Fatigue life determination by acoustic emission monitoring and assessment of fatigue damage accumulation by using acousto-ultrasonic technique

Transcription

1 5th International Symposium on NDT in Aerospace, 13-15th November 213, Singapore Fatigue life determination by acoustic emission monitoring and assessment of fatigue damage accumulation by using acousto-ultrasonic technique Ahmed MASLOUHI and Clément POULIQUEN Department of mechanical engineering, Université de Sherbrooke, Québec, Canada Phone: , Ahmed.Maslouhi@Usherbrooke.ca Abstract This paper proposes a comprehensive analytical and experimental methodology to monitor, in real time, fatigue crack growth and use physics based model for life prediction. The approach uses Acoustic Emission (AE) techniques to detect fatigue crack initiation and crack growth in aluminum materials used in aircraft structures. The quantification of damage rate induced by fatigue loading were investigated by analyzing the global effects of fatigue loading on the Acousto-Ultrasonic (AU) guided wave propagation in cracked samples. Mechanical properties degradation in terms of fatigue life was correlated with signal characteristics related to guided waves propagation. The aluminum alloy samples, with inserted precracks in the fastener holes, were tested mechanically in fatigue tension-tension cyclic loading with NDT monitoring techniques to quantify damage growth versus the fatigue cycle number. Nasgro analytical model, which integrates the crack growth rate, was used to produce a crack growth curve. Based on the correlations between crack propagation rates, acoustic emission rates and stress intensity factor range procedures are suggested for predicting critical fatigue life. The results indicate that by exploiting health monitoring data such; acoustic emission signals and guided waves features, coupled with analytical physic based models provides an effective methodology to estimate safety factor on life of the structure. Keywords: fatigue life, crack growth, acoustic emission, the safety factor on life, Acousto-ultrasonics, lamb waves. 1. Introduction Aluminum alloys, in particular, 224 alloys are widely used in wings and fuselages of civil airplanes. These alloys have to sustain repetitive loading conditions. Fatigue damage is one of the main factors that limits the life of aeronautical components. After repeated load cycles, tiny cracks will form, often at multiple location in the structures, this initial period of cycling is known as the crack nucleation or initiation life. The cracks are too small to cause fracture, but they do extend slowly after repeated cycling. Eventually, some coalesce, leading to a governing crack that continues to grow in a stable manner. Finally, the dominant crack reaches a size that causes a catastrophic fracture of the component. Consequently, detection of fatigue crack onset and fatigue crack propagation is an important issue for aerospace structures. In practice, the boundaries between these different phases are not always easy to figure out. In recent years, many studies focus on monitoring the health of structures (Structural Health Monitoring SHM) [1], which is to control health by using integrated sensors on the structure that provide continued structural integrity monitoring. It should enable the diagnosis and early detection of damage to certain vital components of the structure to make a prognosis estimate that determines the running time for an element of the structure [2]. Therefore, there are a variety of traditional non-destructive evaluation techniques, which are available to ensure the quality of aeronautical structures. Most of these techniques [3] are able to detect defects such as discontinuities of surface or volume and changes of section. However, they are unable to detect initiation and propagation of cracks in real time and continuously during service. These techniques are applied at discrete intervals

2 and require the structure to be out of service load and generate high costs. Presently, Acoustic Emission (AE) and Acousto-Ultrasonics (AU) techniques appear as promising alternatives to monitor, in real time, damage initiation and crack propagation due to fatigue loading [4,5,6,7] 2. Crack propagation modeling The most common crack growth mechanisms in metallic structures are fatigue crack growth [8], and the main issue concerning fatigue crack propagation is how many loading cycles, does it take for crack to grow from an initial size to the maximum permissible size. In general, to predict crack growth behavior, such as illustrated in Figure 1, the following information must be available: The stress-intensity factor; the stress time history; the baseline crack growth properties and finally, a damage integration routine that integrates the crack growth rate to produce a crack growth curve. Figure 1 presents a schematic of typical growth behavior for a crack being observed in a structural element as it moves from an initial damage size (a ) to a critical damage size (a cr ) that causes structural failure. The crack grows in response to the cyclic loading (N) applied to the structure. Any crack will grow a given increment ( a) in a given number of loading events ( N), the rate being measured by a/ N. When the crack length reaches a critical value (a cr ), the growth becomes unstable, thereby inducing failure. The structural life limit N f is a measure of the maximum allowable loading cycle associated with driving the crack from its initial length (a o ) to the critical length (a cr ). Damage tolerance analysis is based upon the stress intensity factor: K = a, where σ is the applied stress, a is the crack size, and β is the non dimensional geometry factor. In fatigue, the crack growth data are expressed as a function of the stress intensity range, K, and the stress ratio, R. By employing material data in term the plane fracture toughness (K IC ) or the plane stress fracture toughness (K IC ), the appropriate growth model da/dn the yield strain, the geometry factor, β, as a function of crack size for the structure and the stress history, the crack growth curve will be sorted out by numerical integration of the equation (1): da = f ( K, R ).. (1) dn K th n 1 da 1 f K C K (2) = q dn R 1 K 1 ( R ) K 1 c Many fatigue crack growth models [2], have been developed to correlate constant amplitude fatigue crack growth rates with various loading parameters. These models are based on curvefitting techniques and are primarily used with numerical programs to interpolate between the experimental data obtained under diverse test conditions. This paper will use the NASGRO model [9], defined by equation (2), which has been developed for use with the NASGRO crack growth analysis software developed by NASA Johnson Space Center [9]. The model can account for retardation, acceleration for fast fracture and the crack closure. The NASGRO crack growth equation is expressed by equation (2). Where da/dn is the crack growth rate, K is the applied stress-intensity factor range, and R is the stress ratio; K th is the fatigue threshold, K max is the stress-intensity factor corresponding to peak applied load, and K c is the critical stress intensity; p and q control the shape of the asymptotes in the threshold and critical crack growth regions, respectively; f is Newman s crack opening function. Where C, n, p, and q are empirically derived. These values are provided by the NASGRO material database for each material. p βσ π

3 Figure 1: Variation of crack length versus fatigue cycles Figure 2 presents the algorithm of calculation of crack length versus fatigue load as described by [1]. Figure 2 : Block diagram of calculation of crack length versus fatigue cycles [1]. Table1 presents the configuration geometries and loading data used in the analysis. The global geometry of the components tested is chosen as rectangular specimens of dimensions 5 8 mm with a 5,4 mm diameter hole at the center. The thickness of the specimens is close to 3,175 mm (1/8 in). The specimen (1) has no incipient crack, the specimen (2) has a single through crack at hole and specimen (3) has a double through crack at hole. Those incipient cracks had a length of 1 mm, and they were made with a milling cutter of 1/16 in diameter. For simulation, the load spectrum oscillated between MPa and 25%, 3% or 35% of the yield stress (91, 19.5 and 128 MPa) with a stress ratio (R) equal to zero. The fatigue crack propagation prediction results under constant amplitude loading, for

4 the specimen (2) with single through crack at hole, is presented above. For this specimen, the resulting range of the stress intensity factor K was calculated by using shape factor, β, defined by [9], where R is the hole radius and a the crack length. The factor β is used to relate gross geometrical features to the stress intensity factor. Table 1: Specimen configurations and fatigue testing data 3. Experimental procedures 3.1 Materials The specimens used throughout this investigation were prepared from aluminum alloy 224- T3. Specimen geometries, dimensions and fatigue crack growth experiments performed are summarized in table1. Such tested material is often used in aeronautical mainframe structures. The mechanical characteristics of the 224-T3 alloy are defined such as; the Young modulus, E=742MPa, the Poisson s ratio, ν=.33, the yield strength was 365 MPa, the plane strain fracture toughness, KIc=36.3 MPa m and the plane stress fracture toughness, Kc= 72.5 MPa m. The fatigue tests were carried out on 1KN servo-hydraulic machine controlled by computer, following ASTM standard recommended procedures, under constant load range at R=σ min /σ max =. Monitoring crack length is done by a traveling microscope and the crack in the specimen surface is observed at the magnification of 2 to 3X. The crack length is measured as a function of cycles at predetermined intervals. To aid in crack-length measurements, scribe marks are applied to the specimens. 3.2 Acoustic emission and acousto-ultrasonic monitoring This study uses AE and AU to detect and to monitor, in real time, the initiation and the propagation of fatigue cracks under cyclic loading and also to establish a life prediction by using physic based model. Acoustic Emission is the term used to elastic stress waves generated in solids as a consequence of the application of the static or dynamic stress. The transient acoustic emission waves are generated by rapid release of energy within the material. Plastic deformation, crack nucleation, micro-crack growth and macro-crack formation are the main source mechanisms generating elastic stress waves in ductile metallic materials such as aluminum alloys. A sensitive piezoelectric transducer attached onto the surface of the specimen can detect the elastic stress waves that propagate in all directions of the material. An analysis of the contents of signals collected during testing allows following

5 crack initiation and damage accumulation in the material [11]. The Acousto-Ultrasonics [6] technique is based on acoustic emission and ultrasonic wave propagation. This method is very promising to measure indirectly the variation of mechanical properties depending on the material loading and to assess its damage state. Consequently, this work investigates the characterization of damage growth induced by fatigue loading, by analyzing the global effects of fatigue loading on the Acousto-ultrasonics guided waves propagating in cracked samples. These waves propagate along the surface of the material and also through a plate structure propagating parallel to the plate s upper and lower boundaries [12]. Guo and Cawley [13] have demonstrated that Lamb waves are generated in Acousto-Ultrasonic measurement and lowest symmetrical (S ) and asymmetrical (A ) modes are mainly excited in Acousto- Ultrasonic inspection.. Figure 3: Symmetrical and antisymmetric modes propagating in Aluminum thin plate Lamb waves are symmetric and asymmetric modes propagated along a thin plate. Since the wavelength is of the order of the plate thickness, these waves are dispersive in nature. Figure 3 shows an example of snapshot of wave propagation of S and A modes in aluminum plate obtained by numerical simulation [14]. Figure 4, shows the dispersion curves of group wave velocity obtained numerically for a larger number of propagating modes in aluminum plate with 3.8mm thick used in the experimental testing. The P-wave (longitudinal) velocity was 632 m/s and the S-wave (Shear) velocity was 31 m/s. 5, 5 S Sy mm e tri ca l mo d e S Sy mm e tri ca l mo d e S 1 An ti sy m m e tri ca l m o d e A An ti sy m m e tri ca l m o d e A 1 5, Group velocity (m/ms) 4, 5 4, 3, 5 3, 2, 5 2, A A 1 S 1 1, 5 1,, 5,, 5 1, 1, 5 F re q ue n cy( M Hz ) Figure 4: Velocity versus frequency dispersion curves for a 3,8mm thick aluminum plate for the first four modes. S= symmetrical mode and A= asymmetrical mode The curve shows that there are many possible propagating Lamb modes and that the waves are in general dispersive, their group velocity is a function of the frequency. In a dispersive

6 medium, the phase velocity [14], not shown here, varies with frequency and is not necessarily the same as the group velocity wave (figure 4), which is the rate that changes in amplitude, known as the envelope of the wave, will propagate [15]. However, in the low-frequency range, below 1MHz, there are four possible fundamental Lamb modes, the symmetrical modes (S ) and (S 1 ) and asymmetric modes (A ) and (A 1 ). Which are often termed the extensional and flexural modes respectively. In the frequency band shown by figure 4, illustrated by shaded area, the S, S 1 and A 1 modes are almost dispersive, while the A mode is non-dispersive. This work, use fundamental wave modes S and A to investigate the characterization of damage growth induced by fatigue loading, by analyzing the global effects of fatigue loading on the Acousto-ultrasonics waveforms injected in cracked samples. The non-dispersive mode, A will be used to assess the state of fatigue damage of the material after cycling. For each sample, crack propagation was monitored by both acoustic emission and Acousto-ultrasonic techniques, and the extracted monitoring data will be correlated with measured crack size evolution obtained visually. In the AU approach, elastic pulse waves were artificially produced by a pulse generator and were injected to the specimen through a piezoelectric emitter. The waves propagating in all directions of the material were detected by a broadband receiver, with a flat frequency response over the range.1-1 MHz. The receiver was placed at a fixed distance from the emitter and collected both AE and AU waves. The received signals were amplified and filtered over the range 1 khz-2 MHz using a bandpass filter, and were then digitized at a sampling period of 3 ns using a signal acquisition and processing system (PAC acquisition system).the The detection threshold was fixed at 48mV. Results and discussions Figure 5, presents the results of AE fatigue damage monitoring done on the un-notched specimen 1 defined by the table 1. The results are plotted in terms of cumulative distributions of the detected number of hits versus the number of loading cycle applied to the sample. For comparison purposes, the distribution curve of the AE hits are plotted in the same graph showing the results of crack lengths versus the fatigue lives obtained by the Nasgro simulation model and by using fracture mechanics based analysis from Beasy software tool, which applies boundary element's technology to predict remaining life in metallic materials[16]. The monitored crack lengths done by a traveling microscope as function of cycles, were also plotted as referencecurve.nce curve. Crack Length (mm) Number of AE Hits NASGRO prediction Traveling microscope measurements Number of Hits ( 1) Number of Cycles Figure 5: Fatigue life predictions and AE hits distribution for un-notched specimen 1

7 Figure 5 clearly confirms that crack propagation and acoustic emission are correlated. Three stages appear in the AE data evolution versus fatigue cycle. The first stage is characterized by low AE activity. At this stage, the edges of the hole in the specimen were subjected of the appearance of micro cracking mechanisms characterized by slippage in the material crystalline structure and the onset of the micro plastic deformation. During the second stage, the evolution of the AE distribution observed between 29,4 and 111,7 cycles, demonstrates the importance of initiation of macro cracking. The theoretical model predicts that the crack reaches,5mm in length at 111,7 cycles. The last stage, corresponding to crack propagation, appears at between 117, and 164,5 cycles and testifies of the high growth rate of damage. During this phase, the crack length increases from 1,5 mm to 37,2 mm for only a variation of 47, cycles. The visual measurement of crack length shows that the critical crack length reaches 37 mm for total life cycles of 164,5. The Nasgro physic based model predicts a critical length of 37.2mm at 146,89 lifetimes. By using AE data only, let us assume that the specimen contains a minimum detectable crack of initial length, a d =1mm, then grows until it reaches a critical length a c, where the brittle fracture occurs at N if cycles of loading. If the number of cycles expected in actual service is defined as N a, then the safety factor on life [15], X N, is defined by equation (3). This situation is illustrated in figure 1. N if X N =. (3) N a The critical point at which the material reaches the brittle fracture is determined by the current AE signal emitted at corresponding lifetime N if, and the actual lifetime, N a, is determined by AE signal detection when crack length reaches a d =1mm. Applying this assumption for AE data distribution obtained during fatigue loading of the specimen 1 (no through crack) at 3% of σ Ys, the safety factor on life from equation (3) is: N if 164,751 X N = = = 12 N a 13, Figure 6 to 7, show the results obtained by using a predictive Nasgro and Beasy models projected on the same graphics, as the AE hit distributions detected on the specimens 2. When a single through crack at the hole model is considered, in the case of the specimen 2 subjected to 25% of the yield stress, the results of crack length evolution shown by figure 6 are close to those predicted by Nasgro model. The figure 6 shows, also, that the crack propagation measured is slower than the ones predicted by numerical calculation. This retardation is probably due to the mode of manufacture of the incipient initial notch. Figure 7, presents the results when the specimen 2 was submitted to 35% of the yield stress constant amplitude loading level. In this specimen, the gap between experience and simulations is less important. The growth of the number of hits appears a bit earlier than the optical detection of the crack propagation. The AE distribution reaches a maximum at 35,25 cycles and for actual crack length of 1mm, the corresponding AE hits were detected at 87 cycles. By using equation 3, the safety factor on life results of the tested specimens, based only on AE hit distribution data, are summarized in table 2. The table shows that the AE monitoring based on the safety factor on life, calculated by using the number cycles at witch crack size reach reference size chosen as 1mm, made it possible to conclude over the lifespan from the samples tested. Indeed, specimen 1 loaded at 3%σ Ys shows a margin of remaining life times higher than the specimens 2 and 3, with single through crack and double through crack respectively were subjected to different load levels. These results demonstrate that the evaluation of the remaining lifetime of the specimens with fatigue cracks requires the determination of the expected number of cycles to a particular moment and by knowing the critical fatigue life, leads the prevention of the catastrophic failure.

8 Crack Length (mm) Traveling microscope measurements NASGRO Prediction BEASY Prediction Number of AE Hits Number of Cycles Number of Hits (x1) Crack Length (mm) Traveling microscope measurements NASGRO prediction Beasy prediction Number of AE Hits Number of Cycles Number of Hits (x1) Figure 6: Fatigue life predictions and AE hits distribution for notched specimen 2(25% σ Ys ) Figure 7: Fatigue life predictions and AE hits distribution for notched specimen 2(35% σ Ys ) Table 2: Safety factor on life Figure 8: Wave modes and crack length versus percent of fatigue life for specimen 2 (25%σ Ys )

9 The figure 8 emphasizes the stages of variation of the A mode according to the cycling loading in terms of fatigue life. The curve shows a progressive growth according to the number of fatigue life and reaches a maximum at 36% of fatigue life. The measurement of the initial crack length indicates that it is always one mm. Indeed when the material is fatigue loaded to 36% of its lifetime, it does not produce any crack propagation observed by travelling microscope. Therefore, the variation noted in the A mode is rather a manifestation of the microstructural transformation associated to the phenomena of strain hardening and plastic deformation in the inserted crack tip and this damage occur before the crack starts to propagate [17]. It s well known, that most metal will undergo hardening under cyclic loading. Dislocation density normally increases with increasing number of cycles. This increase cause strain hardening at the initial crack tip during fatigue prior to the formation of micro-cracks. The figure 8 also exhibits that from 47% in material fatigue life, the evolution of WT curve of flexural mode (A ) decreases rapidly, and that decay is increasing gradually as the cycle number increases. The decay of the curve coincides with the fast growth of the crack length and this continues until reaching the critical length of 37.5 mm that produces the sudden break of the material. The relatively amplification and attenuation of the A mode can be attributed to the dominant out-of-plane displacements of particles, which interact with damage hardening and damage growth occurring during fatigue loading. Due to the physical nature of the non-dispersive wave Lamb propagation of the A mode (figure 4), which travels with a constant velocity for the frequency range used in this work, it carries very rich information related to the microstructural state of the material and the accumulation of fatigue damage. These results further demonstrate that by using theoretical knowledge related to wave modes propagation and AU measurements are very useful in quantitatively characterizing the fatigue damage state of a material, including early damage stage of fatigue life such as plastic deformation. 4. Conclusions This study applies ultrasonic wave propagation, in order to monitor the initiation and propagation of cracks in un-notched and notched hole aluminum samples subjected to cyclic fatigue. The monitoring of crack propagation has been done in real time, until the complete rupture of the samples. The evolution of the distribution of acoustic emission rate, based on the number of cycling, shows three distinct phases characterizing the fatigue crack nucleation and propagation until the sudden break of the material. The experimental results show that the severity of the acoustic emission is proportionate to the initial cracking state of the samples and the amplitude of the applied stresses. Indeed, exploiting AE data permits the diagnosis of the cycle number which corresponds to the nucleation of micro cracks and to determine the lifetime of the materials tested. By applying the AU approach and using wave Lamb modes, quantitatively assessment of the health state of material has been achieved. The distribution curves of the numbers of hits obtained as a function of cycling, have been confronted with deterministic models for predicting the lifetime based on fracture mechanic approach. Notwithstanding that the numerical results show a slight difference in the prediction of lifetimes, with the results obtained by EA, a strong correlation has been obtained. The results demonstrate that the combination of both a passive and active NDE techniques coupled with deterministic physic based models offer a high potential for structural health monitoring and structural damage prognostic applications.

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