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Numerical modelling of resistance changes in symmetric CFRP composite under the influence of structure damage
Composites Science and Technology 88 (2013) 99–105
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Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Numerical modelling of resistance changes in symmetric CFRP composite under the influence of structure damage Paweł Pyrzanowski ⇑, Mirosław Olzak Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 10 June 2013 Accepted 25 August 2013 Available online 5 September 2013 Keywords: A: Carbon fibres A: Polymer–matrix composites (PMCs) B: Electrical properties C: Finite element analysis (FEA)
a b s t r a c t CFRP (Carbon Fibre Reinforced Polymer) composite consists of two materials characterised by different electric properties i.e., carbon fibres – the high strength component with conductive features as well as polymer fillers with insulating properties. For this reason, any structural damage will result in changes in electrical properties of the whole composite. This paper presents a mathematical FEM-based model allowing for simulation of damage in monolayer symmetric laminate structure. The dependences of electrical responses on the size and location of damage as well as the sensitivity of the method for accurate placement of electrodes supplying electric current were investigated. The effectiveness of this method for determining the approximate size and location of the damage and the usefulness of the FEM for modelling the changes in electrical properties of the composite were demonstrated. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction For years of the development of technology, the major construction materials were metals and their alloys. The main advantages of such materials is the ease of testing and modelling their material properties, as well as predictable and simple to predict way of destruction. This is due to isotropic properties of the material strength. In the early 70s of last century, in the advanced industries, especially aerospace, composite materials began to be used, mainly based on glass fibres, and, later, carbon and kevlar ones. Thanks to their high mechanical properties, strength and stiffness, the CFRP (Carbon Fibre-Reinforced Polymer) composites are the most often used for responsible and highly loaded airframe structural components. Strength properties of composites are strongly anisotropic, and depend on the directionality of the fibres and their arrangement, because it can be approximately assumed that the loads may only be carried by the fibres that can be stretched or compressed. The strength in the direction perpendicular to the fibres is ensured only through the binder, and in most cases can be ignored [1]. Such a composite structure can cause considerable problems of modelling its endurance. Especially, it concerns the issues of fatigue strength. So far, there are not any good models for forecasting the time of construction work to the such an extent as it is possible for metals. The most unfavourable situation exists in the case of carbon composites, which show very weak symptoms of a progressive process of fatigue degradation. One may only observe a very slight ⇑ Corresponding author. Tel.: +48 222347512. E-mail address: [email protected] (P. Pyrzanowski). 0266-3538/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2013.08.023
decrease in stiffness, due to destruction of the fibres. A decrease of the order of 1–2% is followed by a rapid destruction of the element. This causes great problems with monitoring the work of the composite and with prediction of its stock of strength, especially in real constructions. Moreover, it may be very difficult to measure the changes e.g., in an aircraft girder during a flight. Ultrasonic methods are popular [6], however, being useful for the periodic diagnosis, they are not suitable for continuous monitoring of the structure because of the difficulty with installing a network of detectors. The mentioned reasons make it necessary to work out new method for diagnosing the degradation process of composites. One of the possible methods is the measurement of changes in composite resistivity. The carbon fibres, whose continuity is to be detected here, are good conductors of electric current, with the resistivity of about 105 X m, and the binder is a very bad one, with the resistivity of about 1010 to 1015 X m. This difference causes that electric current flows only through the carbon fibres, and disruption of even small number of them will reduce the cross-section through which the current flows and thereby will cause an increase in the resistance. This phenomenon has been observed experimentally on several occasions, both in static and fatigue experiments, as well as in shock load tests. One of the first results were presented by Schulte and Baron in the paper [7] in which also influence of electric current, temperature, and time of the test on the resistivity of composite was investigated. Recently experimental investigations of influence of composite damage into its resistivity were presented by research team of Hou [4], Irving [5], Todoroki [8–10] and others [2,3,11], but so far mainly laboratory trials have been carried out. In order to apply the method in practice, there is a need for developing a mathematical model of
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the phenomenon, and to relate resistance changes with the changes in the element’s structure. Such attempts have already been taken, e.g. in work [12] in which the authors proposed a model of an analogue network of resistors simulating the fibres and the contacts between them. The authors also presented a discrete model based on the Finite Element Method, which compares the breaks of composite fibres bands with the resistance changes. 2. Tested material In the constructed models, a single layer of the laminate was simulated. In the case of damage comprising the fibres of only one layer, the changes in resistance were significantly reduced due to the shunt effect caused by intact layers which take a portion of the current flow without significant reduction in whole cross-section of the composite. This effect was achieved also by modelling the damage that encompasses less than the whole skein, because an analogous mechanism appeared. The analysed model, contains the equal amounts of fibres arranged in two directions – along and across the current flow. The geometry of fabric was modelled accurately, also taking into account the weave of skeins passing from the lower to the upper surface of the laminate, and vice versa. Such a model is much more complicated than the simple one, but it takes into consideration more complex situations e.g., the location of the electrodes on the skein along or across the direction of current flow. The geometrical dimensions of the skein of a fabric were taken as averages for a laminate of reinforcement volume ratio of about 65%. Each skein was treated as a single elementary cell, without analyzing the behaviour of individual fibres, but taking into account their average properties in the whole volume of the band. Prior to the calculations, we had carried out test measurements of the resistivity of the modelled fabrics. Unfortunately, this proved to be a very difficult task. The resistance along the fibres for an
individual skein, both before and after the lamination, is relatively easy to measure. Its value is quite stable, and it does not depend on the point of measurement on the sample. The measurement in the transverse direction with respect to the fibres is much less reliable. Theoretically, the value of specific resistance may vary from the values for the fibres along their length (if one assumes isotropic properties of the individual fibres, excellent adhesion of the fibres, lack of insulating properties of the interface and lack of penetration of the resin between the fibres) to infinity (if the skeins is perfectly penetrated by the resin and one assumes lack of contact between the fibres). In practice, the expected value of the actual resistance lies between these two values. Attempts of measurement showed very large variability of the measured parameter, depending on the point of measurement. The authors measured experimentally the resistivity of a single skein prepared from the experimentally created plate as shown in Fig. 1a. Four-wire method, described in details in Section 3.2, was used. The length of the measured band was 100 mm. The result obtained from the measurement depended on the specimen (6 samples were used) and varied from 0.03e3 to 0.08e3 X mm. For measuring the resistivity of the spacer between skeins similar set-up, shown in Fig. 1b was used. The parts of two parallel and two perpendicular bands were prepared what allowed to obtain 4 contact zones between the bands. The measured resistance was recalculated into the resistivity of FEM elements. Transverse resistivity of a skein was not measured. This is very difficult because an arrangement of fibres in skeins is not completely parallel, and electric contacts between the fibres are quite randomly spaced. For this reason, the authors assumed that the average ratio of the values of the specific resistance along the fibres to the ones across the fibres was equal to 1:20. This roughly corresponds to the value of 1:27 given in [9] for unidirectional prepreg and reinforcement ratio of 62%. In this study, we used the numerical model corresponding to the ECC 452 fabric with a weight of 204 g/m2, 2 2 twill. Fig. 2
(a)
(b)
Fig. 1. Measuring of resistivity: (a) single skein; (b) spacer between skein.
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Fig. 2. The tested fabric: (a) real image; (b) FEM model.
(a)
direction of fibres
A
B C D
...............
CE
1 2 3
...............
4
Fig. 3. Geometry of two elementary fabric cells (mm).
82 shows the image of a fragment of a fabric before lamination, and the numerical model made in ANSYS program. Geometrically, the FEM model correspond exactly to a monolayer laminate made of this fabric. The geometrical dimensions of elementary cells are shown in Fig. 3. There are presented two cells that contain fragments of the skeins with fibres of different directionality, and an oblique fragment modelling the transition of the skein between the upper and the lower surfaces of the laminate. The skeins containing single fibres were treated as continuous fragments with cross-sectional dimensions of 1.864 0.1 mm across the fibres and orthotropic electrical properties. An oblique fragment linking the bands on the transition between the upper and the lower surfaces also had orthotropic properties, but its resistivity along fibres was slightly smaller (reduced to 0.897 of the resistivity of the simple band), in order to compensate the reduced thickness of the model on the slants. Between them, there is a layer with a thickness of 0.05 mm and isotropic electrical properties, which models the insulating epoxy resin separating the bands from each other. The current was led into the model and the resistance was measured through the contacts, with very high electrical conductivity. The resistivity of the applied components is presented below: The horizontal band: 0.05e3 X mm (along the fibres); 1.0e3 X mm (across the fibres). The sloping band: 0.0405e3 X mm (along the fibres); 1.0e3 X mm (across the fibres). The spacer between bands (isotropic): 0.7 X mm. The electrodes (isotropic): 1.0e7 X mm. The entire model consisted of 78 skeins along the direction of current flow (x direction – horizontally in the following figures) and 82 skeins laterally (y direction – vertically), so that its dimensions were 161.177 mm 169.453 mm. Such a large model provided sufficient approximation of a laminate of unlimited dimensions. Fig 4 presents the coordinate system for column and row indication and localisation of electrodes for one case (nonshifted current electrodes, central located 3-band length break).
(b) current electrode measurement electrode
break position
Fig. 4. The specimen: (a) coordinate system of bands; (b) electrode localisation.
2.1. Modelling of defects The developed model represented the defects in the laminate involving interruption of half of a skein, one, two or three skeins. In the case of breakage comprising more than one skein, the disruption included the neighbouring, but not a distant skein. The break was modelled by removing a small element connecting the cells (see Fig. 3). 3. Method of measuring the changes of electrical properties 3.1. Model of resistance changes Carbon composite, consisting mainly of carbon fibres, has the typical characteristics of a good conductor of electric current. In particular, its resistance R, given by formula (1), depends on resistivity q, current flow path length l, and cross-sectional area A.
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R¼
P. Pyrzanowski, M. Olzak / Composites Science and Technology 88 (2013) 99–105
Z 0
l
q A
dl
ð1Þ
The integral form of the formula allows for an analytical description of the changes in resistance of a conductor whose cross-section A is large in relation to its length l, and may be applied in the cases in which resistivity is not stable, but changes within the conductor’s volume. For conductors of high length/ diameter ratio, e.g. wires, one may use the generally applicable form of Eq. (2).
R¼
ql
ð2Þ
A
As it results from these equations, the resultant change in resistance may be caused ether by changes in resistivity, or changes in the dimensions of the conductor. The tested laminate sample, in which defects are caused either by fatigue demotion or acute destruction, can be considered as the conductor with structure discontinuities, hence two different models of degradation are possible (as shown in Fig. 5). (a) Small discontinuities arising as a result of a break of individual fibres without any significant rupture in the continuity of the skein appearing in the entire volume of the fragment of sample. Such a defect can be modelled as a change in resistivity of some elements without geometry changes. In the current flow space through the damage area, one can observe a reduction of its density caused by the increase in resistivity. Neither the length of current flow path nor the cross-sectional area are changed. (b) Large discontinuities produced as the result of break of either whole the skein or its significant part. In this case, we observe an increase in the length of current flow path and a decrease in conductor’s cross-section area, but the resistivity of the structure does not change. Since the current flowing through the element must pass round the damaged fragments, the area of the damaged part is subtracted from the total cross-sectional area. In this case, the conductor’s resistivity does not change. This model is especially used for material with anisotropic electrical parameters in which resistivity in the direction perpendicular to the current flow is higher than in parallel one.
Current flow lines (the areas of increased current density)
(a)
(b) Area of microdefect
In this work, we assumed the existence of large discontinuities of the material. They could be as high as at least a half of cross-section of the skein and were situated perpendicularly to current flow line joining the points where current contacts were applied to the sample. Therefore, there was no need for an alteration of the resistivity of the composite elements. 3.2. Measurement of resistance changes In practice, the resistance of a conductor is measured using an appropriate instrument – an ohmmeter. Its principle of operation (as shown in Fig. 6) requires the use of a constant current source (indicated by I) that produces a current of constant intensity, independent of the load resistance, and measuring the voltage drop across the tested resistor R through which the current flows. The voltage is measured with a voltmeter (labelled as V). The simplest ohmmeter uses only two wires connecting the instrument to the tested resistor (the two-wire parallel circuit, Fig. 6a). The current source and the voltage meter are contained within the instrument. The two-wire arrangement is very simple, but its significant disadvantage is that the resistances of connecting cables (Rp) adds up to the measured resistance. If the measured resistance is low, comparable to the resistance of the connecting wires, significant measurement error may arise. For this reason, in more advanced devices, the four-wire method is used, in which the current circuit and the voltage measuring circuit are separated, and two pairs of wires connect the resistor’s contacts to the voltmeter and the current source, respectively (Fig. 6b). This method is much better for measuring small resistances, because the resistance of the voltage circuit has practically no effect on voltage measurement due to high input resistance of the voltmeter (typically several MXs or greater). The resistances in the current circuit do not have any influence on the measurement result, either. Since the resistance of the carbon composite is very low, usually much smaller than the resistance of the contacts between the fibres and wires, the measurement of small changes in the resistance caused by the defects in the structure might be burdened with a high error. For this reason, the four-wire method proved much better and was simulated by the authors in this study. In order to minimize the measuring error, the contacts of the voltmeter leads should be placed as close as possible to the place of damage. In practice, the current source cables and the voltmeter cables are not connected at one point on the sample; the voltage contacts must be closer to the tested damage place than the current contacts. Such a connection scheme is modelled in this work. 4. Samples As it was mentioned in Section 2, the tested model consisted of 78 bands oriented along the current flow (x axis) and 82 bands across it (y axis). In order to facilitate the description, we applied
macrodefect
Fig. 5. The model of composite damage (description in the text).
(b) (a)
Rp
Rp
R
R V
I
V
Rp
Rp Fig. 6. The method of resistance measurement: (a) two-wire circuit; (b) four-wire circuit.
I
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At the end of the electrode 40N, intensity of the current in equals +1 A. At the end of the electrode 40BO, intensity of the current out equals 1 A. At the end of the electrode 40N, potential of 0 V (the reference point for other potentials in the circuit).
Table 1 Location of electrodes. Cell designation
Fibre direction
Electrode description
39N 40N 39BO 40BO 41BO 39AI 40AI 41AI 39AU 40AU 41AU
||| ||| ||| |||
Current left for shift 2 Current left for shift 0 and 1 Current right for shift 1 Current right for shift 0 Current right for shift 2 Voltage left upper Voltage left middle Voltage left lower Voltage right upper Voltage right middle Voltage right lower
We also examined the samples in which the current electrodes were placed on different bands i.e., in the cells 40N and 39N or 39BO and 41BO. The voltages were always determined along one band between the measuring electrodes 39AI and 39AU, 40AI and 40AU or 41AI and 41AU. Actually, we measured the electric potentials with respect to the electrode 40N and then subtracted them, so that the voltage differences between the measuring electrodes lying on the different bands could easily be calculated. Simulated cracks (i.e., the place from which the modelling elements were removed from the bundle) had the following lengths: half the width of the bundle (length 0.5); one bundle width (length 1); two bundle width (length 2); three bundle width (length 3). The cracks were situated between the columns AO–AP, in the rows 37 to 43. Location of a crack was defined by the coordinates of the cells between which the crack was situated. For greater readability of the tables, graphs and results, the position coordinate of the crack was introduced, defined by the distance from the crack centre to the centre line of the row number 40. For example, for the crack crossing three adjacent rows, the position coordinate of 2 corresponds to the rupture between the cells 37AO–37AP, 38AO–38AP and 39AO–39AP, while the position of 0 means that the crack is located between the cells 39AO–39AP, 40AO–40AP and 41AO–41AP. For the crack crossing two rows, the position coordinate may take the following values: 2.5, 1.5, 0 .5, 0.5, 1.5, 2.5, for the cracks between the cells: 37AO–37AP and 38AO–38AP; 38AO–38AP and 39AO–39AP; 39AO–39AP and 40AO–40AP; 40AO–40AP and 41AO–41AP; 41AO–41AP and 42AO–42AP; 42AO–42AP and 43AO–43AP respectively. Direction of fibres (horizontal or vertical) in respective cells was described in Table 1. Obviously, this direction pertained to the place of application of the electrodes. On the other side of the sample the direction of fibres was reversed.
Table 2 Potentials on the electrodes on sample without fracture. Shift
Electrode
Potential (V)
Electrode
Potential (V)
Voltage between electrodes (mV)
0 0 0 0 1 1 1 1 2 2 2 2
39AI 40AI 41AI 40N 39AI 40AI 41AI 40N 39AI 40AI 41AI 39N
1.34960 1.34110 1.35170 0 1.3505E03 1.3404E03 1.3515E03 0 1.3482E03 1.3486E03 1.3512E03 0
39AU 40AU 41AU 40BO 39AU 40AU 41AU 39BO 39AU 40AU 41AU 41BO
1.46850 1.47910 1.46550 2.81550 1.4801E03 1.4676E03 1.4648E03 2.8161E03 1.4612E03 1.4619E03 1.4596E03 2.8036E03
0.1189 0.1380 0.1138 2.8155 0.1296 0.1272 0.1133 2.8161 0.1130 0.1133 0.1084 2.8036
a rectangular table consisting of 78 (horizontal) to 82 (vertical) square cells. The rows of the array are numbered from 1 to 82 and columns are numbered from A to BZ. The location of the electrode on the sample is referred to the coordinates of the cell (the row number and column number) in which the electrode is located (e.g., 41AI), while the location of the break is determined by the coordinates of the cells between which the break occurs (e.g., 43AO–43AP). In most calculations, we assumed that current flows between the electrodes 40N and 40BO (both the electrodes on one band). The following boundary conditions were assumed for the voltage and currents in the sample:
5. Results For the samples described in Section 4 we performed calculations for different positions of the current electrodes, different crack lengths (from mid-width of one band to three adjacent
Table 3 Changes of voltage between electrodes on sample with fracture. Shift
Pair of electrodes
Fracture location 2
0 0 0 0 1 1 1 1 2 2 2 2
39AI–39AU 40AI–40AU 41AI–41AU 40N–40BO 39AI–39AU 40AI–40AU 41AI–41AU 40N–44BQ 39AI–39AU 40AI–40AU 41AI–41AU 39N–41BO
0
1
1
2
U (lV)
%
U (lV)
%
U (lV)
%
U (lV)
%
U (lV)
%
36.6 9.2 11.7 5.5 38.80 9.60 12.10 5.90 34.90 8.80 11.30 5.00
31 7 10 0.2 30 8 11 0.2 31 8 10 0.2
38.3 40.4 14.2 6.3 40.00 38.80 14.20 6.30 35.90 35.30 13.00 5.20
32 29 13 0.2 31 31 13 0.2 32 31 12 0.2
37.7 41.1 15.8 6.4 39.40 39.50 15.60 6.30 35.30 36.00 14.40 5.20
32 30 14 0.2 31 31 14 0.2 31 32 13 0.2
9.9 40.2 16.0 6.2 9.50 38.10 15.50 5.80 9.00 35.10 14.70 5.10
8 29 14 0.2 7 30 14 0.2 8 31 13 0.2
8.0 9.1 14.4 5.4 8.00 9.20 14.20 5.20 7.80 8.80 13.80 4.90
7 7 13 0.2 6 8 13 0.2 7 8 13 0.2
P. Pyrzanowski, M. Olzak / Composites Science and Technology 88 (2013) 99–105
difference of the voltage vs. reference [µV]
104 45
crack length 0.5 band 1 band 2 bands 3 bands
40 35 30 25 20 15 10 5 0 -3
-2
-1
0
1
2
3
distance from the symmetry [band] Fig. 7. Voltage changes for fractures with a variable length as a function of distance between the damage centre and length of the crack.
bands) and different positions of the cracks. In this paper, only some of the simulation are discussed in details, for some others we only present either the obtained values, or the graphs of relationships between the measured voltages and the position of the crack or the current electrode. 5.1. Non-shifted current electrodes
30 25
(b)
shift 0 1 band 2 bands
20 15 10 5
-3
-2
-1
0
1
2
3
distance from the symmetry [band]
difference of the voltage vs. reference [µV]
shift 0 1 band 2 bands
30 25 20 15 10 5 0
0
(c)
40 35
difference of the voltage vs. reference [µV]
(a) difference of the voltage vs. reference [µV]
In the case of simulation of the symmetric textile, the symmetry of current flow was disturbed by interlacing fibres. The values of potentials at the electrodes and the voltages measured between three pairs of voltage electrodes and a pair of current electrodes are given in Table 2 (for 0 shift). It is clear that the greatest poten-
tial gradient between the current electrodes appears along the band connecting the electrodes, which means that current flowing through this band flows is much greater than that in the adjacent bands. Near the centre of the sample, current is much more evenly distributed, because there exist contacts between the bands. As it can be seen, the potential differences between the measuring voltage electrodes are more than twenty times smaller than the voltage applied to the sample (measured with the respect to the ground electrode 40N). This is the main reason for the difficulties in measurement. For currents of 10 mA, commonly encountered in practice, there is a need for measurement of voltages of microvolt values, similar to those existing in the strain gauge in bridge systems. On the other hand, the measurement may be facilitated due to the fact that the measured resistance is smaller, by the several orders of magnitude, than that of a strain gauge (a fraction of an ohm compared to the typical strain gauge resistance of 120– 350 X), which results in greater noise immunity. In the following stage of investigations, we simulated interruptions of the band of different length (half of the band, one, two or three bands). The change of voltages for crack length 3 bands, for three pairs of measuring electrodes, relative to the reference voltages i.e., to the value without the simulated break (see Table 2) are presented in Table 3 (for 0 shift) in the function of fracture location. The table also contains the percentage differences in these voltages, relative to the same reference voltage. The change in voltage is quite large, easy to measure, reaching a value of about 40 lV i.e., 30% of value without crack. A minor change is visible for the pair 41AI–41AU, which is due to the arrangement of fibres that is less beneficial in terms of measurement. At the same time, there was an increase in the total resistance of the sample, by about 6 lX, i.e., about 0.2% of the value without fracture (measured between the current electrodes 40N and 40BO). Such a small value is virtually impossible to measure,
-3
-2
-1
0
1
2
3
distance from the symmetry [band]
45 40 35 30 shift 0 1 band 2 bands
25 20 15 10 5 0 -2
-1
0
1
2
distance from the symmetry [band] Fig. 8. The courses of voltage variability as a function of fracture deviation from zero line depending on current electrodes shift for the crack of a length of: (a) one band; (b) two bands; (c) three bands.
P. Pyrzanowski, M. Olzak / Composites Science and Technology 88 (2013) 99–105
which shows the necessity of measuring with electrodes placed much closer to the defect. Fig. 7 shows the cumulative graph of voltage changes for fractures with a length of 0,5; 1; 2 and 3 band widths as a function of distance between the damage centre and the row 40 (i.e., to line connecting the current electrodes) measured by central electrodes. As it is visible the crack located by more than its own length from the symmetry line (the line connected measuring electrodes) may by undetectable. 5.2. Shifted current electrodes The calculations were carried out also when the current electrodes were not placed along a single band, but slightly shifted. This may occur in practice, because for a longer path it can be difficult to find a band to which the electrode is attached. The model with a shift of two band widths was even more interesting, because the electrodes were attached to the fibres running transversely to the direction of the current flow between the electrodes. Thus, the current flow took place along the path of a greater width, however, this had no significant effect on the voltage difference in the case without fracture (Table 2). Table 3 shows the voltage difference for the fracture with a length of three bands for the shift by one band, and by two bands. Zero position was assumed the same as in the case for calculations for non-shifted electrodes. The distribution of voltage variability for three different fracture lengths (1; 2; 3 bands) and for different current electrode shifts (0; 1; 2 bands) is presented in Fig. 8. As it can be noticed, the value of the measured voltage weakly depends on the length of the fracture (the maximal voltage difference of about 10 lV – see Fig. 7 for crack length of 1 and 3 bands), but also, what is beneficial, on the shift of the current electrodes. The maximal voltage difference due to the electrodes shift is about 5 lV, what is visible in Fig. 8a–c as a difference between the maximal value for the shift 0 and 2 bands. It means that small error in their placement does not lead to drastic changes in the sensitivity of the method, whereas proper location of measuring electrodes is essential. 6. Conclusions The paper presents some results of analysis of resistance changes in carbon polymer composites caused by a damage involving the lack of continuity in a part of a band, in the whole band, or in several bands of the fabric. The tests were aimed at practical implementation in the system allowing for detection of such defects in a composite. The investigations, carried out on accurate models representing geometry and properties of the fabrics, have shown the usefulness of the method. It conforms to the initial assumptions, allowing for confirming the formation of damage in the composite. In the case of a more elaborated system, having a greater number of electrodes and ensuring proper location of the electrodes that measure the voltage between the corresponding points on the surface of the composite, it may also be possible to determine, with satisfactory accuracy, the approximate location and size of the defect. However, for correct interpretation of the results obtained experimentally, the preliminary, necessary task is to build and test a composite model, including simulation of the expected damage. Such a model
105
should represent, as accurately as possible, the structure of a real object. Nevertheless, there are some fairly significant difficulties hindering broader application of the method. Above all, there is a need for: Acquiring a preliminary, very accurate knowledge of material properties, often stochastic, of the investigated composites, and carrying out multiple simulations. Measuring of relatively low voltages, for which one should use measuring systems with high gain and thus with high susceptibility to interferences and place the measuring amplifiers close to the tested structure. Using multiple electrodes placed around the expected location of the defect in order to estimate the location and size of the damage. Despite these drawbacks, it seems that the method is worth further development. For example, in the case of multilayer laminates used in practice, it is possible to add a single layer of carbon fabric for measuring purposes in the construction made, in its essential part, of the glass fabric. It is also possible to separate one layer of a fabric in a composite made entirely of carbon fibres with very thin layers of glass fabric of a small weight. In this way, a single layer isolated from the rest of the structure would be created, and the measuring electrodes may be placed on it. Acknowledgement This work has been supported by the Scientific Research Communities of Poland, Project No 4034/B/T02/2008/35. References [1] Aboudi J. Mechanics of composite materials. Elsevier; 1991. [2] Angelidis N, Khemiri N, Irving PE. Experimental and finite element study of the electrical potential technique for damage detection in CFRP laminates. Smart Mater Struct 2005;14:147–54. [3] Gadomski J, Pyrzanowski P. Damage identification in strongly loaded carbonreinforced composite using the electric resistance change procedure. Mater Test 2011;53:351–5. [4] Hou L, Hayes SA. A resistance-based damage location sensor for carbon-fibre composites. Smart Mater Struct 2002;11:966–9. [5] Irving PE, Thiagarajan C. Fatigue damage characterization in carbon fibre composite materials using an electrical potential technique. Smart Mater Struct 1998;7:456–66. [6] Mouritz AP, Townsend C, Shah Khan MZ. Non-destructive detection of fatigue damage in thick composites by pulse-echo ultrasonics. Compos Sci Technol 2000;60:23–32. [7] Schulte K, Baron Ch. Load and failure analysis of CFRP laminates by electrical resistivity measurements. Compos Sci Technol 1989;36:63–76. [8] Todoroki A, Omagari K, Shimamura Y, Kobayashi H. Matrix crack detection of CFRP using electrical resistance change with integrated surface probes. Compos Sci Technol 2006;66:1539–45. [9] Todoroki A, Tanaka M, Shimamura Y. Measurement of orthotropic electric conductance of CFRP laminates and analysis of the effect on delamination monitoring with an electric resistance change method. Compos Sci Technol 2002;62:619–28. [10] Todoroki A, Tanaka Y. Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method. Compos Sci Technol 2002;62:629–39. [11] Wang S, Chung DDL, Chung JH. Impact damage of carbon fiber polymer–matrix composites, studied by electrical resistance measurement. Composites Part A 2005;36:1707–15. [12] Xia Z, Okabe T, Park JB, Curtin WA, Takeda N. Quantitative damage detection in CFRP composites: coupled mechanical and electrical models. Compos Sci Technol 2003;63:1411–22.
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Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Numerical modelling of resistance changes in symmetric CFRP composite under the influence of structure damage Paweł Pyrzanowski ⇑, Mirosław Olzak Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 10 June 2013 Accepted 25 August 2013 Available online 5 September 2013 Keywords: A: Carbon fibres A: Polymer–matrix composites (PMCs) B: Electrical properties C: Finite element analysis (FEA)
a b s t r a c t CFRP (Carbon Fibre Reinforced Polymer) composite consists of two materials characterised by different electric properties i.e., carbon fibres – the high strength component with conductive features as well as polymer fillers with insulating properties. For this reason, any structural damage will result in changes in electrical properties of the whole composite. This paper presents a mathematical FEM-based model allowing for simulation of damage in monolayer symmetric laminate structure. The dependences of electrical responses on the size and location of damage as well as the sensitivity of the method for accurate placement of electrodes supplying electric current were investigated. The effectiveness of this method for determining the approximate size and location of the damage and the usefulness of the FEM for modelling the changes in electrical properties of the composite were demonstrated. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction For years of the development of technology, the major construction materials were metals and their alloys. The main advantages of such materials is the ease of testing and modelling their material properties, as well as predictable and simple to predict way of destruction. This is due to isotropic properties of the material strength. In the early 70s of last century, in the advanced industries, especially aerospace, composite materials began to be used, mainly based on glass fibres, and, later, carbon and kevlar ones. Thanks to their high mechanical properties, strength and stiffness, the CFRP (Carbon Fibre-Reinforced Polymer) composites are the most often used for responsible and highly loaded airframe structural components. Strength properties of composites are strongly anisotropic, and depend on the directionality of the fibres and their arrangement, because it can be approximately assumed that the loads may only be carried by the fibres that can be stretched or compressed. The strength in the direction perpendicular to the fibres is ensured only through the binder, and in most cases can be ignored [1]. Such a composite structure can cause considerable problems of modelling its endurance. Especially, it concerns the issues of fatigue strength. So far, there are not any good models for forecasting the time of construction work to the such an extent as it is possible for metals. The most unfavourable situation exists in the case of carbon composites, which show very weak symptoms of a progressive process of fatigue degradation. One may only observe a very slight ⇑ Corresponding author. Tel.: +48 222347512. E-mail address: [email protected] (P. Pyrzanowski). 0266-3538/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2013.08.023
decrease in stiffness, due to destruction of the fibres. A decrease of the order of 1–2% is followed by a rapid destruction of the element. This causes great problems with monitoring the work of the composite and with prediction of its stock of strength, especially in real constructions. Moreover, it may be very difficult to measure the changes e.g., in an aircraft girder during a flight. Ultrasonic methods are popular [6], however, being useful for the periodic diagnosis, they are not suitable for continuous monitoring of the structure because of the difficulty with installing a network of detectors. The mentioned reasons make it necessary to work out new method for diagnosing the degradation process of composites. One of the possible methods is the measurement of changes in composite resistivity. The carbon fibres, whose continuity is to be detected here, are good conductors of electric current, with the resistivity of about 105 X m, and the binder is a very bad one, with the resistivity of about 1010 to 1015 X m. This difference causes that electric current flows only through the carbon fibres, and disruption of even small number of them will reduce the cross-section through which the current flows and thereby will cause an increase in the resistance. This phenomenon has been observed experimentally on several occasions, both in static and fatigue experiments, as well as in shock load tests. One of the first results were presented by Schulte and Baron in the paper [7] in which also influence of electric current, temperature, and time of the test on the resistivity of composite was investigated. Recently experimental investigations of influence of composite damage into its resistivity were presented by research team of Hou [4], Irving [5], Todoroki [8–10] and others [2,3,11], but so far mainly laboratory trials have been carried out. In order to apply the method in practice, there is a need for developing a mathematical model of
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the phenomenon, and to relate resistance changes with the changes in the element’s structure. Such attempts have already been taken, e.g. in work [12] in which the authors proposed a model of an analogue network of resistors simulating the fibres and the contacts between them. The authors also presented a discrete model based on the Finite Element Method, which compares the breaks of composite fibres bands with the resistance changes. 2. Tested material In the constructed models, a single layer of the laminate was simulated. In the case of damage comprising the fibres of only one layer, the changes in resistance were significantly reduced due to the shunt effect caused by intact layers which take a portion of the current flow without significant reduction in whole cross-section of the composite. This effect was achieved also by modelling the damage that encompasses less than the whole skein, because an analogous mechanism appeared. The analysed model, contains the equal amounts of fibres arranged in two directions – along and across the current flow. The geometry of fabric was modelled accurately, also taking into account the weave of skeins passing from the lower to the upper surface of the laminate, and vice versa. Such a model is much more complicated than the simple one, but it takes into consideration more complex situations e.g., the location of the electrodes on the skein along or across the direction of current flow. The geometrical dimensions of the skein of a fabric were taken as averages for a laminate of reinforcement volume ratio of about 65%. Each skein was treated as a single elementary cell, without analyzing the behaviour of individual fibres, but taking into account their average properties in the whole volume of the band. Prior to the calculations, we had carried out test measurements of the resistivity of the modelled fabrics. Unfortunately, this proved to be a very difficult task. The resistance along the fibres for an
individual skein, both before and after the lamination, is relatively easy to measure. Its value is quite stable, and it does not depend on the point of measurement on the sample. The measurement in the transverse direction with respect to the fibres is much less reliable. Theoretically, the value of specific resistance may vary from the values for the fibres along their length (if one assumes isotropic properties of the individual fibres, excellent adhesion of the fibres, lack of insulating properties of the interface and lack of penetration of the resin between the fibres) to infinity (if the skeins is perfectly penetrated by the resin and one assumes lack of contact between the fibres). In practice, the expected value of the actual resistance lies between these two values. Attempts of measurement showed very large variability of the measured parameter, depending on the point of measurement. The authors measured experimentally the resistivity of a single skein prepared from the experimentally created plate as shown in Fig. 1a. Four-wire method, described in details in Section 3.2, was used. The length of the measured band was 100 mm. The result obtained from the measurement depended on the specimen (6 samples were used) and varied from 0.03e3 to 0.08e3 X mm. For measuring the resistivity of the spacer between skeins similar set-up, shown in Fig. 1b was used. The parts of two parallel and two perpendicular bands were prepared what allowed to obtain 4 contact zones between the bands. The measured resistance was recalculated into the resistivity of FEM elements. Transverse resistivity of a skein was not measured. This is very difficult because an arrangement of fibres in skeins is not completely parallel, and electric contacts between the fibres are quite randomly spaced. For this reason, the authors assumed that the average ratio of the values of the specific resistance along the fibres to the ones across the fibres was equal to 1:20. This roughly corresponds to the value of 1:27 given in [9] for unidirectional prepreg and reinforcement ratio of 62%. In this study, we used the numerical model corresponding to the ECC 452 fabric with a weight of 204 g/m2, 2 2 twill. Fig. 2
(a)
(b)
Fig. 1. Measuring of resistivity: (a) single skein; (b) spacer between skein.
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Fig. 2. The tested fabric: (a) real image; (b) FEM model.
(a)
direction of fibres
A
B C D
...............
CE
1 2 3
...............
4
Fig. 3. Geometry of two elementary fabric cells (mm).
82 shows the image of a fragment of a fabric before lamination, and the numerical model made in ANSYS program. Geometrically, the FEM model correspond exactly to a monolayer laminate made of this fabric. The geometrical dimensions of elementary cells are shown in Fig. 3. There are presented two cells that contain fragments of the skeins with fibres of different directionality, and an oblique fragment modelling the transition of the skein between the upper and the lower surfaces of the laminate. The skeins containing single fibres were treated as continuous fragments with cross-sectional dimensions of 1.864 0.1 mm across the fibres and orthotropic electrical properties. An oblique fragment linking the bands on the transition between the upper and the lower surfaces also had orthotropic properties, but its resistivity along fibres was slightly smaller (reduced to 0.897 of the resistivity of the simple band), in order to compensate the reduced thickness of the model on the slants. Between them, there is a layer with a thickness of 0.05 mm and isotropic electrical properties, which models the insulating epoxy resin separating the bands from each other. The current was led into the model and the resistance was measured through the contacts, with very high electrical conductivity. The resistivity of the applied components is presented below: The horizontal band: 0.05e3 X mm (along the fibres); 1.0e3 X mm (across the fibres). The sloping band: 0.0405e3 X mm (along the fibres); 1.0e3 X mm (across the fibres). The spacer between bands (isotropic): 0.7 X mm. The electrodes (isotropic): 1.0e7 X mm. The entire model consisted of 78 skeins along the direction of current flow (x direction – horizontally in the following figures) and 82 skeins laterally (y direction – vertically), so that its dimensions were 161.177 mm 169.453 mm. Such a large model provided sufficient approximation of a laminate of unlimited dimensions. Fig 4 presents the coordinate system for column and row indication and localisation of electrodes for one case (nonshifted current electrodes, central located 3-band length break).
(b) current electrode measurement electrode
break position
Fig. 4. The specimen: (a) coordinate system of bands; (b) electrode localisation.
2.1. Modelling of defects The developed model represented the defects in the laminate involving interruption of half of a skein, one, two or three skeins. In the case of breakage comprising more than one skein, the disruption included the neighbouring, but not a distant skein. The break was modelled by removing a small element connecting the cells (see Fig. 3). 3. Method of measuring the changes of electrical properties 3.1. Model of resistance changes Carbon composite, consisting mainly of carbon fibres, has the typical characteristics of a good conductor of electric current. In particular, its resistance R, given by formula (1), depends on resistivity q, current flow path length l, and cross-sectional area A.
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R¼
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Z 0
l
q A
dl
ð1Þ
The integral form of the formula allows for an analytical description of the changes in resistance of a conductor whose cross-section A is large in relation to its length l, and may be applied in the cases in which resistivity is not stable, but changes within the conductor’s volume. For conductors of high length/ diameter ratio, e.g. wires, one may use the generally applicable form of Eq. (2).
R¼
ql
ð2Þ
A
As it results from these equations, the resultant change in resistance may be caused ether by changes in resistivity, or changes in the dimensions of the conductor. The tested laminate sample, in which defects are caused either by fatigue demotion or acute destruction, can be considered as the conductor with structure discontinuities, hence two different models of degradation are possible (as shown in Fig. 5). (a) Small discontinuities arising as a result of a break of individual fibres without any significant rupture in the continuity of the skein appearing in the entire volume of the fragment of sample. Such a defect can be modelled as a change in resistivity of some elements without geometry changes. In the current flow space through the damage area, one can observe a reduction of its density caused by the increase in resistivity. Neither the length of current flow path nor the cross-sectional area are changed. (b) Large discontinuities produced as the result of break of either whole the skein or its significant part. In this case, we observe an increase in the length of current flow path and a decrease in conductor’s cross-section area, but the resistivity of the structure does not change. Since the current flowing through the element must pass round the damaged fragments, the area of the damaged part is subtracted from the total cross-sectional area. In this case, the conductor’s resistivity does not change. This model is especially used for material with anisotropic electrical parameters in which resistivity in the direction perpendicular to the current flow is higher than in parallel one.
Current flow lines (the areas of increased current density)
(a)
(b) Area of microdefect
In this work, we assumed the existence of large discontinuities of the material. They could be as high as at least a half of cross-section of the skein and were situated perpendicularly to current flow line joining the points where current contacts were applied to the sample. Therefore, there was no need for an alteration of the resistivity of the composite elements. 3.2. Measurement of resistance changes In practice, the resistance of a conductor is measured using an appropriate instrument – an ohmmeter. Its principle of operation (as shown in Fig. 6) requires the use of a constant current source (indicated by I) that produces a current of constant intensity, independent of the load resistance, and measuring the voltage drop across the tested resistor R through which the current flows. The voltage is measured with a voltmeter (labelled as V). The simplest ohmmeter uses only two wires connecting the instrument to the tested resistor (the two-wire parallel circuit, Fig. 6a). The current source and the voltage meter are contained within the instrument. The two-wire arrangement is very simple, but its significant disadvantage is that the resistances of connecting cables (Rp) adds up to the measured resistance. If the measured resistance is low, comparable to the resistance of the connecting wires, significant measurement error may arise. For this reason, in more advanced devices, the four-wire method is used, in which the current circuit and the voltage measuring circuit are separated, and two pairs of wires connect the resistor’s contacts to the voltmeter and the current source, respectively (Fig. 6b). This method is much better for measuring small resistances, because the resistance of the voltage circuit has practically no effect on voltage measurement due to high input resistance of the voltmeter (typically several MXs or greater). The resistances in the current circuit do not have any influence on the measurement result, either. Since the resistance of the carbon composite is very low, usually much smaller than the resistance of the contacts between the fibres and wires, the measurement of small changes in the resistance caused by the defects in the structure might be burdened with a high error. For this reason, the four-wire method proved much better and was simulated by the authors in this study. In order to minimize the measuring error, the contacts of the voltmeter leads should be placed as close as possible to the place of damage. In practice, the current source cables and the voltmeter cables are not connected at one point on the sample; the voltage contacts must be closer to the tested damage place than the current contacts. Such a connection scheme is modelled in this work. 4. Samples As it was mentioned in Section 2, the tested model consisted of 78 bands oriented along the current flow (x axis) and 82 bands across it (y axis). In order to facilitate the description, we applied
macrodefect
Fig. 5. The model of composite damage (description in the text).
(b) (a)
Rp
Rp
R
R V
I
V
Rp
Rp Fig. 6. The method of resistance measurement: (a) two-wire circuit; (b) four-wire circuit.
I
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At the end of the electrode 40N, intensity of the current in equals +1 A. At the end of the electrode 40BO, intensity of the current out equals 1 A. At the end of the electrode 40N, potential of 0 V (the reference point for other potentials in the circuit).
Table 1 Location of electrodes. Cell designation
Fibre direction
Electrode description
39N 40N 39BO 40BO 41BO 39AI 40AI 41AI 39AU 40AU 41AU
||| ||| ||| |||
Current left for shift 2 Current left for shift 0 and 1 Current right for shift 1 Current right for shift 0 Current right for shift 2 Voltage left upper Voltage left middle Voltage left lower Voltage right upper Voltage right middle Voltage right lower
We also examined the samples in which the current electrodes were placed on different bands i.e., in the cells 40N and 39N or 39BO and 41BO. The voltages were always determined along one band between the measuring electrodes 39AI and 39AU, 40AI and 40AU or 41AI and 41AU. Actually, we measured the electric potentials with respect to the electrode 40N and then subtracted them, so that the voltage differences between the measuring electrodes lying on the different bands could easily be calculated. Simulated cracks (i.e., the place from which the modelling elements were removed from the bundle) had the following lengths: half the width of the bundle (length 0.5); one bundle width (length 1); two bundle width (length 2); three bundle width (length 3). The cracks were situated between the columns AO–AP, in the rows 37 to 43. Location of a crack was defined by the coordinates of the cells between which the crack was situated. For greater readability of the tables, graphs and results, the position coordinate of the crack was introduced, defined by the distance from the crack centre to the centre line of the row number 40. For example, for the crack crossing three adjacent rows, the position coordinate of 2 corresponds to the rupture between the cells 37AO–37AP, 38AO–38AP and 39AO–39AP, while the position of 0 means that the crack is located between the cells 39AO–39AP, 40AO–40AP and 41AO–41AP. For the crack crossing two rows, the position coordinate may take the following values: 2.5, 1.5, 0 .5, 0.5, 1.5, 2.5, for the cracks between the cells: 37AO–37AP and 38AO–38AP; 38AO–38AP and 39AO–39AP; 39AO–39AP and 40AO–40AP; 40AO–40AP and 41AO–41AP; 41AO–41AP and 42AO–42AP; 42AO–42AP and 43AO–43AP respectively. Direction of fibres (horizontal or vertical) in respective cells was described in Table 1. Obviously, this direction pertained to the place of application of the electrodes. On the other side of the sample the direction of fibres was reversed.
Table 2 Potentials on the electrodes on sample without fracture. Shift
Electrode
Potential (V)
Electrode
Potential (V)
Voltage between electrodes (mV)
0 0 0 0 1 1 1 1 2 2 2 2
39AI 40AI 41AI 40N 39AI 40AI 41AI 40N 39AI 40AI 41AI 39N
1.34960 1.34110 1.35170 0 1.3505E03 1.3404E03 1.3515E03 0 1.3482E03 1.3486E03 1.3512E03 0
39AU 40AU 41AU 40BO 39AU 40AU 41AU 39BO 39AU 40AU 41AU 41BO
1.46850 1.47910 1.46550 2.81550 1.4801E03 1.4676E03 1.4648E03 2.8161E03 1.4612E03 1.4619E03 1.4596E03 2.8036E03
0.1189 0.1380 0.1138 2.8155 0.1296 0.1272 0.1133 2.8161 0.1130 0.1133 0.1084 2.8036
a rectangular table consisting of 78 (horizontal) to 82 (vertical) square cells. The rows of the array are numbered from 1 to 82 and columns are numbered from A to BZ. The location of the electrode on the sample is referred to the coordinates of the cell (the row number and column number) in which the electrode is located (e.g., 41AI), while the location of the break is determined by the coordinates of the cells between which the break occurs (e.g., 43AO–43AP). In most calculations, we assumed that current flows between the electrodes 40N and 40BO (both the electrodes on one band). The following boundary conditions were assumed for the voltage and currents in the sample:
5. Results For the samples described in Section 4 we performed calculations for different positions of the current electrodes, different crack lengths (from mid-width of one band to three adjacent
Table 3 Changes of voltage between electrodes on sample with fracture. Shift
Pair of electrodes
Fracture location 2
0 0 0 0 1 1 1 1 2 2 2 2
39AI–39AU 40AI–40AU 41AI–41AU 40N–40BO 39AI–39AU 40AI–40AU 41AI–41AU 40N–44BQ 39AI–39AU 40AI–40AU 41AI–41AU 39N–41BO
0
1
1
2
U (lV)
%
U (lV)
%
U (lV)
%
U (lV)
%
U (lV)
%
36.6 9.2 11.7 5.5 38.80 9.60 12.10 5.90 34.90 8.80 11.30 5.00
31 7 10 0.2 30 8 11 0.2 31 8 10 0.2
38.3 40.4 14.2 6.3 40.00 38.80 14.20 6.30 35.90 35.30 13.00 5.20
32 29 13 0.2 31 31 13 0.2 32 31 12 0.2
37.7 41.1 15.8 6.4 39.40 39.50 15.60 6.30 35.30 36.00 14.40 5.20
32 30 14 0.2 31 31 14 0.2 31 32 13 0.2
9.9 40.2 16.0 6.2 9.50 38.10 15.50 5.80 9.00 35.10 14.70 5.10
8 29 14 0.2 7 30 14 0.2 8 31 13 0.2
8.0 9.1 14.4 5.4 8.00 9.20 14.20 5.20 7.80 8.80 13.80 4.90
7 7 13 0.2 6 8 13 0.2 7 8 13 0.2
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difference of the voltage vs. reference [µV]
104 45
crack length 0.5 band 1 band 2 bands 3 bands
40 35 30 25 20 15 10 5 0 -3
-2
-1
0
1
2
3
distance from the symmetry [band] Fig. 7. Voltage changes for fractures with a variable length as a function of distance between the damage centre and length of the crack.
bands) and different positions of the cracks. In this paper, only some of the simulation are discussed in details, for some others we only present either the obtained values, or the graphs of relationships between the measured voltages and the position of the crack or the current electrode. 5.1. Non-shifted current electrodes
30 25
(b)
shift 0 1 band 2 bands
20 15 10 5
-3
-2
-1
0
1
2
3
distance from the symmetry [band]
difference of the voltage vs. reference [µV]
shift 0 1 band 2 bands
30 25 20 15 10 5 0
0
(c)
40 35
difference of the voltage vs. reference [µV]
(a) difference of the voltage vs. reference [µV]
In the case of simulation of the symmetric textile, the symmetry of current flow was disturbed by interlacing fibres. The values of potentials at the electrodes and the voltages measured between three pairs of voltage electrodes and a pair of current electrodes are given in Table 2 (for 0 shift). It is clear that the greatest poten-
tial gradient between the current electrodes appears along the band connecting the electrodes, which means that current flowing through this band flows is much greater than that in the adjacent bands. Near the centre of the sample, current is much more evenly distributed, because there exist contacts between the bands. As it can be seen, the potential differences between the measuring voltage electrodes are more than twenty times smaller than the voltage applied to the sample (measured with the respect to the ground electrode 40N). This is the main reason for the difficulties in measurement. For currents of 10 mA, commonly encountered in practice, there is a need for measurement of voltages of microvolt values, similar to those existing in the strain gauge in bridge systems. On the other hand, the measurement may be facilitated due to the fact that the measured resistance is smaller, by the several orders of magnitude, than that of a strain gauge (a fraction of an ohm compared to the typical strain gauge resistance of 120– 350 X), which results in greater noise immunity. In the following stage of investigations, we simulated interruptions of the band of different length (half of the band, one, two or three bands). The change of voltages for crack length 3 bands, for three pairs of measuring electrodes, relative to the reference voltages i.e., to the value without the simulated break (see Table 2) are presented in Table 3 (for 0 shift) in the function of fracture location. The table also contains the percentage differences in these voltages, relative to the same reference voltage. The change in voltage is quite large, easy to measure, reaching a value of about 40 lV i.e., 30% of value without crack. A minor change is visible for the pair 41AI–41AU, which is due to the arrangement of fibres that is less beneficial in terms of measurement. At the same time, there was an increase in the total resistance of the sample, by about 6 lX, i.e., about 0.2% of the value without fracture (measured between the current electrodes 40N and 40BO). Such a small value is virtually impossible to measure,
-3
-2
-1
0
1
2
3
distance from the symmetry [band]
45 40 35 30 shift 0 1 band 2 bands
25 20 15 10 5 0 -2
-1
0
1
2
distance from the symmetry [band] Fig. 8. The courses of voltage variability as a function of fracture deviation from zero line depending on current electrodes shift for the crack of a length of: (a) one band; (b) two bands; (c) three bands.
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which shows the necessity of measuring with electrodes placed much closer to the defect. Fig. 7 shows the cumulative graph of voltage changes for fractures with a length of 0,5; 1; 2 and 3 band widths as a function of distance between the damage centre and the row 40 (i.e., to line connecting the current electrodes) measured by central electrodes. As it is visible the crack located by more than its own length from the symmetry line (the line connected measuring electrodes) may by undetectable. 5.2. Shifted current electrodes The calculations were carried out also when the current electrodes were not placed along a single band, but slightly shifted. This may occur in practice, because for a longer path it can be difficult to find a band to which the electrode is attached. The model with a shift of two band widths was even more interesting, because the electrodes were attached to the fibres running transversely to the direction of the current flow between the electrodes. Thus, the current flow took place along the path of a greater width, however, this had no significant effect on the voltage difference in the case without fracture (Table 2). Table 3 shows the voltage difference for the fracture with a length of three bands for the shift by one band, and by two bands. Zero position was assumed the same as in the case for calculations for non-shifted electrodes. The distribution of voltage variability for three different fracture lengths (1; 2; 3 bands) and for different current electrode shifts (0; 1; 2 bands) is presented in Fig. 8. As it can be noticed, the value of the measured voltage weakly depends on the length of the fracture (the maximal voltage difference of about 10 lV – see Fig. 7 for crack length of 1 and 3 bands), but also, what is beneficial, on the shift of the current electrodes. The maximal voltage difference due to the electrodes shift is about 5 lV, what is visible in Fig. 8a–c as a difference between the maximal value for the shift 0 and 2 bands. It means that small error in their placement does not lead to drastic changes in the sensitivity of the method, whereas proper location of measuring electrodes is essential. 6. Conclusions The paper presents some results of analysis of resistance changes in carbon polymer composites caused by a damage involving the lack of continuity in a part of a band, in the whole band, or in several bands of the fabric. The tests were aimed at practical implementation in the system allowing for detection of such defects in a composite. The investigations, carried out on accurate models representing geometry and properties of the fabrics, have shown the usefulness of the method. It conforms to the initial assumptions, allowing for confirming the formation of damage in the composite. In the case of a more elaborated system, having a greater number of electrodes and ensuring proper location of the electrodes that measure the voltage between the corresponding points on the surface of the composite, it may also be possible to determine, with satisfactory accuracy, the approximate location and size of the defect. However, for correct interpretation of the results obtained experimentally, the preliminary, necessary task is to build and test a composite model, including simulation of the expected damage. Such a model
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should represent, as accurately as possible, the structure of a real object. Nevertheless, there are some fairly significant difficulties hindering broader application of the method. Above all, there is a need for: Acquiring a preliminary, very accurate knowledge of material properties, often stochastic, of the investigated composites, and carrying out multiple simulations. Measuring of relatively low voltages, for which one should use measuring systems with high gain and thus with high susceptibility to interferences and place the measuring amplifiers close to the tested structure. Using multiple electrodes placed around the expected location of the defect in order to estimate the location and size of the damage. Despite these drawbacks, it seems that the method is worth further development. For example, in the case of multilayer laminates used in practice, it is possible to add a single layer of carbon fabric for measuring purposes in the construction made, in its essential part, of the glass fabric. It is also possible to separate one layer of a fabric in a composite made entirely of carbon fibres with very thin layers of glass fabric of a small weight. In this way, a single layer isolated from the rest of the structure would be created, and the measuring electrodes may be placed on it. Acknowledgement This work has been supported by the Scientific Research Communities of Poland, Project No 4034/B/T02/2008/35. References [1] Aboudi J. Mechanics of composite materials. Elsevier; 1991. [2] Angelidis N, Khemiri N, Irving PE. Experimental and finite element study of the electrical potential technique for damage detection in CFRP laminates. Smart Mater Struct 2005;14:147–54. [3] Gadomski J, Pyrzanowski P. Damage identification in strongly loaded carbonreinforced composite using the electric resistance change procedure. Mater Test 2011;53:351–5. [4] Hou L, Hayes SA. A resistance-based damage location sensor for carbon-fibre composites. Smart Mater Struct 2002;11:966–9. [5] Irving PE, Thiagarajan C. Fatigue damage characterization in carbon fibre composite materials using an electrical potential technique. Smart Mater Struct 1998;7:456–66. [6] Mouritz AP, Townsend C, Shah Khan MZ. Non-destructive detection of fatigue damage in thick composites by pulse-echo ultrasonics. Compos Sci Technol 2000;60:23–32. [7] Schulte K, Baron Ch. Load and failure analysis of CFRP laminates by electrical resistivity measurements. Compos Sci Technol 1989;36:63–76. [8] Todoroki A, Omagari K, Shimamura Y, Kobayashi H. Matrix crack detection of CFRP using electrical resistance change with integrated surface probes. Compos Sci Technol 2006;66:1539–45. [9] Todoroki A, Tanaka M, Shimamura Y. Measurement of orthotropic electric conductance of CFRP laminates and analysis of the effect on delamination monitoring with an electric resistance change method. Compos Sci Technol 2002;62:619–28. [10] Todoroki A, Tanaka Y. Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method. Compos Sci Technol 2002;62:629–39. [11] Wang S, Chung DDL, Chung JH. Impact damage of carbon fiber polymer–matrix composites, studied by electrical resistance measurement. Composites Part A 2005;36:1707–15. [12] Xia Z, Okabe T, Park JB, Curtin WA, Takeda N. Quantitative damage detection in CFRP composites: coupled mechanical and electrical models. Compos Sci Technol 2003;63:1411–22.