Evaluation of Al-specimen fatigue using a «Smart sensor» Текст научной статьи по специальности «Физика»

Evaluation of Al-specimen fatigue using a «smart sensor»

U. Cikalova, M. Kroening, J. Schreiber, Ye. Vertyagina1

Fraunhofer-Institut für Zerstörungsfreie Prüfverfahren (IZFP), Institutsteil Dresden, Dresden, 01109, Germany 1 L.N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan

We develope a new methodology for the characterization and evaluation of precritical crack propagation. Our experiments were performed with Al-alloy specimens that had special thin Al single crystal films, the so-called a "smart sensor" glued to their surfaces. These sensors were used as tools for evaluation of damage developed in the specimen bulk. The specimens were plastified by tensile tests and fatigued by low cycles fatigue load. The on-line measurement for damage characterisation were done for the different stage of fatigue tests on the thin-film sensor. Two techniques were applied for experiments, namely the optical microscopy and pulsed eddy current method. We introducted the fractal dimension Df of the surface topography as a parameter for evaluation of the fatigue damage. The optical images were evaluated by the use of Gaussian smoothing algorithm and the eddy current signals by use of the autocorrelation function. The two approaches confirmed that the mesostructural changes of the Al-film surface are characteristic for the fatigued material and can be described and evaluated by the fractal dimension quantitatity Df. It was found that the values of the Df parameter calculated from the optical images increased as the fatigue damage evolved with the indications of the transition to characteristic pattern. A similar analysis of the pulsed eddy current measurements in tension tests results in similar characteristics. However, in the case of fatigue tests the fractal analysis of the pulsed eddy current signals yields to ambiguous results.

Keywords: non-destructive testing, plastic deformation, fatigue, mesomechanics, fractal dimension, eddy currents

1. Introduction

There is a need for an improvement in accuracy of forecasting of residual service life of commercially available components. Therefore, easy in use and precise non-destructive testing (NDT) methods for determination of the material fatigue are especially attractive. The developments in evaluation of provided signals by standard non-destructive testing techniques such as optical microscopy and pulsed eddy current give possibilities in characterization of the current material state and structural health.

The aircraft industry is especially interested in the so-called structural health monitoring (SHM). Structural health monitoring has been identified as amongst the most needed technology for the industries over the next twenty years. This approach is based on regular or even in-situ monitoring of fatigue damage progressing in various structures and elements, including components that are critical for aircraft industry. Structural health monitoring offers direct cost reduction and reduced structural weight, as well as safety and improved aircraft operability. Various techniques have been identified for local inspection, e.g. comparative vacuum monitoring, crack wire, corrosion sensors, eddy current foil sensors, and strain gauge. The application of the thin me-

tallic foil sensors for structural health monitoring was proposed in [1] by performing real-time monitoring of the smart-designed multilayer thin film sensors («multiscale smart skin»). Fatigue damage of an aviation component could be evaluated by the changes of the topography of such «smart sensors», applied to the component surface. Numerous experiments were performed to investigate the evolution of the deformation structures by the optical images taken from the surfaces of a single crystalline Al thin film glued to Al specimens [1, 2-5]. The results shown that sensor surface underwent a sharp transition from initially solid flat state to the band-like surface pattern with increasing cyclic load, and then overflowed to the more pronounced labyrinth-like bulk structure [5-8, 9].

The aim of the presented paper is to deeper understand the substructure transformations on the basis of mesome-chanics principles, using a fractal analysis of characteristic mesostructure formation occurring during increasing plastic deformation before the crack initiation starts.

The structural development is a very complex process, causing non-regular structures, initially beginning on microscopic level and expanding on mesoscopic and macroscopic level. The theory of mesomechanics reveals build-

© Cikalova U., Kroening M., Schreiber J., Vertyagina Ye., 2011

ing of tree classes of deformation structures at the micro-and mesolevels. The mesomechanical microlevel corresponds to the formation of line and screw dislocations and the generation of dislocation clusters or dissipative structure within original grains of material. At the next level the formation of the cell structures or persistent glide bands corresponds to level meso I. The formation of multi-band structure corresponds to third level, i.e. meso II [9]. Such development of hierarchical structures leads to the hypothesis that the deformation structure is of fractal nature. Furthermore we suggest that each of these structures displays a self-similarity behaviour which can be evaluated by the fractal analysis. Hence the derived fractal dimension Df should be a suitable parameter to characterize the change of the structure at different load stages.

This approach was successful verified in [10, 11]. For austenitic fatigue specimens it was found that the parameter Df derived from the surface topography increases during fatigue load. A step-like behaviour of Df as a function of the number of load cycles was observed with the help of online tests, by which the change of the surface topography was investigated always at the same place of the test specimen. The individual plateaus of the fractal dimension together with the absolute value of Df characterise the level of deformation structure, namely first plateau with the micro, second plateau with the meso I and third plateau with the meso II levels. This result was obtained on the basis of scanning electron microscopic images (SEM) taken from the surface of the austenitic steel sample during the whole fatigue procedure until fracture. The similar Df curve dependency from the number of cycles was founded by evaluation of magnetic time-dependent Barkhausen noise signals of the deformation structure [12].

In the case non-ferromagnetic metals like Al alloys surface changes were detected by a video system and acoustic emission [13]. The mesostructure development during fatigue damage was demonstrated quite well, however, fractal analysis did not lead to conclusive results. The fractal analysis was then used for the evaluation of the deformation state of the thin single crystal Al stripes [6, 7]. It was found that the fractal analysis could be convenient for characterisation the plastic deformed structures of the Al stripes.

In this paper the surface topography of single crystal Al stripes glued to samples of 2024 Al-alloy will be investigated by the help of optical imaging with microscopical resolution as well as with pulsed eddy current testing to characterise the damaged state of the Al-bulk material.

2. Materials, specimen preparation and experimental setup

Flat bar tension specimens made of the aluminium sheet metal were provided by the Airbus Company. They were of Al alloy 2024 AlCu4Mg1 with the yield stress a y = 260 MPa, ultimate strength au = 420 MPa and total elongation of et = 8 %. In the centre of each specimen a single crystal Al stripe («smart skin sensor»), which was provided by Institute of Metal Physics in Kiev, was glued at the front and back side of the specimen with thickness of 3 mm (Fig. 1). The sensor size was about 10x25 mm and thickness about 0.17 mm. Tensile tests were performed in the elastic and later in the plastic range of the bulk material. The tensile stresses were increased in 2 % strain steps up to maximum stress of 450 MPa. For optical and eddy current measurements the testing machine was stopped. The optical measurement was carried out in the centre of the single crystal Al stripe at the front side of the smart sensor and the eddy current signals — at the back side.

The low cycle fatigue (LCF) tests were stress controlled and carried out with a stress amplitude near to ay with the constant frequency u = 20 Hz. The maximum stress was equal to 300 MPa and the minimum one was 20 MPa (R = 0.07). The measurement of the optical images (10x magnification) and eddy current signals was obtained at the minimum stresses.

Eddy current testing belongs to the oldest electromagnetic non-destructive testing methods and it is commonly used for surface defect detection in aircraft industry. Conventional eddy current probes apply an oscillated magnetic field that induced eddy currents in the sample. However, in our investigation we used pulsed eddy current signals generated by a waveform generator. For measurement two different probes were utilized; where for the tensile tests the probe 1 with diameter of 0 = 5 mm (repetition rate 2 MHz, pulse width 180 ns, and amplitude 2.5 V) and for fatigue tests the probe 2 with 0 = 9 mm (repetition rate 0.7 MHz, pulse width 280 ns, and amplitude 2.5 V) were applied. Since the depth of penetration of the eddy current signals is dependent on the frequency of excitation, in our case the penetration depth of induced eddy current signals is approximately 1p.m.

3. Methods for fractal analysis

3.1. Optical images

The optical images of the single crystal Al stripe was transformed into a map with a 256 gray scale. By taking the

Single crystal Al stripe

300 mm 4-►

Fig.1. Al alloy specimen with glued single crystal Al stripe — the so-called "smart sensor"

a |

-4-

■ Excitation EC signal - Recieved EC signal

250 Time, ns

500

w

-A-

E <

■ Excitation EC signal - Recieved EC signal

250 Time, ns

500

Fig 2. Signals of eddy current probe 1 (a) and probe 2 (b). Dot line shows excitation signal as a function of the time; full line is the eddy current (EC) signal as received from Al-stripe

gray values as a measure of heights algorithms the fractal dimension Df of rough surfaces can be determined. Here we apply the method proposed by Mussigmann [14]. Using of successively smoothing the surface by the help of a Gaussian kernel with different peak width a and calculating the content of the surface F, the parameter Df can be obtained by the relations

AF (a) = F (a) - F0

-2a

and

Df = 2 + a,

(1)

(2)

F0 is the size of the basis area in (x, y)-plane. The fractal dimension of the Al-stripe surface topography can be determined by the slope a of ln(AF(a)) as a function of lna. The measured data can be rather good analyzed in the region lna ~ 2-4.

3.2. Pulsed eddy current signals

Eddy current time series are analyzed by using the difference autocorrelation function:

Mmax -n

1 (IS (tp +Tn) -IS (tp ))q

p=i_

C(Tn, q) = -

(3)

Mmax - n + 1

IS(tp) are the digital values of the integrated time series which is defined by the equation

ISn =

1 (Sp - Pv) p=0

(4)

Mmax is the total number of used signals and t is the time shift.

Using the autocorrelation function C(t, q) defined above, the fractal behaviour occurs in the form

C(t, q)~ TqH(q), (5)

from which a q-dependent fractal dimension can be derived follows:

Df (q) = 2 - H (q), (6)

where H is the Hurst-parameter. An example of the auto-

correlation function of the integrated eddy current signal with the analyzed region and the result of the Df computation is shown in Fig. 2.

The parameter q »1 helps to eliminate the influence of random noise contribution. In [10] the Df dependency on the value of the parameter q was tested for a finite mathematical fractal known as the Koch curve superimposed by stochastic noise. It was proven that the exact value of the Koch curve can be extracted only for q »1. The same procedure yields reasonable results for the Barkhausen noise signals, too.

Figure 3 shows pulsed eddy current noise signals for the two tested probes. Dot line shows excitation signal as a function of the time represented taken without the contact of the single crystal Al stripe, the so-called air excitation signal, the full line is a received eddy current signal measured for the "smart sensor". The fractal dimension of the received eddy current time series was computed for the whole signal range.

Fit curve

t/jr

r =>Df = 1.065

/ * • •

/ m • •

Fig. 3. Autocorrelation function of the integrated series for the pulsed eddy current signal as a function of the time difference between the two individual signals (time shift Tn). The straight line is the curve fitted according to Eq. (4). The fractal dimension for this case was Df = 1.065

Fig. 4. The fractal dimension Df as a function of the applied strain computed from the optical images taken for the surface of single crystal Al stripe (points). The last point was computed after the specimen fracture. The line shows the stress-strain curve

4. Results and discussion

4.1. Tensile test

Application of a mechanical strain to material causes changes on its surface and at the surface of the Al stripe. Thus, correlation between the changes on the sensor surface and the fractal dimension Df of the deformation structure was searched in order to have a parameter for describing the changes occurring on the specimen surface. Furthermore a connection of this parameter to the changes in the bulk material is expected.

At first the p arameter Df was calculated with the help of the optical surface images for the Al stripe at different stages of tensile tests, as shown in Fig. 4. The test results show that the values of Df were not changed as long as the strain of the bulk material remained lower than 2 %. Then the fractal dimension was slowly growing as a function of the strain. After specimen cracking slightly Df decreased. The maximal value of Df detected before the specimen failure was 2.12. This value was much lower than the ex-

Fig. 5. The fractal dimension Df as a function of the applied strain computed from the eddy current time series taken for the surface of single crystal Al stripe (points). The last point was computed after the sample fracture. The last circle point shows the Df of the bulk material. The line shows the stress-strain curve

pected value of about Df = 2.3 (see below). It turned out that the bulk material fractured before the failure of the "smart sensor". Hence the Al stripe was strongly plastically strained shortly after the sample was fractured. This plastically load may have flatted the already developed meso-structure of the sensor stripe, hence, the value Df determined by the images of the ruptured stripe will be reduced as compared to the values determined before the fracture of the bulk specimen.

The values of the fractal dimension parameter calculated for the pulsed eddy current signals also increased as a function of the applied strain, as shown in Fig. 5, however, the observed increase was much less pronounced as compared with the behaviour shown in Fig. 4. The most rapid increase of Df was observed between 2 and 4 % of strain, which agrees with the findings of the optical analysis. The maximum value was slightly smaller than for the optical images, however, no decrease of Df value was observed after the specimen fracture. The reason for that could be the effect of the roughening of the border observed for strain larger than 6 % (Fig. 6), since the eddy current sensor size was as large as the width of the stripe.

Additionally, a measurement was performed on the back side of the specimen opposite to the measuring position of the front side with the stripe to compare the results of the pulsed eddy current measurements obtained for the stripe and for the bulk material. The value Df found there was nearly the same as that determined for the Al stripe.

e = 0 %

e = 6.2 %

Fig. 6. Al stripe in the initial state (e = 0 %) and after the 6.2 % strain with the visible sensor delamination

Zone 1

Transition zone (zone 3}

Zone 2

Fig. 7. The Al stripe with the marked zones for fractal analysis; zone 1 — band-pattern zone, zone 2 — grid-pattern zone and zone 3 — transition zone of the both pattern (a). Development of deformation structures at Al stripe obtained by optical microscopy at zone 1, zone 2 and zone 3 in dependence of the number of cycles N (b)

4.2. Fatigue test

To examine the development of the fractal parameters under fatigue damage a cyclic tension experiment was applied. At first, the state of the single crystal Al surface layer was investigated by the optical method at specimen 1. At the beginning the surface of the Al plate was smooth and flat. After 2000 cycles a regular band pattern appeared. The bands were oriented approximately along the loading direction. After 10000 cycles the band pattern changed to rectangular grid-like pattern but not for whole the investigated area. The behaviour of the two characteristic areas at the surface of the "smart sensors" was more pronounced with the increasing fatigue damage. It is likely that the difference in the development of both structures is caused by various adhesion forces of both plate areas, i.e. the altered constraint yield to rather different mesostructure development for the same fatigue damage of the bulk-material. Taking into account a transition region between the two defor-

Fig. 8. The fractal dimension as a function of cycles number (Nb is the number of the cycles till the specimen breakage) calculated of optical images by the use of Gaussian method during the on-line measurement of specimen 1. The itemized zones correspond to three zones described in Fig. 6

mation areas three zones were investigated for the optical examination. Zone 1 in Fig. 7 contains band pattern, zone 2 — rectangular grid-like pattern and transition zone 3 has a topography mixture of both zones 1 and 2.

Fractal analysis was performed for each of the three zones of the Al plate using the Gaussian algorithm for the optical images. Corresponding results are collected in Fig. 8. At the initial stage of cycling loading the fractal dimension for all three zones increased with the number of cycling. The band structure at the zone 1 was observed after 4103 cycles of loading (log N/Nb = -1.7) and did not change further. It is expected that the appearance of the band structure is accompanied by drastic reduction of the adhesion of the bands to the bulk material and hence the reduced forces applied to the bands could not provide the development of the new mesostructures.

The grid structure which was formed in zone 2 was well established after 7104 cycles (log N/Nb = -0.52). The grid pattern of zone 2 has a significant higher value Df than that obtained for zone 1. The fatigue damage of zone 2 shows qualitatively more advanced mesostructures in comparison with the 1 and 3 zones and the corresponding Df rises more significant. It is worth to mention that slope of the curve Df(N/Nb) changes for the characteristic value of N/Nb, where the band structure appears in zone 1 and 3. The decrease in the values Df before the specimen fracture can be explained by partial lost of adhesion force of the glue. The cyclic load with reduced stress amplitudes may help to relax a non-equilibrium state which brings the structure back to less developed mesostructures. The values of Df curve for the transition zone 3 are placed between curves of zones 1 and 2.

The fatigue experiment was repeated with a Al stripe glued to the bulk material in a better way. In this case the fatigue damage of the stripe was homogeneous over the whole stripe and the parameter Df increases till the speci-

Fig. 9. The fractal dimension D{ as a function of cycles number calculated from optical images by the use of Gaussian method during the on-line measurement of the specimens 2 and 3. The examples of the three different deformation structures developed during these tests are included in the diagram

men fracture (Fig. 9). Furthermore some indications were found that the function Df (log N/Nb ) may have three stages observed for bulk materials [12,13]. The first stage is characterized by irregular random microstructure, the bandlike pattern are typical for next structural stage, and in the last stage multi-band or band crossing grid-like structure are developed. However, the results of the first experiment show that the effect of the glue-joint can not only modify those patterns and thus also the absolute values of Df but even suppress the expected plateau like behaviour.

Finally a fractal analysis of the data which were obtained by a fatigue experiment performed in Tomsk [9] was carried out. In this paper a fractal dimension was evalu-

ated, too, using the method of difference correlation function

C(r) = £ (I(R + r) -1(R))2, (7)

where I(R) is the intensity of the optical image at the place R, while r is the difference between the two images the correlation of which are investigated by Eq. (7). However, the authors in [9] don't take into account the disturbing fluctuations originated by electronically noise and numerical failures. This noise is usually a random noise with a correlation radius approximately zero. In this case the difference correlation function did not go to zero for vanishing lateral distances of the both measured quantities, i.e.

C(r ^ 0) * 0. (8)

25 50 75 100 125 150 175 103 N

50 75 100 125 150 175 103 N

Fig. 10. The values of the parameter H (the Hurst parameter) as a function of the cycle number calculated in [9] (a). The recalculated results by the use of the Gaussian algorithm (b)

rn

Fig. 11. The fractal dimension Df as a function of cycles number calculated of optical images by the use of difference-autocorrelation function during the on-line measurement of the specimens 2 (a) and 3 (b)

In the case of fractal nature of the images the following behaviour is expected

C(r) ~ C0 + Cxr2H with Df = 3 - H. (9)

Hence, determination of the slope of the correlation function in a double logarithmic coordinate system cannot give the correct exponent 2H of the algebraic behaviour in Eq. (9). Usually the constant C0 becomes smaller during the fatigue load and hence the parameter Hincreases (Fig. 10, a). The correct analysis using Gaussian algorithm yields a decreasing value ofH and increasing parameter Df (Fig. 10, b). The qualitative behaviour in this figure corresponds well with that one in Fig. 8 in spite of the fact, that in the Tomsk experiment the loading stress was lying between 20 and 200 MPa and the frequency was only 1 Hz. However, the structural development was completed in the band structure stage. The type of surface pattern and the absolute values of Df points at such a conclusion.

The Al stripes were also investigated by the help of pulsed eddy current technique. The eddy current measurement was done at the same position for which the optical images were measured. The evaluation of the fractal dimension values by the method of the difference-autocorrelation function were performed between 0 and 600 ns of the real time eddy current signals (cf. Fig. 2). The result of this procedure is shown in Fig. 11. The initial level of the fractal dimension in both experiments was approximately 1.2. The fractal dimension grew up the appearance of bandlike pattern at the Al-stripe surface with increasing fatigue damage. Then the behaviour of the fractal dimension stays constant or slightly decreases, to finally fall down nearly to the initial values. For specimen 2 this behaviour was caused by visible delamination of the «smart sensors». In the case of specimen 1 a larger number of cracks was observed, which would reduce the current dimension so that mainly one dimensional current paths would take part at the eddy current signal. For comparison Df was determined for the bulk material, where the values were very similar to that one of the initial state of the «smart sensor».

5. Conclusion and outlook

This paper has briefly described the application of a new non-destructive testing method in order to monitor the fatigue state of industrial components. The method is based on the application of smart-designed thin film sensors — "multiscale smart skin". In our approach the optical images or pulsed eddy current signals were measured during the deformation of the specimens. The deformation state of the whole specimens was detected by optical images and eddy current signals and was evaluated by use of the fractal analysis with the fractal dimension as most relevant parameter.

During the tensile test the fractal dimension increase only slightly and no mesostructural patterns were observed until fracture of the bulk material. On the other side, the development of the surface structure of the Al-stripe sensors reflected the characteristics ofthe fatigue damage during cyclic load. At the same time the fractal dimension changes correspondingly. However, the plateau-like behaviour, found for various steel specimens in online fatigue experiments [11, 12], did not appear in pronounced way. Nevertheless, in the function Df(N/Nb) clear indications of the change in mesostructural pattern were found. Hence the fractal dimension Df grows with certain indication of three different stages: a) stochastic, b) band formation, c) multiband/grid state.

The fatigue damage of the bulk material was quite strongly correlated with the change of the fractal dimension Df of the Al stripe, however, the observed stages were not unique for the whole specimen, since there are inhomoge-neous adhesive forces and differences in the loading type were possible as well due to the different modules E of the single crystal stripe and the bulk material.

Furthermore crack structures in the Al stripe had to be taken into account as an additional level of mesomechanical structure development in order to follow the fatigue damage towards the end of life time of the bulk material. The cracks take off the constraints for structure development, consequently, rough structures were be flattened by further loading. As a consequences Df decreased.

The fractal analysis of pulsed eddy current signal did yield non-conclusive results, so far. Insufficient sensor features, delamitation and crack appearance influence the obtained results and the result of fractal analysis in a different way. To have a quick and reliable engineering non-destructive test procedure to read out the information of smart sensor layers applied to components, it is necessary to design special eddy current sensors, which has best contrast for detecting changes in deformation structures. However, it makes sense to search for other techniques to estimate the structural state of the smart sensor. First of all optical fibre technique should be discussed because of easy application and advantage of fibre technology in aircraft structural health monitoring. The use of magnetic sensor material seems to be the second road to reach our goal. The Barkhausen noise is sensitive to structural changes and material can be optimised for fatigue assessment.

The authors are very grateful for having the opportunity to take part at the INTAS project No. 04-80-7078 „RealTime Multiscale Composite System for Structural Health Monitoring of Fatigue Damage", especially to collaborate in a fruitful way with Dr. Ch. Paget, Prof. E. Zasimchuk, Dr. Y. Gordienko, Prof. V.E. Panin and Dr. P. Kusnetzov. For providing support in specimen preparation we would like to thank the Airbus division in UK and the Institute of Metal Physics in Kiev, Ukraine. The authors express the gratitude to the teams of Siempelkamp Prüf- und GutachterGesellschaft mbH Dresden for their support and supplying of experimental facilities. The authors are obliged to Dr. P. Kuznetsov for leaving the experimental data of his fatigue experiment at the Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russia.

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Поступила в редакцию 20.06.2011 г.

Сведения об авторах

Cikalova Ulana, Ph.D., Researcher, IZFP, Dresden, Germany, ulana.cikalova@izfp-d.fraunhofer.de Schreber Juergen, Prof., Dr., Division Director, IZFP, Dresden, Germany, Juergen.Schreiber@izfp-d.fraunhofer.de Michael Kröning, Prof., IZFP, Dresden, Germany, michael@kroening.com Vertyagina Yelena, Ph.D., Lecturer, ENU, Astana, Kazakhstan