191 1.8110 46 383521 1.7323 44 396091 1.9449 49.4381051 1.8504 47 386000 1.7717 45 397580 1.9843 50.4383507 1.8937 48.1 388487 1.8110 46 399028 2.0079 51385224 1.9331 49.1 390836 1.8543 47.1 400696 2.0472 52387269 1.9685 50 393020 1.8898 48 402511 2.0866 53389066 2.0079 51 395133 1.9291 49 404096 2.1339 54.2390917 2.0472 52 397223 1.9646 49.9 405355 2.1654 55392786 2.0866 53 399511 2.0039 50.9 406740 2.2047 56394967 2.1260 54 402741 2.0866 53 408103 2.2441 57396440 2.1654 55 405791 2.1575 54.8 409360 2.2835 58397997 2.2047 56 407427 2.1969 55.8 410461 2.3228 59399395 2.2441 57 408800 2.2362 56.8 411534 2.3622 60400601 2.2835 58 410133 2.2638 57.5 412441 2.4016 61402580 2.3622 60 411680 2.2992 58.4 413541 2.4409 62404645 2.4409 62 412762 2.3268 59.1 414288 2.4803 63406155 2.5197 64 414910 2.3976 60.9 415041 2.5197 64407479 2.5984 66 416855 2.4685 62.7 416066 2.5827 65.6408660 2.6772 68 418561 2.5236 64.1 416936 2.6378 67409543 2.7402 69.6 419841 2.5906 65.8 417377 2.6772 68410149 2.8110 71.4 421165 2.6575 67.5 417790 2.7165 69410672 2.8661 72.8 422247 2.7244 69.2 418121 2.7559 70410976 2.9252 74.3 423257 2.8031 71.2 418448 2.7953 71411257 2.9843 75.8 424081 2.8661 72.8 418807 2.8346 72411466 3.0591 77.7 424810 2.8858 73.3 419012 2.8740 73411698 3.1181 79.2 425230 3.0157 76.6 419378 2.9134 74411831 3.1890 81 425859 3.1693 80.5 419598 2.9528 75411961 3.2480 82.5 426138 3.1890 81 419817 2.9921 76412075 3.3031 83.9 426138 3.2087 81.5 419985 3.0315 77412176 3.3937 86.2 426432 3.3268 84.5 420082 3.0709 78412255 3.4843 88.5 420223 3.1102 79412326 3.6496 92.7 420325 3.1496 80

420406 3.1929 81.1420463 3.2283 82420587 3.3031 83.9

420692 3.3937 86.2420758 3.4606 87.9420807 3.5866 91.1

Table 3: Crack Growth Data for the Dented SpecimensDented Specimens: Cycles vs. Crack Length

Specimen #1 Specimen #2 Specimen #3Cycles (inch) (mm) Cycles (inch) (mm) Cycles (inch) (mm)

0 0.3701 9.4 0 0.3701 9.4 0 0.3701 9.413981 0.3937 10 33112 0.4094 10.4 24846 0.4094 10.442870 0.4370 11.1 59167 0.4488 11.4 61767 0.4724 1260392 0.4724 12 84563 0.4882 12.4 81918 0.5118 1385533 0.5236 13.3 98310 0.5276 13.4 95300 0.5512 1493374 0.5512 14 126325 0.5906 15 116147 0.6063 15.4115317 0.5906 15 140917 0.6299 16 123554 0.6299 16140245 0.6732 17.1 162647 0.6890 17.5 133577 0.6693 17149136 0.7087 18 182682 0.7480 19 145242 0.7087 18158848 0.7480 19 191669 0.7874 20 153309 0.7480 19167012 0.7874 20 199865 0.8268 21 164503 0.7874 20178016 0.8425 21.4 207977 0.8661 22 172267 0.8268 21185330 0.8819 22.4 214931 0.9055 23 183027 0.8661 22189630 0.9055 23 221659 0.9449 24 191768 0.9173 23.3196396 0.9449 24 228191 0.9843 25 196527 0.9449 24 203103 0.9843 25 232982 1.0236 26 202135 0.9843 25208920 1.0236 26 238211 1.0630 27 208550 1.0236 26214542 1.0630 27 242555 1.1024 28 213153 1.0630 27219868 1.1024 28 247677 1.1417 29 218847 1.1024 28224781 1.1457 29.1 251482 1.1811 30 222848 1.1417 29234333 1.2205 31 255447 1.2205 31 226074 1.1811 30239588 1.2598 32 259099 1.2598 32 230754 1.2205 31244947 1.2992 33 269099 1.3386 34 234006 1.2598 32251055 1.3386 34 273433 1.3780 35 237649 1.2992 33257605 1.3780 35 281345 1.4567 37 241647 1.3386 34264443 1.4173 36 286736 1.4961 38 246819 1.3780 35271149 1.4567 37 291161 1.5354 39 253203 1.4173 36277156 1.4961 38 295550 1.5748 40 258030 1.4567 37283383 1.5354 39 299640 1.6142 41 263923 1.4961 38288552 1.5748 40 302683 1.6535 42 268120 1.5354 39292849 1.6142 41 306984 1.6929 43 275169 1.5748 40297066 1.6535 42 309329 1.7323 44 278992 1.6142 41300389 1.6929 43 311255 1.7598 44.7 283113 1.6535 42302953 1.7323 44 314479 1.8110 46 286374 1.6929 43305800 1.7717 45 315995 1.8504 47 289696 1.7323 44308256 1.8110 46 318903 1.9291 49 292060 1.7717 45310450 1.8504 47 321745 1.9921 50.6 295225 1.8110 46312694 1.8898 48 323581 2.0472 52 297160 1.8504 47314784 1.9291 49 324850 2.0866 53 299465 1.8898 48317214 1.9685 50 326336 2.1260 54 301039 1.9291 49320024 2.0079 51 327408 2.1654 55 302998 1.9685 50322411 2.0472 52 328833 2.2047 56 304277 2.0079 51324964 2.0866 53 330053 2.2441 57 306093 2.0472 52

327095 2.1260 54 337128 2.4213 61.5 307219 2.0866 53329843 2.1654 55 338904 2.4882 63.2 308807 2.1260 54332916 2.2047 56 340137 2.5197 64 310022 2.1654 55335897 2.2441 57 340881 2.5591 65 311701 2.2047 56338983 2.2835 58 341651 2.5984 66 313211 2.2441 57341503 2.3228 59 342114 2.6378 67 314937 2.2835 58344844 2.3622 60 342633 2.6772 68 316705 2.3228 59347792 2.4016 61 342885 2.7165 69 318945 2.3622 60349920 2.4409 62 343269 2.7559 70 320433 2.4016 61351828 2.4803 63 343486 2.7953 71 322454 2.4409 62354043 2.5197 64 343746 2.8346 72 323271 2.4764 62.9356377 2.5591 65 343937 2.8740 73 324752 2.5197 64358548 2.6063 66.2 344169 2.9134 74 325535 2.5591 65359856 2.6378 67 344284 2.9528 75 326798 2.5984 66361159 2.6772 68 344431 2.9921 76 327507 2.6378 67362185 2.7165 69 344528 3.0315 77 328495 2.6772 68363128 2.7559 70 344671 3.0709 78 328925 2.7165 69363923 2.7953 71 344736 3.1102 79 329446 2.7559 70364604 2.8346 72 344867 3.1496 80 329749 2.7953 71364942 2.8740 73 344913 3.1890 81 330254 2.8346 72365304 2.9173 74.1 345012 3.2677 83 330499 2.8740 73365707 2.9528 75 345154 3.3465 85 331106 2.9528 75366027 2.9921 76 345220 3.4252 87 331340 2.9921 76366311 3.0433 77.3 345276 3.5433 90 331498 3.0118 76.5366462 3.0748 78.1 345329 3.7283 94.7 331687 3.1024 78.8366670 3.1102 79 331866 3.1496 80366495 3.1496 80 331962 3.1890 81366944 3.1890 81 332168 3.2677 83367070 3.2283 82 332323 3.3976 86.3367129 3.2677 83 332396 3.5039 89367217 3.3071 84 332443 3.6181 91.9367284 3.3465 85 332479 3.8740 98.4367348 3.3976 86.3367408 3.4606 87.9367467 3.5630 90.5367509 3.6457 92.6367541 3.8268 97.2

Table 4: Crack Growth Data for the Reworked SpecimensReworked Specimens: Cycles vs. Crack Length

Specimen #1 Specimen #2 Specimen #4Cycles (inch) (mm) Cycles (inch) (mm) Cycles (inch) (mm)

0 0.3701 9.4 0 0.3701 9.4 0 0.3701 9.416436 0.4331 11 22533 0.4094 10.4 17299 0.3937 1030214 0.4724 12 41201 0.4488 11.4 37562 0.4331 1152277 0.5512 14 56715 0.4882 12.4 63494 0.4803 12.262322 0.5906 15 77881 0.5276 13.4 83622 0.5394 13.769661 0.6299 16 94726 0.5669 14.4 100353 0.5906 1578516 0.6693 17 104112 0.6063 15.4 112146 0.6417 16.385156 0.7087 18 113865 0.6457 16.4 120202 0.6693 1791788 0.7480 19 126439 0.6850 17.4 127842 0.7087 18

97727 0.7874 20 133786 0.7087 18 135493 0.7480 19103979 0.8268 21 140990 0.7480 19 147631 0.8031 20.4110844 0.8661 22 147631 0.7874 20 162481 0.8268 21119064 0.9055 23 154550 0.8268 21 193793 0.8898 22.6127684 0.9449 24 162546 0.8661 22 217464 0.9488 24.1139354 0.9843 25 167617 0.9055 23 223607 0.9843 25146898 1.0118 25.7 173733 0.9449 24 235318 1.0512 26.7157487 1.0630 27 178465 0.9843 25 240030 1.0906 27.7169535 1.1339 28.8 184496 1.0236 26 244884 1.1299 28.7180303 1.1929 30.3 189234 1.0591 26.9 251087 1.1693 29.7207856 1.2598 32 193887 1.0984 27.9 261181 1.2087 30.7213504 1.2992 33 197505 1.1378 28.9 266026 1.2480 31.7239510 1.3386 34 202460 1.1457 29.1 284660 1.2874 32.7255714 1.4134 35.9 206626 1.1850 30.1 298797 1.3268 33.7261522 1.4567 37 215575 1.2362 31.4 310009 1.3661 34.7268233 1.4961 38 219877 1.2598 32 320101 1.4055 35.7271906 1.5354 39 241736 1.2992 33 324803 1.4449 36.7275693 1.5748 40 255509 1.3386 34 332887 1.4843 37.7278056 1.6142 41 277348 1.3780 35 336826 1.5236 38.7281072 1.6535 42 302346 1.4370 36.5 341573 1.5630 39.7282818 1.6929 43 309148 1.4567 37 345311 1.6024 40.7285068 1.7323 44 318122 1.4961 38 348756 1.6417 41.7286597 1.7717 45 330212 1.5591 39.6 351889 1.6811 42.7289272 1.8110 46 332485 1.5748 40 354295 1.7205 43.7291008 1.8504 47 336483 1.6142 41 357452 1.7598 44.7293769 1.8898 48 340731 1.6535 42 359836 1.7992 45.7296120 1.9291 49 343864 1.6929 43 362534 1.8386 46.7300114 1.9685 50 346914 1.7323 44 365575 1.8819 47.8302850 2.0079 51 349142 1.7717 45 368158 1.9252 48.9306416 2.0472 52 351232 1.8110 46 369107 1.9567 49.7309438 2.0866 53 353265 1.8504 47 371495 1.9961 50.7314436 2.1260 54 355441 1.8898 48 373988 2.0354 51.7319341 2.1850 55.5 357199 1.9291 49 378246 2.0748 52.7322331 2.2047 56 358986 1.9685 50 381671 2.1142 53.7326027 2.2441 57 360232 2.0079 51 386549 2.1535 54.7329577 2.2835 58 361434 2.0472 52 391541 2.1929 55.7332963 2.3228 59 362401 2.0866 53 395854 2.2323 56.7336742 2.3622 60 363793 2.1260 54 398769 2.2717 57.7339280 2.4016 61 364985 2.1654 55 401475 2.3110 58.7342271 2.4409 62 366613 2.2047 56 404171 2.3504 59.7343853 2.4803 63 368266 2.2441 57 407200 2.3898 60.7345461 2.5197 64 370041 2.2835 58 407200 2.4291 61.7346704 2.5591 65 371914 2.3228 59 408957 2.4685 62.7347962 2.5984 66 374523 2.3622 60 410528 2.5079 63.7348993 2.6378 67 376857 2.4016 61 412447 2.5472 64.7349918 2.6575 67.5 379538 2.4409 62 413756 2.5866 65.7350496 2.6969 68.5 381190 2.4803 63 414896 2.6260 66.7351445 2.7165 69 382434 2.5197 64 415898 2.6654 67.7352052 2.7559 70 383295 2.5591 65 416669 2.7047 68.7352438 2.8189 71.6 384053 2.5984 66 417138 2.7441 69.7353335 2.8740 73 384635 2.6378 67 417623 2.7835 70.7353627 2.9134 74 385284 2.6772 68 417939 2.8228 71.7353920 2.9528 75 385687 2.7165 69 418228 2.8622 72.7

354117 2.9921 76 386117 2.7559 70 418421 2.9016 73.7354450 3.0315 77 386435 2.7953 71 418675 2.9409 74.7354703 3.0709 78 386739 2.8346 72 418896 2.9803 75.7355164 3.1496 80 386995 2.8740 73 419063 3.0197 76.7355545 3.2283 82 387272 2.9134 74 419319 3.0984 78.7355860 3.3071 84 387471 2.9528 75 419549 3.1378 79.7356145 3.3858 86 387708 2.9921 76 419713 3.2205 81.8356332 3.4646 88 387844 3.0315 77 419831 3.2992 83.8356493 3.5433 90 387986 3.0748 78.1 419952 3.3819 85.9356571 3.6220 92 388097 3.1102 79 420041 3.5000 88.9356620 3.7402 95 388208 3.1496 80 420090 3.6142 91.8356670 3.8189 97 388310 3.1890 81

388458 3.2677 83388574 3.3465 85388665 3.4252 87388714 3.5472 90.1388754 3.6811 93.5388775 3.7677 95.7388791 3.9370 100

Graphic Results from Crack Growth Testing

The following plots provide a graphic representation of crack length versus cyclesfor each of the three conditions (pristine, dented, and reworked). Figure 4 shows theresults for the three pristine specimens. The data is very consistent from specimen tospecimen, as the three curves are bunched very close together. Figure 5 shows the resultsfor the dented specimens. The results for the three dented specimens are consistent, butnot as consistent as the pristine specimens. Figure 6 shows the results for the reworkedspecimens. The results for the three reworked specimens are not nearly as consistent asthe pristine and dented specimens, because of the reworking procedure. The life of thedented specimens is considerably shortened when compared with the pristine specimens.The life of the reworked specimens is also shortened, but not quite as much as the dentedspecimens. A better comparison of the three conditions is provided in Figures 7 and 8,where the results for the different conditions are plotted on the same set of axes.

Figure 5. Crack Length vs Cycles (DentedSpecimens)

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Figure 4. Crack Length vs Cycles (Pristine Specimens)

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Comparisons between Pristine, Dented, and Reworked Conditions

A comparison of the crack length versus number of cycles data between thepristine and dented conditions and between the pristine and reworked conditions is shownin Figures 7 and 8 respectively. Figure 7, which is a plot of both the pristine and dentedconditions, shows that there is a significant reduction in crack life for the specimens withdents compared with the pristine specimens. Figure 8 shows the results from the pristinespecimens, as well as the reworked specimens. The reworking helped, but did not, on theaverage, restore the fatigue life to that of the pristine specimens.

Figure 6. Crack Length vs. Cycles (ReworkedSpecimens)

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Figure 7. Crack Length vs Cycles (Pristine andDented Specimens)

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Figure 8. Crack Length vs Cycles (Pristine andReworked Specimens)

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Crack Growth Rate da/dN vs. Kmax:

Damage tolerance assessment requires a data base of growth rate information forthe various materials used. Growth rate information is often expressed as the crackgrowth rate (da/dN) versus the maximum stress intensity factor (KImax) or change in stressintensity factor (∆KI ) for a given constant amplitude cyclic loading. The following plots(Figures 9, 10 and 11) provide a graphic representation of da/dN vs. KImax for each of thethree conditions (pristine, dented and reworked) and for each of the three replications foreach condition. These plots are always given on log-log paper, since the data tends to belinear in the mid-range region. Figure 9 has the crack growth rate plots for the threereplications of the pristine condition. Figures 10 and 11 have the same data for thedented and reworked conditions respectively. The KImax and da/dN values for thespecimens are determined as follows:

KImax = σmax (π a) 0.5 β

β = 1.122-0.231(a/w) +10.550(a/w) 2-21.71(a/w) 3 +30.82(a/w) 4

σmax = maximum stress in the constant amplitude cyclic loading

∆KI = (1-R)KImax R = σmin/σmax = 0.2

σmin = minimum stress in the constant amplitude cyclic loadinig

da/dN = slope of the crack length vs. cycles curve, (ai+4-ai-4)/ (Ni+4-Ni-4)

The slope da/dN was also determined from (ai+3-ai-3)/ (Ni+3-Ni-3) as well as (ai+5-ai-5)/ (Ni+5-Ni-5); however, they produced results that were almost identical to the slopedetermined from (ai+4-ai-4)/ (Ni+4-Ni-4). Tables giving the values of KImax and ∆KI foreach of the three pristine, dented and reworked specimens are not included herein.Although da/dN vs. KImax is considered a material property (independent of structuralgeometry), there is considerable difference between the crack growth rate curves forpristine, dented and reworked specimens of same material. Growth rate information isnormally presented for pristine material. It is shown here for the dented and reworkedspecimens, as well as the pristine specimens, to attain a better understanding of thedifferences between these three conditions.

Figure 9. da/dN vs Kmax for Pristine Specimens

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Figure 10. da/dN vs Kmax for Dented Specimens

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The overall crack growth rate for the dented specimens is faster than the pristinespecimens, however, there are some interesting observations that can be made by carefulinspection of the crack length versus cycles plots for the dented specimens (Figure 5).Crack growth in the dented specimens is faster than in the pristine specimens until thecrack gets near the first dent. When the crack tip is near the first dent the growth isslowed until the crack passes through the first dent, after which the growth is againaccelerated until the tip gets near the second dent. The growth is again slowed until thetip passes through the second dent, when, again it is accelerated.

Figure 11. da/dN vs Kmax all Reworked Specimens

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A Further Comparison between Pristine and Dented Specimens.

An additional comparison can be made between the pristine specimens and thedented specimens that shows the crack growth in the dented specimens under constantamplitude cyclic loading is approximately equal to the crack growth in the pristinespecimens if the magnitude of the cyclic loading for the pristine specimens is increasedby about 8%.

The crack growth in one of the pristine specimens (specimen #1) was simulatedwith the software Air Force Grow, known as AFGROW (5) as follows: The softwareAFGROW provides growth rate information da/dN vs. ∆KI in the form of an equation ifthe constants are known for the particular material being used. The software also allowsfor growth rate to be input in tabulated form. The da/dN vs. ∆KI data for specimen #1was input into AFGROW, and a crack was grown analytically cycle-by-cycle with theconstant amplitude cyclic loading used to generate the experimental data (σmax = 6.25 ksiand σmin = 1.25 ksi). When compared with the crack length vs. cycles experimental data,the analytically determined results matched favorably, as they should; the crack length vs.cycles curve grown with the use of AFGROW for the pristine specimen #1 is comparedwith the experimental results for pristine specimen #1 in Figure 12.

The maximum and minimum stresses were adjusted (keeping their ratio constantat R = 0.2) until the analytical curve produced by AFGROW matched the experimentaldata from the dented specimens as well as could be. Figure 13 shows the analyticalresults for the pristine specimen with an 8% increase in stresses compares favorably withthe experimental results for the three dented specimens. That is, for the specimengeometry and dent metrics used in this study, it can be concluded that the pristinespecimen with an 8% increase in remote stress will produce crack growth about the sameas a dented specimen. Similar results may be shown by using pristine specimen #2 or #3.

Figure 12. Crack Length vs Cycles (Pristine Specimens)

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Specimen #1 (AFGROW) Specimen #1 (Experimental)

Discussion of Results and Recommendations

An investigation of the stable crack propagation in 2024-T3 aluminum alloyspecimens under three conditions (pristine, dented, and reworked) was made. An 8 inchwide 0.04 inch thick edge-cracked specimen with multiple dents along the crack line wasused. Constant amplitude cyclic loading was used with a maximum stress of 6,250 psiand a minimum stress of 1,250 psi (stress ratio of 0.2). The initial crack length wasapproximately 0.37 inches. Two dents were placed along the crack line 1.25 inches and2.25 inches from the edge of the specimen. Crack length vs. cycles was recorded withthe use of an optical microscope (160X). Stable crack propagation was observed to takeplace on a line perpendicular to the load and through both dents before failure occurred.The overall crack propagation in the dented specimens was significantly faster than in thepristine specimens. It was also faster in the reworked specimens; however, the crackpropagation in the reworked specimens was not as consistent as the pristine and dentedspecimens. The crack growth in the dented specimens was accelerated, as compared withthe pristine specimens, until the crack tip came close to a dent, after which thepropagation was retarded until the tip of the crack grew completely through the dent,where the growth again became accelerated.

The data was also displayed in the form of da/dN vs. KImax. The growth rate forthe pristine specimens displayed the classical "almost" linear pattern on log-log paper.However, when the data for the dented and reworked specimens was displayed in this

Figure 13. Crack Length vs Cycles (Dented Specimens)

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Dented #1 AFGROW (1.08%)

manner, the pattern was highly non-linear. It is clear from this study that denting causescracks to grow faster, and the type of reworking done resulted in little or no help inregaining the characteristics of the pristine condition. The denting procedure producedcold working, geometric changes, and residual stresses, and it is not clear which of thesehas the greatest effect.

A comparison was made between the crack growth for the dented specimens(under the cyclic loading of σmax = 6.25 ksi and σmin = 1.25 ksi) and the crack growth forthe pristine specimens with increased remote stresses. It was determined that, for thespecimen geometry and dent metrics used in this study, a pristine specimen with itsremote stress increased by about 8% resulted in similar crack growth to the dentedspecimens. The crack growth for the pristine specimen was simulated with theAFGROW software based on experimental da/dN vs. ∆KI data from pristine specimen#1. This software was used to produce crack growth curves with increasing values ofremote stress until a curve was produced that most closely matched the experimental datafor the dented specimens.

The data presented herein is limited. Only one material was used. All specimenswere tested under the same cyclic loading stresses. Only one dent depth and one indenterdiameter was used. The population of data needs to be expanded to include differentstress levels, different dent depths and different indenter diameters (or configurations).Advanced methods of reworking such as rotary-peening and shot-peening should be usedand the results compared with the reworking method used here. In order to use theresults for purposes of damage tolerance calculations, either the growth rate curves mustbe altered or the analytical models should incorporate the residual stresses caused by thedenting. Growth rate curves represent material properties, independent of structuralgeometry, therefore, the second of the afore-mentioned approaches is the most promisingapproach to take. For example, the crack propagation software Air Force Grow(AFGROW) allows for the inclusion of residual stresses.

Reference:

1. Ekstrand, G.,and Asnafi, N., "Testing of the Stiffness and the Dent Resistance ofAutobody Panels", Materials and Design 19, pp.145-156, Elsevier Science Publishers,1998.2. Smith, B. L., and Jacob, K., "The Effect of Dents on Crack Growth of 2024-T3, 7475-T7351, and 7050-T7451 Aluminum Alloys" NIS Project 05-013, National Institute for 3.Aviation research, Wichita State University, July 2005.3. Simmons, F., Veciana, J., and Wallace, J., "Effects of Dent Removal on the DesignProperties of Fuselage Skin Material," 41st IAA/ASME/AHS/ASC Structures, StructuralDynamics, and Materials Conference, AIAA 2000-1467.4. ASTM-E-647, "Standard Test Method for Measurement of Fatigue Crack GrowthRates", 2000.5. Harter, J. A., AFGROW for Windows 2k/XP, Version 4.0009.12, Air Force ResearchLaboratory, Wright Patterson Air force Base, OH, June 2004