Engineering Fracture Mechanics

Transcription

1 Engineering Fracture Mechanics 76 (2009) Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: Crack closure under high load-ratio conditions for Inconel-718 near threshold behavior Y. Yamada, J.C. Newman Jr. * Department of Aerospace Engineering, Mississippi State University, Mississippi State, MS 39762, United States article info abstract Article history: Received 2 July 2008 Received in revised form 26 September 2008 Accepted 27 September 2008 Available online 17 October 2008 Keywords: Fatigue-crack growth Crack closure K max effect Threshold Compression precracking Load ratio Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 6 R ) and a constant K max test condition. Previous research had indicated that high R (>0.7) and constant K max test conditions near threshold conditions were suspected to be crack-closure-free and that any differences were attributed to K max effects. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crack-opening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. The crack-opening loads were increasing as the crack approached threshold conditions at R = 0.7. Based on these measurements, crack-closure-free FCG data (DK eff against rate) were calculated. The DK eff -rate data fell at lower DK values and higher rates than the constant K max test results. In addition, constant R tests at extremely high R (0.9 and 0.95) were also performed and compared with the constant K max test results. The constant R test results at 0.95 agreed well with the DK eff -rate data, while the R = 0.9 data agreed well with constant K max test data in the low-rate regime. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold was approached, while the R = 0.9 and K max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R P 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces in the nearthreshold regime. Tests at low R also showed darkening of the fatigue surfaces only in the near-threshold regime. These results suggest that the DK eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Cracks in high-cycle fatigue (HCF) components spend a large portion of their fatigue life near threshold conditions. In order to characterize the evolution of damage and crack propagation during these conditions, fatigue-crack-growth (FCG) rate data at threshold and near-threshold conditions are essential in predicting service life and in determining the proper inspection intervals. Based on linear elastic fracture mechanics, FCG rate (dc/dn) data are quantified in terms of the stress-intensity factor range, DK, at a given load ratio (R = minimum to maximum load ratio) [1]. The relation between DK and dc/dn was shown to be nearly linear on a log(dk) log(dc/dn) scale. The relationship becomes nonlinear when the crack approaches * Corresponding author. Tel.: ; fax: address: j.c.newman.jr@ae.msstate.edu (J.C. Newman) /$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi: /j.engfracmech

2 210 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) Nomenclature B thickness, mm c crack length, mm c f crack length at failure, mm dc/dn crack growth rate, m/cycle E modulus of elasticity, MPa K cp compressive (minimum) stress-intensity factor during pre-cracking, MPa m 1/2 K F elastic plastic fracture toughness, MPa m 1/2 K Ie elastic fracture toughness or maximum stress-intensity factor at failure, MPa m 1/2 K max maximum stress-intensity factor, MPa m 1/2 m fracture toughness parameter P max maximum applied load, N P min minimum applied load, N P o crack opening load, N R load (P min /P max ) ratio U crack-opening function, (1 P o /P max )/(1 R) W specimen width, mm DK stress-intensity factor range, MPa m 1/2 DK c critical stress-intensity factor range at failure, MPa m 1/2 DK eff effective stress-intensity factor range (U DK), MPa m 1/2 r ys yield stress (0.2% offset), MPa r u ultimate tensile strength, MPa BFS back-face strain gage CPCA compression pre-cracking and constant-amplitude test method CPLR compression pre-cracking and load-reduction test method C(T) compact specimen DICC debris-induced crack closure FCG fatigue-crack growth OPn crack-opening load (P o /P max ) ratio at n% compliance offset PICC plasticity-induced crack closure RICC roughness-induced crack closure fracture [2] or when the FCG rate is very slow [3]. One of the significant mechanisms that influences crack-growth behavior is crack closure, which is partly caused by residual plastic deformations remaining in the wake of an advancing crack [4,5], roughness of the crack surfaces [6], and debris created along the crack surfaces [7]. The discovery of the crack-closure mechanism and development of the crack-closure concept led to a better understanding of FCG behavior, like the load-ratio (R) effect on crack growth. The crack-closure concept has been used to correlate crack-growth-rate data under constant-amplitude loading over a wide range in rates from threshold to fracture over a wide range in load ratios and load levels [8]. Difficulties have occurred in the threshold and near-threshold regimes using only plasticity-induced crack-closure modeling [9]. The load range where the crack tip is fully open is considered to be the effective range controlling crack growth. To calculate the effective stress-intensity factor range, DK eff, the crack-opening load, P o, was initially determined from load-displacement records using a local displacement gage placed near the crack tip [4,5]. For convenience, however, more recent measurement methods have used either remote crack-mouth-opening-displacement (CMOD) gages or back-face strain gages (BFS). These remote measurement methods have indicated that cracks are fully open under high load-ratio conditions. Thus, high load ratio (R P 0.7) data have been considered to be closure free, even in the threshold regime, and R-ratio effects were attributed to K max effects. In the low rate regime, at and near threshold conditions, roughness-induced crack closure (RICC) [6,10] and debris-induced crack closure (DICC) [7,11], have been considered more relevant, but plasticity-induced crack closure (PICC) [8,9] is still relevant under low load-ratio conditions. The crack-closure concept has not yet been able to correlate data in the threshold regime, either from load-reduction tests at constant R or constant K max tests. Variations in the threshold and near-threshold behavior with load ratio cannot be explained from PICC alone [9], but RICC and DICC mechanisms may be needed to correlate these data. The constant K max test procedure [12] also produces what has been referred to as the K max effect, in that, lower thresholds are obtained using higher K max values [13 15]. Compared with the constant R test method, constant K max tests gradually decrease P max and increase P min to obtain a reduction in DK as the crack grows. One advantage of this test method is that it is commonly considered to produce crack-closure-free data (R P 0.7). But constant K max testing also produces data at variable load ratios (R) and fatigue-crack-growth thresholds at high load ratios (>0.8). For aluminum alloys and larger K max values, more dimpling and tunneling on the fatigue surfaces were observed [14], as the threshold was approached. This behavior indicated a change in the damage mechanism from classical fatigue-crack growth to more of a tensile fracture mode due to the K max levels approaching the elastic fracture toughness. But extensive literature data reviewed by Vasudevan et al [16] and test data by Marci [17] on a wide variety of

3 Y. Yamada, J.C. Newman / Engineering Fracture Mechanics 76 (2009) materials do not show the so-called K max effect. These mixed results suggest that something is different in either the test procedures or test specimens that exhibit different behavior in the near-threshold regime. Most of the test data reviewed by Vasudevan et al. [16] was determined by European and Japanese authors from 1979 to 1984 on unspecified crack configurations. These data may have been determined from different test methods and/or other crack configurations than those currently used in ASTM E (method approved about 1983) [18]. The so-called K max effects have been observed on a number of materials using the constant-k max test procedures on C(T) and ESE(T) specimens, as specified in E647-05, where larger K max values have produced lower thresholds [13 15]. But what has caused this behavior? Was K max close to the elastic fracture toughness, which would induce a static fracture mode [14] on cyclic crack growth? Is there a K max effect for values much lower than the elastic fracture toughness, as currently used in the two-parameter, DK m K max n, curve-fitting equations [1,19]? Could crack-closure behavior at high-r (>0.7) explain the variations in the DK-rate curves for different K max values? This paper will address these issues by conducting local and remote measurements of crack-closure behavior in the threshold regime. To generate constant load-ratio data in the threshold and near-threshold regimes, ASTM E [18] proposes the loadreduction test method. This method is basically a K-reduction scheme to maintain a constant load ratio. But the load-reduction test method has been shown to produce higher thresholds and lower rates in the near-threshold regime than steadystate constant-amplitude data on a wide variety of materials [20 22]. In addition, the load-reduction test method produces fanning with the load ratio in the threshold regime for some materials. It has been shown that the test method induces a load-history effect, which may be caused by remote closure [9,23]. Thus, the load-reduction test method does not, in general, produce constant-amplitude FCG data, as was originally intended in ASTM E In order to produce steady-state constant-amplitude data, compression compression pre-cracking methods have been proposed [24 27]. A pre-notched specimen is cycled under compression compression loading to produce an initial crack, which naturally stops growing (a threshold is reached under compression compression loading). (Standard notches, as specified in E647-05, are satisfactory with either a 45 or 60 included notch angle with a notch-root radius of about 0.1-mm. Notch surfaces do not contact during compressive loading, as specified herein.) Then the specimen is subjected to the desired constant-amplitude loading. If the crack has not grown after a million or so cycles, then the load is slightly increased (few percent). This process is repeated until the crack has begun to grow. Then the constant-amplitude loading is held constant and FCG rate data is generated at the desired stress ratio. The crack must be grown a small amount (about three compressive plastic-zone sizes) to eliminate the crack-starter notch and tensile residual-stress effects, and to stabilize the crack-closure behavior [21,27]. This method is called compression pre-cracking constant-amplitude (CPCA) loading threshold testing. Another method is to grow the crack at a low DK value, after compression pre-cracking, and then use the standard load-reduction test method. Compression precracking allows the initial DK value or rate, before load reduction, to be much lower than would be needed or allowed in the ASTM standard load-reduction test method. This method is called the compression pre-cracking load-reduction (CPLR) threshold test method. Both the CPCA and CPLR methods are used herein. In this paper, FCG tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 6 R ) and a constant K max test condition from threshold to near fracture conditions. During a test at a load ratio of 0.7, strain gages (about 3-mm gage length) were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth, as shown in Fig. 1. The placement of the local strain gages was about one-half of a thickness away from the crack tip, so that an average value of crack-opening load could be measured. In addition, a BFS gage (3-mm) was also used to monitor crack lengths and to measure remote loadstrain records during the same test. Based on the load-strain measurements (BFS and local), crack-opening loads were determined and crack-closure-free FCG data, DK eff, were calculated. In addition, constant R test at extremely high R (0.9 and 0.95) conditions were also performed and compared with the constant K max test results and the DK eff against rate Fig. 1. Compact specimen with local (crack tip) and remote (BFS) strain gages beveled holes.

4 212 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) relation. For low R (0.1 and 0.4), only the BFS gage was used to determine crack-opening loads using the 1% complianceoffset method [18]. Crack surface appearances in the threshold regime are discussed in relation to the measured crackopening behavior. 2. Material and test procedures Compact, C(T), specimens (B = 9.5 mm) were used to generate FCG rate data on Inconel-718 alloy. The specimens were obtained from Boeing-Rockwell (Ken Garr) and he had tested some of the specimens under the ASTM load-reduction method and constant-amplitude loading. He had previously tested a similar material [28], which had shown a width effect on threshold behavior using C(T) specimens and the load-reduction method. The chemical composition was: Al 0.53, C 0.03, Cb + Ta 5.03, Co 0.84, Cr 18.23, Mo 3.01, Ti 1.02, Ni 53.01% and balance Fe. The yield stress and the ultimate tensile strength were 1060 and 1350 MPa, respectively, with an elongation of 27.9%. Specimens had a width (W) of 76.2 mm and an initial notch length (measured from the pin-hole centerline) of 26 mm, as shown in Fig. 1. In addition, the edges of the pin holes in the specimens were beveled to avoid or minimize undesired out-of-plane bending moments (pins forced to contact near midthickness of specimen), see Fig. 1b. The load sequences applied to the C(T) specimens are shown in Fig. 2. All specimens were pre-cracked under constant-amplitude compression compression loading (R 20 24) to initiate a crack at the machined crack-starter V-notch with a 60 -included angle ( K cp /E m 1/2 ). FCG rate tests were then conducted using either constant K max testing (shed rate of 0.4 mm 1 ), constant-amplitude (CPCA) loading, or load reduction (CPLR) at constant R after a small amount of crack extension under constant-amplitude (CPCA) loading. Load-reduction tests were conducted when the FCG rate was 8E-10 to 2E-9 m/cycle, which is nearly an order of magnitude lower than the maximum rate allowed in the ASTM E standard [18]. FCG tests were performed under computer control on servo hydraulic testing machines Fig. 2. Load sequences for threshold and constant-amplitude testing.

5 Y. Yamada, J.C. Newman / Engineering Fracture Mechanics 76 (2009) (25 kn capacity) in laboratory air at room temperature and humidity (30 50% RH). The loads were applied in sinusoidal waveform at 18 Hz in the low-rate regime and about 3 Hz in the high-rate regime. Crack lengths were monitored by using a BFS gage and occasionally calibrated with measurements made from a traveling optical microscope. To measure load-strain records near the crack tip, strain gages were mounted close to the crack path for the specimen tested at a load ratio of 0.7 only. The locations of the strain gages were chosen to be slightly off the anticipated crack path by about the crack-starter notch height (2 mm) and about 5 mm away from the crack tip after compression compression pre-cracking (Fig. 1). A number of strain gages were mounted along the anticipated crack path to record load-strain records as the crack approached these gages. The optimum signals were obtained when the crack tip was about 2 3 mm away from the strain gage during threshold testing. Approximately 20 load-strain records were recorded when the target FCG rates were achieved. During measurements, the frequency of cyclic loadings was reduced to 0.5 Hz to minimize external noise. 3. Experimental results FCG tests were conducted over a wide range in load-ratio conditions (0.95 P R P 0.1) and a constant K max test. Fig. 3a shows the test data, which generally ranged from threshold to near fracture. At high rates, the asymptote to fracture, as expected, was a function of the load ratio, R. In this regime, the critical stress-intensity factor range at failure, DK c, is given by K Ie (1 R), where K Ie is the elastic fracture toughness or maximum stress-intensity factor at failure. Thus, at higher R-values, a crack will grow to failure at lower values of DK c. In the near-threshold regime, the R = 0.95 rates were slightly higher than the R = 0.9 rates at the same DK value. In the mid-rate regime, the R = 0.9 results gave slightly higher rates than the R = 0.7 results, but the R = 0.8 results agreed well with the R = 0.7 results. The results from the low R (0.4 and 0.1) tests show the usually parallel shift with load ratio. But at low rates, the FCG rate data exhibited severe fanning with the load ratio. (Fanning gives a larger shift in the threshold regime with R than in the mid-region.) The R = 0.9 test data agreed well with the constant K max test data at low rates, which had R-values ranging from 0.64 at the start of the test to 0.92 near threshold conditions. The constant K max test and most of the other tests had the same characteristic shape of the crack-growth-rate curve in the threshold regime, except the results from the R = 0.1 test. Here the test results showed the development of a lower plateau, which was not observed in the other tests. In this region, the fatigue surfaces were dark and lightened up as the rates increased (>1E-9 m/cycle). The R = 0.1 tests were the only ones conducted with the CPCA loading and it could not be determined whether these differences were related to either the CPCA or CPLR loading sequences. Further study is required to help resolve these issues. Fig. 3b shows a comparison of test data generated at R = 0.1 and 0.7 using the ASTM load-reduction (LR) test method [18] or the CPCA/CPLR test methods. The ASTM load-reduction tests were conducted by Ken Garr (Boeing-Rockwell, private communication) on specimens machined from the same plate of material used in this test program. These results show that the LR test method produced higher thresholds (DK th at 1E-10 m/cycle) and lower rates than the CPCA or CPLR test methods. At rates greater than about 1E-8 m/cycles, the test results from the two different laboratories and methods agreed well. At R = 0.1, differences were also observed between the CPCA and CPLR test methods, even though the CPLR test was initiated at a rate 20 times lower than the LR test (1E-8 m/cycle). Both LR and CPCA tests showed the development of a lower plateau Fig. 3. (a) FCG rate data for a constant K max and constant R tests and (b) FCG rate data at low and high R for load-reduction (LR) and CPCA/CPLR testing.

6 214 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) below a rate less than about 1E-9 m/cycle. The plateau region also corresponded to a darkening of the fatigue surfaces, which may indicate the accumulation of fretting debris. At higher rates, the fatigue surfaces did not show the dark regions. Because high R and constant K max tests were conducted, the ratio of K max to the elastic fracture toughness (K Ie ) was of concern, since previous research [14] had shown that lower thresholds were obtained as the K max values approach the fracture toughness. The series of C(T) specimens that were cycled to failure at various load ratios was used to determine the fracture toughness. Here, the critical stress-intensity factor range, asymptote to fracture, DK c was used to determine the elastic fracture toughness, K Ie. The K Ie value is the K max value at failure and was calculated from DK c /(1 R). These results are shown in Fig. 4. The K Ie values ranged from 125 to 175 MPa m 1/2 depending on the ratio of final crack-length-to-specimen-width (c f / W) ratio at failure. From the Two-Parameter Fracture Criterion (TPFC) [29], the elastic plastic fracture toughness, K F, was 650 MPa m 1/2 and the fracture toughness parameter, m, was 0.6. These values were selected to fit the test data in Fig. 4. The TPFC equation is K F ¼ K Ie =ð1 ms n =S u Þ for S n < r ys ; ð1þ where K F and m are the two fracture parameters, K Ie is the elastic fracture toughness (elastic stress-intensity factor at failure), S n is the net-section stress and S u is the plastic-hinge stress based on the ultimate tensile strength. For example, for a center crack in a finite-width specimen, S u is equal to r u, the ultimate tensile strength; for a pure bend cracked specimen, S u = 1.5r u ; and for a C(T) specimen, S u 1.62r u. A similar equation was derived for S n > r ys, see Ref. [29]. Once K F and m are known for a material, thickness and specimen configuration, then K Ie is calculated as K Ie ¼ K F =f1 mk F =½S u p ðpcþfn Šg for S n < r ys ð2þ for a given crack length and specimen width. (Note that F n is the usual boundary-correction factor, F, on the stress-intensity factor with a net-to-gross section conversion [29], because the net-section stress is used in Eq. (1).) For S n > r ys, a more complicated equation, which is a function of the stress strain behavior, is given in Ref. [29]. The TPFC fit the test results quite well and predicted that the K Ie values are a function of the crack length and width; and approaches zero as the crack length approaches the width. Later, the TPFC will be used to calculate the elastic fracture toughness to compare with the K max values used in the tests near threshold. Fig. 5 shows the results of only the constant K max test and the CPLR/CA test at R = 0.7. (After CP, the LR test was initiated at a rate of 1E-9 m/cycle. Once reaching threshold conditions, CA loading was applied for rates greater than 1E-9 m/cycle.) A large difference was observed between these two data sets, even though the constant K max and R test data were both considered crack-closure-free data. The K max test exhibited a lower threshold than the R = 0.7 tests, which may be considered as a K max effect. However, the K max value was only about 15% of the calculated elastic fracture toughness (K Ie = 240 MPa m 1/2 ), so it is highly unlikely that this low value would have caused a K max effect. The constant K max test data started deviating from the R = 0.7 data at a rate of about 2.5E-09 m/cycle. Several FCG rates were then selected to make near crack-tip load-strain measurements to determine crack-opening loads. They were chosen as 2.5E-09, 9.0E-10, 5.0E-10, 3.6E-10, 2.5E-10 and 1.5E- 10 m/cycle. Thus, the change in crack-opening loads could be captured as the FCG rate approaches the threshold condition. Fig. 6 shows typical load-reduced-strain records measured from a near crack-tip strain gage (local) and the BFS gage (remote) at a FCG rate of 9.0E-10 m/cycle (The method used to generate the load-reduced-strain, or load-reduced-displacement, Fig. 4. Elastic fracture toughness (K Ie ) as a function of crack length and width.

7 Y. Yamada, J.C. Newman / Engineering Fracture Mechanics 76 (2009) Fig. 5. Comparison of result from constant K max test and constant R test at 0.7. Fig. 6. Comparison of reduced load-strain records measured with local and BFS gage. records is described in Ref. [30] and will not be presented here). Levels of noise were almost the same between the local and remote gages, but the shape of the load-reduced-strain records were quite different. Obviously, the signal-to-noise ratio in these data is poor. Smoothing methods were attempted but they did not work well (future efforts are being made to try to reduce the noise in these signals). But the local gage did measured a clear indication of crack closure, even at R = 0.7, which was quite surprising. The local gages almost always showed some amounts of crack closure in the near threshold regime; whereas, the remote gage consistently showed no indication of crack closure at the high R-values. This indicated that the remote gages are not sufficient to determine crack-opening loads from remote measurements, especially at high R; and that local measurements have a great advantage in capturing the near crack-tip behavior. ASTM E [18] suggests using a 2% offset compliance change to determine crack-opening loads from load-reducedstrain or displacement records. However, because of the amplitude of noise and size of crack-closure tail-swing in the reduced load-strain record, the use of an offset value was not practical. In Fig. 6, the amplitude of noise was approximately 1-le and the size of the crack-closure tail-swing was about 2.5-le for the R = 0.7 local measurements at 9.0E-10 m/cycle; whereas other tests at lower R (0.1) showed orders-of-magnitude larger tail swings from the BFS gage. On a load-reduced-stain record, the abrupt change from a non-linear curve (tail swing) to a near vertical (linear) trace indicates the crack-opening load. Several smoothing techniques were attempted to determine adequate crack-opening values, however, the opening values were very sensitive to the smoothing parameters. Instead of trying to determine one single crack-opening value, a range of opening values for each load-reduced-strain record was determined and some of these are shown in Fig. 7. First, the tail swing caused by crack closure was very obvious for all FCG rates and the range of crack-opening-load ratios rose

8 216 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) Fig. 7. Reduced-load strain records for several FCG rates near threshold conditions. Fig. 8. Region of calculated DK eff based on crack-opening measurements using local gages. as the rate approached the threshold condition. Based on the ranges of crack-opening load determined for each rate, a region of DK eff was calculated and this region is shown in Fig. 8. Surprisingly, the region of DK eff was located at DK values lower than the constant K max test. At the ASTM defined threshold (1E-10 m/cycle), the (DK eff ) th ranged from 2.7 to 3.1 MPa m 1/2, whereas DK th from the constant K max test was 3.15 MPa m 1/2. This is a very minor difference, but constant K max tests were believed to generate crack-closure-free test data at high R. But the crack-closure-free region indicated that varying amounts of crack closure may be present in the constant K max test results from R = 0.64 to Since differences where observed between the constant K max test and the DK eff -rate region, constant R tests at extremely high R conditions (0.9 and 0.95) were conducted to search for a proper R-value to obtain crack-closure-free data. The test results for R = 0.9 and 0.95 are shown on Fig. 9. Again, the K max values in these two high R tests were 14% and 25% of the corresponding calculated elastic fracture toughness at threshold and, thus, K max effects are unlikely. The results from the R = 0.95 test, which were analyzed by the secant method, agreed well with the DK eff -rate region determined from the R = 0.7 test. Likewise, the test results at R = 0.9 agreed well with the K max test data in the low-rate regime (<1.0E-9 m/cycle), and merged with the DK eff region at higher rates. Unfortunately, the number of specimens was depleted and further studies with the local strain gages on specimens tested under constant K max, low and high R conditions could not be tested. However, for the low R ratio tests at 0.1 and 0.4, the BFS and crack-monitoring software had recorded various complianceoffset values using Elber s reduced-strain approach [30]. Comparisons between the BFS and local-strain gages could not be

9 Y. Yamada, J.C. Newman / Engineering Fracture Mechanics 76 (2009) Fig. 9. Comparison of high R, constant K max test data and DK eff rate behaviour. Fig. 10. Local and BFS load-against reduced strain for low R = 0.1 test on 7075-T651 alloy. made on the Inconel-718 alloy, but a comparison could be made on a 7075-T651 alloy. Fig. 10 shows the load-reduced-strain records measured on a test at R = 0.1. The results from the BFS shows the tail-swing associated with crack closure and the compliance-offset values from 1% (OP1) to 16% (OP16). The solid horizontal line shows the crack-opening-load ratio from FASTRAN [31] for a constraint factor of 2, which was required to correlate the FCG rate data over a wide range in load ratios [32]. The compliance-offset values gave progressively lower values of the crack-opening-load ratio. The near crack-tip gage showed a similar load-reduced-strain record as the BFS gage, but showed a slightly larger tail-swing and indicated that the crack-opening load would be slightly higher than the 1% offset value, like that shown by FASTRAN. The 1% offset values were then used from the Inconel-718 alloy tests at R = 0.1 and 0.4; and the results of these measurements and calculations are shown in Fig. 11. Several DK-rate values were selected from the R = 0.1 and 0.4 tests, and the OP1 values were used to calculate the corresponding DK eff values. In general, the DK eff values fell short of the DK eff -rate region determined from the R = 0.7 local-strain measurements, except for the lowest rates from the CPLR tests. The R = 0.4 CPLR data agreed fairly well with the DK eff -rate curve, while the R = 0.4 CA data fell short. The 1% offset values underestimated the true crack-opening values (as shown in Fig. 10) and that the true opening loads would have resulted in a closer agreement. These results suggest that the DK eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime, if the true crack-opening values could have been measured.

10 218 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) Fig. 11. High R constant K max test and appropriate low-r DK eff data on Inconel-718 alloy. Fig. 12. Photographs of fatigue surfaces showing darkened surfaces in the near-threshold regimes.

11 Y. Yamada, J.C. Newman / Engineering Fracture Mechanics 76 (2009) Discussion of results Crack-opening measurements made on a C(T) specimen test at a load ratio (R) of 0.7 indicated a significant amount of crack closure as the threshold condition was approached. The test method was compression compression pre-cracking with load reduction (CPLR), but the FCG rate at the start of the load-reduction procedure was an order-of-magnitude less than the maximum rate allowed in the ASTM E standard. Thus, load-history effects may not have been present in the data at R = 0.7. During all tests, the fatigue-crack surfaces were very flat and straight, as shown in Fig. 12. The fatigue-crack surface from one of the R = 0.1 tests is shown in Fig. 12a, which shows a dark surface in the rate regime from 3E-10 to 3E-9 m/cycle (near-threshold regime). Fig. 12b shows the fatigue surface for the R = 0.7 test, which did not show a darkened surface in the near-threshold regime, but appeared to have a white metallic powder. But the R = 0.9 test did show a slight darkening on the fatigue surface in the near threshold regime (Fig. 12c). Why the R = 0.7 test did not show the darkened fatigue surfaces as seen on both the R = 0.1 and 0.9 tests was not known. Based on these limited data, the constant K max and R = 0.9 test may have also developed some slight amounts of crack closure. For the R = 0.9 test, the U-value (DK eff = UDK) would have ranged from 1 at 2E-9 m/cycle to 0.92 at the threshold condition to agree with the DK eff -rate region. Even the R = 0.1 and 0.4 tests may have agreed with the DK eff -rate region, if local-strain-gage measurements could have been made. The BFS gage method (OP1) under estimates the true crack-opening-load behavior for low R and was not able to determine any closure behavior for high R tests. 5. Concluding remarks Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 6 R ) and a constant K max test condition. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crackopening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold condition was approached, while the R = 0.9 and K max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R P 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces only in the near-threshold regime. Tests at lower R also showed darkening of the fatigue surfaces on most of the tests only in the near-threshold regime, which may be caused by a combination of plasticity and fretting-product-debris induced crack closure. Crack-opening measurements made at low R using the back-face strain gage and the 1% compliance offset values nearly correlated the crack-growth-rate date on a DK eff against rate basis. These results suggest that the DK eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime. Further studies on the Inconel-718 alloy and other materials using local load-strain records may provide further verification of high-r crack closure from DICC and RICC mechanisms in the near-threshold regimes. Acknowledgements The authors thank Mr. Ken Garr, Pratt-Whitney Corporation, for providing the Inconel-718 alloy C(T) specimens and the test data on similar C(T) specimens using the ASTM standard load-reduction test method. Thanks to Dr. A. Vasudevan, Office of Naval Research, for supporting development of the compression pre-cracking test procedures at MSU under grant N ; and to Dr. Keith Donald, Fracture Technology Associates, for his valuable advice on the use of his crack-monitoring software. References [1] Paris PC, Erdogan F. A critical analysis of crack propagation laws. J Basic Engng 1963;85(3): [2] Barsom JM. Fatigue-crack propagation in steels of various yield strengths. J Engng Ind 1971;93(4): [3] McEvily Jr AJ, Illg W. The rate of fatigue-crack propagation in two aluminum alloys. NACA TN 1958;4394. [4] Elber W. Fatigue crack closure under cyclic tension. Engng Fract Mech 1970;2(1): [5] Elber W. The significance of fatigue crack closure damage tolerance in aircraft structures ASTM STP 486. American Society for Testing and Materials 1971;22: [6] Walker N, Beevers CJ. A fatigue crack closure mechanism in titanium. Fatigue Engng Mater Struct 1979;1(1): [7] Paris PC, Bucci RJ, Wessel ET, Clark WG, Mager TR. Extensive study of low fatigue crack growth rates in A533 and A508 steels. ASTM STP : [8] Newman Jr JC. Effects of constraint on crack growth under aircraft spectrum loading. Fatigue of Aircraft Materials. The Netherlands: Delft University Press; [9] Newman Jr JC. Analysis of fatigue crack growth and closure near threshold conditions. ASTM STP : [10] Kirby BR, Beevers CJ. Slow fatigue crack growth and threshold behaviour in air and vacuum of commercial aluminium alloys. Fatigue Fract Engng Mater Struct 1979;1: [11] Suresh S, Zaminski GF, Ritchie RO. Oxide induced crack closure: an explanation for near-threshold corrosion fatigue crack growth behavior. Metall Trans 1981;A12A: [12] Herman W, Hertzberg R, Jaccard R. A simplified laboratory approach for the prediction of short crack behavior in engineering structures. Fatigue Engng Mater Struct 1988;11(4):

12 220 Y. Yamada, J.C. Newman Jr. / Engineering Fracture Mechanics 76 (2009) [13] Donald JK, Bray GH, Bush RW. An evaluation of the adjusted compliance ratio technique for determining the effective stress intensity factor ASTM STP West Conshohocken, PA: American Society for Testing and Materials; p [14] Newman JA, Riddell WT, Piascik RS. Effects of K max on fatigue crack growth threshold in aluminum alloys. ASTM STP : [15] Smith SW, Piascik RS. An indirect technique for determining closure-free fatigue crack growth behavior ASTM STP West Conshohocken, PA: American Society for Testing and Materials; p [16] Vasudevan AK, Sadananda K, Louat N. A review of crack closure, fatigue crack threshold and related phenomena. Mater Sci Engng 1994;A188:1 22. [17] Marci G. Fatigue crack growth threshold concept and test results for al- and ti-alloys. ASTM STP : [18] Standard test method for measurement of fatigue crack growth rates, ASTM E-647; [19] Bray GH, Donald JK. Separating the influence of K max from closure-related stress ratio effects using the adjusted compliance ratio technique ASTM STP West Conshohocken, PA: American Society for Testing and Materials; p [20] Forth SC, Newman Jr JC, Forman RG. On generating fatigue crack growth thresholds. Int J Fatigue 2003;25:9 15. [21] Newman Jr JC, Schneider J, Daniel A, McKnight D. Compression pre-cracking to generate near threshold fatigue-crack-growth rates in two aluminum alloys. Int J Fatigue 2005;27: [22] Ruschau J, Newman Jr JC. Compression precracking to generate near threshold fatigue crack growth rates in an aluminum and titanium alloy. In: Fatigue and fracture mechanics: 36th symposium, Tampa, FL; November [23] McClung RC. Analysis of fatigue crack closure during simulated threshold testing. ASTM STP : [24] Pippan R. The growth of short cracks under cyclic compression. Fatigue Fract Eng Mater Struct J 1987;9: [25] Pippan R, Plöchl L, Klanner F, Stüwe HP. The use of fatigue specimens precracked in compression for measuring threshold values and crack growth. ASTM J Test Evaluat 1994;22:98. [26] Topper TH, Au P. Fatigue test methodology AGARD Lecture Series 118. Fatigue test methodology. AGARD Lecture Series 118. Berlin: The Technical University of Denmark; [27] Yamada Y, Newman JC, III, Newman Jr JC. Elastic plastic finite-element analyses of compression precracking and its influence on subsequent fatiguecrack growth. In: Fatigue and fracture mechanics: 36th symposium, Tampa, FL; November [28] Garr KR, Hresko GC. A size effect on the fatigue crack growth rate threshold of alloy 718. W. Conshohocken, PA: ASTM STP-1372; p [29] Newman Jr JC. Fracture analysis of various cracked configurations in sheet and plate materials. Properties related to fracture toughness, ASTM STP-605; p [30] Elber W. Crack-closure and crack-growth measurements in surface-flawed titanium alloy Ti 6Al 4V. NASA TN D ;12:21. September. [31] Newman Jr JC. FASTRAN II a fatigue crack growth structural analysis program. NASA TM [32] Newman Jr JC, Jordon JB, Anagnostou EL, Fridline D, Rusk, D. Fatigue and crack-growth analyses on specimens simulating details in wing panels of naval aircraft. In: Aging aircraft conference, Phoenix, AZ; April 2008.