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In situ ultrasonic monitoring of surface fatigue crack initiation and growth from surface cavity
International Journal of Fatigue 25 (2003) 41–49 www.elsevier.com/locate/ijfatigue
In situ ultrasonic monitoring of surface fatigue crack initiation and growth from surface cavity S.I. Rokhlin ∗, J.-Y. Kim The Ohio State University Nondestructive Evaluation Program, Edison Joining Technology Center, 1248 Arthur E. Adams Drive, Columbus, OH 43221, USA Received 27 March 2001; received in revised form 21 February 2002; accepted 3 May 2002
Abstract A surface acoustic wave method for in situ monitoring of fatigue crack initiation and evolution from a pit-type surface flaw is described. The method is demonstrated for fatigue tests on Al 2024-T3 and Inconel 718 samples with different surface pit sizes. The surface acoustic wave signature is acquired continuously during the fatigue cycle without stopping the fatigue test. Crack initiation and propagation are identified clearly from the ultrasonic surface wave reflection signals. Crack initiation in the Inconel 718 sample is observed to occur at a much later stage of fatigue life than in the Al-2024-T3 sample. The ultrasonic results are supported by fractographs of fracture surfaces. Small crack sizing is performed from the ultrasonic signatures using the low frequency scattering model. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue; Ultrasonic crack depth measurement; Surface acoustic wave; Ultrasonic nondestructive evaluation; In situ fatigue experiment
1. Introduction Material degradation due to pitting corrosion and surface fatigue crack initiation from pits has been known to be a cause of widespread damage in aging aircraft structures [1]. Therefore, detection and measurement of a surface fatigue crack initiated from a surface flaw are of great significance for the prediction of remaining fatigue life and for timely maintenance of aging aircraft. Ultrasonic bulk [2] and surface [3–6] wave methods for surface and subsurface crack detection have been well developed. Resch and Nelson [3] and Yuce et al. [4] described measurements of small fatigue crack depth and crack opening load by ultrasonic surface waves. Tittman and Buck [5] performed experiments to determine the size and closure load of a surface fatigue crack in a titanium alloy. Tien et al. [6] applied surface waves to study the effect of indentation-induced residual stress on
Corresponding author. Tel.: +1-614-292-7823; fax: +1-614-2923395. E-mail address: [email protected] (S.I. Rokhlin). ∗
crack extension by comparing results for heat-treated and as-indented samples. Most previous work on ultrasonic characterization of surface breaking cracks has been concerned with a crack on a flawless surface or an artificial saw-cut as a simulated crack. However, actual cracks often initiate from surface flaws (foreign object impact damage, corrosion pit, etc.). The additional interaction of scattered waves with the surface flaw complicates crack detection and prevents immediate application of existing methods for small crack evaluation. Also, these surface flaws as stress risers lead to plasticity-induced crack closure that affects the crack reflectivity [2,7,8]. All these complicate the sizing of the small fatigue cracks emanating from a surface flaw. To address this problem activities in this direction were started in our group several years ago. Preliminary experimental results on surface wave reflectivity from a pit with crack have been reported by Dai et al. [9]. Kim and Rokhlin [10] developed a surface acoustic wave scattering model to evaluate the depths of small cracks emanating from pits. Crack closure measurement using surface waves is discussed in Ref. [11]. In this paper, an experimental method is developed
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S.I. Rokhlin, J..-Y. Kim / International Journal of Fatigue 25 (2003) 41–49
for in situ surface wave monitoring of fatigue crack initiation and propagation with data taken during fatigue cycling. The method is demonstrated for two widely used aerospace materials: Al 2024-T3 and Inconel 718. A small pit is produced to simulate surface flaws caused by pitting corrosion or foreign object impact damages. Surface acoustic wave reflections from cracks have been obtained as functions of fatigue load and number of cycles. The ultrasonically determined crack sizes are compared with fractographs.
2. Experiment 2.1. Sample preparation The materials used in this study were Al 2024-T3 alloy and Inconel 718. The Al 2024-T3 alloy fatigue sample was 1.6 mm thick, yield stress sY ⫽ 340Mpa, ultimate tensile stress sU ⫽ 483MPa, and elongation 17.5%. The Inconel fatigue sample was 1.97 mm thick, yield stress 1100 MPa, ultimate tensile stress 1310 MPa and elongation 17.0%. The specimens were machined according to ASTM standard E-466-96. The cross section of the aluminum sample was 1.6 × 6mm2 and that of the Inconel sample was 1.97 × 6mm2. Controlled-size small pits with nominal depths 250 and 750 µm and diameter 250 µm were produced by an electrical discharge machine (EDM) in the center of the specimen. 2.2. Fatigue test Fatigue tests were carried out on a servo-hydraulic MTS (mechanical testing system, Model 810) in the stress-controlled mode. The normalized fatigue load parameters were the same for both aluminum and Inconel samples. The frequency of loading was 15 Hz and the maximum stress level was 76% of the yield stress. The stress ratio R was 0.1, so that the stress range ⌬s was 231 MPa for the aluminum sample and 756 MPa for the Inconel sample. The high stress concentration (kt⬇3.45) leads to the development of a plastic zone around the pit. Considering that the onset of the long crack regime for our samples is about 650 µm [12] the measurements performed in this study are during and immediately after the short-crack regime of the fatigue life. Post-fracture surfaces were examined with scanning electron microscope (SEM) fractographs and actual sizes of crack and pit were measured. In total, 10 samples were used for ultrasonic monitoring; however, a large number of similar fatigue experiments on Al 2024-T3 samples with pits have been performed in our prior work [12].
2.3. In situ ultrasonic measurements In order to monitor crack initiation and propagation during the fatigue cycle, ultrasonic surface wave reflections from a pit with a crack were measured. The experimental system includes ultrasonic pulser/receiver, oscilloscope, control computer for MTS and ultrasonic data collection as shown in Fig. 1(a). A commercial wide-band longitudinal-wave transducer with 5 MHz center frequency was assembled on a specially designed polystyrene wedge and used for generating and receiving surface acoustic waves (Fig. 1(a)). The wedge design is critical for acceptable signal-to-noise ratio. For an in situ measurement, the transducer assembly is mounted using a small clamp on the sample undergoing the fatigue test so that the ultrasonic signals are collected during fatigue cycling (Fig. 1(b)) and at different load levels. A liquid ultrasonic couplant was applied between the ultrasonic wedge and the sample. At predetermined numbers of cycles, the computer controlled fatigue load was changed to a step-up or step-down–up (10 steps) load (Fig. 1(c)) and ultrasonic reflections were recorded and averaged, to suppress measurement noise, at each step-load level. The ultrasonic signature was repeatable for different samples.
3. Ultrasonic results and interpretation 3.1. Surface wave reflection from pit with crack in Al 2024-T3 sample Typical reflected ultrasonic signatures from a pit with an emanating fatigue crack are shown in Fig. 2 at different numbers of cycles. Surface wave reflection signals were obtained on an Al 2024-T3 sample for two load levels at different fatigue cycles. The depth and diameter of the pit were 252 and 246 µm, respectively. The fatigue life of this sample was 142,856 cycles. The surface acoustic wave reflections are composed of waves reflecting from different parts of the pit with crack (2) (A(1) N ), followed by the plate bottom reflection (AN ) of a mode-converted shear wave; the subscript N represents the number of cycles. In Fig. 2(b), the amplitudes are marked for N ⫽ 0, i.e. reflections from the pit prior to fatigue. Detailed interpretations of the pit and plate-bottom reflected signals have been presented in Ref. [10]. As seen in Fig. 2, the A(1) and A(2) groups of signals are separated in the time domain. As a result of the crack initiation and growth during the fatigue test the amplitudes of both the first (A(1)) and plate bottom (A(2)) reflections change continuously. It is interesting to compare the signals (Fig. 2(a)and (b)) taken at the same number of cycles, but only under different load levels. While the reflection signal recorded at 400 lb load changes significantly as the number of cycles increases, no change
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Fig. 1. In situ ultrasonic experiment for monitoring of surface crack emanating from a pit. (a) SAW monitoring system. (b) Ultrasonic transducer mounted on the sample. (c) Load profile to monitor crack initiation and evolution.
is observed until 52% of the fatigue life when the signal is recorded at 100 lb load. Fig. 3 shows peak-to-peak amplitudes A(1) N of the first reflection normalized by the signal amplitude before the fatigue test A(1) 0 as a function of the number of cycles N. The ultrasonic signals at different load levels were normalized with the same quantities A(1) 0 since they depend only negligibly on the load. The first reflection has minima near 60,000 and 130,000 cycles as indicated in Fig. 3. Since the crack emanates approximately from the mid-plane of the pit as shown in Fig. 4, the path difference 2R of waves reflected from the pit front and crack surface is about half the surface wave wavelength lR at 5 MHz: 2R / lR⬇0.5. Hence, the interference of reflected waves from pit front and crack surfaces is destructive resulting in decrease of the first
reflection amplitude. The first reflection starts to decrease at around 20,000 cycles and has minimum at 60,000 cycles as marked by arrow (A) in Fig. 3. This effect is also observed in Fig. 2(b) starting from 25,000 cycles as a decrease of the first reflected signal. As an alternative measure one can monitor the tail part of the first reflection which is associated with the crack reflection. However, the amplitude pattern resulting from the signal interference is more sensitive to crack initiation and enhances crack sizing analysis [10]. To illustrate the signal interference Fig. 5 shows a simulation of the overlapping of two reflected signals with time delay ⌬t ⫽ 2R / nR. The simulated signal is very similar to the actual reflected signal from the pit with crack at 65,000 fatigue cycles. From this, one can
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Fig. 2. Change of reflection signal at different fatigue cycles at two different loads (a) 100 lb, (b) 400 lb during fatigue test for an Al 2024-T3 sample. The fatigue life of the sample is 142,856 cycles.
Fig. 4. Difference of path lengths for signals reflected from pit front and crack surfaces. Fig. 3. Change of the normalized first reflection signal amplitude during fatigue life of Al 2024-T3 sample.
deduce that at 25,000 cycles, the crack has grown enough to be detectable by ultrasonic waves. Fig. 6 shows the SEM fractograph of a similar sample that was broken in tension after 25,000 cycles. The fatigue cracks
on both sides of the pit can be identified. Crack sizes are about 42–54 µm. As the crack grows further, wave reflection from the crack eventually dominates the reflecting signal. Thus, the peak amplitude of the reflection signal shifts by ⌬t ⫽ 0.178µs which corresponds to the time for the surface wave to travel twice the pit radius (2R / vR) as indicated by the dashed line in Fig.
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forms a weak resonance on the crack surface because of the low reflection coefficient (~0.2) from the crack tip [14]. The dips in reflection signal amplitudes can, therefore, result from surface wave resonance reinforced by constructive interference of creeping waves that reflect back and forth on the front half of the pit between the two crack surfaces. For one sample, the fatigue cycle was stopped and the sample was fractured in tension after the first reflection reached a minimum (B) at 100,000 cycles (Fig. 7(a)). From the fractograph for this sample shown in Fig. 7(b), the crack length on the surface from the edge of the pit is about 350 µm, just above half a surface wavelength lR ⫽ 600µm. Since the fatigue life of the samples varies from one sample to another, the number of cycles at which the first reflection has the minimum may be different from the one shown
Fig. 5. Simulation of interference of reflected surface waves.
Fig. 6. Fractograph of an Al 2024-T3 fatigue sample fractured at 25,000 cycles. Fatigue crack is initiated near the sample surface around the pit. Cracks about 42 and 54 µm width are indicated on two sides of the pit.
2(b). As was described in Ref. [12], the fatigue cracks first initiate at the edges of the pit forming two corner cracks. These cracks grow downward separately on both sides of the pit (see Fig. 6) until their depths reach the pit bottom. As these cracks grow further beyond the root of the pit, they combine into a single semi-elliptical crack whose aspect ratio is dependent on the ratio of depth to diameter of the pit [12]. In Fig. 3, the first reflections show dips at about 130,000 cycles. This can be attributed to the lowest order resonance of surface waves on the crack surface excited when the crack grows to half a wavelength of the surface wave [13]. However, it is known that the surface wave
Fig. 7. (a) Normalized first reflection versus number of cycles (Al 2024-T3 sample). The minimum of the reflection amplitude is indicated. The fatigue cycle was stopped just after reflection minimum was detected. (b) Fracture surface at number of fatigue cycles 104,000 (Al 2024-T3 sample).
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in Fig. 3, but should exhibit the same trend (in some samples, this minimum is less pronounced). 3.2. Plate bottom reflection signals in Al 2024-T3 sample The mode-converted shear wave is launched on the bottom of the pit and propagates down toward the bottom of the plate where it is reflected, mode-converted back to the surface wave at the bottom of the pit, and returned to and received by the surface wave. One can measure the depth of the surface discontinuity by analyzing the time delay and amplitude of the bottom reflection signal. As evident in Fig. 2, the plate bottom reflection signal is narrower and better defined than the first reflec-
tion. As we will see below, the bottom reflection provides useful information on fatigue crack depth and also the crack closure behavior [11]. The time of arrival of the bottom reflection increases with the sample thickness and for thicker bodies its amplitude will decrease due to attenuation which depends on material microstructure. However, for many practical cases this signal may be resolved and provide useful information. Fig. 8 shows the plate bottom reflections A(2) N versus number of cycles N normalized by the signal amplitude before the fatigue test A(2) 0 , as for the first reflection signals shown in Fig. 3. The amplitude of the plate bottom
Fig. 8. Change of normalized plate bottom reflection signal amplitude during fatigue life of Al 2024-T3 sample.
Fig. 9. Fracture surface at number of fatigue cycles 65,000 (Al 2024T3 sample).
Fig. 10. Change of the normalized surface wave reflection signal during fatigue life of Al 2024-T3 sample with a pit whose depth is 750 µm and diameter 247 µm. (a) First reflection, (b) Plate bottom reflection signal.
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reflection increases slightly with the number of cycles since it is not affected by wave interference. At around 60,000 cycles the second reflection starts to increase rapidly. This occurs when the crack reaches the pit depth substantially increasing surface wave transformation to shear wave, thus increasing the plate bottom signal. Therefore, one can expect that crack depth be about pit depth at around 60,000 cycles. To support this conclusion, Fig. 9 shows the fractograph of the sample broken after 65,000 cycles where the actual crack depth is 265 µm and half-width 200 µm, which is slightly larger than the pit depth of 250 µm. A similar in situ ultrasonic experiment was performed for the sample with a pit depth 750 µm. The sample fatigue life was 61,253 cycles. Fig. 10 shows the first and bottom reflections as a function of the number of cycles. Change of the pit reflection signal due to crack initiation starts at about 5000 cycles (Fig. 10(a)). Due to the previously mentioned interference between the pit and the crack surface reflection signals, the first reflection amplitude decreases as for the sample with 250 µm deep pit. The depth of the crack reaches the pit bottom around 45,000 fatigue cycles. The plate bottom reflection (Fig. 10(b)) does not change until this point and then starts to increase with the number of cycles. The results for the sample with the deep pit are very similar to those from the shallow pit, indicating that the ultrasonic result obtained for the sample with the 250 µm pit can be generalized to pits of different depths. As observed in Figs. 2 and 10, the ultrasonic signals are sensitive to the load level at which they are meas-
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ured. This phenomenon is related to crack opening–closing behavior as discussed in Ref. [11]. 3.3. Surface wave reflections from a pit with crack in Inconel The surface wave reflection signals for an Inconel 718 sample measured at the load level of 800 lb are shown for different fatigue cycles in Fig. 11. The depth and diameter of the pit were 182 and 254 µm, respectively. The fatigue life of the sample was 147,346 cycles. The change of ultrasonic signal due to crack initiation and evolution is similar to that for Al alloy samples. However, the monitored ultrasonic signals begin to change above 113,000 cycles indicating that the crack is detected in the Inconel 718 sample at a much later stage of fatigue life (76% of the fatigue life) than in aluminum samples (17% of the fatigue life). Similar to Al 2024T3 samples, the shift of the first reflection signal in time due to crack growth is observed. In Fig. 12 the peak-to-peak amplitude of the first and plate bottom reflections are shown as a function of number of cycles at different load levels. Very little change in the signals is observed before 113,000 cycles probably due to the high grain noise and the small reflection caused by the shallow pit (182 µm). A rapid change of the reflected signals occurs from 113,000 cycles until failure. Also a clear dependence of signal amplitudes on the load is observed. While the aforementioned conclusion seems to be correct, in general one should be careful when assessing
Fig. 11. In situ monitoring of fatigue surface crack initiation and propagation in Inconel 718 sample.
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being detected by surface waves in this sample, which is quite different from the case of the Al 2024 sample (compare Fig. 12(a)and (b) with Figs. 3 and 8).
4. Model-based ultrasonic sizing of small cracks Small corner cracks emanating from a pit can be sized from their ultrasonic signature using a low frequency surface wave scattering model proposed in Ref. [10]. According to the model, the normalized time domain reflection signature from the pit with crack is represented by the sum of the crack and the pit reflected signals as follows: r(t,a) ⫽ r(t,a ⫽ 0)
冕
(1)
⬁
⫹
Rc11(w,a)V(w)eiw(t⫺D/V R) dw,
⫺⬁
where Vi(w) is the frequency response of the measurement system, i the imaginary unit, w the angular frequency, D the pit diameter and VR is the surface wave velocity. The pit reflection coefficient in the presence of the crack is approximated by the pit reflection coefficient without the crack r(t,a ⫽ 0) that is measured prior to fatigue. The crack reflection coefficient Rc11 is approximated as Rc11(w,a) ⫽
Fig. 12. Change of surface wave reflection amplitude versus number of fatigue cycle for Inconel 718 sample with pit whose diameter is 254 µm and depth 182 µm. (a) First reflection, (b) second (bottom) reflection.
crack initiation in the Inconel sample. Comparing Figs. 2 and 11 one can note that the grain noise in the Inconel sample is much higher than in the Al alloy sample. The maximum signal-to-noise ratio in the Inconel sample for the reflection from the pit before the fatigue test is 8 dB while that in the Al alloy sample is 30 dB. Therefore, the grain noise masks small changes of the signal reflected from the pit due to crack initiation and small crack propagation. Since changes of the first (Fig. 12(a)) and the plate-bottom (Fig. 12(b)) reflected signals began to occur at the same number of cycles (113K) the crack depth may reach the pit depth (about 180 µm) before
冕
iw(1⫺n2) r(r)K2I(a)dl, 3EP ⌫
(2)
where KI(a) is the mode-I stress intensity factor of the corner crack [12], a the crack depth, n the Poisson’s ratio, E the Young’s modulus, P the input power into the transducer, dl the line element on the crack front ⌫ and r(r) is defined in Ref. [10]. Using Eq. (1), the normalized time domain reflected signals were calculated as a function of the crack depth. Then, by comparing the calculated reflected amplitude versus crack depth with the normalized amplitude coefficient versus number of cycles (Fig. 3), the crack depth versus number of cycles was determined. The corner crack model is valid while the crack grows to the pit bottom; therefore, calculated crack depths are bounded by pit depths. Fig. 13 shows the crack depths determined from the measured ultrasonic signatures for four different samples with different pit depths. The crack depths measured from SEM fractographs of the similar samples broken in tension after certain numbers of cycles are also shown by solid triangles. The experimental and predicted crack depths are in very good agreement. It is observed from SEM fractographs that the sizes of the two corner cracks are not equal immediately after initiation; however,
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University Research Initiative (MURI) under Air Force Office of Scientific Research grant #F49620-96-1-0442 and in part by the Federal Aviation Administration (FAA) under contract #97-C-001. The authors are thankful to Mr Dai for his assistance in data collection.
References
Fig. 13. Comparison of ultrasonically predicted crack depths and measured from SEM fractographs.
eventually their sizes get closer with growth. It is interesting to note that once the crack reaches the pit bottom, the crack does not grow downward but grows around the pit bottom until the two cracks merge into one crack. This results in temporary decrease of the crack growth rate as one can observe in Fig. 13. 5. Summary An in situ method using surface acoustic waves for the evaluation of small fatigue cracks emanating from pit-type surface flaws is presented. The method is demonstrated by monitoring fatigue crack initiation and propagation during fatigue cycling on Al 2024-T3 and Inconel 718 samples. By interpreting ultrasonic reflection signals, crack initiation and growth are described quantitatively. After breaking samples in tension at different stages of fatigue life, the ultrasonic results were verified by SEM fractography. It is demonstrated that the results are similar for Al and Inconel alloy samples with different pit sizes if the fatigue-loading parameters are normalized with respect to the yield stress. Sizes of small fatigue cracks are determined from the ultrasonic signatures using the low frequency scattering model. Acknowledgements This work was sponsored in part by the Defense Advanced Projects Agency (DARPA) Multidisciplinary
[1] Chang JCI. Aging aircraft science and technology issues and challenge and USAF aging aircraft program. Structural integrity of aging aircraft, AD-vol. 47, ASME 1995; 1–7. [2] Buck O, Thompson RB, Rehbein DK. Using acoustic waves for the characterization of closed fatigue cracks. In: Newman Jr. JC, Elber W, editors. Mechanics of fatigue crack closure, ASTM STP 982. 1988. p. 536–47. [3] Resch MT, Nelson DV. An ultrasonic method for measurement of size and opening behavior of small fatigue cracks. In: Larsen JM, Allison JE, editors. Small-crack test methods, ASTM STP 1149. 1992. p. 169–96. [4] Yuce HH, Nelson DV, Resch MT. The use of surface acoustic waves to study small fatigue cracks in 7075-T651 aluminum and 4340 steel. In: Thompson DO, Chimenti DE, editors. Review of progress in quantitative nondestructive evaluation, vol. 3A. New York: Plenum Press; 1985. p. 105–13. [5] Tittman BR, Buck O. Fatigue lifetime prediction with the aid of SAW NDE. In: Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE. 1980. p. 411–21. [6] Tien JJW, Khuri-Yakub BT, Kino GS, Marshall DB, Evans AG. Surface acoustic wave measurement of surface cracks in ceramics. J Nondestruct Eval 1981;2(3, 4):219–29. [7] Buck O, Skillings BJ, Reed LK. Simulation of closure: effect on crack detection probability and stress distributions. In: Thompson DO, Chimenti DE, editors. Review of progress in quantitative nondestructive evaluation, vol. 2A. New York: Plenum Press; 1983. p. 345–52. [8] Buck O, Thompson RB, Rehbein DK. The interaction of ultrasound with contacting asperities: application to crack closure and fatigue crack growth. J Nondestruct Eval 1984;4:203–12. [9] Dai W, Kim J-Y, Rokhlin SI. In-situ surface acoustic wave monitoring of fatigue crack initiation and propagation. In: Thompson DO, Chimenti DE, editors. Review of progress in quantitative nondestructive evaluation, Vol. 18B. New York: Plenum Press; 1999. p. 2225–33. [10] Kim J-Y, Rokhlin SI. Surface acoustic wave measurements of small fatigue cracks initiated from a surface cavity. Int J Solids Struct 2002;39:1487–504. [11] Rokhlin SI, Kim J-Y. In situ ultrasonic measurement of crack closure. Int J Fatigue 2002;25(1):510–58. [12] Rokhlin SI, Kim J-Y, Nagy H, Zoofan B. Effect of pitting corrosion on the fatigue crack initiation and fatigue life. Engng Frac Mech 1999;62:425–44. [13] Ayter S, Auld BA. On the resonances of surface breaking cracks. In: Proceedings of the DARPA/AFML Review of Progress in Quantitative NDE. 1980. p. 394–402. [14] Freund LB. The oblique reflection of a Rayleigh wave from a crack tip. Int J Solids Struct 1971;7:1199–210.
In situ ultrasonic monitoring of surface fatigue crack initiation and growth from surface cavity S.I. Rokhlin ∗, J.-Y. Kim The Ohio State University Nondestructive Evaluation Program, Edison Joining Technology Center, 1248 Arthur E. Adams Drive, Columbus, OH 43221, USA Received 27 March 2001; received in revised form 21 February 2002; accepted 3 May 2002
Abstract A surface acoustic wave method for in situ monitoring of fatigue crack initiation and evolution from a pit-type surface flaw is described. The method is demonstrated for fatigue tests on Al 2024-T3 and Inconel 718 samples with different surface pit sizes. The surface acoustic wave signature is acquired continuously during the fatigue cycle without stopping the fatigue test. Crack initiation and propagation are identified clearly from the ultrasonic surface wave reflection signals. Crack initiation in the Inconel 718 sample is observed to occur at a much later stage of fatigue life than in the Al-2024-T3 sample. The ultrasonic results are supported by fractographs of fracture surfaces. Small crack sizing is performed from the ultrasonic signatures using the low frequency scattering model. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue; Ultrasonic crack depth measurement; Surface acoustic wave; Ultrasonic nondestructive evaluation; In situ fatigue experiment
1. Introduction Material degradation due to pitting corrosion and surface fatigue crack initiation from pits has been known to be a cause of widespread damage in aging aircraft structures [1]. Therefore, detection and measurement of a surface fatigue crack initiated from a surface flaw are of great significance for the prediction of remaining fatigue life and for timely maintenance of aging aircraft. Ultrasonic bulk [2] and surface [3–6] wave methods for surface and subsurface crack detection have been well developed. Resch and Nelson [3] and Yuce et al. [4] described measurements of small fatigue crack depth and crack opening load by ultrasonic surface waves. Tittman and Buck [5] performed experiments to determine the size and closure load of a surface fatigue crack in a titanium alloy. Tien et al. [6] applied surface waves to study the effect of indentation-induced residual stress on
Corresponding author. Tel.: +1-614-292-7823; fax: +1-614-2923395. E-mail address: [email protected] (S.I. Rokhlin). ∗
crack extension by comparing results for heat-treated and as-indented samples. Most previous work on ultrasonic characterization of surface breaking cracks has been concerned with a crack on a flawless surface or an artificial saw-cut as a simulated crack. However, actual cracks often initiate from surface flaws (foreign object impact damage, corrosion pit, etc.). The additional interaction of scattered waves with the surface flaw complicates crack detection and prevents immediate application of existing methods for small crack evaluation. Also, these surface flaws as stress risers lead to plasticity-induced crack closure that affects the crack reflectivity [2,7,8]. All these complicate the sizing of the small fatigue cracks emanating from a surface flaw. To address this problem activities in this direction were started in our group several years ago. Preliminary experimental results on surface wave reflectivity from a pit with crack have been reported by Dai et al. [9]. Kim and Rokhlin [10] developed a surface acoustic wave scattering model to evaluate the depths of small cracks emanating from pits. Crack closure measurement using surface waves is discussed in Ref. [11]. In this paper, an experimental method is developed
0142-1123/02/$ - see front matter. 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 0 2 ) 0 0 0 5 5 - 5
42
S.I. Rokhlin, J..-Y. Kim / International Journal of Fatigue 25 (2003) 41–49
for in situ surface wave monitoring of fatigue crack initiation and propagation with data taken during fatigue cycling. The method is demonstrated for two widely used aerospace materials: Al 2024-T3 and Inconel 718. A small pit is produced to simulate surface flaws caused by pitting corrosion or foreign object impact damages. Surface acoustic wave reflections from cracks have been obtained as functions of fatigue load and number of cycles. The ultrasonically determined crack sizes are compared with fractographs.
2. Experiment 2.1. Sample preparation The materials used in this study were Al 2024-T3 alloy and Inconel 718. The Al 2024-T3 alloy fatigue sample was 1.6 mm thick, yield stress sY ⫽ 340Mpa, ultimate tensile stress sU ⫽ 483MPa, and elongation 17.5%. The Inconel fatigue sample was 1.97 mm thick, yield stress 1100 MPa, ultimate tensile stress 1310 MPa and elongation 17.0%. The specimens were machined according to ASTM standard E-466-96. The cross section of the aluminum sample was 1.6 × 6mm2 and that of the Inconel sample was 1.97 × 6mm2. Controlled-size small pits with nominal depths 250 and 750 µm and diameter 250 µm were produced by an electrical discharge machine (EDM) in the center of the specimen. 2.2. Fatigue test Fatigue tests were carried out on a servo-hydraulic MTS (mechanical testing system, Model 810) in the stress-controlled mode. The normalized fatigue load parameters were the same for both aluminum and Inconel samples. The frequency of loading was 15 Hz and the maximum stress level was 76% of the yield stress. The stress ratio R was 0.1, so that the stress range ⌬s was 231 MPa for the aluminum sample and 756 MPa for the Inconel sample. The high stress concentration (kt⬇3.45) leads to the development of a plastic zone around the pit. Considering that the onset of the long crack regime for our samples is about 650 µm [12] the measurements performed in this study are during and immediately after the short-crack regime of the fatigue life. Post-fracture surfaces were examined with scanning electron microscope (SEM) fractographs and actual sizes of crack and pit were measured. In total, 10 samples were used for ultrasonic monitoring; however, a large number of similar fatigue experiments on Al 2024-T3 samples with pits have been performed in our prior work [12].
2.3. In situ ultrasonic measurements In order to monitor crack initiation and propagation during the fatigue cycle, ultrasonic surface wave reflections from a pit with a crack were measured. The experimental system includes ultrasonic pulser/receiver, oscilloscope, control computer for MTS and ultrasonic data collection as shown in Fig. 1(a). A commercial wide-band longitudinal-wave transducer with 5 MHz center frequency was assembled on a specially designed polystyrene wedge and used for generating and receiving surface acoustic waves (Fig. 1(a)). The wedge design is critical for acceptable signal-to-noise ratio. For an in situ measurement, the transducer assembly is mounted using a small clamp on the sample undergoing the fatigue test so that the ultrasonic signals are collected during fatigue cycling (Fig. 1(b)) and at different load levels. A liquid ultrasonic couplant was applied between the ultrasonic wedge and the sample. At predetermined numbers of cycles, the computer controlled fatigue load was changed to a step-up or step-down–up (10 steps) load (Fig. 1(c)) and ultrasonic reflections were recorded and averaged, to suppress measurement noise, at each step-load level. The ultrasonic signature was repeatable for different samples.
3. Ultrasonic results and interpretation 3.1. Surface wave reflection from pit with crack in Al 2024-T3 sample Typical reflected ultrasonic signatures from a pit with an emanating fatigue crack are shown in Fig. 2 at different numbers of cycles. Surface wave reflection signals were obtained on an Al 2024-T3 sample for two load levels at different fatigue cycles. The depth and diameter of the pit were 252 and 246 µm, respectively. The fatigue life of this sample was 142,856 cycles. The surface acoustic wave reflections are composed of waves reflecting from different parts of the pit with crack (2) (A(1) N ), followed by the plate bottom reflection (AN ) of a mode-converted shear wave; the subscript N represents the number of cycles. In Fig. 2(b), the amplitudes are marked for N ⫽ 0, i.e. reflections from the pit prior to fatigue. Detailed interpretations of the pit and plate-bottom reflected signals have been presented in Ref. [10]. As seen in Fig. 2, the A(1) and A(2) groups of signals are separated in the time domain. As a result of the crack initiation and growth during the fatigue test the amplitudes of both the first (A(1)) and plate bottom (A(2)) reflections change continuously. It is interesting to compare the signals (Fig. 2(a)and (b)) taken at the same number of cycles, but only under different load levels. While the reflection signal recorded at 400 lb load changes significantly as the number of cycles increases, no change
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Fig. 1. In situ ultrasonic experiment for monitoring of surface crack emanating from a pit. (a) SAW monitoring system. (b) Ultrasonic transducer mounted on the sample. (c) Load profile to monitor crack initiation and evolution.
is observed until 52% of the fatigue life when the signal is recorded at 100 lb load. Fig. 3 shows peak-to-peak amplitudes A(1) N of the first reflection normalized by the signal amplitude before the fatigue test A(1) 0 as a function of the number of cycles N. The ultrasonic signals at different load levels were normalized with the same quantities A(1) 0 since they depend only negligibly on the load. The first reflection has minima near 60,000 and 130,000 cycles as indicated in Fig. 3. Since the crack emanates approximately from the mid-plane of the pit as shown in Fig. 4, the path difference 2R of waves reflected from the pit front and crack surface is about half the surface wave wavelength lR at 5 MHz: 2R / lR⬇0.5. Hence, the interference of reflected waves from pit front and crack surfaces is destructive resulting in decrease of the first
reflection amplitude. The first reflection starts to decrease at around 20,000 cycles and has minimum at 60,000 cycles as marked by arrow (A) in Fig. 3. This effect is also observed in Fig. 2(b) starting from 25,000 cycles as a decrease of the first reflected signal. As an alternative measure one can monitor the tail part of the first reflection which is associated with the crack reflection. However, the amplitude pattern resulting from the signal interference is more sensitive to crack initiation and enhances crack sizing analysis [10]. To illustrate the signal interference Fig. 5 shows a simulation of the overlapping of two reflected signals with time delay ⌬t ⫽ 2R / nR. The simulated signal is very similar to the actual reflected signal from the pit with crack at 65,000 fatigue cycles. From this, one can
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Fig. 2. Change of reflection signal at different fatigue cycles at two different loads (a) 100 lb, (b) 400 lb during fatigue test for an Al 2024-T3 sample. The fatigue life of the sample is 142,856 cycles.
Fig. 4. Difference of path lengths for signals reflected from pit front and crack surfaces. Fig. 3. Change of the normalized first reflection signal amplitude during fatigue life of Al 2024-T3 sample.
deduce that at 25,000 cycles, the crack has grown enough to be detectable by ultrasonic waves. Fig. 6 shows the SEM fractograph of a similar sample that was broken in tension after 25,000 cycles. The fatigue cracks
on both sides of the pit can be identified. Crack sizes are about 42–54 µm. As the crack grows further, wave reflection from the crack eventually dominates the reflecting signal. Thus, the peak amplitude of the reflection signal shifts by ⌬t ⫽ 0.178µs which corresponds to the time for the surface wave to travel twice the pit radius (2R / vR) as indicated by the dashed line in Fig.
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forms a weak resonance on the crack surface because of the low reflection coefficient (~0.2) from the crack tip [14]. The dips in reflection signal amplitudes can, therefore, result from surface wave resonance reinforced by constructive interference of creeping waves that reflect back and forth on the front half of the pit between the two crack surfaces. For one sample, the fatigue cycle was stopped and the sample was fractured in tension after the first reflection reached a minimum (B) at 100,000 cycles (Fig. 7(a)). From the fractograph for this sample shown in Fig. 7(b), the crack length on the surface from the edge of the pit is about 350 µm, just above half a surface wavelength lR ⫽ 600µm. Since the fatigue life of the samples varies from one sample to another, the number of cycles at which the first reflection has the minimum may be different from the one shown
Fig. 5. Simulation of interference of reflected surface waves.
Fig. 6. Fractograph of an Al 2024-T3 fatigue sample fractured at 25,000 cycles. Fatigue crack is initiated near the sample surface around the pit. Cracks about 42 and 54 µm width are indicated on two sides of the pit.
2(b). As was described in Ref. [12], the fatigue cracks first initiate at the edges of the pit forming two corner cracks. These cracks grow downward separately on both sides of the pit (see Fig. 6) until their depths reach the pit bottom. As these cracks grow further beyond the root of the pit, they combine into a single semi-elliptical crack whose aspect ratio is dependent on the ratio of depth to diameter of the pit [12]. In Fig. 3, the first reflections show dips at about 130,000 cycles. This can be attributed to the lowest order resonance of surface waves on the crack surface excited when the crack grows to half a wavelength of the surface wave [13]. However, it is known that the surface wave
Fig. 7. (a) Normalized first reflection versus number of cycles (Al 2024-T3 sample). The minimum of the reflection amplitude is indicated. The fatigue cycle was stopped just after reflection minimum was detected. (b) Fracture surface at number of fatigue cycles 104,000 (Al 2024-T3 sample).
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in Fig. 3, but should exhibit the same trend (in some samples, this minimum is less pronounced). 3.2. Plate bottom reflection signals in Al 2024-T3 sample The mode-converted shear wave is launched on the bottom of the pit and propagates down toward the bottom of the plate where it is reflected, mode-converted back to the surface wave at the bottom of the pit, and returned to and received by the surface wave. One can measure the depth of the surface discontinuity by analyzing the time delay and amplitude of the bottom reflection signal. As evident in Fig. 2, the plate bottom reflection signal is narrower and better defined than the first reflec-
tion. As we will see below, the bottom reflection provides useful information on fatigue crack depth and also the crack closure behavior [11]. The time of arrival of the bottom reflection increases with the sample thickness and for thicker bodies its amplitude will decrease due to attenuation which depends on material microstructure. However, for many practical cases this signal may be resolved and provide useful information. Fig. 8 shows the plate bottom reflections A(2) N versus number of cycles N normalized by the signal amplitude before the fatigue test A(2) 0 , as for the first reflection signals shown in Fig. 3. The amplitude of the plate bottom
Fig. 8. Change of normalized plate bottom reflection signal amplitude during fatigue life of Al 2024-T3 sample.
Fig. 9. Fracture surface at number of fatigue cycles 65,000 (Al 2024T3 sample).
Fig. 10. Change of the normalized surface wave reflection signal during fatigue life of Al 2024-T3 sample with a pit whose depth is 750 µm and diameter 247 µm. (a) First reflection, (b) Plate bottom reflection signal.
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reflection increases slightly with the number of cycles since it is not affected by wave interference. At around 60,000 cycles the second reflection starts to increase rapidly. This occurs when the crack reaches the pit depth substantially increasing surface wave transformation to shear wave, thus increasing the plate bottom signal. Therefore, one can expect that crack depth be about pit depth at around 60,000 cycles. To support this conclusion, Fig. 9 shows the fractograph of the sample broken after 65,000 cycles where the actual crack depth is 265 µm and half-width 200 µm, which is slightly larger than the pit depth of 250 µm. A similar in situ ultrasonic experiment was performed for the sample with a pit depth 750 µm. The sample fatigue life was 61,253 cycles. Fig. 10 shows the first and bottom reflections as a function of the number of cycles. Change of the pit reflection signal due to crack initiation starts at about 5000 cycles (Fig. 10(a)). Due to the previously mentioned interference between the pit and the crack surface reflection signals, the first reflection amplitude decreases as for the sample with 250 µm deep pit. The depth of the crack reaches the pit bottom around 45,000 fatigue cycles. The plate bottom reflection (Fig. 10(b)) does not change until this point and then starts to increase with the number of cycles. The results for the sample with the deep pit are very similar to those from the shallow pit, indicating that the ultrasonic result obtained for the sample with the 250 µm pit can be generalized to pits of different depths. As observed in Figs. 2 and 10, the ultrasonic signals are sensitive to the load level at which they are meas-
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ured. This phenomenon is related to crack opening–closing behavior as discussed in Ref. [11]. 3.3. Surface wave reflections from a pit with crack in Inconel The surface wave reflection signals for an Inconel 718 sample measured at the load level of 800 lb are shown for different fatigue cycles in Fig. 11. The depth and diameter of the pit were 182 and 254 µm, respectively. The fatigue life of the sample was 147,346 cycles. The change of ultrasonic signal due to crack initiation and evolution is similar to that for Al alloy samples. However, the monitored ultrasonic signals begin to change above 113,000 cycles indicating that the crack is detected in the Inconel 718 sample at a much later stage of fatigue life (76% of the fatigue life) than in aluminum samples (17% of the fatigue life). Similar to Al 2024T3 samples, the shift of the first reflection signal in time due to crack growth is observed. In Fig. 12 the peak-to-peak amplitude of the first and plate bottom reflections are shown as a function of number of cycles at different load levels. Very little change in the signals is observed before 113,000 cycles probably due to the high grain noise and the small reflection caused by the shallow pit (182 µm). A rapid change of the reflected signals occurs from 113,000 cycles until failure. Also a clear dependence of signal amplitudes on the load is observed. While the aforementioned conclusion seems to be correct, in general one should be careful when assessing
Fig. 11. In situ monitoring of fatigue surface crack initiation and propagation in Inconel 718 sample.
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being detected by surface waves in this sample, which is quite different from the case of the Al 2024 sample (compare Fig. 12(a)and (b) with Figs. 3 and 8).
4. Model-based ultrasonic sizing of small cracks Small corner cracks emanating from a pit can be sized from their ultrasonic signature using a low frequency surface wave scattering model proposed in Ref. [10]. According to the model, the normalized time domain reflection signature from the pit with crack is represented by the sum of the crack and the pit reflected signals as follows: r(t,a) ⫽ r(t,a ⫽ 0)
冕
(1)
⬁
⫹
Rc11(w,a)V(w)eiw(t⫺D/V R) dw,
⫺⬁
where Vi(w) is the frequency response of the measurement system, i the imaginary unit, w the angular frequency, D the pit diameter and VR is the surface wave velocity. The pit reflection coefficient in the presence of the crack is approximated by the pit reflection coefficient without the crack r(t,a ⫽ 0) that is measured prior to fatigue. The crack reflection coefficient Rc11 is approximated as Rc11(w,a) ⫽
Fig. 12. Change of surface wave reflection amplitude versus number of fatigue cycle for Inconel 718 sample with pit whose diameter is 254 µm and depth 182 µm. (a) First reflection, (b) second (bottom) reflection.
crack initiation in the Inconel sample. Comparing Figs. 2 and 11 one can note that the grain noise in the Inconel sample is much higher than in the Al alloy sample. The maximum signal-to-noise ratio in the Inconel sample for the reflection from the pit before the fatigue test is 8 dB while that in the Al alloy sample is 30 dB. Therefore, the grain noise masks small changes of the signal reflected from the pit due to crack initiation and small crack propagation. Since changes of the first (Fig. 12(a)) and the plate-bottom (Fig. 12(b)) reflected signals began to occur at the same number of cycles (113K) the crack depth may reach the pit depth (about 180 µm) before
冕
iw(1⫺n2) r(r)K2I(a)dl, 3EP ⌫
(2)
where KI(a) is the mode-I stress intensity factor of the corner crack [12], a the crack depth, n the Poisson’s ratio, E the Young’s modulus, P the input power into the transducer, dl the line element on the crack front ⌫ and r(r) is defined in Ref. [10]. Using Eq. (1), the normalized time domain reflected signals were calculated as a function of the crack depth. Then, by comparing the calculated reflected amplitude versus crack depth with the normalized amplitude coefficient versus number of cycles (Fig. 3), the crack depth versus number of cycles was determined. The corner crack model is valid while the crack grows to the pit bottom; therefore, calculated crack depths are bounded by pit depths. Fig. 13 shows the crack depths determined from the measured ultrasonic signatures for four different samples with different pit depths. The crack depths measured from SEM fractographs of the similar samples broken in tension after certain numbers of cycles are also shown by solid triangles. The experimental and predicted crack depths are in very good agreement. It is observed from SEM fractographs that the sizes of the two corner cracks are not equal immediately after initiation; however,
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University Research Initiative (MURI) under Air Force Office of Scientific Research grant #F49620-96-1-0442 and in part by the Federal Aviation Administration (FAA) under contract #97-C-001. The authors are thankful to Mr Dai for his assistance in data collection.
References
Fig. 13. Comparison of ultrasonically predicted crack depths and measured from SEM fractographs.
eventually their sizes get closer with growth. It is interesting to note that once the crack reaches the pit bottom, the crack does not grow downward but grows around the pit bottom until the two cracks merge into one crack. This results in temporary decrease of the crack growth rate as one can observe in Fig. 13. 5. Summary An in situ method using surface acoustic waves for the evaluation of small fatigue cracks emanating from pit-type surface flaws is presented. The method is demonstrated by monitoring fatigue crack initiation and propagation during fatigue cycling on Al 2024-T3 and Inconel 718 samples. By interpreting ultrasonic reflection signals, crack initiation and growth are described quantitatively. After breaking samples in tension at different stages of fatigue life, the ultrasonic results were verified by SEM fractography. It is demonstrated that the results are similar for Al and Inconel alloy samples with different pit sizes if the fatigue-loading parameters are normalized with respect to the yield stress. Sizes of small fatigue cracks are determined from the ultrasonic signatures using the low frequency scattering model. Acknowledgements This work was sponsored in part by the Defense Advanced Projects Agency (DARPA) Multidisciplinary
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