CONTACT AND ACOUSTIC MEASUREMENTS ON A ...

CONTACT AND ACOUSTIC MEASUREMENTS ON A FATIGUING, CANTILEVER BEAM K. Klein Centre for Cold Ocean Resources Engineering Memorial University of Newfoundland St. John’s, Newfoundland, Canada, AlB 3X5 J.Y. Guigne’ A.S.J. Swamidas Faculty of Engineering and Applied Science Memorial University of Newfoundland St. John’s, Newfoundland, Canada, AlB 3X5

parameters within these functions exhibited change that correlated with fatigue crack growth. This paper summarizes the results to date.

‘GuignC International Ltd. 82 St. Thomas Line Site 21, Box 13, RR#l Paradise, Newfoundland, Canada, AIL lC1

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ABSTRACT This work was a part of a continuing study on changes in the modal properties of a structure that occur with fatigue cracking. The bending mode transfer functions (accelerationand near field pressure) oftwo cantileverbeams were measured. Both beams were subjected to repetitive cyclic loads. In the first case, measurementswere periodically made as fatigue cycles accumulated, from the unfatigued state to the final cracked condition. Ink staining and beachmarking were applied at various stages of cracking to delineate the crack depth profile. The second case was a cracked beam with results already partially reported at IMAC XII. Additional measurements of the final cracked state were made to further examine an apparent variation in modal frequency with position attributed to cracking. Previous work has established that pressure transfer functions near the plate surface have a strong relationship to the frequency response of the beam. Frequency response functions of acceleration and pressure were examined in the natural frequency regions for changes attributable to cracking. The component of normalized acoustic intensity normal to the plate’s surface was constructed from pairs of pressure transfer functions collectedat different altitudesand likewise examined. The objective was to identify which

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INTRODUCTION

When a structure experiences cyclic load reversals (e.g. offshore structure subjected to wave loads), fatigue cracking can occur at the hot spot regions of the welded joints. This wilI affect the dynamic properties of the stmcture. Attention has been focused on developing inspection techniques that will detect cracks and defects in the welded joints of stmctures [1,2]. One such technique under development during tbe last decade is vibration monitoring. Within this field researchers have investigated methods involving contact with the structure, such as accelerometersand strain gauges [3]. Researchers have also investigated the acoustic field radiatedby modal vibrations, as a non contact method of measuring structural dynamic properties [4,5]. The research group at Memorial University has been investigating acoustic techniques in conjunction with vibrational based crack detection methods [6]. We are interested in the damage information that can be obtained both from contact measurements and from acoustic measurements. The parameters of interest include natural frequency, damping and the net radiated acoustic power (acoustic intensity). This paper presents our most recent experimental observations on fatigue-dama,ged cantilever plates. 2. EXPERIMENTAL MEASUREMENTS

Specimen F, shown in Figure 1, was a cantilever beam with a welded stub that was subjected to constant amplitude cyclic loading to produce approximately 250 MPa stress at the weld toe closest to the clamped end, the eventual crack location. Periodically the loading was stopped to make FRF and PTF (pressure transfer function) measurements. This beam remained clamped in its support throughout its fatigue life from installation (no fatigue) until it had lost 213 of its cross sectional area to cracking. Cracking initiated just prior to 834,000 cycles of fatigue. At 834,000 cycles, a 20 mm surface crack was present along the back weld toe, starting from the side of the beam Figure 2 shows the crack cross sectional boundaries (identitied from the pattern of ink staining and beach marking procedures during fatiguing). Table I lists the relative crack cross sectional area as a function of the total accumulated number of fatigue cycles, and identifies the crack boundaries in Figure 2. Fourteen sets of data were collected, of which eight were collected prior to crack initiation, and six were collected at different stages of fatigue. Measurements were made on the first 5 beam bending modes. FRFs were measured at 5 equally spaced positions on beam centre. PTFs were measured at altitudes of 35 and 85 mm above beam centre. The number of x-y positions for the PTF measurements varied with the order of the bending mode. One x-y location was used for the first mode, two for second mode increasing linearly to 5 locations for the fifth mode. Zoom FFTs were collected with a frequency resolution of 0.125 Hz. At this resolution there were sufficient data points to curve tit the natural frequency regions of the second, third, fourth and fifth modes, but not the first mode. FRF and PTF spectra were processed individually for modal parameters (natural frequency, damping, etc.) using a single degree of freedom model. PTF spectra were also used to constmct the spectrum of acoustic intensity normal to the beam surface, 60 mm above the centreline of the beam. The natural frequencies obtained from FRF measurements are tabulated in Table 2 as a function of cumulative fatigue cycles. At the final cracked cross sectional area of 65 % of the beam cross section, the natural frequencies had decreased from their initial values by IO l/2 % for the first mode, 8 % for the second, 5 l/2 % for the third, 3 % for the fourth and 2 I12 % for the fifth mode. Figure 3 illustrates the shape of natural frequency vs fatigue cycles plotted for the first and fifth modes. This shape was typical of the other modes as well. Looking at Figure 3, the shifts in the natural frequencies are not noticeable until some point on or after 1,384,OOO fatigue cycles when the crack had gone through at least 30 % of the beam cross section.

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The natural frequencies calculated from PTF’s were observed to be the same at both altitudes. The natural frequencies from PTFs measured 35 mm above the beam are given in Table 3. Their values compare well with the FRF frequencies and exhibit the same shape. Figure 4 illustrates the shape of natural frequency from PTFs vs fatigue cycles for the first and fifth modes. For some of the modes, PTFs showed a slightly greater relative reduction in frequency with cracking. However this only occurred at or after 1,374,OOO cycles. As with FRFs, the frequency shifts were not noticeable until the crack cross sectional area reached 30 % of the beam cross section. The damping ratios of the: modes provided different information. The ratios for modes 2, 3, 4 and 5 are pIotted in Figure 5. At 750,000 cycles the third mode damping ratio increased significantly. This raised our expectations for crack initiation. Crack initiation did indeed occur shortly thereafter at 834,000 icycles. In hindsight however, the scatter in the damping ratio values for each mode makes interpretation difficult. There is no obvious event associated with the increase in the 4th mode’s damping ratio at 350,000 cycles (which correlates with a small increase in the 2nd mode). The increase in the 3rd mode, at 750,000 cycles correlates with an increase in the 4th mode and a small increase in the second mode. This is presumably associatedwith accumulationof the conditions for cracking. The increase in the tifih mode at 834,000 cycles is assumed to be due to crack initiation. Overall, the modes exhibited an increase in the damping ratio that either preceded or coincided with crack initiation. Scatter in the values and increases in the damping ratio of single modes at other times certainly obscured these events somewhat. The damping ratio calculated from PTFs for modes 2, 3 and 4 did not correlate that well with the damping ratio calculated from the FRF data. This was attributed to the combined scatter of the two data sets. The PTF scatter was probably greater than the FRF scatter because of the inherently noisier acoustic signal and because fewer x.y locations were measured for modes 2, 3 and 4 than for FRF’s. By comparison, there was good agreement in the 5th mode. Consequently, there was no obvious correlation between cracking and the damping ratio calculated for the second mode (not shown), the 3rd mode (shown in Figure 6), or the fourth mode (not shown). The damping ratio from the PTFs of the fifth mode, shown in Figure 7, overlays the FRF data quite well, exhibiting the same increasejust after crack initiation (834,000 cycles). Acoustic intensity, constructed from the PTFs (vector component normal to beam surface) was examined both for

spectral content and for net radiated power. Being constructed from PTFs, the spectra exhibited the same frequency shifts with cumulative fatigue cycles as the PTFs. The calculated error bounds on spectra from the first 2 modes swamped the mean values, excluding them from further consideration. Intensity from modes 3 and 4 exhibited sufficient variability from data set to data set to preclude correlating cracking to the observed changes in spectral shape. In some cases, the shape and scale of the no fatigue spectrum and the final spectrum collected at 1.550,OOO cycles were still similar for the same location. intensity spectra from the fifth mode were more consistent from data set to data set. There were changes in the 5th mode spectral content at 834,000 cycles, but these changes were only obvious in the spectra from 2 of 5 measurement locations. Similar comments apply to net power. Figure 8 shows that at each of 4 measurement locations for the 4th mode, the scatter in the net power measurements was large. The fifth mode exhibited a drop in net power at 834,000 cycles at 3 of 5 measurement locations (shown in figure 9). Overall, there was no additional information in the normal component of acoustic intensity that could not be obtained directly from the PTFs. Specimen E was a cantilever beam very similar to specimen F (see figure 1) that had been fatigued with constant amplitude loading that produced about 2.80 MPa stress at the eventual crack location. At 294,000 cycles it had progressed from the no fatigue condition to the cracked state with the crack profile shown in Figure 10. The cracked cross sectional area was approximately 65 % of the beam cross sectional area. In the original installation in 1993, this specimen had exhibited natural frequencies after cracking that appeared to vary with position [6]. Tables 4 and 5 illustrate what was observed for the 4th and 5th bending modes as a function of position down the centreline of the beam. In 1994, we reinstalled this specimen in its cracked state to make more measurements of this apparent phenomena and found that the natural frequenciesno longer varied significantly with position (last column of Tables 4 and 5) and were as large OT larger than the highest values measured after cracking. Looking for another explanation, we noted that the 1993 measurements had taken place over several days and had progressed inwards from the free end of the beam with time. The changes in frequencies in 1993, 7 Hz for the fourth mode, 8 Hz for the fifth mode, although a small percentage of the natural frequencies, were significantly larger than previously observed changes attributed to day to day measurement drift and system instability. Even disassembling and reassembling the measurement setup on 4 separate days could not produce the observed changes in natural frequency.

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It was then hypothesized that perhaps the increase in frequency with time was connected to the interval behveen end of fatigue and measurement. We wanted to subject the beam to additional fatigue ad observe whether the natural frequenciesshifted with time. In order to subject the beam to m”re fatigue without risking loss of the specimen, the specimen was subjected to 5,000 cycles of beachmarking. Measurementswere then made repetitively at two locations (x= 448 & 632 mm) back and forth over 48 hours, to obtain the natural frequencies of the 4th and 5th modes with time. Figure 11 illustrates the change in the frequencies for both positions with time. For each mode, the frequencies at the two positions are close together at similar times. The natural frequencies were not dependent on position. The natural frequencies of both modes did increase with the time interval since end of fatigue. In 48 hours, the 4th mode frequency increased by about 4 Hz and the 5th mode frequency increased by about 5 Hz. It was therefore concluded that the observed change in natural frequency after cracking in 1993 was most likely due to the time interval between end of fatigue and measurement. A possible explanation may be that at 294,000 cycles, the affected zone had large plasticity associated with cracking and consequently the frequencies were lower; with the passage of time the crack tip plasticity was relieved producing a stronger material. 3.

DISCUSSION

The first indication of damage in specimen F came from a change in the damping ratios, not the natural frequencies. In spite of some scatter in the data, the damping ratios showed a significant increase just before or at crack initiation, depending on the mode. After cracking had initiated, the damping ratios returned to their previous values. By comparison, the natural frequencies of specimen F did not shift noticeably until the cracked area of the beam had reached 30 % of the beam cross section. From that point on all natural frequencies decreased with cumulative fatigue cycles and crack growth. As a” indication of limiting values, when the crackedhad reached 65 % of the beam cross section, the total maximum frequency decreases ranged from 10 l/2 % for the 1st mode to 2 l/2 % for the 5th mode. PTFs provided the same natural tiequency information over 5 modes as FRFs. For the lower 4 modes, damping ratios calculated from PTFs suffered from excessive scatter in values. This was partially due to a lesser number of measurement locations for PTFs than FRFs in all but the 5th mode. In the fifth mode the damping ratio agreement between FRFs and PTFs was quite good, including the increase associated with crack initiation.

The normal component of acoustic intensity for the lower 4 modes suffered from too much variability between spectra. A drop in the 5th mode net power did occur with crack initiation. However, there was no additional information in the normal component of acoustic intensity that could not be obtained directly from the PTFs. The scatter of values for the damping ratio and the isolated increases that appear in single modes highlight the need to reduce scatter to make real events more obvious or identify the significance of these isolated events. It was fortunate that we had an opportunity to re-examine specimen E. It was observed that for this cracked beam, after subjecting it to additional fatigue, the natural frequencies increased with time, correlating very well with time interval following end of fatigue. From these results, it was concluded that the observed change in natural frequency after cracking in 1993 was most likely due to the time interval between end of fatigue and measurement, and was not related to measurement position. 4. ACKNOWLEDGEMENT The authors gratefully acknowledge the support of this work by the Narural Sciences and Engineering Research Council of Canada. 5. REFERENCES 1. Dover, W.D., 1991. “Condition Monitoring and Damage Assessment in Structures”, Proc. ofInternational Symposium on Fatigue and Failure in Steel and Concrete Structures, Dec. 19-21, Madras, India, Vol. 2, pp. 1087-1110. 2. Rytter, A., 1993. “Vibrational Based Inspection of Civil Engineering Structures”, Ph.D. thesis, Dept. of Building Technology and Structural Engineering, University of Aalborg, Denmark. 3. Swamidas, A.S.J., Chen, Y., Perchard, D.R. and Budipriyanto, A., 1994. “DetectionofCracking in Structures Using Experimental and Analytical Modal Analysis”, Proc. of the Annual Forum ofthe Canadian Society of Mechanical Engineers, McGill University, Montreal, June 27-29,25 pp. 4. Okubo, N. and Masuda, K., 1990. “Acoustic Sensitivity Analysis Based on the Results of Acoustic Modal Testing”, Proc. of Vlllth Int’l. Modal Analy. Conf., Vol.1, pp.270-274 5. Jifang, T., 1991. “The Modal Analysis of Motion Response, Dynamic Stress and Acoustic Radiation”, Proceedings of IXth Int’l. Modal Analysis Conference, Vol. II, pp. X53-855. 6. Klein, K., Guignt, J.Y. and Swamidas, A.S.J., 1994. “Monitoring the Change in Modal ParametersDuring Crack Growth in a Cantilever Plate”, Proceedings, XIIth Int’l. Modal Analysis Conference,Hawaii, U.S.A., pp. 1792-1800.

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Tahlc 4: Natural Freauencies of Fourth Mode

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