- Email: [email protected]
The impedance method of non-destructive inspection
The impedance method of non-destructive inspection P. Cawley The physical basis of the impedance method of non-destructive testing has been investigated. A theoretical study has been backed up by impedance measurements on structures with deliberately introduced disbonds. It has been shown that defects such as disbonds and delaminations may be modelled as a spring beneath which is the undamaged structure, the spring stiffness being infinite if no defect is present. The impedance at the top of the spring is a strong function of the spring stiffness, so impedance measurements may be used to detect damage. The technique is most sensitive when the defect is close to the surface and the base structure is relatively stiff. The limiting factor on the sensitivity of the technique is the stiffness of the dry point-contact between the impedance transducer and the structure. The results show that the technique ;is potentially a simple and rapid means of non-destructive testing.
Keywords: acoustic testing, mechanical impedance, defect detection
The impedance method of non-destructive inspection has been used in the Soviet Union for almost 30 yearsllt and its use in the West has now increased with the marketing of the Acoustic Flaw Detector, which is based on the Soviet design, by Inspection Instruments Ltd. The technique uses measurements of the point impedance Z of a structure defined as
F
Z = -
(1)
v
where F is the harmonic force input to the structure and v is the resultant velocity of the structure at the same point. The measurements are carried out at a single frequency, the frequency used being typically between 1 and 10 kHzlll. The method is used to detect defects such as disbonds in adhesive joints, delaminations and voids in laminated structures and defective honeycomb constructions. These are all 'plana£ defecis which result in one or more layers of the construction being separated from the base layer(s). The method is not suitable for detecting transverse cracks. The technique is attractive because the test is quick to carry out and, since the frequencies used are low, a dry contact between the transducer and the test structure is satisfactory. This removes the need for the coupling fluids which are required in higher frequency ultrasonic testing. Also, because the lower frequencies result in longer wavelengths, the measured impedance of a honeycomb structure is less dependent on whether the transducer is placed directly above or between the corrugations. This makes the inspection of honeycomb structures easier than with ultrasonics. Conversely, the longer wavelengths
mean that the minimum detectable size in solid laminates is increased. The~re is therefore considerable interest in the technique, particularly from the aerospace industry, but uncertainty about what physical parameters are measured and the relationship between these and the presence of defects has limited its application. Lange has published over 20 papers on the impedance method in the Soviet literature (see, for example, References 1-3). However, these are more concerned with the design and operation of the transducer than with the investigation of the impedance changes produced by defects. It was therefore decided to carry out a theoretical and experimental study of the effect of disbonds and similar defects on the impedance of a structure. This study is described here.
Physical basis of the method Model of damage The impedance method seeks to detect areas of a structure where one or more layers are separated from the base layer(s) as shown in Figure I a. A localized defect of this type has little effect on the overall dynamic properties of the structure~ It has been shownl"s] that the changes in mode shapes and structural natural frequencies produced by localized defects, while measurable, are in general small. Clearly, however, the local stiffness of the structure is significantly reduced. The defect may therefore be modelled as a spring, below which is the rest of the structure whose properties are unaltered, as shown in Figure lb. The spring stiffness is given by the stiffness of the layers above the defect which may be considered clamped around the edges of the defect. In the absence of a defect, the spring stiffness is
0308-9126/84/020059-07 ~3.00 © 1984 ButterworthEt Co (Publishers) Ltd NDT INTERNATIONAL. VOL 17. NO 2. APRIL 1984
59
Disband
i
J
! a
b Fig. 1
Glue line (exaggerated thickness)
Adherends
I
l
.,P-Slxing, stiffness k
l
I
Undamaged structure
a - - Typical defect; b - - mathematical model of defect
infinite. The variation of the impedance measured at the top of the spring as the spring stiffness is changed must therefore be investigated. In practice, the impedance method of non-destructive inspection uses a dry point-contact between the transducer and the structure. This contact has a finite stiffnesslnl so the spring stiffness in the model becomes the defect stiffness in series with the contact stiffness. The spring stiffness over a good area of the structure is the contact stiffness alone. The effect of this on the sensitivity of the technique is discussed in the following sections.
factor of the beam was taken as 0.05, which corresponds to a Q factor of 20. The resonances correspond to positions of m i n i m u m impedance. As expected, the resonant frequencies are little changed as the spring stiffness is decreased. However, the resonances become much less pronounced and the anti-resonances (frequencies at which the impedance is a maximum) move closer to the resonances. Between spring stiffnesses of 10~2 and 108 N m -~ there is little change in the basic shape of the curve though the position of the higher anti-resonances does shift. This indicates that the system behaviour is controlled by the beam. Below a spring stiffness of 10s N m-L however, the system impedance is increasingly spring controlled, the impedance decreasing with spring stiffness. This indicates that measurements of point impedance can be used to indicate the spring stiffness and hence the presence of defects. When the impedance of the system is completely controlled by the spring, the impedance is that of a grounded spring (the beam is relatively stiff and so acts as a rigid abutment). Now the deflection u at the top of the spring for a force F is given by F u = -k
(3)
and for harmonic motion at frequency to the velocity is v = icou -
icoF k
The impedance is therefore given by
The plate formed by the layers above the defect can resonate. The model of the defect as a spring whose stiffness is the static stiffness of this plate is only valid at frequencies well below the first resonant frequency. This is the frequency of the m e m b r a n e resonance in which all areas of the plate move in phase with each other. The frequency of this modefn is dependent on the size of the defect, For a circular defect considered clamped at its edges, the frequency is given by
f"
0.47 h - a2
/ E ' X / P ( 1 - v ~)
Fe
Theoretical prediction of impedance changes due to defects For ease of analysis, the theoretical predictions were carried out on the beam structure shown in Figure 2. The method is, however, readily generalizable to plate and shell structures. The impedance at the top of the spring was predicted for a variety of spring stiffnesses, positions of the spring along the beam, and beam stiffnesses and damping using the receptance analysis program, COUPLE, which was developed at Imperial CollegeH.
r- N \Knife Fig. 2
60
u
Beam 40 mm wide; various thicknesses
300 m m edge supports
System analysed
I00 \
~
k = I012N m-t \
6o
20
0
Figure 3 shows a family of curves of the modulus of the impedance (in dB re 1 N s m -~) against frequency for a beam 300 m m long, 40 m m wide and 10 m m deep with the spring placed 100 m m from one end, as the spring stiffness k is changed from 10~2 to 105 N m-L The hysteretic damping
i~t
4~,~- - !
(2)
where h is the thickness of the layer above the defect, a is the defect radius andE, p and v are the material modulus, density and Poisson's ratio respectively. Thus, a defect 0.5 m m deep and 10 m m in radius in aluminium has a m e m b r a n e resonance at 12.5 kHz. This is above the normal operating range of the impedance method.
(4)
-Nm"
0
I 2
4
6
8
i
!0
Frequency (kHz) Fig. 3 Predicted impedance against frequency curves for 10 mm thick beam at different spring stiffnesses: ..beam + spring,------grounded spring
NDT I N T E R N A T I O N A L . APRIL 1 9 8 4
Z
F =
k
(5)
-
v
iw
+
8O
and
S
k IZl = -
(6)
t.o
6O
Curves of IzI calculated from Equation (6) for the lower spring stiffnesses used in the analysis are shown dotted in Figure 3. These reemphasize the degree of spring control at the different values of stiffness. If the behaviour of the system is completely spring controlled the frequency at which the inspection measurements are made is immaterial. However, in the intermediate region, the frequency can be critical. For example, at 4.2 kHz, the impedance shown in Figure 3 for a stiffness of 107 N m -~ is greater than that for a stiffness of 108 N m -~ because of an anti-resonance in the former curve. If stiffnesses in this intermediate region are to be detected, the inspection frequency should be chosen to be as far as possible from the resonant frequencies. If the spring has a major effect on the impedance curve, this will also ensure that the anti-resonances are avoided as the resonances and anti-resonances will then be close together. The spring stiffness at which the system behaviour becomes spring controlled depends on the stiffness of the structure. Figure 4 shows a family of curves similar to that of Figure 3 except that the beam thickness has been reduced to 2 mm. The more flexible structure has many more resonances below 10 kHz and there is little change in the curves between spring stiffnesses of l0 s and 10~ N m-L Below 107 N m -1, however, spring control is achieved. This indicates that the technique is more sensitive on stiffer structures, a conclusion which accords with Soviet experience[ll. From Equation (6), log I l l = log k - log ~o
(7)
Hence, if the behaviour of the system is spring controlled, a graph of log ] Z [ against log k at a constant frequency should be a straight line. Figure 5 shows this relationship at a frequency of 5 kHz for different beam thicknesses. The graph shows that the thinner the beam, the lower the spring stiffness at which the impedance departs from the spring controlled line. When the impedance leaves this line it can either increase or decrease, depending on
8
40
E
20
I 6
I 7
I 8
LOglo spring stiffness ( N m"t) Fig. 5 Predicted impedance against spring stiffness for system of Figure 2 for different beam thicknesses: 0 - - 1 O0 mm, + - - 10 mm, I - I - - 5 mm, A - - 2 mm
whether the frequency is near a resonance or an antiresonance. It is worth noting that some change in impedance with spring stiffness is obtained even when the system behaviour is not spring controlled. For example, the curves of Figure 4 for spring stiffnesses of l0 s and 107 N m -~ are not coincident. However, the impedance can either increase or decrease with stiffness depending on the frequency chosen. This would make test results difficult to interpret. The effects of varying spring position and beam damping have also been investigated. It was found that in between resonances neither parameter had much effect on the impedance, the range in impedance for a 10 m m deep beam and a spring stiffness of 10~ N m -~ at a frequency of 5 kHz being 2 dB as the springwas moved along the beam. The variation as the Q factor of the beam was changed from 10 to 1000 was less than this. Hence, provided inspection is not carried out at resonances or antiresonances, the damping of the structure is not important and the results should not vary greatly with position (unless the section of the structure changes).
I00
Experimental investigation of the impedance of defects
\ 80
-
~ .
k = l O S N m -I
Tests on a thick beam
/
The validity of the predictions of the previous section was investigated by testing the thick beam shown in Figure 6a. This comprised a steel beam 290 m m long, 60 m m wide and 30 m m deep with an aluminium sheet 45 m m wide and 3.3 m m deep bonded to one face with an epoxy adhesive. Two areas of the sheet, one 39 m m long and the other 17 m m long, were not coated with adhesive and so formed disbonds.
6O
~= 40 E
20
~
0 0
k~l= i d N m-I
~
k : I0- Nm I 2
- --
I 4
I 6
I 8
I0
Frequency ( kHz ) Fig, 4 Predicted impedance against frequency curves for 2 mm thick beam at different spring stiffnesses: , beam + s p r i n g ~ - - - g r o u n d e d spring
NDT INTERNATIONAL. APRIL 1984
The impedance of the structure at different points was measured using a Bruel & Kjaer type 8001 impedance head which essentially consists of a force gauge and accelerometer in one unitlsl. Provided a number of criteria are satisfiedlgl, the division of the force by the integrated
61
acceleration signal gives a direct measurement of the impedance of the structure at the point of attachment. The impedance head was connected to the structure via cementing studs which were bonded to the structure at the required measurement points as shown in Figure 6a. White-noise excitation was applied to the structure via a small electromagnetic shaker, the impedance-frequency curve being produced by a fast Fourier transform based signal analyser. The experimental configuration used is shown in Figure 7.
Cementinq studs
thick aluminium sheet
a
thick steel beom
(thickness exaggerated)
Disbands
~Smm
120 n~n
I
I
I
I
I
I
I
I
'IT I I
1.63mm thick aluminium sheet
b
II
T
510x 150x 6mm steel plate
Disbonds
I
I
12,m.7 I i
I I
l'8"m l J Two 3 0 0 x 6 5 x l . 7 5 mm aluminium sheets bonded together
Fig. 6
a - - Thick beam; b - - thick plate; c - - thin beam
White noise signal
Fast Fourier transform analyser
Power amplifier
Figure 8 shows the impedance modulus against frequency curve for a good area and the middle of the two defective zones from a frequency of 0 to 12 kHz. The static stiffness of the defective zones was calculated using a finite element analysis of a plate free on two parallel edges and either clamped or simply supported on the other two edges. The predicted stiffnesses for the larger defect were 18 )< 10+ N m -1 (clamped) and 7 × 10+ N m-' (simply supported). The impedance curves corresponding to these predicted stiffnesses are shown dotted in Figure 8. It is clear that the spring model is appropriate up to a frequency of about 4.5 kHz, the stiffness being between that predicted for simply supported and clamped edges. This is reasonable since the sound areas of the bond do not rigidly clamp the zone above the defect but some moment constraint is provided. The spring model breaks down as the membrane resonance of the layer above the defect is approached. Figure 8 shows that this resonance occurs at about 6 kHz which accords well with simple predictions based on the stiffness and mass of the layer. The predictions for the smaller defect were not as accurate. This is not surprising since the cementing stud used to attach the impedance head to the structure was 14 mm in diameter and the defect was only 17 mm long. The impedance measured was therefore a poor approximation to the impedance at the centre of the defect. The stiffness prediction is also very sensitive to the length of the defect and a small error in the assumed length due to, for example, uneven adhesive spreading would have a large effect on the stiffness of the smaller defect. However, the curve for this defect shown in Figure 8 accords well with the trend of the predictions made in the previous section, the impedance being intermediate between those of the good area and the larger defective zone. The impedance of both defects is essentially spring controlled and the defective zones can clearly be detected by impedance measurements.
100
:::~ Charge amplifiers
Small shaker
Push
._~ I-
"-~
Force signal
Acceleration signal
=
I
Clamped 20
Impedance head
Fig. 7
62
Test piece
Schematic of test arrangement
ubber mat
0
:39 mm defect
I 4
J 8
~2
Frequency (kHz) Fig. 8 Measured impedance against frequency curves for thick beam: - measured, ------predicted for spring stiffness of 39 mm defect
NDT INTERNATIONAL. APRIL 1984
300 m m long. 65 m m wide and 1.75 m m thick bonded together. Disbonds 27 and 18 m m long were incorporated as shown in Figure 6c.
60
~ L ~
"
" ' W " " " ~ -~
~E~ 40
Clamped edges
20
0
~'~._.~l~Xj~.~_j
,,~.,._~"'# ~
~ ~--~I._~ Siml~y supported edges I 4 Frequency (kHz)
I 2
I.122rnrn def ecl ~'jl8mm
~'/__~¢~"2Ornrn ~'~
detect 25 mm defect I 6
Fig. 9 Measured impedance against frequency curves for thick plate: - - m e a s u r e d , - - - - - - p r e d i c t e d for spring stiffness of 25 rnm defect
,oo
i
8O
8
60
40
The impedance curves obtained are shown in Figure 10. The impedance is clearly not spring controlled for either defect and, while there are differences between the curves, the impedance of a defective zone can be higher or lower than that of a good zone depending on the frequency. This would make inspection difficult. These findings confirm the theoretical prediction that defects of a given size are more readily detected on stiffer structures.
The contact stiffness b e t w e e n transducer and structure It was mentioned in the previous section 'Physical basis of the method - - model of damage" that a dry point-contact is usually used between the impedance transducer and the structure. This facilitates rapid inspection without the need for the coupling fluids which are usually required in ultrasonic testing, However, the finite stiffness of this contact does limit the sensitivity of the method. The analysis of the previous section showed that the presence of a defect effectively introduces a spring kd between the transducer and the structure, whose stiffness decreases as the defect size increases. This spring is in series with the contact stiffness k c, so the total stiffness k is given by 1
27 mrn defect 20 0
I 2
I 4 Frequency (kHz)
Fig. 10
k
1 -
The next series of tests was designed to test the method on a structure which had many more resonances in the frequency range of interest than the thick beam used previously, but whose base was still stiff compared with the layer above the adhesive. This was done using the testpiece shown in Figure 6b which comprised a steel plate 310 mm long, 150 m m wide and 6 mm deep with an aluminium sheet 64 mm wide and 1.63 m m thick bonded to one face. Disbonds 25, 20, 18 and 12 mm long were placed as shown in Figure 6b. The testing technique was identical to that used in the previous tests. Figure 9 shows the impedance-frequency relationships for the good and defective zones. (Curves for other sound areas were produced and were very similar to the one shown.) The curves corresponding to the predicted stiffnesses of the largest defect for simply supported and clamped edges are also shown. Again, a spring stiffness between the two provides a good model of the defect behaviour at frequencies around 4 kHz where inspection is usually carried out. The large number of structural resonances makes the curves more complicated than those shown in Figure 8 but it is clear that provided inspection frequencies between the resonances are chosen, the defects can readily be detected and placed in order of size from the impedance measurements. All the defects show essentially springcontrolled behaviour. on a thin b e a m
The last series of tests was carried out on a much more flexible testpiece. This comprised two aluminium sheets
NDT INTERNATIONAL. APRIL 1984
--
1 +
kc
--
(8)
kd
or
k-
Measured impedance against frequency curves for thin beam
Tests on a thick plate
Tests
-
kckd kc + kd
(9)
Therefore, ifkc is small compared with kd, a change in kd will produce a relatively small change in the total stiffness k. Since the impedance transducer can only measure the total stiffness, this has serious implications for the sensitivity of the technique. Lange and Teumin[+l have studied the stiffness of a dry point-contact both theoretically and experimentally. Using standard elastic contact theoryll°l they showed that for small vibrations,
1.82(FR) 1/a kc -
B
(10)
where F is the static force clamping the transducer onto the structure, R is the radius of curvature of the contact tip of the transducer, and B ;
1-vl 2
E1
+ 1
E2
]
where E~, vl and E~, v2 are the Young's moduli and Poisson's ratios of the materials of the contact tip and structure respectively. The experimental results quoted in Reference 6 show good agreement with the values calculated using Equation (10). The contact stiffnesses calculated using Equation (10) for brass and steel transducer contact tips of radius 15.75 mm, which is the radius used on the Soviet transducerl~l and a clamping force of 3 N on structure surfaces of steel, aluminium and carbon fibre reinforced p l a s t i c (CFRP) are given in Table 1. The values for CFRP are low because the modulus perpendicular to the plane of the fibres determines the contact stiffness. This modulus is approximately 8 G N m-~[lq.
63
Table 1. materials
Contact
stiffness
between
different
2°°I
dB, CFRP
Contact stiffness (x 10 6 N m -1) Structure surface material
Steel contact tip
Brass contact tip
Steel Aluminium CFRP
15.4 9.7 2.7
11.9 8.4 2.6
Clamping force (F) Radius of contact tip
= 3 N = 15.75 mm
3 dB, CFRP
150
v
E
E O ~6
6 dB,
IO0
3dB, aluminium
If the clamping force is increased to 10 N, the stiffnesses are increased by 50%. It is therefore important that the clamping force is kept constant during testing. 50
Discussion It has been shown that defects such as disbonds, delaminations and voids may be modelled as a spring whose stiffness is approximately that of the layer above the defect clamped around the defect edges, A practical impedance measuring system for nondestructive testing will use a dry point-contact between the transducer and the structure, whereas the tests described in the section on the 'Physical basis of the method" used a contact with a much higher stiffness. This contact stiffness is effectively in series with the defect stiffness. The impedance transducer measures the overall stiffness so the sensitivity of the technique is greatly reduced when the defect stiffness is of the same order or greater than the contact stiffness. The results of the test are clearest when the impedance of the system is effectively spring controlled. The spring stiffness at which this occurs depends on the stiffness of the structure under test. Figure 5 shows that the impedance is effectively spring controlled at a spring stiffness of 107 N m -~ on aluminium structures 5 m m thick, while for a 2 mm thick structure spring control is attained at a stiffness of 10+ N m-'. Table 1 shows that contact stiffnesses are of the order of 107 N m -I. s o on all but the thinnest structures the impedance measured by the transducer will be spring controlled. Defects can still be detected when the impedance is not spring controlled, but in this regime the impedance of a defective zone may be greater or less than that of a sound region depending on the excitation frequency. If the measured impedance is spring controlled, it is possible to plot the m i n i m u m detectable defect diameter against defect depth. For a steel contact tip on an aluminium structure, the contact stiffness is approximately 10~N m -t. Therefore, this is the effective stiffness of a sound area. Assuming that a 6 dB change in impedance can reliably be detected, the m i n i m u m detectable defect size must reduce the overall stiffness by 6 dB. Therefore, from Equation (9), the defect stiffness kd is 107 N m-', The central stiffness of a clamped circalar plate of radius a and depth h is 16rtD (ii) kd --
a2
where Eh 3 D-
64
12(1 - v2)
0
~ 0
I 2
I
I 4
1
I 6
l
Defect depth (mrn) Fig, 11 Minimum detectable defect diameter against defect depth in aluminium and CFRP assuming 3 dB and 6 dS reliabilities in impedance measurement
and E, v are the Young's modulus and Poisson's ratio for the plate material, Hence, for a given ka, the relationship between defect diameter and depth may be found. Figure 11 shows graphs of the minimum detectable defect diameter against depth for aluminium and CFRP structures using a steel transducer contact tip giving the contact stiffnesses shown in Table 1, assuming 3 dB and 6 dB reliabilities in impedance measurement. (The CFRP structure was assumed to be cross plied with Ex = Ey -----70 G N m-2.) The defect sizes in CFRP are larger because of the lower contact stiffness shown in Table 1. At depths greater than 3 - 4 ram, the m i n i m u m diameters shown are probably pessimistic since the membrane resonances of the defects would come into the inspection frequency range resulting in a reduction in the effective defect stiffness from that calculated using Equation (l l). Also, if the plate were assumed to be simply supported rather than clamped, the predicted m i n i m u m detectable defect size would be smaller than that shown in Figure 1 I. The theoretical and experimental investigations have shown that the most reliable results will be obtained if the excitation frequency is chosen to avoid structural resonances. If this is done, structural damping has little effect on the results and the impedance of a sound structure is insensitive to position on the structure if the section is constant. The study of the effect of contact stiffness has shown the importance of keeping the clamping force between the transducer and the structure constant. The predictions of the section on the 'Physical basis of the method' and the graph of m i n i m u m detectable defect size against depth (Figure 11) all concerned structures fabricated from solid material. In a honeycomb structure the local stiffness is critically dependent on the bond between the skin and core. The skins also tend to be very thin so it is likely that the method will be very suitable for use with honeycomb structures.
NDT INTERNATIONAL. APRIL 1 9 8 4
The advantages of the impedance method of inspection can only be realized if the impedance transducer and associated instrumentation is satisfactory. Problems have arisen with the systems currently employed both in the Soviet Union and the West because the transducers used, unlike the impedance head used in the tests reported here, give an output which is a highly nonlinear function of the structural impedance and the simple physical interpretation which can be made of the results, as shown in this paper, is lost. This tends to relegate the technique to the realms of t h e ' b l a c k box'. The practical implementation of the method will be the subject of a future paper.
Conclusions It has been shown that defects such as disbonds, delaminations and voids may be modelled as a spring, beneath which is the sound structure whose properties are unchanged. The spring stiffness is approximately that of the layer above the defect clamped around the defect edges. The predicted impedances obtained using this model agree well with those obtained experimentally. The theoretical predictions, supported by experimental investigations, have shown that impedance measurements have considerable potential for detecting defects in a plane parallel to the structure surface, such as disbonds and delaminations. The sensitivity of the method is greatest when the layer above the defect is thin and the base structure is relatively stiff These findings are in line with experience in the Soviet Union. The stiffness of the dry point-contact between the transducer and the structure surface has been shown to be the limiting factor on the sensitivity of the technique.
This work has been carded out with the support of the Procurement Executive, Ministry of Defence.
References 1 [,sage, Yu.Y. "Low frequency acoustic NDT methods', Soy J NDT (1978) pp 788-797 2 Lunge, Yu.V. 'Characteristics of the impedance method of inspection and of impedance inspection transducers', SovJNDT 0978) pp 958-966 3 Lunge, Yu.V. 'Design of the transducer in differential probe heads of impedance type defectoscopes', Soy J NDT 0975) pp 295-302 4 Cawley,P. and Adams, R.D. "Thelocation of defects in structures from measurements of natural frequencies', J Strain Analysis (1979) 5 Cawley,P. and Adams, R.D. 'Defect location in structures by a vibration technique', ProcASME Design Engineering Technical Conference. St Louis, USA (September 1979) 6 Lunge,Yu.V,and Teamin, l.l. 'Dynamic flexibility of a dry point contact', Soy J NDT (1971) pp i 57-165 7 Sainslmry, M.G. "Users guide to structural dynamic analysis computer program COUPLE2",Imperial CollegeMech Eng Dept 8
Dynamics Section Report No 81008 (1981) Ewias, D.J. 'Measurement and application of mechanical impedance data, Part 2, measurement techniques',JSoc En vEng
(1976) 9
Brownjohn, J.M.W., Steel, G.H., Cawley, P. and Adams, R.D.
"Errors in mechanical impedance data obtained with impedance heads', J Sound Vib 73 (1980) 10 Timeeheako, S.P. and Goodier, J.N. Theory of elasticity (McGraw-Hill, 1951) l l Cawley,P. and Adams, R.D. "The predicted and experimental natural modes of free-free CFRP plates', J Composite Materials (1978)
Author P. Cawley is in the Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London SW7 2BX, UK.
Paper received 17 November 1983
NDT INTERNATIONAL. APRIL 1984
65
ULTRASONICS INTERNATIONAL
'83
Conference Proceedings This book contains the proceedings of the 14th conference in the Ultrasonic International series which took place in Canada in July 1983. Papers were presented from all the main areas of ultrasound research, including defect sizing, medical scanning, macrosonics, surface waves and acoustic microscopy. The specialist authors came from a wide range of countries. Ultrasonics plays an increasingly important role in many diverse areas of technology, and this new collection of papers provides the research worker with an up-to-date record of the latest developments and advances in this field. So#cover
680pages
246 x 170mm
0 408 22163 1
£40.00 in the UK only
Ordersshouldbesentto theappropriateButterworthoffice listedbelow. Fordetailsof otherButterworthScientificor AnnArbortitles,pleasecontacttheappropriateButterworthoffice
Butterworth United Kingdom Butterworth & Co (Publishers) Ltd Borough Green, Sevenoaks Kent, TN15 8PH
USA Butterworth & Co (Publishers) Inc 10 Tower Office Park Woburn, MA 01801
Scientific
South Afdca Butterworth & Co (SA) (Pty) Ltd PO Box 792 152-154Gale Street Durban 4000
,,
Australia Butterworths Pty Ltd POB 345 North Ryde, NSW 2113
New Zealand Butterworths of New Zealand Ltd 33-35 Cumberland Place CPO Box 472 Wellington 1
DIE C A S T I N G M E T A L L U R G Y Alan Kaye and Arthur Street Butterworths Monographs in Materials series Th~s new book, the first in the Monographs in Materials series, concentrates on the recent developments in the metallurgical, as opposed to design and engineering, aspects of efficient and economic die casting. The importance of metals in the cost of die casting is now fully appreciated, and this authoritative reference work examines new methods of improving metal reclamation, reducing losses and increasing the efficiency of melting and handling equipment. As the durability of dies developed for large and complex castings is still far from satisfactory, the metallurgy and treatment of steels are discussed to give an insight into such phenomena as die failure by thermal fatigue. Die Casting Metallurgy will fulfil the need for an authoritative, up-to-date reference source for technical managers, metallurgists, engineers and suppliers to the industry. Hardcover 320 pages 234x 156mm 0408 10717 0 £21.00in the UK only 1982 Orders should be sent to the appropriate Butterworth office listed below. For details of other Butterworth Scientific or Ann Arbor titles, please contact the appropriate Butterworth office
Butterworth Scientific United Kingdom Butterworth & Co (Publishers) Ltd Borough Green, Sevenoaks Kent, TN15 8PH
66
USA Butterworth & Co (Publishers) Inc 10 Tower Office Park Woburn, MA 01801
South Afdca Butterworth & Co (SA) (Pry) Ltd PO Box 792 152-154Gale Street Durban 4000
Australia Butterworths Pty Ltd POB 345 North Ryde, NSW 2113
New Zealand Butterworths of New Zealand Ltd 33-35 Cumberland Place CPO Box 472 Wellington 1
NDT INTERNATIONAL. APRIL 1984
Keywords: acoustic testing, mechanical impedance, defect detection
The impedance method of non-destructive inspection has been used in the Soviet Union for almost 30 yearsllt and its use in the West has now increased with the marketing of the Acoustic Flaw Detector, which is based on the Soviet design, by Inspection Instruments Ltd. The technique uses measurements of the point impedance Z of a structure defined as
F
Z = -
(1)
v
where F is the harmonic force input to the structure and v is the resultant velocity of the structure at the same point. The measurements are carried out at a single frequency, the frequency used being typically between 1 and 10 kHzlll. The method is used to detect defects such as disbonds in adhesive joints, delaminations and voids in laminated structures and defective honeycomb constructions. These are all 'plana£ defecis which result in one or more layers of the construction being separated from the base layer(s). The method is not suitable for detecting transverse cracks. The technique is attractive because the test is quick to carry out and, since the frequencies used are low, a dry contact between the transducer and the test structure is satisfactory. This removes the need for the coupling fluids which are required in higher frequency ultrasonic testing. Also, because the lower frequencies result in longer wavelengths, the measured impedance of a honeycomb structure is less dependent on whether the transducer is placed directly above or between the corrugations. This makes the inspection of honeycomb structures easier than with ultrasonics. Conversely, the longer wavelengths
mean that the minimum detectable size in solid laminates is increased. The~re is therefore considerable interest in the technique, particularly from the aerospace industry, but uncertainty about what physical parameters are measured and the relationship between these and the presence of defects has limited its application. Lange has published over 20 papers on the impedance method in the Soviet literature (see, for example, References 1-3). However, these are more concerned with the design and operation of the transducer than with the investigation of the impedance changes produced by defects. It was therefore decided to carry out a theoretical and experimental study of the effect of disbonds and similar defects on the impedance of a structure. This study is described here.
Physical basis of the method Model of damage The impedance method seeks to detect areas of a structure where one or more layers are separated from the base layer(s) as shown in Figure I a. A localized defect of this type has little effect on the overall dynamic properties of the structure~ It has been shownl"s] that the changes in mode shapes and structural natural frequencies produced by localized defects, while measurable, are in general small. Clearly, however, the local stiffness of the structure is significantly reduced. The defect may therefore be modelled as a spring, below which is the rest of the structure whose properties are unaltered, as shown in Figure lb. The spring stiffness is given by the stiffness of the layers above the defect which may be considered clamped around the edges of the defect. In the absence of a defect, the spring stiffness is
0308-9126/84/020059-07 ~3.00 © 1984 ButterworthEt Co (Publishers) Ltd NDT INTERNATIONAL. VOL 17. NO 2. APRIL 1984
59
Disband
i
J
! a
b Fig. 1
Glue line (exaggerated thickness)
Adherends
I
l
.,P-Slxing, stiffness k
l
I
Undamaged structure
a - - Typical defect; b - - mathematical model of defect
infinite. The variation of the impedance measured at the top of the spring as the spring stiffness is changed must therefore be investigated. In practice, the impedance method of non-destructive inspection uses a dry point-contact between the transducer and the structure. This contact has a finite stiffnesslnl so the spring stiffness in the model becomes the defect stiffness in series with the contact stiffness. The spring stiffness over a good area of the structure is the contact stiffness alone. The effect of this on the sensitivity of the technique is discussed in the following sections.
factor of the beam was taken as 0.05, which corresponds to a Q factor of 20. The resonances correspond to positions of m i n i m u m impedance. As expected, the resonant frequencies are little changed as the spring stiffness is decreased. However, the resonances become much less pronounced and the anti-resonances (frequencies at which the impedance is a maximum) move closer to the resonances. Between spring stiffnesses of 10~2 and 108 N m -~ there is little change in the basic shape of the curve though the position of the higher anti-resonances does shift. This indicates that the system behaviour is controlled by the beam. Below a spring stiffness of 10s N m-L however, the system impedance is increasingly spring controlled, the impedance decreasing with spring stiffness. This indicates that measurements of point impedance can be used to indicate the spring stiffness and hence the presence of defects. When the impedance of the system is completely controlled by the spring, the impedance is that of a grounded spring (the beam is relatively stiff and so acts as a rigid abutment). Now the deflection u at the top of the spring for a force F is given by F u = -k
(3)
and for harmonic motion at frequency to the velocity is v = icou -
icoF k
The impedance is therefore given by
The plate formed by the layers above the defect can resonate. The model of the defect as a spring whose stiffness is the static stiffness of this plate is only valid at frequencies well below the first resonant frequency. This is the frequency of the m e m b r a n e resonance in which all areas of the plate move in phase with each other. The frequency of this modefn is dependent on the size of the defect, For a circular defect considered clamped at its edges, the frequency is given by
f"
0.47 h - a2
/ E ' X / P ( 1 - v ~)
Fe
Theoretical prediction of impedance changes due to defects For ease of analysis, the theoretical predictions were carried out on the beam structure shown in Figure 2. The method is, however, readily generalizable to plate and shell structures. The impedance at the top of the spring was predicted for a variety of spring stiffnesses, positions of the spring along the beam, and beam stiffnesses and damping using the receptance analysis program, COUPLE, which was developed at Imperial CollegeH.
r- N \Knife Fig. 2
60
u
Beam 40 mm wide; various thicknesses
300 m m edge supports
System analysed
I00 \
~
k = I012N m-t \
6o
20
0
Figure 3 shows a family of curves of the modulus of the impedance (in dB re 1 N s m -~) against frequency for a beam 300 m m long, 40 m m wide and 10 m m deep with the spring placed 100 m m from one end, as the spring stiffness k is changed from 10~2 to 105 N m-L The hysteretic damping
i~t
4~,~- - !
(2)
where h is the thickness of the layer above the defect, a is the defect radius andE, p and v are the material modulus, density and Poisson's ratio respectively. Thus, a defect 0.5 m m deep and 10 m m in radius in aluminium has a m e m b r a n e resonance at 12.5 kHz. This is above the normal operating range of the impedance method.
(4)
-Nm"
0
I 2
4
6
8
i
!0
Frequency (kHz) Fig. 3 Predicted impedance against frequency curves for 10 mm thick beam at different spring stiffnesses: ..beam + spring,------grounded spring
NDT I N T E R N A T I O N A L . APRIL 1 9 8 4
Z
F =
k
(5)
-
v
iw
+
8O
and
S
k IZl = -
(6)
t.o
6O
Curves of IzI calculated from Equation (6) for the lower spring stiffnesses used in the analysis are shown dotted in Figure 3. These reemphasize the degree of spring control at the different values of stiffness. If the behaviour of the system is completely spring controlled the frequency at which the inspection measurements are made is immaterial. However, in the intermediate region, the frequency can be critical. For example, at 4.2 kHz, the impedance shown in Figure 3 for a stiffness of 107 N m -~ is greater than that for a stiffness of 108 N m -~ because of an anti-resonance in the former curve. If stiffnesses in this intermediate region are to be detected, the inspection frequency should be chosen to be as far as possible from the resonant frequencies. If the spring has a major effect on the impedance curve, this will also ensure that the anti-resonances are avoided as the resonances and anti-resonances will then be close together. The spring stiffness at which the system behaviour becomes spring controlled depends on the stiffness of the structure. Figure 4 shows a family of curves similar to that of Figure 3 except that the beam thickness has been reduced to 2 mm. The more flexible structure has many more resonances below 10 kHz and there is little change in the curves between spring stiffnesses of l0 s and 10~ N m-L Below 107 N m -1, however, spring control is achieved. This indicates that the technique is more sensitive on stiffer structures, a conclusion which accords with Soviet experience[ll. From Equation (6), log I l l = log k - log ~o
(7)
Hence, if the behaviour of the system is spring controlled, a graph of log ] Z [ against log k at a constant frequency should be a straight line. Figure 5 shows this relationship at a frequency of 5 kHz for different beam thicknesses. The graph shows that the thinner the beam, the lower the spring stiffness at which the impedance departs from the spring controlled line. When the impedance leaves this line it can either increase or decrease, depending on
8
40
E
20
I 6
I 7
I 8
LOglo spring stiffness ( N m"t) Fig. 5 Predicted impedance against spring stiffness for system of Figure 2 for different beam thicknesses: 0 - - 1 O0 mm, + - - 10 mm, I - I - - 5 mm, A - - 2 mm
whether the frequency is near a resonance or an antiresonance. It is worth noting that some change in impedance with spring stiffness is obtained even when the system behaviour is not spring controlled. For example, the curves of Figure 4 for spring stiffnesses of l0 s and 107 N m -~ are not coincident. However, the impedance can either increase or decrease with stiffness depending on the frequency chosen. This would make test results difficult to interpret. The effects of varying spring position and beam damping have also been investigated. It was found that in between resonances neither parameter had much effect on the impedance, the range in impedance for a 10 m m deep beam and a spring stiffness of 10~ N m -~ at a frequency of 5 kHz being 2 dB as the springwas moved along the beam. The variation as the Q factor of the beam was changed from 10 to 1000 was less than this. Hence, provided inspection is not carried out at resonances or antiresonances, the damping of the structure is not important and the results should not vary greatly with position (unless the section of the structure changes).
I00
Experimental investigation of the impedance of defects
\ 80
-
~ .
k = l O S N m -I
Tests on a thick beam
/
The validity of the predictions of the previous section was investigated by testing the thick beam shown in Figure 6a. This comprised a steel beam 290 m m long, 60 m m wide and 30 m m deep with an aluminium sheet 45 m m wide and 3.3 m m deep bonded to one face with an epoxy adhesive. Two areas of the sheet, one 39 m m long and the other 17 m m long, were not coated with adhesive and so formed disbonds.
6O
~= 40 E
20
~
0 0
k~l= i d N m-I
~
k : I0- Nm I 2
- --
I 4
I 6
I 8
I0
Frequency ( kHz ) Fig, 4 Predicted impedance against frequency curves for 2 mm thick beam at different spring stiffnesses: , beam + s p r i n g ~ - - - g r o u n d e d spring
NDT INTERNATIONAL. APRIL 1984
The impedance of the structure at different points was measured using a Bruel & Kjaer type 8001 impedance head which essentially consists of a force gauge and accelerometer in one unitlsl. Provided a number of criteria are satisfiedlgl, the division of the force by the integrated
61
acceleration signal gives a direct measurement of the impedance of the structure at the point of attachment. The impedance head was connected to the structure via cementing studs which were bonded to the structure at the required measurement points as shown in Figure 6a. White-noise excitation was applied to the structure via a small electromagnetic shaker, the impedance-frequency curve being produced by a fast Fourier transform based signal analyser. The experimental configuration used is shown in Figure 7.
Cementinq studs
thick aluminium sheet
a
thick steel beom
(thickness exaggerated)
Disbands
~Smm
120 n~n
I
I
I
I
I
I
I
I
'IT I I
1.63mm thick aluminium sheet
b
II
T
510x 150x 6mm steel plate
Disbonds
I
I
12,m.7 I i
I I
l'8"m l J Two 3 0 0 x 6 5 x l . 7 5 mm aluminium sheets bonded together
Fig. 6
a - - Thick beam; b - - thick plate; c - - thin beam
White noise signal
Fast Fourier transform analyser
Power amplifier
Figure 8 shows the impedance modulus against frequency curve for a good area and the middle of the two defective zones from a frequency of 0 to 12 kHz. The static stiffness of the defective zones was calculated using a finite element analysis of a plate free on two parallel edges and either clamped or simply supported on the other two edges. The predicted stiffnesses for the larger defect were 18 )< 10+ N m -1 (clamped) and 7 × 10+ N m-' (simply supported). The impedance curves corresponding to these predicted stiffnesses are shown dotted in Figure 8. It is clear that the spring model is appropriate up to a frequency of about 4.5 kHz, the stiffness being between that predicted for simply supported and clamped edges. This is reasonable since the sound areas of the bond do not rigidly clamp the zone above the defect but some moment constraint is provided. The spring model breaks down as the membrane resonance of the layer above the defect is approached. Figure 8 shows that this resonance occurs at about 6 kHz which accords well with simple predictions based on the stiffness and mass of the layer. The predictions for the smaller defect were not as accurate. This is not surprising since the cementing stud used to attach the impedance head to the structure was 14 mm in diameter and the defect was only 17 mm long. The impedance measured was therefore a poor approximation to the impedance at the centre of the defect. The stiffness prediction is also very sensitive to the length of the defect and a small error in the assumed length due to, for example, uneven adhesive spreading would have a large effect on the stiffness of the smaller defect. However, the curve for this defect shown in Figure 8 accords well with the trend of the predictions made in the previous section, the impedance being intermediate between those of the good area and the larger defective zone. The impedance of both defects is essentially spring controlled and the defective zones can clearly be detected by impedance measurements.
100
:::~ Charge amplifiers
Small shaker
Push
._~ I-
"-~
Force signal
Acceleration signal
=
I
Clamped 20
Impedance head
Fig. 7
62
Test piece
Schematic of test arrangement
ubber mat
0
:39 mm defect
I 4
J 8
~2
Frequency (kHz) Fig. 8 Measured impedance against frequency curves for thick beam: - measured, ------predicted for spring stiffness of 39 mm defect
NDT INTERNATIONAL. APRIL 1984
300 m m long. 65 m m wide and 1.75 m m thick bonded together. Disbonds 27 and 18 m m long were incorporated as shown in Figure 6c.
60
~ L ~
"
" ' W " " " ~ -~
~E~ 40
Clamped edges
20
0
~'~._.~l~Xj~.~_j
,,~.,._~"'# ~
~ ~--~I._~ Siml~y supported edges I 4 Frequency (kHz)
I 2
I.122rnrn def ecl ~'jl8mm
~'/__~¢~"2Ornrn ~'~
detect 25 mm defect I 6
Fig. 9 Measured impedance against frequency curves for thick plate: - - m e a s u r e d , - - - - - - p r e d i c t e d for spring stiffness of 25 rnm defect
,oo
i
8O
8
60
40
The impedance curves obtained are shown in Figure 10. The impedance is clearly not spring controlled for either defect and, while there are differences between the curves, the impedance of a defective zone can be higher or lower than that of a good zone depending on the frequency. This would make inspection difficult. These findings confirm the theoretical prediction that defects of a given size are more readily detected on stiffer structures.
The contact stiffness b e t w e e n transducer and structure It was mentioned in the previous section 'Physical basis of the method - - model of damage" that a dry point-contact is usually used between the impedance transducer and the structure. This facilitates rapid inspection without the need for the coupling fluids which are usually required in ultrasonic testing, However, the finite stiffness of this contact does limit the sensitivity of the method. The analysis of the previous section showed that the presence of a defect effectively introduces a spring kd between the transducer and the structure, whose stiffness decreases as the defect size increases. This spring is in series with the contact stiffness k c, so the total stiffness k is given by 1
27 mrn defect 20 0
I 2
I 4 Frequency (kHz)
Fig. 10
k
1 -
The next series of tests was designed to test the method on a structure which had many more resonances in the frequency range of interest than the thick beam used previously, but whose base was still stiff compared with the layer above the adhesive. This was done using the testpiece shown in Figure 6b which comprised a steel plate 310 mm long, 150 m m wide and 6 mm deep with an aluminium sheet 64 mm wide and 1.63 m m thick bonded to one face. Disbonds 25, 20, 18 and 12 mm long were placed as shown in Figure 6b. The testing technique was identical to that used in the previous tests. Figure 9 shows the impedance-frequency relationships for the good and defective zones. (Curves for other sound areas were produced and were very similar to the one shown.) The curves corresponding to the predicted stiffnesses of the largest defect for simply supported and clamped edges are also shown. Again, a spring stiffness between the two provides a good model of the defect behaviour at frequencies around 4 kHz where inspection is usually carried out. The large number of structural resonances makes the curves more complicated than those shown in Figure 8 but it is clear that provided inspection frequencies between the resonances are chosen, the defects can readily be detected and placed in order of size from the impedance measurements. All the defects show essentially springcontrolled behaviour. on a thin b e a m
The last series of tests was carried out on a much more flexible testpiece. This comprised two aluminium sheets
NDT INTERNATIONAL. APRIL 1984
--
1 +
kc
--
(8)
kd
or
k-
Measured impedance against frequency curves for thin beam
Tests on a thick plate
Tests
-
kckd kc + kd
(9)
Therefore, ifkc is small compared with kd, a change in kd will produce a relatively small change in the total stiffness k. Since the impedance transducer can only measure the total stiffness, this has serious implications for the sensitivity of the technique. Lange and Teumin[+l have studied the stiffness of a dry point-contact both theoretically and experimentally. Using standard elastic contact theoryll°l they showed that for small vibrations,
1.82(FR) 1/a kc -
B
(10)
where F is the static force clamping the transducer onto the structure, R is the radius of curvature of the contact tip of the transducer, and B ;
1-vl 2
E1
+ 1
E2
]
where E~, vl and E~, v2 are the Young's moduli and Poisson's ratios of the materials of the contact tip and structure respectively. The experimental results quoted in Reference 6 show good agreement with the values calculated using Equation (10). The contact stiffnesses calculated using Equation (10) for brass and steel transducer contact tips of radius 15.75 mm, which is the radius used on the Soviet transducerl~l and a clamping force of 3 N on structure surfaces of steel, aluminium and carbon fibre reinforced p l a s t i c (CFRP) are given in Table 1. The values for CFRP are low because the modulus perpendicular to the plane of the fibres determines the contact stiffness. This modulus is approximately 8 G N m-~[lq.
63
Table 1. materials
Contact
stiffness
between
different
2°°I
dB, CFRP
Contact stiffness (x 10 6 N m -1) Structure surface material
Steel contact tip
Brass contact tip
Steel Aluminium CFRP
15.4 9.7 2.7
11.9 8.4 2.6
Clamping force (F) Radius of contact tip
= 3 N = 15.75 mm
3 dB, CFRP
150
v
E
E O ~6
6 dB,
IO0
3dB, aluminium
If the clamping force is increased to 10 N, the stiffnesses are increased by 50%. It is therefore important that the clamping force is kept constant during testing. 50
Discussion It has been shown that defects such as disbonds, delaminations and voids may be modelled as a spring whose stiffness is approximately that of the layer above the defect clamped around the defect edges, A practical impedance measuring system for nondestructive testing will use a dry point-contact between the transducer and the structure, whereas the tests described in the section on the 'Physical basis of the method" used a contact with a much higher stiffness. This contact stiffness is effectively in series with the defect stiffness. The impedance transducer measures the overall stiffness so the sensitivity of the technique is greatly reduced when the defect stiffness is of the same order or greater than the contact stiffness. The results of the test are clearest when the impedance of the system is effectively spring controlled. The spring stiffness at which this occurs depends on the stiffness of the structure under test. Figure 5 shows that the impedance is effectively spring controlled at a spring stiffness of 107 N m -~ on aluminium structures 5 m m thick, while for a 2 mm thick structure spring control is attained at a stiffness of 10+ N m-'. Table 1 shows that contact stiffnesses are of the order of 107 N m -I. s o on all but the thinnest structures the impedance measured by the transducer will be spring controlled. Defects can still be detected when the impedance is not spring controlled, but in this regime the impedance of a defective zone may be greater or less than that of a sound region depending on the excitation frequency. If the measured impedance is spring controlled, it is possible to plot the m i n i m u m detectable defect diameter against defect depth. For a steel contact tip on an aluminium structure, the contact stiffness is approximately 10~N m -t. Therefore, this is the effective stiffness of a sound area. Assuming that a 6 dB change in impedance can reliably be detected, the m i n i m u m detectable defect size must reduce the overall stiffness by 6 dB. Therefore, from Equation (9), the defect stiffness kd is 107 N m-', The central stiffness of a clamped circalar plate of radius a and depth h is 16rtD (ii) kd --
a2
where Eh 3 D-
64
12(1 - v2)
0
~ 0
I 2
I
I 4
1
I 6
l
Defect depth (mrn) Fig, 11 Minimum detectable defect diameter against defect depth in aluminium and CFRP assuming 3 dB and 6 dS reliabilities in impedance measurement
and E, v are the Young's modulus and Poisson's ratio for the plate material, Hence, for a given ka, the relationship between defect diameter and depth may be found. Figure 11 shows graphs of the minimum detectable defect diameter against depth for aluminium and CFRP structures using a steel transducer contact tip giving the contact stiffnesses shown in Table 1, assuming 3 dB and 6 dB reliabilities in impedance measurement. (The CFRP structure was assumed to be cross plied with Ex = Ey -----70 G N m-2.) The defect sizes in CFRP are larger because of the lower contact stiffness shown in Table 1. At depths greater than 3 - 4 ram, the m i n i m u m diameters shown are probably pessimistic since the membrane resonances of the defects would come into the inspection frequency range resulting in a reduction in the effective defect stiffness from that calculated using Equation (l l). Also, if the plate were assumed to be simply supported rather than clamped, the predicted m i n i m u m detectable defect size would be smaller than that shown in Figure 1 I. The theoretical and experimental investigations have shown that the most reliable results will be obtained if the excitation frequency is chosen to avoid structural resonances. If this is done, structural damping has little effect on the results and the impedance of a sound structure is insensitive to position on the structure if the section is constant. The study of the effect of contact stiffness has shown the importance of keeping the clamping force between the transducer and the structure constant. The predictions of the section on the 'Physical basis of the method' and the graph of m i n i m u m detectable defect size against depth (Figure 11) all concerned structures fabricated from solid material. In a honeycomb structure the local stiffness is critically dependent on the bond between the skin and core. The skins also tend to be very thin so it is likely that the method will be very suitable for use with honeycomb structures.
NDT INTERNATIONAL. APRIL 1 9 8 4
The advantages of the impedance method of inspection can only be realized if the impedance transducer and associated instrumentation is satisfactory. Problems have arisen with the systems currently employed both in the Soviet Union and the West because the transducers used, unlike the impedance head used in the tests reported here, give an output which is a highly nonlinear function of the structural impedance and the simple physical interpretation which can be made of the results, as shown in this paper, is lost. This tends to relegate the technique to the realms of t h e ' b l a c k box'. The practical implementation of the method will be the subject of a future paper.
Conclusions It has been shown that defects such as disbonds, delaminations and voids may be modelled as a spring, beneath which is the sound structure whose properties are unchanged. The spring stiffness is approximately that of the layer above the defect clamped around the defect edges. The predicted impedances obtained using this model agree well with those obtained experimentally. The theoretical predictions, supported by experimental investigations, have shown that impedance measurements have considerable potential for detecting defects in a plane parallel to the structure surface, such as disbonds and delaminations. The sensitivity of the method is greatest when the layer above the defect is thin and the base structure is relatively stiff These findings are in line with experience in the Soviet Union. The stiffness of the dry point-contact between the transducer and the structure surface has been shown to be the limiting factor on the sensitivity of the technique.
This work has been carded out with the support of the Procurement Executive, Ministry of Defence.
References 1 [,sage, Yu.Y. "Low frequency acoustic NDT methods', Soy J NDT (1978) pp 788-797 2 Lunge, Yu.V. 'Characteristics of the impedance method of inspection and of impedance inspection transducers', SovJNDT 0978) pp 958-966 3 Lunge, Yu.V. 'Design of the transducer in differential probe heads of impedance type defectoscopes', Soy J NDT 0975) pp 295-302 4 Cawley,P. and Adams, R.D. "Thelocation of defects in structures from measurements of natural frequencies', J Strain Analysis (1979) 5 Cawley,P. and Adams, R.D. 'Defect location in structures by a vibration technique', ProcASME Design Engineering Technical Conference. St Louis, USA (September 1979) 6 Lunge,Yu.V,and Teamin, l.l. 'Dynamic flexibility of a dry point contact', Soy J NDT (1971) pp i 57-165 7 Sainslmry, M.G. "Users guide to structural dynamic analysis computer program COUPLE2",Imperial CollegeMech Eng Dept 8
Dynamics Section Report No 81008 (1981) Ewias, D.J. 'Measurement and application of mechanical impedance data, Part 2, measurement techniques',JSoc En vEng
(1976) 9
Brownjohn, J.M.W., Steel, G.H., Cawley, P. and Adams, R.D.
"Errors in mechanical impedance data obtained with impedance heads', J Sound Vib 73 (1980) 10 Timeeheako, S.P. and Goodier, J.N. Theory of elasticity (McGraw-Hill, 1951) l l Cawley,P. and Adams, R.D. "The predicted and experimental natural modes of free-free CFRP plates', J Composite Materials (1978)
Author P. Cawley is in the Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London SW7 2BX, UK.
Paper received 17 November 1983
NDT INTERNATIONAL. APRIL 1984
65
ULTRASONICS INTERNATIONAL
'83
Conference Proceedings This book contains the proceedings of the 14th conference in the Ultrasonic International series which took place in Canada in July 1983. Papers were presented from all the main areas of ultrasound research, including defect sizing, medical scanning, macrosonics, surface waves and acoustic microscopy. The specialist authors came from a wide range of countries. Ultrasonics plays an increasingly important role in many diverse areas of technology, and this new collection of papers provides the research worker with an up-to-date record of the latest developments and advances in this field. So#cover
680pages
246 x 170mm
0 408 22163 1
£40.00 in the UK only
Ordersshouldbesentto theappropriateButterworthoffice listedbelow. Fordetailsof otherButterworthScientificor AnnArbortitles,pleasecontacttheappropriateButterworthoffice
Butterworth United Kingdom Butterworth & Co (Publishers) Ltd Borough Green, Sevenoaks Kent, TN15 8PH
USA Butterworth & Co (Publishers) Inc 10 Tower Office Park Woburn, MA 01801
Scientific
South Afdca Butterworth & Co (SA) (Pty) Ltd PO Box 792 152-154Gale Street Durban 4000
,,
Australia Butterworths Pty Ltd POB 345 North Ryde, NSW 2113
New Zealand Butterworths of New Zealand Ltd 33-35 Cumberland Place CPO Box 472 Wellington 1
DIE C A S T I N G M E T A L L U R G Y Alan Kaye and Arthur Street Butterworths Monographs in Materials series Th~s new book, the first in the Monographs in Materials series, concentrates on the recent developments in the metallurgical, as opposed to design and engineering, aspects of efficient and economic die casting. The importance of metals in the cost of die casting is now fully appreciated, and this authoritative reference work examines new methods of improving metal reclamation, reducing losses and increasing the efficiency of melting and handling equipment. As the durability of dies developed for large and complex castings is still far from satisfactory, the metallurgy and treatment of steels are discussed to give an insight into such phenomena as die failure by thermal fatigue. Die Casting Metallurgy will fulfil the need for an authoritative, up-to-date reference source for technical managers, metallurgists, engineers and suppliers to the industry. Hardcover 320 pages 234x 156mm 0408 10717 0 £21.00in the UK only 1982 Orders should be sent to the appropriate Butterworth office listed below. For details of other Butterworth Scientific or Ann Arbor titles, please contact the appropriate Butterworth office
Butterworth Scientific United Kingdom Butterworth & Co (Publishers) Ltd Borough Green, Sevenoaks Kent, TN15 8PH
66
USA Butterworth & Co (Publishers) Inc 10 Tower Office Park Woburn, MA 01801
South Afdca Butterworth & Co (SA) (Pry) Ltd PO Box 792 152-154Gale Street Durban 4000
Australia Butterworths Pty Ltd POB 345 North Ryde, NSW 2113
New Zealand Butterworths of New Zealand Ltd 33-35 Cumberland Place CPO Box 472 Wellington 1
NDT INTERNATIONAL. APRIL 1984