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Fatigue and crack-growth analyses of riveted lap-joints in a retired aircraft
Accepted Manuscript Fatigue and Crack-Growth Analyses of Riveted Lap-Joints in a Retired Aircraft J.C. Newman Jr., R. Ramakrishnan PII: DOI: Reference:
S0142-1123(15)00126-7 http://dx.doi.org/10.1016/j.ijfatigue.2015.04.010 JIJF 3575
To appear in:
International Journal of Fatigue
Received Date: Accepted Date:
21 October 2014 26 April 2015
Please cite this article as: Newman, J.C. Jr., Ramakrishnan, R., Fatigue and Crack-Growth Analyses of Riveted LapJoints in a Retired Aircraft, International Journal of Fatigue (2015), doi: http://dx.doi.org/10.1016/j.ijfatigue. 2015.04.010
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Fatigue and Crack-Growth Analyses of Riveted Lap-Joints in a Retired Aircraft J. C. Newman, Jr.1,a, R. Ramakrishnan2 1
Department of Aerospace Engineering, Mississippi State University, MS, USA 39762 2
a
Delta Air Lines Inc., Atlanta, GA, USA 30320
Corresponding author: [email protected]
ABSTRACT For aluminum alloys, research has shown that fatigue behavior of notched and unnotched specimens can be characterized by fatigue-crack growth from micro-structural features, such as inclusion-particle sizes. A crack-growth model using small- and large-crack data was used to calculate fatigue lives and crack growth in lap-joints in laboratory specimens. The tightness of the rivets dictated the type of crack configurations that occurred in the joint and equivalent initial flaw sizes (EIFS) were selected to fit the fatigue test data. These crack configurations and EIFS values were then used to predict fatigue lives in fuselage lap-joints in a retired passenger aircraft and for curved panels cut from the retired aircraft. The paper demonstrates that fuselage lap-joint fatigue-life-prediction methods based on fatigue-crack growth alone (i.e., with accounting for any time spent in crack nucleation) are very adequate to model the lifetimes in fuselage riveted lap joints. KEYWORDS: Aircraft, fatigue, cracks, riveted lap joints, aluminum alloy NOMENCLATURE a
Crack depth in thickness (B) direction, mm
ai
Initial flaw or crack depth in B-direction, mm
B
Specimen thickness, mm
Ci
Coefficients in multi-linear crack-growth equation (i = 1 to m)
c
Crack half-length in width (W) direction, mm
ci
Initial flaw or crack half-length in W-direction, mm
D
Rivet-hole diameter, mm
F
Boundary-correction factor
K
Stress-intensity factor, MPa√m
Ko
Crack-opening stress-intensity factor, MPa√m
Li
Riveted joint load factors
M
Bending moment, Nm
N
Number of cycles
Nf
Number of cycles to failure
1
ni
Powers in multi-linear crack-growth equation (i = 1 to m)
P
Rivet force, N
R
Stress ratio (Smin /Smax)
r
Hole radius, mm
S
Remote applied stress, MPa
Sb
Fastener by-pass stress, MPa
SB
Outer-fiber bending stress, MPa
Sp
Fastener bearing stress, MPa
Smax
Maximum applied stress, MPa
Smin
Minimum applied stress, MPa
W
Specimen half-width, mm
wr
Rivet spacing, mm
α
Constraint factor
γ
Bending factor
∆
Interference, µm
∆K
Stress-intensity factor range, MPa√m
∆Keff
Effective stress-intensity factor range, MPa√m
(∆Keff)T Effective stress-intensity factor range at flat-to-slant transition, MPa√m λ
Biaxial loading factor
σo
Flow stress (average of σys and σu), MPa
σys
Yield stress (0.2 percent offset), MPa
σu
Ultimate tensile strength, MPa
1.0 INTRODUCTION The Federal Aviation Administration (FAA) and Delta Air Lines [1-6] had teamed to conduct a destructive evaluation of a retired narrow-body passenger aircraft that had nearly 60,000 revenue service flights (one design service goal). Some objectives of the program were to characterize the state of multiplesite damage (MSD) at riveted fastener holes in the fuselage of an aircraft at the design service goal; and to develop or verify analysis methods that can correlate and predict the state of MSD at any point in time. For the retired aircraft, observations from the destructive examination of the fuselage joints indicated that one side of the aircraft appeared to have tight (within specifications) rivets with no detectable cracks present, whereas on the other side of the aircraft the rivets appear to have under-driven rivets with a large number of
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cracks present [5, 6]. For these cracks, faying surface origins were predominant, despite a majority of rivets being under driven. A large number of cracks have been examined with a scanning-electron-microscope (SEM) to count striations and to back-track the cracking history to reconstruct the crack length against flight cycle behavior [4]. The measured crack length against flight cycle results tended to fall within a fairly narrow band considering the complexity of real aircraft structural joints under actual operational loads and service environments. Several curved fuselage panels were cut from the other side of the fuselage and two panels with lap joints that had tight, correctly driven rivets were tested using the Full-scale Aircraft Structural Test Evaluation and Research facility (FASTER) at the FAA William J. Hughes Technical Center, Atlantic City, NJ. The FASTER facility uses a pressure box to fatigue test large fuselage panel by cyclic hydraulic loading. Prior to testing, both panels were verified to be crack free to the extent detectable by high frequency eddy current non-destructive test methods. These pressure box tests extended the fatigue cycles already experienced by these two panels during aircraft revenue service of 59,497 cycles, and added 43,500 cycles in one case and 120,000 cycles in another case. Both extended fatigue tests showed that these two panels with the very tight joints were extremely durable with no cracks formed at the end of the extended test cycles. These widely differing fatigue lives in the relatively loose joints with the under driven rivets versus the tight joints with the correctly driven rivets, had to be modeled and shown to be amenable for analyses in consistent manner. Some of the first approaches to improve the calculation of fatigue lives of riveted lap-joints were made in the mid-1960’s [7, 8].
These approaches were based on stress-life (S-N) behavior and the
calculation of local stress concentrations due to rivet loading, by-pass loading, and local bending. The effects of hole preparation (drilling, reaming, or cold-working) and of hole filling (rivets, bolts, or interference-fit fasteners) were accounted for by using either empirical factors derived from fatigue tests [8] or, more recently, on the use of “reference” S-N curves [9] from fatigue tests conducted on joints made with the particular manufacturing process of interest. The fracture-mechanics approach, used herein, is based on similar reasoning but calculates stressintensity factors and crack-opening stresses for small cracks under rivet loading, by-pass loading, and local bending. Effects of hole preparation are accounted for by selection of an “equivalent initial flaw size (EIFS)”; and the effects of hole filling on the selection of an “effective” level of interference to account for riveting interference, clamp-up, and frictional effects. The selection of an EIFS also indirectly accounts for any nucleation cycles.
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During the last two decades, research on small-crack behavior [10] and analysis methods [11], especially for aluminum alloys, have shown that the entire fatigue process can be effectively modeled as “crack propagation” from a micro-structural discontinuity in the material (e.g., precipitate particles). Thus, for the lap-joint configuration, an initial flaw size exists that will characterize the material or manufacturing quality.
The analysis methodology to predict crack growth from the micro-scale has been based on
traditional fracture-mechanics and crack-closure concepts. (Small-crack theory is the use of small-crack data accounting for micro-structural effects on crack growth in the low-rate regime and using a closure model to capture the transient closure effects as a small crack grows and develops a plastic wake.) Herein, these principles will be applied to the lap-joint configuration using some of the results obtained from the two- and three-dimensional analyses of the NLR lap-joint specimen [12]. Stress-intensity factors for small corner and through cracks growing under rivet loading, by-pass loading, and local bending have been developed [12]. The crack-closure model [13] will be used to calculate crack-opening stresses for a crack growing from an open hole, but using the stress-intensity factors for the lap-joint specimen. The rivet liftoff stress (applied stress required to separate the rivet from the fastener hole) will be used to account for rivet contact at the minimum load. (Ideally, a closure model should be developed to model the rivet in the hole and account for interference and contact analytically, but this is beyond the scope of the present paper.) Effects of hole preparation (e.g., tool marks or burrs) are accounted for by the selection of an EIFS; and the effects of hole filling on the selection of an “effective” level of interference to account for riveting interference, clamp-up, and frictional effects. The objective of this paper is to use FASTRAN [13] and small-crack theory to calculate fatigue lives and crack growth in laboratory lap-joint specimens made of 2024-T3 clad aluminum alloy. Tightness of the rivets led to different crack configurations (corner cracks at the rivet hole or surface cracks along the fraying surface) and different EIFS values. Two types of laboratory specimens were analyzed: (1) three-rivet-row countersunk specimens and (2) two-rivet-row countersunk specimens with a doubler.
Several rivet
conditions were considered: (1) standard-driven rivets, (2) tight or over-driven rivets, and (3) under-driven rivets. The appropriate crack configuration and the EIFS values were then used to calculate crack growth in the retired aircraft and curved fuselage test panels cut from the aircraft and tested in the FASTER Test Facility at the FAA William J. Hughes Technical Center [14]. Comparisons are made between AFGROW [15] and FASTRAN for crack growth in the retired aircraft and the reconstructed crack-length-against-flightpressure-cycle history. Fatigue life and crack-growth behavior are also predicted on the curved fuselage test panels and compared with test results.
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2.0 STRESS ANALYSIS OF CRACKS AT RIVET-LOADED FASTENER HOLES Stress-intensity factors for a corner crack or a through crack emanating from a typical fastenerloaded hole under remote applied stress (S = Sp + Sb), remote outer-fiber bending stress (SB) due to bending moment (M), by-pass stress (Sb), fastener load (Sp = P/(wrB)), where wr is rivet spacing and B is sheet thickness), and interference (∆), as shown in Figure 1, are given in Reference 12. The influence of biaxial loading (λSb) on stress-intensity factors for cracks emanating from the fastener hole are given in the Appendix. One of the restrictions for the corner-crack equations is that the crack aspect ratio, a/c, is fixed, and the influence of rivet interference is based on a simple approximation [12]. Stress-intensity factor equations for a surface crack in a plate under remote tension (St) and bending (SB) stresses are given in Reference 16. To calculate the growth of a corner crack initiating at a critically-loaded rivet hole in a lap-joint (see Fig. 1), the stress-intensity factors for rivet loading (Sp), by-pass loading (Sb), local bending (M or σb), and interference (∆) must be obtained and added as K = Kp + Kb + KM + K∆
(1)
Herein, to calculate the maximum stress-intensity factor, Kmax, it was assumed that the maximum applied loading is such that the rivet will not be in contact, that is, the applied stress will be greater than the rivet liftoff stress, SLO. Thus, at maximum load it was assumed, for simplicity, that K∆ = 0. The influence of the rivet being in the hole, however, is reflected in the calculation of the other values of stress-intensity factor due to the radial pressure distribution. Therefore, the stress-intensity factor in terms of applied stress is K = Sp √(πc) Fp + Sb √(πc) Gb Fλn + σb √(πc) Hb
(2)
Expressing equation (2) in terms of the total remote stress S with the bending stress expressed as
σb = kb S
gives K = S √(πc) [ Lp Lf Fp + Lb (1 – Lf) Gb Fλn + kb Hb ] = S √(πc) F
(3)
where Lp is the load factor (Sp/S) for the critical rivet (crack location), Lb is the load factor (Sb/S) for the bypass loading, Lf is the rivet-load factor, and kb is the Hartman-Schijve bending factor [17]. The term Fλn is the correction factor for bi-axial loading and the equation is given in the Appendix. Reference 12 gives the equations for the boundary-correction factors Fp, Gb, and Hb, for rivet load, by-pass load and bending, respectively. Thus, F is the boundary-correction factor for a through crack at a rivet-loaded hole in the lap joint. To convert equation (3) to a corner crack at the edge of the rivet-loaded hole, F is multiplied by the corner-crack-to-through-crack (Kcc/Ktc) ratio [12] as:
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Kcc/Ktc = 0.8 + 0.2 a/B – 0.2 (1 – a/B) (a/c) – 0.05 (1 – a/B)15
(4)
Equation (4) is very accurate for small a/B ratios and the Kcc/Ktc ratio approaches unity as the corner crack becomes a through crack (a/B = 1). 3.0 MATERIAL CRACK GROWTH PROPERTIES The material used in the laboratory lap-joint specimens and the retired fuselage structure was 2024T3 thin-sheet (B = 1 mm) clad aluminum alloy. Surprisingly, fatigue-crack-growth-rate data for the 1-mm thick sheet could not be found in the literature. But crack-growth-rate data on a 2-mm thick clad aluminum alloy were obtained from Schijve et.al. [18]. The yield stress (σys) was 360 MPa, ultimate tensile strength (σu) was 490 MPa and the flow stress (σo) was 425 MPa. These data covered a wide range in stress ratios (R = -0.1 to 0.73). Previously, Newman [19] developed steady-state crack-opening stress equations from the FASTRAN crack-closure model for middle-crack tension, M(T), specimens subjected to constant-amplitude loading at various stress levels (S max/σo ), stress ratios (R), and constraint factor (α). These equations were then used to develop the effective-stress-intensity-factor-range-against-rate relation for the clad alloy, as shown in Figure 2. The symbols show the test data for the various stress ratio tests. The data correlated very well with the same constraint factors that had been used for the bare material [20] with B = 2.3 mm. The crack transitions from flat-to-slant crack growth (assumed constraint-loss regime) at a value of (∆Keff) T given by 0.5 σo √B [20], as shown by the vertical dashed lines at B = 1 and 2 mm, respectively. Small-crack data on the thin-sheet 2024-T3 bare alloy [11] were used to estimate the effective stress-intensity factor range results at extremely low crack growth rates near threshold. The solid curve shows the ∆Keff baseline relation (see Table 1) used in all subsequent fatigue and crack-growth calculations. However, because the fuselage material was thinner (B = 1 mm), the constraint-loss regime was estimated to occur at lower rates (see Table 1) than the 2-mm thick material data shown in Figure 2. The dashed curve shows the relation obtained for the bare material. For most of the data, the clad and bare results agreed quite well. Fatigue-crack-growth rates were calculated from a multi-linear equation as dc/dN = Ci (∆Keff)ni
(5)
where Ci and ni are determined from the values shown in Table 1 for each linear segment (i) and ∆Keff = Kmax – Ko. The crack-opening stress-intensity factor, Ko, was calculated from the crack-closure model, FASTRAN [13, 20]. 4.0 LABORATORY LAP-JOINT SPECIMENS AND ANALYSES Research on the aging aircraft fleets by the FAA, NASA and the DoD have generated test and analysis data on riveted lap-joints from simple laboratory specimens to curved test panels [21]. The results
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on the laboratory specimens have been used to improve and verify the fatigue and crack-growth methodologies for lap-joint configurations. Herein, two studies on simple lap-joint specimens were used to establish appropriate crack configurations and the equivalent initial flaw sizes (EIFS).
These crack
configurations and EIFS values were then used to calculate fatigue lives and crack growth in fuselage lap joints in a retired narrow-body passenger aircraft and for curved panels cut from the retired aircraft and tested in a pressure-box facility. 4.1 Northwestern University Conner et.al. [22] conducted a large number of lap-joint tests on specimens, as shown in Figure 3. The specimens were prepared by riveting together two Alclad 2024-T3 aluminum alloy panels, one with three countersunk rivet holes and one with three straight shank holes. The rivets were made of 2017-T4 aluminum alloy and the hole diameter was about 4.8 mm. The specimens were fatigue tested at remote stress levels of 103 to 180 MPa at a stress ratio (R) of 0.1. When the specimens were fatigued at the lowest stress levels (103 and 129 MPa) the cracks initiated and grew as “eyebrow” surface cracks at the faying surface on the straight-shank hole side, but when the higher stress levels were applied (154 and 180 MPa) the cracks initiated as corner cracks at the hole along the faying surface. FASTRAN was used to calculate the fatigue lives of these specimens using two different crack models. The first was the eyebrow type crack—a crack initiating on the faying surface near the bottom of the rivet that appeared like surface cracks. Thus, a surface crack was assumed to initiate along the faying surface and the crack was subjected to both remote tension and bending loads. The rivet was totally neglected in these analyses. The bending stress was estimated from the Hartman-Schijve equations [18] and was 0.34 times the remote applied stress. Figures 4(a) shows the results of tests conducted at 103 MPa at R = 0.1. The crack length, 2c, was measured using an acoustic microscope and includes the hole diameter plus crack growth on both sides of the hole. In the analyses for the eyebrow crack, an initial surface crack length, ci, of 2.4 mm (radius of rivet head) was assumed. The initial crack depth, ai, was then chosen to fit the bounds of the three test specimens. The 9-µm deep crack gave nearly an upper bound; whereas, the 15-µm deep crack gave a lower bound. These values were selected by trial-and-error to fit the test data. For tests conducted at the higher applied stress level, Figure 4(b), the crack configuration in the tests and analyses was a corner crack located at the edge of the straight-shank hole. The bending stress was calculated to be 0.39 times the applied stress and the rivet-load factor (Lf) was 0.37. Again, the crack length, 2c, was measured with the acoustic or optical microscope and the crack length included the hole diameter. The initial corner-crack size was, again, chosen to fit the upper and lower bounds of the test data. For this
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cracking mode, a 60- and 120-µm crack fit the results fairly well. These initial crack sizes were quite large for the 2024 alloy (inclusion particle clusters range from 3 to 30-µm in size), but these sizes could have been caused by drilling marks and burrs at the outer edges of the fastener hole. 4.2 Georgia Institute of Technology Two-rivet-row lap-joint specimens were tested at Georgia Tech [23]. The lap-joint specimen is shown in Figure 5. Several rivet conditions were considered: (1) standard-driven rivets, (2) over-driven (tight) rivets, or (3) under-driven (loose) rivets. All specimens were subjected to a remote stress of 124 MPa. Figure 6(a) shows the fatigue tests results on the under-driven rivet condition, which had an average life of about 80,000 cycles. (Crack growth was not monitored in these tests, in contrast to the previous Northwestern tests.) In the fatigue analyses, a semi-circular corner crack (a/c = 1) was assumed to occur along the faying surface of straight-shank hole. Various EIFS values were assumed. It was found that a 6µm crack fit the average results quite well. The upper and lower bounds were captured quite well by the 4and 15-µm initial crack, respectively. The test results for the standard- and over-driven rivets are shown in Figure 6(b). Here it was found that the standard-and over-driven rivets produced nearly the same cycles to failure. The average fatigue life was about 60% longer than that for the under-driven rivets. Here a semicircular corner crack was assumed as the EIFS and a 7-µm interference value was needed to fit the mean of the test results with a 6-µm initial crack. Again, the fatigue scatter was captured quite well by the 4- to 15µm initial crack. 5.0 RETIRED AIRCRAFT LAP-JOINT CONFIGURATION AND ANALYSES A retired passenger aircraft was destructively examined to determine the state of cracking in the fuselage lap-joint regions on one side of the aircraft [1-6]. On the other side, several curved fuselage panels were removed from the aircraft and two of them (FT-1 and FT-2) were subjected to extended fatigue testing in a pressure box at the FAA’s William J. Hughes Technical Center in Atlantic City, NJ [3]. A drawing of structural details around the horizontal lap joint is shown in Figure 7. Fatigue cracks would be expected to be present and grow in the horizontal three-rivet row lap joint near the center of the panel. Figure 8 shows the cross section at a rivet location showing the inner and outer sheets with an internal doubler and the countersunk rivet. Cracks would be expected to initiate and grow from the faying surface as corner cracks or surface cracks. In the following, comparisons are made between the measured and calculated cracking in the retired aircraft fuselage structure and cracking in curved fuselage panels removed from the aircraft and tested at the FAA Technical Center.
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5.1 Aircraft Fuselage Lap-Joint Cracking Behavior A large number of rivet locations had been examined from the retired passenger aircraft and a number of cracks were found emanating from the rivet holes [2, 4]. These cracks had been examined in a scanning-electron-microscope (SEM) to count striations and to back-track the cracking history to reconstruct the crack-length-against-flight-cycle behavior [4]. The primary fuselage loading comes from the ground-airground (GAG) pressurization cycle. Some of these results are shown in Figure 9. The open symbols show results on a surface crack emanating along the faying surface but near the fastener hole and the solid symbols show a corner or surface crack emanating from the edge of the fastener hole. AFGROW [15] and FASTRAN [13] have both been used to calculate the cracking in the retired aircraft fuselage joints during its 60,000-pressure cycle history.
Of concern was the restriction in
FASTRAN that the a/c ratio had to be held constant, such as a/c = 1, while the a/c ratio was variable in AFGROW. In AFGROW, the growth of a corner crack is independent in the a- and c-directions. An AFGROW analysis of an initial ai/ci = 1 corner crack in a lap-joint was made with 37% fastener load, 63% by-pass load and 85% bending; and the predicted a/c-ratio was nearly unity until the crack began to break through the sheet thickness (a/B = 1; a/c = 0.92). For a/B ratios greater than unity, AFGROW analyses modeled an oblique crack front until the crack transitions into a straight-through crack.
However,
FASTRAN assumes that the a/c ratio is held constant at unity until breakthrough. Thereafter, a straightthrough crack is assumed until failure. Because of compensating effects of the remote loads causing higher stress-intensity factors along the depth, a-direction, and bending causing lower stress-intensity factors along the depth direction, the crack in AFGROW was predicted to grow as a nearly quarter-circular (a/c ~ 1) crack. The dashed curve in Figure 9 is a calculated result from AFGROW using an EIFS of 5-µm radius corner crack. The EIFS value was chosen to roughly fit the mean of the measured data. The solid curves show calculations made with FASTRAN for values of EIFS ranging from a 9 to 30-µm radius corner crack. Both codes produced essentially the same results, in that, the shape of the crack length against flights curves were similar for cracks larger than about 300-µm. The only major difference was in the small-crack regime (5 to 30-µm). (Note that the AFGROW calculations did not include the effects of biaxial loading; whereas, the FASTRAN calculations did included the influence of biaxial loading, λ = 0.5, on stress-intensity factors, as shown in the Appendix.) FASTRAN calculations were also carried out to failure, which indicated that if not repaired or replaced, the fuselage is predicted to go to failure between 71,000 to 93,000 flights. Note that the Aloha Airlines Boeing 737 with a similar fuselage lap-joint design, but without a bonded doubler, had a fuselage failure at about 89,680 flight cycles [24], as shown by the diamond symbol.
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5.2 Curved Fuselage Test Panels Two of the curved fuselage test (FT) panels removed from the retired aircraft after about 60,000 pressure cycles were tested in a pressure-box at the FAA Technical Center [3, 25]. Because these panels were removed from the side of the aircraft, which apparently had tight joints and rivet connections, there were two types of crack configurations that could be selected: (1) surface crack at the edge of the rivet head, as in Figure 4(a) or (2) corner crack at the edge of the fastener hole, as in Figure 6(b). Herein, the surface-crack model was used to make fatigue life and crack growth predictions. Note that the surface- or through-crack model (without a rivet hole) would not be influenced by biaxial loading [26]. Figure 10 shows the predicted crack length, 2c, against cycles, N, for two levels of secondary bending. The two levels of bending were estimated from lap-joints with and without a bonded doubler [3, 27, 28]. The flight history (GAG loading) on this section in the fuselage was calculated to be at 94.5 MPa at R = 0 for 59,497 cycles [2], and the stress applied to FT-2 and FT-1 panels was 98 MPa at R = 0.1 for 43,500 cycles and 120,000 additional simulated in-service cycles, respectively, as shown by the solid vertical lines [3]. But close examination of the lap-joint region indicated no cracking. The predicted cycles on the curved fuselage test panels depended greatly upon the magnitude of secondary bending used in the analyses. The higher bending factor (0.85) indicated that both FT-2 and FT-1 panels should have cracked in 100,000 to 180,000 total (flight plus simulated) cycles, but they had no evidence of cracking. However, using the bending factor of 0.38 indicated that both panels should not have significantly cracked in less than 200,000 cycles, which agreed well with the curved panel tests. Panel FT-1 with improved loading fixtures withstood about 180,000 total cycles (flight loading plus 120,000 cycles of in-service simulated loading for load condition A), but a detailed examination revealed no cracking in the lap-joints. Thus, damage in the form of saw-cuts were inserted at some particular rivet holes [3] and the panel was subjected to residual strength loads (113 MPa at R = 0.1 for condition B) for 10,000 cycles, but no crack growth was observed at the saw-cuts. Loads were then increased to the design limit loads (130 MPa at R = 0.1 for condition C) for 5,000 cycles and some crack growth was detected. Finally, loads were increased 147 MPa at R = 0.1 (load condition D) and the panel was cycled for an additional 6,770 cycles. Some measured crack growth against cycles is shown in Figure 11. In the FT-1 analysis, an initial through crack (equal area of the saw-cut, ci = 1.65 mm) was placed at the forward and aft edges of a damaged rivet hole. Because the number of cycles to initiate a crack from the saw-cut was not known, the number of cycles in load condition B was changed until the crack length at 135,000 cycles was about 4.4 mm. Thus, the computed crack growth under load condition D would be
10
compared to the measured crack growth during the same loading sequence. Three levels of secondary bending were assumed. The high bending level (0.85) was obtained from reference 3, which was based on results from reference 23. However, Fawaz [28] had tested 4 joints and measured secondary bending factors from 0.2 to 0.34. None of these joints, however, were exactly the same as the retired fuselage joints, but Joint I was the closest. Joint I had 1.6-mm skin with 0.64-mm thick doubler, while the aircraft joint had 1mm skin and 0.5-mm thick doubler. The calculated results with the highest bending factor (0.85) produced the shortest crack growth behavior, while the results with the nominal bending factor (0.38) was fairly close. A bending factor of 0.25 was required to match the test results. Further study is needed on the appropriate bending factor (or other parameters in the crack-growth analysis) for the panels tested in the pressure box. If panels from the other side of the fuselage had been selected for pressure-box testing, then further cracking would have been expected. 6.0 DISCUSSION OF RESULTS Testing and analyses made on lap-joints in this paper have involved two types of laboratory coupons, results from curved panel tests, and destructive examination of cracking in lap-joints of a retired passenger aircraft. For each case, a particular crack configuration was selected based on whether the rivet installation could have been characterized as tight, standard or loose.
Using the selected crack
configuration, an equivalent-initial-flaw-size (EIFS) was selected to best fit the test crack-length-againstcycle results.
For each case, different EIFS values were found.
These different EIFS values could
possibility be explained by some observations that have been made during the aging aircraft studies conducted in the 1990’s (see e.g., Ref. 21). Installation of rivets into laboratory coupons have generally resulted in tighter rivet connections (higher rivet-hole interference and frictional forces between layers); whereas, rivet installation in full-scale aircraft is more difficult and could lead to a loose joint. Due to manufacturing and installation variations, the two sides of the retired aircraft’s fuselage had very different joint quality. The left side had tight joints with standard or overdriven rivets while the right side had loose joints with under driven rivets. The left side with the tight joints was used to manufacture the curved panels (FT-1 and 2). In addition, fastener holes drilled in the laboratory environment may be more pristine (less burrs and machining marks) than those drilled in a large fuselage. Thus, the EIFS values for the actual fuselage were larger than those for the laboratory coupons.
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7.0 CONCLUDING REMARKS The crack-growth model, FASTRAN, was used to calculate fatigue lives and crack growth in laboratory lap-joint specimens made of a thin-sheet clad aluminum alloy to establish appropriate crack configurations and to select equivalent initial flaw sizes (EIFS). Various loading and rivet conditions were considered, such as high loads or low loads, and standard, over-driven (tight) or under-driven (loose) rivets. For the standard-driven and under-driven rivets, a corner crack at a fastener hole was assumed; whereas, for the tight-rivet condition, a surface crack coming from the faying surface was considered. The calculated fatigue lives and crack growth in the laboratory specimens agree well with the test data. Using the effective stress-intensity-factor-range-against-rate relation for the clad alloy, a corner crack at a fastener hole was used to calculate the fatigue lives and crack growth in the retired aircraft fuselage joints (under-driven rivet side) and a surface crack in a plate was used to calculate the fatigue life and crack growth in the curved test panel from the tight rivet side. The calculated crack length against flight pressure cycles in the retired aircraft fuselage was quite similar to the results found from fractographic examinations. The predicted cycles on the curved fuselage test panels depended greatly upon the magnitude of secondary bending used in the analyses. For simulated in-service loading, the higher bending factor (0.85) indicated that both FT-1 and FT-2 panels should have cracked in 100,000 to 180,000 cycles, but they had no evidence of cracking. However, using the bending factor of 0.38 indicated that both panels should not have cracked in less than 200,000 cycles. In addition, predicted crack growth in the FT-1 panel at higher applied loading with the lower bending factors agreed better with test measurements. Further study is needed on the appropriate bending factor or other parameters in the crack-growth analysis for the panels tested in the pressure box. Overall, the paper demonstrated that fuselage lap-joint fatigue-life-prediction methods based on crack growth are very adequate. This suggests that the portion of fatigue life spent in nucleating fatigue cracks in real aircraft joints is very small. 8.0 REFERENCES 1.
Steadman, D. and Bakuckas, J. G., Jr. Destructive evaluation and extended fatigue testing of retired transport aircraft: Program overview. DOT/FAA/AR-07/22, V1, 2007.
2.
Ramakrishnan, R. and Jury, D. Destructive evaluation and extended fatigue testing of retired transport aircraft: Damage characterization. DOT/FAA/AR-07/22, V2, 2007.
3.
Mosinyi, B., Bakuckas, J. G., Jr. and Steadman, D. Destructive evaluation and extended fatigue testing of retired transport aircraft: Extended fatigue testing. DOT/FAA/AR-07/22, V4, 2007.
12
4.
Ramakrishnan, R., Steadman, D. and Carter, A. Crack history reconstruction of lap joint fatigue cracks. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
5.
Jury, D., Ramakrishnan, R. and Carter, A. Rivet installation and faying surface quality studies in a lap joint removed from a retired commercial aircraft. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
6.
Ramakrishnan, R. and Steadman, D. Analysis of the influence of fastener installation and faying surface quality on fatigue cracking in aircraft lap joints. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
7.
Jongebreur, A. A., “The Fatigue Strength at Fluctuating Tension of Two Row Rivited Single Lap Joints of Clad Sheet of the Aluminum Alloys 2024-T3 or 7075-T6”, Fokker Report S-116, October 1965.
8.
Jarfall, L. E., “Optimum Design of Joints: The Stress Severity Factor Concept”, 5th ICAF Symposium, Aircraft Fatigue -- Design, Operational and Economic Aspects, Melbourne, Australia, May 1967.
9.
Homan, J.J. and Jongebreur, A.A., “Calculation Method for Predicting the Fatigue Life of Riveted Joints”, 17th ICAF Symposium, Durability and Structural Integrity of Airplanes, Stockholm, Sweden, 1993, pp. 175-190.
10.
Short-Crack Growth Behaviour in an Aluminum Alloy -- an AGARD Cooperative Test Programme, AGARD R-732, 1988.
11.
Newman, J. C., Jr. A review of modeling small-crack behavior and fatigue-life predictions for aluminum alloys. Fatigue and Fracture of Engineering Materials and Structures, 1994; 17(4):429-440.
12.
Newman, J. C., Jr., Harris, C. E., James, M. A. and Shivakumar, K. N. Fatigue-life prediction of riveted lap-splice joints using small-crack theory. In: Fatigue in New and Aging Aircraft, ICAF, EMAS Publishing, UK, 1997; I:523-539.
13.
Newman, J. C., Jr. FASTRAN II - Fatigue Crack Growth Structural Analysis Program. NASA TM 104159, 1992.
14.
Bakuckas, J. G., Jr. Full-scale testing of fuselage structure containing multiple cracks. DOT/FAA/AR-01/46, 2002.
15.
AFGROW Users Guide, Version 4.0005.12.10 (2002) J. A. Harter, WPAFB OH.
16.
Newman, J. C., Jr. and Raju, I. S. Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads. In: Computational Methods in the Mechanics of Fracture, S. N. Atluri (ed.), 1986;2:311-334.
13
17.
Hartman, A. and Schijve, J. The effect of secondary bending on fatigue strength of 2024-T3 alclad riveted joints. NLR TR 69116 U, National Aerospace Laboratory, 1969.
18.
Schijve, J., Jacobs, F. A., and Tromp, P. J. Crack propagation in aluminum alloy sheet materials under flight simulation loading. NLR-TR 68117 U, National Aerospace Lab, 1968.
19.
Newman, J. C., Jr. A crack opening stress equation for fatigue crack growth. Int. J. Fract., 1984;24:R131-Rl35.
20.
Newman, J. C., Jr. Effects of constraint on crack growth under aircraft spectrum loading. Fatigue of Aircraft Materials, Delft University Press, 1992, 83-109.
21.
Second Joint NASA/FAA/DoD Conference on Aging Aircraft. NASA CP-208982, 1999.
22.
Conner, Z., Fine, M. E. and Achenbach, J. D. Quantitative investigation of surface and subsurface cracks near rivets in riveted joints using acoustic, electron and optical microscopy. In: NASA CP208982, Part 1, 1999, pp. 240-243.
23.
Atre, A. P., Johnson, W. S. and Newman, J. C., Jr. Assessment of residual stresses and hole quality on the fatigue behavior of aircraft structural Joints: Finite element simulation of riveting process and fatigue lives, DOT/FAA/AR-07/56, V3, 2009.
24.
Aircraft Accident Report—Aloha Airlines, Flight 243, Boeing 737-200. National Transportation Safety Board, NTSB/AAR-89/03, 1989.
25.
Mosinyi, B., Bakuckas, J., Steadman, D., Awerbuch, J., Lau, A. and Tan, T. Full-scale extended fatigue testing of fuselage structure from a retired passenger service airplane. Ninth Joint FAA/DoD/NASA Aging Aircraft Conference, 2006, Atlanta, GA.
26.
Tada, H., Paris, P. C. and Irwin, G. R. The stress analysis of cracks handbook. Third Edition, ASME Press, New York, NY, 2000:125.
27.
de Rijck, J. J. M. and Fawaz, S. A simplified approach for stress analysis of mechanically fastened joints. Fourth Joint DoD, FAA and NASA Conference on Aging Aircraft, St. Louis, MO, May 2000.
28.
Fawaz, S. A. Equivalent initial flaw size testing and analysis. AFRL-VA-WP-TR-2000-3024, June 2000.
29.
Chang, C. and Mear, M. E. A boundary element method for two-dimensional linear elastic fracture analysis. Int J Fracture, 1996;74:219-251.
14
Appendix – Effects of Biaxial Loading on Stress-Intensity Factors for Through Cracks Emanating from a Circular Hole A fastener hole in an aircraft fuselage is subjected to a wide variety of loading conditions, as shown in Figure 1. A single crack or two-symmetric cracks of length, c, emanating from an open hole and subjected to only remote uniform stress, Sb, and biaxial stress, λSb, were analyzed with the two-dimensional boundary-element code, FADD2D [29], to determine the influence of biaxial loading on stress-intensity factors. Figure 12 shows, Fλn, ratio of the stress-intensity factor for a crack under biaxial loading (λ) to that for only uniaxial remote stress (λ = 0) against crack-length-to-hole-radius (c/r) ratio. The open symbols show the results for two-symmetry cracks (n = 2) and the solid symbols show the results for a single crack (n = 1). For small c/r ratios, the results for one or two cracks agreed very well, but some slight differences were observed for larger c/r ratios. For c/r > 3, biaxial loading had less than 1% influence on the stressintensity factors. Equations were developed to fit these results and they are given by Fλ1 = 1 + λ/[3 + 4.5 (c/r) + 4.7 (c/r)2 + 4.9 (c/r)3]
(A1)
Fλ2 = 1 + λ/[3 + 4.5 (c/r) + 6.2 (c/r)2 + 1.1 (c/r)3]
(A2)
Equations A1 and A2 are within about ±0.8% of the numerical results from the boundary-element analyses for any value of c/r. The stress-intensity factor for either two- or three-dimensional cracks is then given by Kλ = Kλ=0 Fλn
(A3)
where Kλ=0 is the stress-intensity factor for either a surface crack, corner crack or through crack at a fastener hole.
15
Figure Captions: Figure 1. - Crack configuration and loading for rivet-loaded hole Figure 2. - Fatigue-crack-growth-rate properties for 2024-T3 clad material Figure 3. - Three-rivet-row lap joint specimen tested at Northwestern University [22] Figure 4(a). - Crack growth in riveted lap joint at a low-applied stress level Figure 4(b). - Crack growth in riveted lap joint at a high-applied stress level Figure 5. - Two-rivet-row lap joint specimen tested at Georgia Institute of Technology [23] Figure 6(a). - Fatigue lives of lap-joint specimens with under driven rivets Figure 6(b). - Fatigue lives of lap-joint specimens with standard and over driven rivets Figure 7. - Curved panel (FT-2) from retired aircraft tested at FAA Technical Center [25] Figure 8. - Typical rivet configuration in retired aircraft [2, 5] Figure 9. - Measured and calculated crack growth from riveted joints in retired aircraft Figure 10. - Predicted crack growth in the FT panels and continued testing at FAA Technical Center Figure 11. - Influence of secondary bending on predicted and measured crack growth in FT-1 panel tested at FAA Technical Center Figure 12. - Influence of biaxial loading on stress-intensity factors for single- and two-symmetric cracks at an open hole
16
TABLE
Table 1 – Effective-stress-intensity-factor-against-rate relation for 2024-T3 (Alclad) B = 1 mm
∆Keff, MPa-√m
dc/dN, m/cycle
0.75
1.00e-11
1.05
1.00e-10
1.37
6.00e-10
1.75
1.90e-09
4.00
7.00e-09
7.60
1.00e-07
10.7
4.00e-07
17.0
3.00e-06
35.0
1.00e-04
85.0
1.00e-02
α = 2.0
≤ 4.00e-08
α = 1.0
≥ 2.00e-07
17
S0142-1123(15)00126-7 http://dx.doi.org/10.1016/j.ijfatigue.2015.04.010 JIJF 3575
To appear in:
International Journal of Fatigue
Received Date: Accepted Date:
21 October 2014 26 April 2015
Please cite this article as: Newman, J.C. Jr., Ramakrishnan, R., Fatigue and Crack-Growth Analyses of Riveted LapJoints in a Retired Aircraft, International Journal of Fatigue (2015), doi: http://dx.doi.org/10.1016/j.ijfatigue. 2015.04.010
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Fatigue and Crack-Growth Analyses of Riveted Lap-Joints in a Retired Aircraft J. C. Newman, Jr.1,a, R. Ramakrishnan2 1
Department of Aerospace Engineering, Mississippi State University, MS, USA 39762 2
a
Delta Air Lines Inc., Atlanta, GA, USA 30320
Corresponding author: [email protected]
ABSTRACT For aluminum alloys, research has shown that fatigue behavior of notched and unnotched specimens can be characterized by fatigue-crack growth from micro-structural features, such as inclusion-particle sizes. A crack-growth model using small- and large-crack data was used to calculate fatigue lives and crack growth in lap-joints in laboratory specimens. The tightness of the rivets dictated the type of crack configurations that occurred in the joint and equivalent initial flaw sizes (EIFS) were selected to fit the fatigue test data. These crack configurations and EIFS values were then used to predict fatigue lives in fuselage lap-joints in a retired passenger aircraft and for curved panels cut from the retired aircraft. The paper demonstrates that fuselage lap-joint fatigue-life-prediction methods based on fatigue-crack growth alone (i.e., with accounting for any time spent in crack nucleation) are very adequate to model the lifetimes in fuselage riveted lap joints. KEYWORDS: Aircraft, fatigue, cracks, riveted lap joints, aluminum alloy NOMENCLATURE a
Crack depth in thickness (B) direction, mm
ai
Initial flaw or crack depth in B-direction, mm
B
Specimen thickness, mm
Ci
Coefficients in multi-linear crack-growth equation (i = 1 to m)
c
Crack half-length in width (W) direction, mm
ci
Initial flaw or crack half-length in W-direction, mm
D
Rivet-hole diameter, mm
F
Boundary-correction factor
K
Stress-intensity factor, MPa√m
Ko
Crack-opening stress-intensity factor, MPa√m
Li
Riveted joint load factors
M
Bending moment, Nm
N
Number of cycles
Nf
Number of cycles to failure
1
ni
Powers in multi-linear crack-growth equation (i = 1 to m)
P
Rivet force, N
R
Stress ratio (Smin /Smax)
r
Hole radius, mm
S
Remote applied stress, MPa
Sb
Fastener by-pass stress, MPa
SB
Outer-fiber bending stress, MPa
Sp
Fastener bearing stress, MPa
Smax
Maximum applied stress, MPa
Smin
Minimum applied stress, MPa
W
Specimen half-width, mm
wr
Rivet spacing, mm
α
Constraint factor
γ
Bending factor
∆
Interference, µm
∆K
Stress-intensity factor range, MPa√m
∆Keff
Effective stress-intensity factor range, MPa√m
(∆Keff)T Effective stress-intensity factor range at flat-to-slant transition, MPa√m λ
Biaxial loading factor
σo
Flow stress (average of σys and σu), MPa
σys
Yield stress (0.2 percent offset), MPa
σu
Ultimate tensile strength, MPa
1.0 INTRODUCTION The Federal Aviation Administration (FAA) and Delta Air Lines [1-6] had teamed to conduct a destructive evaluation of a retired narrow-body passenger aircraft that had nearly 60,000 revenue service flights (one design service goal). Some objectives of the program were to characterize the state of multiplesite damage (MSD) at riveted fastener holes in the fuselage of an aircraft at the design service goal; and to develop or verify analysis methods that can correlate and predict the state of MSD at any point in time. For the retired aircraft, observations from the destructive examination of the fuselage joints indicated that one side of the aircraft appeared to have tight (within specifications) rivets with no detectable cracks present, whereas on the other side of the aircraft the rivets appear to have under-driven rivets with a large number of
2
cracks present [5, 6]. For these cracks, faying surface origins were predominant, despite a majority of rivets being under driven. A large number of cracks have been examined with a scanning-electron-microscope (SEM) to count striations and to back-track the cracking history to reconstruct the crack length against flight cycle behavior [4]. The measured crack length against flight cycle results tended to fall within a fairly narrow band considering the complexity of real aircraft structural joints under actual operational loads and service environments. Several curved fuselage panels were cut from the other side of the fuselage and two panels with lap joints that had tight, correctly driven rivets were tested using the Full-scale Aircraft Structural Test Evaluation and Research facility (FASTER) at the FAA William J. Hughes Technical Center, Atlantic City, NJ. The FASTER facility uses a pressure box to fatigue test large fuselage panel by cyclic hydraulic loading. Prior to testing, both panels were verified to be crack free to the extent detectable by high frequency eddy current non-destructive test methods. These pressure box tests extended the fatigue cycles already experienced by these two panels during aircraft revenue service of 59,497 cycles, and added 43,500 cycles in one case and 120,000 cycles in another case. Both extended fatigue tests showed that these two panels with the very tight joints were extremely durable with no cracks formed at the end of the extended test cycles. These widely differing fatigue lives in the relatively loose joints with the under driven rivets versus the tight joints with the correctly driven rivets, had to be modeled and shown to be amenable for analyses in consistent manner. Some of the first approaches to improve the calculation of fatigue lives of riveted lap-joints were made in the mid-1960’s [7, 8].
These approaches were based on stress-life (S-N) behavior and the
calculation of local stress concentrations due to rivet loading, by-pass loading, and local bending. The effects of hole preparation (drilling, reaming, or cold-working) and of hole filling (rivets, bolts, or interference-fit fasteners) were accounted for by using either empirical factors derived from fatigue tests [8] or, more recently, on the use of “reference” S-N curves [9] from fatigue tests conducted on joints made with the particular manufacturing process of interest. The fracture-mechanics approach, used herein, is based on similar reasoning but calculates stressintensity factors and crack-opening stresses for small cracks under rivet loading, by-pass loading, and local bending. Effects of hole preparation are accounted for by selection of an “equivalent initial flaw size (EIFS)”; and the effects of hole filling on the selection of an “effective” level of interference to account for riveting interference, clamp-up, and frictional effects. The selection of an EIFS also indirectly accounts for any nucleation cycles.
3
During the last two decades, research on small-crack behavior [10] and analysis methods [11], especially for aluminum alloys, have shown that the entire fatigue process can be effectively modeled as “crack propagation” from a micro-structural discontinuity in the material (e.g., precipitate particles). Thus, for the lap-joint configuration, an initial flaw size exists that will characterize the material or manufacturing quality.
The analysis methodology to predict crack growth from the micro-scale has been based on
traditional fracture-mechanics and crack-closure concepts. (Small-crack theory is the use of small-crack data accounting for micro-structural effects on crack growth in the low-rate regime and using a closure model to capture the transient closure effects as a small crack grows and develops a plastic wake.) Herein, these principles will be applied to the lap-joint configuration using some of the results obtained from the two- and three-dimensional analyses of the NLR lap-joint specimen [12]. Stress-intensity factors for small corner and through cracks growing under rivet loading, by-pass loading, and local bending have been developed [12]. The crack-closure model [13] will be used to calculate crack-opening stresses for a crack growing from an open hole, but using the stress-intensity factors for the lap-joint specimen. The rivet liftoff stress (applied stress required to separate the rivet from the fastener hole) will be used to account for rivet contact at the minimum load. (Ideally, a closure model should be developed to model the rivet in the hole and account for interference and contact analytically, but this is beyond the scope of the present paper.) Effects of hole preparation (e.g., tool marks or burrs) are accounted for by the selection of an EIFS; and the effects of hole filling on the selection of an “effective” level of interference to account for riveting interference, clamp-up, and frictional effects. The objective of this paper is to use FASTRAN [13] and small-crack theory to calculate fatigue lives and crack growth in laboratory lap-joint specimens made of 2024-T3 clad aluminum alloy. Tightness of the rivets led to different crack configurations (corner cracks at the rivet hole or surface cracks along the fraying surface) and different EIFS values. Two types of laboratory specimens were analyzed: (1) three-rivet-row countersunk specimens and (2) two-rivet-row countersunk specimens with a doubler.
Several rivet
conditions were considered: (1) standard-driven rivets, (2) tight or over-driven rivets, and (3) under-driven rivets. The appropriate crack configuration and the EIFS values were then used to calculate crack growth in the retired aircraft and curved fuselage test panels cut from the aircraft and tested in the FASTER Test Facility at the FAA William J. Hughes Technical Center [14]. Comparisons are made between AFGROW [15] and FASTRAN for crack growth in the retired aircraft and the reconstructed crack-length-against-flightpressure-cycle history. Fatigue life and crack-growth behavior are also predicted on the curved fuselage test panels and compared with test results.
4
2.0 STRESS ANALYSIS OF CRACKS AT RIVET-LOADED FASTENER HOLES Stress-intensity factors for a corner crack or a through crack emanating from a typical fastenerloaded hole under remote applied stress (S = Sp + Sb), remote outer-fiber bending stress (SB) due to bending moment (M), by-pass stress (Sb), fastener load (Sp = P/(wrB)), where wr is rivet spacing and B is sheet thickness), and interference (∆), as shown in Figure 1, are given in Reference 12. The influence of biaxial loading (λSb) on stress-intensity factors for cracks emanating from the fastener hole are given in the Appendix. One of the restrictions for the corner-crack equations is that the crack aspect ratio, a/c, is fixed, and the influence of rivet interference is based on a simple approximation [12]. Stress-intensity factor equations for a surface crack in a plate under remote tension (St) and bending (SB) stresses are given in Reference 16. To calculate the growth of a corner crack initiating at a critically-loaded rivet hole in a lap-joint (see Fig. 1), the stress-intensity factors for rivet loading (Sp), by-pass loading (Sb), local bending (M or σb), and interference (∆) must be obtained and added as K = Kp + Kb + KM + K∆
(1)
Herein, to calculate the maximum stress-intensity factor, Kmax, it was assumed that the maximum applied loading is such that the rivet will not be in contact, that is, the applied stress will be greater than the rivet liftoff stress, SLO. Thus, at maximum load it was assumed, for simplicity, that K∆ = 0. The influence of the rivet being in the hole, however, is reflected in the calculation of the other values of stress-intensity factor due to the radial pressure distribution. Therefore, the stress-intensity factor in terms of applied stress is K = Sp √(πc) Fp + Sb √(πc) Gb Fλn + σb √(πc) Hb
(2)
Expressing equation (2) in terms of the total remote stress S with the bending stress expressed as
σb = kb S
gives K = S √(πc) [ Lp Lf Fp + Lb (1 – Lf) Gb Fλn + kb Hb ] = S √(πc) F
(3)
where Lp is the load factor (Sp/S) for the critical rivet (crack location), Lb is the load factor (Sb/S) for the bypass loading, Lf is the rivet-load factor, and kb is the Hartman-Schijve bending factor [17]. The term Fλn is the correction factor for bi-axial loading and the equation is given in the Appendix. Reference 12 gives the equations for the boundary-correction factors Fp, Gb, and Hb, for rivet load, by-pass load and bending, respectively. Thus, F is the boundary-correction factor for a through crack at a rivet-loaded hole in the lap joint. To convert equation (3) to a corner crack at the edge of the rivet-loaded hole, F is multiplied by the corner-crack-to-through-crack (Kcc/Ktc) ratio [12] as:
5
Kcc/Ktc = 0.8 + 0.2 a/B – 0.2 (1 – a/B) (a/c) – 0.05 (1 – a/B)15
(4)
Equation (4) is very accurate for small a/B ratios and the Kcc/Ktc ratio approaches unity as the corner crack becomes a through crack (a/B = 1). 3.0 MATERIAL CRACK GROWTH PROPERTIES The material used in the laboratory lap-joint specimens and the retired fuselage structure was 2024T3 thin-sheet (B = 1 mm) clad aluminum alloy. Surprisingly, fatigue-crack-growth-rate data for the 1-mm thick sheet could not be found in the literature. But crack-growth-rate data on a 2-mm thick clad aluminum alloy were obtained from Schijve et.al. [18]. The yield stress (σys) was 360 MPa, ultimate tensile strength (σu) was 490 MPa and the flow stress (σo) was 425 MPa. These data covered a wide range in stress ratios (R = -0.1 to 0.73). Previously, Newman [19] developed steady-state crack-opening stress equations from the FASTRAN crack-closure model for middle-crack tension, M(T), specimens subjected to constant-amplitude loading at various stress levels (S max/σo ), stress ratios (R), and constraint factor (α). These equations were then used to develop the effective-stress-intensity-factor-range-against-rate relation for the clad alloy, as shown in Figure 2. The symbols show the test data for the various stress ratio tests. The data correlated very well with the same constraint factors that had been used for the bare material [20] with B = 2.3 mm. The crack transitions from flat-to-slant crack growth (assumed constraint-loss regime) at a value of (∆Keff) T given by 0.5 σo √B [20], as shown by the vertical dashed lines at B = 1 and 2 mm, respectively. Small-crack data on the thin-sheet 2024-T3 bare alloy [11] were used to estimate the effective stress-intensity factor range results at extremely low crack growth rates near threshold. The solid curve shows the ∆Keff baseline relation (see Table 1) used in all subsequent fatigue and crack-growth calculations. However, because the fuselage material was thinner (B = 1 mm), the constraint-loss regime was estimated to occur at lower rates (see Table 1) than the 2-mm thick material data shown in Figure 2. The dashed curve shows the relation obtained for the bare material. For most of the data, the clad and bare results agreed quite well. Fatigue-crack-growth rates were calculated from a multi-linear equation as dc/dN = Ci (∆Keff)ni
(5)
where Ci and ni are determined from the values shown in Table 1 for each linear segment (i) and ∆Keff = Kmax – Ko. The crack-opening stress-intensity factor, Ko, was calculated from the crack-closure model, FASTRAN [13, 20]. 4.0 LABORATORY LAP-JOINT SPECIMENS AND ANALYSES Research on the aging aircraft fleets by the FAA, NASA and the DoD have generated test and analysis data on riveted lap-joints from simple laboratory specimens to curved test panels [21]. The results
6
on the laboratory specimens have been used to improve and verify the fatigue and crack-growth methodologies for lap-joint configurations. Herein, two studies on simple lap-joint specimens were used to establish appropriate crack configurations and the equivalent initial flaw sizes (EIFS).
These crack
configurations and EIFS values were then used to calculate fatigue lives and crack growth in fuselage lap joints in a retired narrow-body passenger aircraft and for curved panels cut from the retired aircraft and tested in a pressure-box facility. 4.1 Northwestern University Conner et.al. [22] conducted a large number of lap-joint tests on specimens, as shown in Figure 3. The specimens were prepared by riveting together two Alclad 2024-T3 aluminum alloy panels, one with three countersunk rivet holes and one with three straight shank holes. The rivets were made of 2017-T4 aluminum alloy and the hole diameter was about 4.8 mm. The specimens were fatigue tested at remote stress levels of 103 to 180 MPa at a stress ratio (R) of 0.1. When the specimens were fatigued at the lowest stress levels (103 and 129 MPa) the cracks initiated and grew as “eyebrow” surface cracks at the faying surface on the straight-shank hole side, but when the higher stress levels were applied (154 and 180 MPa) the cracks initiated as corner cracks at the hole along the faying surface. FASTRAN was used to calculate the fatigue lives of these specimens using two different crack models. The first was the eyebrow type crack—a crack initiating on the faying surface near the bottom of the rivet that appeared like surface cracks. Thus, a surface crack was assumed to initiate along the faying surface and the crack was subjected to both remote tension and bending loads. The rivet was totally neglected in these analyses. The bending stress was estimated from the Hartman-Schijve equations [18] and was 0.34 times the remote applied stress. Figures 4(a) shows the results of tests conducted at 103 MPa at R = 0.1. The crack length, 2c, was measured using an acoustic microscope and includes the hole diameter plus crack growth on both sides of the hole. In the analyses for the eyebrow crack, an initial surface crack length, ci, of 2.4 mm (radius of rivet head) was assumed. The initial crack depth, ai, was then chosen to fit the bounds of the three test specimens. The 9-µm deep crack gave nearly an upper bound; whereas, the 15-µm deep crack gave a lower bound. These values were selected by trial-and-error to fit the test data. For tests conducted at the higher applied stress level, Figure 4(b), the crack configuration in the tests and analyses was a corner crack located at the edge of the straight-shank hole. The bending stress was calculated to be 0.39 times the applied stress and the rivet-load factor (Lf) was 0.37. Again, the crack length, 2c, was measured with the acoustic or optical microscope and the crack length included the hole diameter. The initial corner-crack size was, again, chosen to fit the upper and lower bounds of the test data. For this
7
cracking mode, a 60- and 120-µm crack fit the results fairly well. These initial crack sizes were quite large for the 2024 alloy (inclusion particle clusters range from 3 to 30-µm in size), but these sizes could have been caused by drilling marks and burrs at the outer edges of the fastener hole. 4.2 Georgia Institute of Technology Two-rivet-row lap-joint specimens were tested at Georgia Tech [23]. The lap-joint specimen is shown in Figure 5. Several rivet conditions were considered: (1) standard-driven rivets, (2) over-driven (tight) rivets, or (3) under-driven (loose) rivets. All specimens were subjected to a remote stress of 124 MPa. Figure 6(a) shows the fatigue tests results on the under-driven rivet condition, which had an average life of about 80,000 cycles. (Crack growth was not monitored in these tests, in contrast to the previous Northwestern tests.) In the fatigue analyses, a semi-circular corner crack (a/c = 1) was assumed to occur along the faying surface of straight-shank hole. Various EIFS values were assumed. It was found that a 6µm crack fit the average results quite well. The upper and lower bounds were captured quite well by the 4and 15-µm initial crack, respectively. The test results for the standard- and over-driven rivets are shown in Figure 6(b). Here it was found that the standard-and over-driven rivets produced nearly the same cycles to failure. The average fatigue life was about 60% longer than that for the under-driven rivets. Here a semicircular corner crack was assumed as the EIFS and a 7-µm interference value was needed to fit the mean of the test results with a 6-µm initial crack. Again, the fatigue scatter was captured quite well by the 4- to 15µm initial crack. 5.0 RETIRED AIRCRAFT LAP-JOINT CONFIGURATION AND ANALYSES A retired passenger aircraft was destructively examined to determine the state of cracking in the fuselage lap-joint regions on one side of the aircraft [1-6]. On the other side, several curved fuselage panels were removed from the aircraft and two of them (FT-1 and FT-2) were subjected to extended fatigue testing in a pressure box at the FAA’s William J. Hughes Technical Center in Atlantic City, NJ [3]. A drawing of structural details around the horizontal lap joint is shown in Figure 7. Fatigue cracks would be expected to be present and grow in the horizontal three-rivet row lap joint near the center of the panel. Figure 8 shows the cross section at a rivet location showing the inner and outer sheets with an internal doubler and the countersunk rivet. Cracks would be expected to initiate and grow from the faying surface as corner cracks or surface cracks. In the following, comparisons are made between the measured and calculated cracking in the retired aircraft fuselage structure and cracking in curved fuselage panels removed from the aircraft and tested at the FAA Technical Center.
8
5.1 Aircraft Fuselage Lap-Joint Cracking Behavior A large number of rivet locations had been examined from the retired passenger aircraft and a number of cracks were found emanating from the rivet holes [2, 4]. These cracks had been examined in a scanning-electron-microscope (SEM) to count striations and to back-track the cracking history to reconstruct the crack-length-against-flight-cycle behavior [4]. The primary fuselage loading comes from the ground-airground (GAG) pressurization cycle. Some of these results are shown in Figure 9. The open symbols show results on a surface crack emanating along the faying surface but near the fastener hole and the solid symbols show a corner or surface crack emanating from the edge of the fastener hole. AFGROW [15] and FASTRAN [13] have both been used to calculate the cracking in the retired aircraft fuselage joints during its 60,000-pressure cycle history.
Of concern was the restriction in
FASTRAN that the a/c ratio had to be held constant, such as a/c = 1, while the a/c ratio was variable in AFGROW. In AFGROW, the growth of a corner crack is independent in the a- and c-directions. An AFGROW analysis of an initial ai/ci = 1 corner crack in a lap-joint was made with 37% fastener load, 63% by-pass load and 85% bending; and the predicted a/c-ratio was nearly unity until the crack began to break through the sheet thickness (a/B = 1; a/c = 0.92). For a/B ratios greater than unity, AFGROW analyses modeled an oblique crack front until the crack transitions into a straight-through crack.
However,
FASTRAN assumes that the a/c ratio is held constant at unity until breakthrough. Thereafter, a straightthrough crack is assumed until failure. Because of compensating effects of the remote loads causing higher stress-intensity factors along the depth, a-direction, and bending causing lower stress-intensity factors along the depth direction, the crack in AFGROW was predicted to grow as a nearly quarter-circular (a/c ~ 1) crack. The dashed curve in Figure 9 is a calculated result from AFGROW using an EIFS of 5-µm radius corner crack. The EIFS value was chosen to roughly fit the mean of the measured data. The solid curves show calculations made with FASTRAN for values of EIFS ranging from a 9 to 30-µm radius corner crack. Both codes produced essentially the same results, in that, the shape of the crack length against flights curves were similar for cracks larger than about 300-µm. The only major difference was in the small-crack regime (5 to 30-µm). (Note that the AFGROW calculations did not include the effects of biaxial loading; whereas, the FASTRAN calculations did included the influence of biaxial loading, λ = 0.5, on stress-intensity factors, as shown in the Appendix.) FASTRAN calculations were also carried out to failure, which indicated that if not repaired or replaced, the fuselage is predicted to go to failure between 71,000 to 93,000 flights. Note that the Aloha Airlines Boeing 737 with a similar fuselage lap-joint design, but without a bonded doubler, had a fuselage failure at about 89,680 flight cycles [24], as shown by the diamond symbol.
9
5.2 Curved Fuselage Test Panels Two of the curved fuselage test (FT) panels removed from the retired aircraft after about 60,000 pressure cycles were tested in a pressure-box at the FAA Technical Center [3, 25]. Because these panels were removed from the side of the aircraft, which apparently had tight joints and rivet connections, there were two types of crack configurations that could be selected: (1) surface crack at the edge of the rivet head, as in Figure 4(a) or (2) corner crack at the edge of the fastener hole, as in Figure 6(b). Herein, the surface-crack model was used to make fatigue life and crack growth predictions. Note that the surface- or through-crack model (without a rivet hole) would not be influenced by biaxial loading [26]. Figure 10 shows the predicted crack length, 2c, against cycles, N, for two levels of secondary bending. The two levels of bending were estimated from lap-joints with and without a bonded doubler [3, 27, 28]. The flight history (GAG loading) on this section in the fuselage was calculated to be at 94.5 MPa at R = 0 for 59,497 cycles [2], and the stress applied to FT-2 and FT-1 panels was 98 MPa at R = 0.1 for 43,500 cycles and 120,000 additional simulated in-service cycles, respectively, as shown by the solid vertical lines [3]. But close examination of the lap-joint region indicated no cracking. The predicted cycles on the curved fuselage test panels depended greatly upon the magnitude of secondary bending used in the analyses. The higher bending factor (0.85) indicated that both FT-2 and FT-1 panels should have cracked in 100,000 to 180,000 total (flight plus simulated) cycles, but they had no evidence of cracking. However, using the bending factor of 0.38 indicated that both panels should not have significantly cracked in less than 200,000 cycles, which agreed well with the curved panel tests. Panel FT-1 with improved loading fixtures withstood about 180,000 total cycles (flight loading plus 120,000 cycles of in-service simulated loading for load condition A), but a detailed examination revealed no cracking in the lap-joints. Thus, damage in the form of saw-cuts were inserted at some particular rivet holes [3] and the panel was subjected to residual strength loads (113 MPa at R = 0.1 for condition B) for 10,000 cycles, but no crack growth was observed at the saw-cuts. Loads were then increased to the design limit loads (130 MPa at R = 0.1 for condition C) for 5,000 cycles and some crack growth was detected. Finally, loads were increased 147 MPa at R = 0.1 (load condition D) and the panel was cycled for an additional 6,770 cycles. Some measured crack growth against cycles is shown in Figure 11. In the FT-1 analysis, an initial through crack (equal area of the saw-cut, ci = 1.65 mm) was placed at the forward and aft edges of a damaged rivet hole. Because the number of cycles to initiate a crack from the saw-cut was not known, the number of cycles in load condition B was changed until the crack length at 135,000 cycles was about 4.4 mm. Thus, the computed crack growth under load condition D would be
10
compared to the measured crack growth during the same loading sequence. Three levels of secondary bending were assumed. The high bending level (0.85) was obtained from reference 3, which was based on results from reference 23. However, Fawaz [28] had tested 4 joints and measured secondary bending factors from 0.2 to 0.34. None of these joints, however, were exactly the same as the retired fuselage joints, but Joint I was the closest. Joint I had 1.6-mm skin with 0.64-mm thick doubler, while the aircraft joint had 1mm skin and 0.5-mm thick doubler. The calculated results with the highest bending factor (0.85) produced the shortest crack growth behavior, while the results with the nominal bending factor (0.38) was fairly close. A bending factor of 0.25 was required to match the test results. Further study is needed on the appropriate bending factor (or other parameters in the crack-growth analysis) for the panels tested in the pressure box. If panels from the other side of the fuselage had been selected for pressure-box testing, then further cracking would have been expected. 6.0 DISCUSSION OF RESULTS Testing and analyses made on lap-joints in this paper have involved two types of laboratory coupons, results from curved panel tests, and destructive examination of cracking in lap-joints of a retired passenger aircraft. For each case, a particular crack configuration was selected based on whether the rivet installation could have been characterized as tight, standard or loose.
Using the selected crack
configuration, an equivalent-initial-flaw-size (EIFS) was selected to best fit the test crack-length-againstcycle results.
For each case, different EIFS values were found.
These different EIFS values could
possibility be explained by some observations that have been made during the aging aircraft studies conducted in the 1990’s (see e.g., Ref. 21). Installation of rivets into laboratory coupons have generally resulted in tighter rivet connections (higher rivet-hole interference and frictional forces between layers); whereas, rivet installation in full-scale aircraft is more difficult and could lead to a loose joint. Due to manufacturing and installation variations, the two sides of the retired aircraft’s fuselage had very different joint quality. The left side had tight joints with standard or overdriven rivets while the right side had loose joints with under driven rivets. The left side with the tight joints was used to manufacture the curved panels (FT-1 and 2). In addition, fastener holes drilled in the laboratory environment may be more pristine (less burrs and machining marks) than those drilled in a large fuselage. Thus, the EIFS values for the actual fuselage were larger than those for the laboratory coupons.
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7.0 CONCLUDING REMARKS The crack-growth model, FASTRAN, was used to calculate fatigue lives and crack growth in laboratory lap-joint specimens made of a thin-sheet clad aluminum alloy to establish appropriate crack configurations and to select equivalent initial flaw sizes (EIFS). Various loading and rivet conditions were considered, such as high loads or low loads, and standard, over-driven (tight) or under-driven (loose) rivets. For the standard-driven and under-driven rivets, a corner crack at a fastener hole was assumed; whereas, for the tight-rivet condition, a surface crack coming from the faying surface was considered. The calculated fatigue lives and crack growth in the laboratory specimens agree well with the test data. Using the effective stress-intensity-factor-range-against-rate relation for the clad alloy, a corner crack at a fastener hole was used to calculate the fatigue lives and crack growth in the retired aircraft fuselage joints (under-driven rivet side) and a surface crack in a plate was used to calculate the fatigue life and crack growth in the curved test panel from the tight rivet side. The calculated crack length against flight pressure cycles in the retired aircraft fuselage was quite similar to the results found from fractographic examinations. The predicted cycles on the curved fuselage test panels depended greatly upon the magnitude of secondary bending used in the analyses. For simulated in-service loading, the higher bending factor (0.85) indicated that both FT-1 and FT-2 panels should have cracked in 100,000 to 180,000 cycles, but they had no evidence of cracking. However, using the bending factor of 0.38 indicated that both panels should not have cracked in less than 200,000 cycles. In addition, predicted crack growth in the FT-1 panel at higher applied loading with the lower bending factors agreed better with test measurements. Further study is needed on the appropriate bending factor or other parameters in the crack-growth analysis for the panels tested in the pressure box. Overall, the paper demonstrated that fuselage lap-joint fatigue-life-prediction methods based on crack growth are very adequate. This suggests that the portion of fatigue life spent in nucleating fatigue cracks in real aircraft joints is very small. 8.0 REFERENCES 1.
Steadman, D. and Bakuckas, J. G., Jr. Destructive evaluation and extended fatigue testing of retired transport aircraft: Program overview. DOT/FAA/AR-07/22, V1, 2007.
2.
Ramakrishnan, R. and Jury, D. Destructive evaluation and extended fatigue testing of retired transport aircraft: Damage characterization. DOT/FAA/AR-07/22, V2, 2007.
3.
Mosinyi, B., Bakuckas, J. G., Jr. and Steadman, D. Destructive evaluation and extended fatigue testing of retired transport aircraft: Extended fatigue testing. DOT/FAA/AR-07/22, V4, 2007.
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4.
Ramakrishnan, R., Steadman, D. and Carter, A. Crack history reconstruction of lap joint fatigue cracks. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
5.
Jury, D., Ramakrishnan, R. and Carter, A. Rivet installation and faying surface quality studies in a lap joint removed from a retired commercial aircraft. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
6.
Ramakrishnan, R. and Steadman, D. Analysis of the influence of fastener installation and faying surface quality on fatigue cracking in aircraft lap joints. In: Proc. Int. Fatigue Congress 2006, Atlanta, GA.
7.
Jongebreur, A. A., “The Fatigue Strength at Fluctuating Tension of Two Row Rivited Single Lap Joints of Clad Sheet of the Aluminum Alloys 2024-T3 or 7075-T6”, Fokker Report S-116, October 1965.
8.
Jarfall, L. E., “Optimum Design of Joints: The Stress Severity Factor Concept”, 5th ICAF Symposium, Aircraft Fatigue -- Design, Operational and Economic Aspects, Melbourne, Australia, May 1967.
9.
Homan, J.J. and Jongebreur, A.A., “Calculation Method for Predicting the Fatigue Life of Riveted Joints”, 17th ICAF Symposium, Durability and Structural Integrity of Airplanes, Stockholm, Sweden, 1993, pp. 175-190.
10.
Short-Crack Growth Behaviour in an Aluminum Alloy -- an AGARD Cooperative Test Programme, AGARD R-732, 1988.
11.
Newman, J. C., Jr. A review of modeling small-crack behavior and fatigue-life predictions for aluminum alloys. Fatigue and Fracture of Engineering Materials and Structures, 1994; 17(4):429-440.
12.
Newman, J. C., Jr., Harris, C. E., James, M. A. and Shivakumar, K. N. Fatigue-life prediction of riveted lap-splice joints using small-crack theory. In: Fatigue in New and Aging Aircraft, ICAF, EMAS Publishing, UK, 1997; I:523-539.
13.
Newman, J. C., Jr. FASTRAN II - Fatigue Crack Growth Structural Analysis Program. NASA TM 104159, 1992.
14.
Bakuckas, J. G., Jr. Full-scale testing of fuselage structure containing multiple cracks. DOT/FAA/AR-01/46, 2002.
15.
AFGROW Users Guide, Version 4.0005.12.10 (2002) J. A. Harter, WPAFB OH.
16.
Newman, J. C., Jr. and Raju, I. S. Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads. In: Computational Methods in the Mechanics of Fracture, S. N. Atluri (ed.), 1986;2:311-334.
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17.
Hartman, A. and Schijve, J. The effect of secondary bending on fatigue strength of 2024-T3 alclad riveted joints. NLR TR 69116 U, National Aerospace Laboratory, 1969.
18.
Schijve, J., Jacobs, F. A., and Tromp, P. J. Crack propagation in aluminum alloy sheet materials under flight simulation loading. NLR-TR 68117 U, National Aerospace Lab, 1968.
19.
Newman, J. C., Jr. A crack opening stress equation for fatigue crack growth. Int. J. Fract., 1984;24:R131-Rl35.
20.
Newman, J. C., Jr. Effects of constraint on crack growth under aircraft spectrum loading. Fatigue of Aircraft Materials, Delft University Press, 1992, 83-109.
21.
Second Joint NASA/FAA/DoD Conference on Aging Aircraft. NASA CP-208982, 1999.
22.
Conner, Z., Fine, M. E. and Achenbach, J. D. Quantitative investigation of surface and subsurface cracks near rivets in riveted joints using acoustic, electron and optical microscopy. In: NASA CP208982, Part 1, 1999, pp. 240-243.
23.
Atre, A. P., Johnson, W. S. and Newman, J. C., Jr. Assessment of residual stresses and hole quality on the fatigue behavior of aircraft structural Joints: Finite element simulation of riveting process and fatigue lives, DOT/FAA/AR-07/56, V3, 2009.
24.
Aircraft Accident Report—Aloha Airlines, Flight 243, Boeing 737-200. National Transportation Safety Board, NTSB/AAR-89/03, 1989.
25.
Mosinyi, B., Bakuckas, J., Steadman, D., Awerbuch, J., Lau, A. and Tan, T. Full-scale extended fatigue testing of fuselage structure from a retired passenger service airplane. Ninth Joint FAA/DoD/NASA Aging Aircraft Conference, 2006, Atlanta, GA.
26.
Tada, H., Paris, P. C. and Irwin, G. R. The stress analysis of cracks handbook. Third Edition, ASME Press, New York, NY, 2000:125.
27.
de Rijck, J. J. M. and Fawaz, S. A simplified approach for stress analysis of mechanically fastened joints. Fourth Joint DoD, FAA and NASA Conference on Aging Aircraft, St. Louis, MO, May 2000.
28.
Fawaz, S. A. Equivalent initial flaw size testing and analysis. AFRL-VA-WP-TR-2000-3024, June 2000.
29.
Chang, C. and Mear, M. E. A boundary element method for two-dimensional linear elastic fracture analysis. Int J Fracture, 1996;74:219-251.
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Appendix – Effects of Biaxial Loading on Stress-Intensity Factors for Through Cracks Emanating from a Circular Hole A fastener hole in an aircraft fuselage is subjected to a wide variety of loading conditions, as shown in Figure 1. A single crack or two-symmetric cracks of length, c, emanating from an open hole and subjected to only remote uniform stress, Sb, and biaxial stress, λSb, were analyzed with the two-dimensional boundary-element code, FADD2D [29], to determine the influence of biaxial loading on stress-intensity factors. Figure 12 shows, Fλn, ratio of the stress-intensity factor for a crack under biaxial loading (λ) to that for only uniaxial remote stress (λ = 0) against crack-length-to-hole-radius (c/r) ratio. The open symbols show the results for two-symmetry cracks (n = 2) and the solid symbols show the results for a single crack (n = 1). For small c/r ratios, the results for one or two cracks agreed very well, but some slight differences were observed for larger c/r ratios. For c/r > 3, biaxial loading had less than 1% influence on the stressintensity factors. Equations were developed to fit these results and they are given by Fλ1 = 1 + λ/[3 + 4.5 (c/r) + 4.7 (c/r)2 + 4.9 (c/r)3]
(A1)
Fλ2 = 1 + λ/[3 + 4.5 (c/r) + 6.2 (c/r)2 + 1.1 (c/r)3]
(A2)
Equations A1 and A2 are within about ±0.8% of the numerical results from the boundary-element analyses for any value of c/r. The stress-intensity factor for either two- or three-dimensional cracks is then given by Kλ = Kλ=0 Fλn
(A3)
where Kλ=0 is the stress-intensity factor for either a surface crack, corner crack or through crack at a fastener hole.
15
Figure Captions: Figure 1. - Crack configuration and loading for rivet-loaded hole Figure 2. - Fatigue-crack-growth-rate properties for 2024-T3 clad material Figure 3. - Three-rivet-row lap joint specimen tested at Northwestern University [22] Figure 4(a). - Crack growth in riveted lap joint at a low-applied stress level Figure 4(b). - Crack growth in riveted lap joint at a high-applied stress level Figure 5. - Two-rivet-row lap joint specimen tested at Georgia Institute of Technology [23] Figure 6(a). - Fatigue lives of lap-joint specimens with under driven rivets Figure 6(b). - Fatigue lives of lap-joint specimens with standard and over driven rivets Figure 7. - Curved panel (FT-2) from retired aircraft tested at FAA Technical Center [25] Figure 8. - Typical rivet configuration in retired aircraft [2, 5] Figure 9. - Measured and calculated crack growth from riveted joints in retired aircraft Figure 10. - Predicted crack growth in the FT panels and continued testing at FAA Technical Center Figure 11. - Influence of secondary bending on predicted and measured crack growth in FT-1 panel tested at FAA Technical Center Figure 12. - Influence of biaxial loading on stress-intensity factors for single- and two-symmetric cracks at an open hole
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TABLE
Table 1 – Effective-stress-intensity-factor-against-rate relation for 2024-T3 (Alclad) B = 1 mm
∆Keff, MPa-√m
dc/dN, m/cycle
0.75
1.00e-11
1.05
1.00e-10
1.37
6.00e-10
1.75
1.90e-09
4.00
7.00e-09
7.60
1.00e-07
10.7
4.00e-07
17.0
3.00e-06
35.0
1.00e-04
85.0
1.00e-02
α = 2.0
≤ 4.00e-08
α = 1.0
≥ 2.00e-07
17