Modeling and analysis of the electrical resistance measurement of carbon fiber polymer matrix composites

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1 Composites Science and Technology 67 (2007) COMPOSITES SCIENCE AND TECHNOLOGY Modeling and analysis of the electrical resistance measurement of carbon fiber polymer matrix composites Lianxi Shen a, Jackie Li b, *, Benjamin M. Liaw b, Feridun Delale b, Jaycee H. Chung c a Package Technology Group, National Semiconductor Corporation, 2900 Semiconductor Dr., P.O. Box 58090, Santa Clara, CA , USA b Mechanical Engineering Department, The City College of New York, New York, NY 10031, USA c Global Contour Ltd., 1145 Ridge Road West, Rockwall, TX 75087, USA Received 3 August 2006; received in revised form 13 December 2006; accepted 19 December 2006 Available online 18 January 2007 Abstract The self-sensing damage detection method based on the electrical resistance measurement of carbon fiber polymer matrix composites has been investigated for a decade. In order to eliminate the effect of contact resistance when using the two-probe method, the four-probe methods, which include the resistance, potential and voltage change methods, were proposed in literature. However, the basic problems involved in the four-probe methods remain unclear, i.e., the validity range and the applicability of the four-probe methods. In this paper, beam-type specimens with and without delamination damage are used to carry out numerical analyses for the above-mentioned problems. It is found that the four-probe resistance method is valid only when the through-thickness conductivity is comparable to or larger than the longitudinal conductivity. For the potential method, which measures directly the voltage values between the voltage contacts, the present results show that the percentage change in damage-induced voltage between a pair of voltage contacts is not consistent with the percentage change in resistance. The underlying reason is that the damage-induced voltage change depends on the location of the applied current, while the resistance change does not. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Polymer matrix composites; B. Electrical resistance; C. Finite element method (FEM) 1. Introduction Composite laminates are used extensively in aerospace systems due to their light weight, high ratios of stiffness and strength to weight, and flexibility for adoption to complex structural configurations. Because the reliability of aerospace systems is crucial for safe operation, it is very much desirable to monitor the integrity of the composite laminate-based structures during service. Several methods have been developed for the structural health monitoring of composite structures using fiber optic sensors [1,2], piezoelectric sensors [3 5], and self-sensing approaches [6 17]. In contrast to fiber optic or piezoelectric sensors, which need to be embedded in or attached to the * Corresponding author. Tel.: ; fax: address: j.li@ccny.cuny.edu (J. Li). composite laminate structure, the multifunctional property-based self-sensing method does not require additional sensors, and thus, from a practical point of view, it is more attractive. The self-sensing method for damage monitoring in carbon fiber-reinforced plastic (CFRP) laminates takes advantage of the electrically conductive feature of the carbon fibers. As a result, no extra sensors are required, leading to lower cost and higher efficiency. Its basic principle is that damage such as fiber breakage or delamination between lamina will cause a decrease of the electrical conductivity in the damaged local region, leading to a resistance or voltage change measured using electrode pairs, which may be placed relatively far away from the damaged region. The goal of the self-sensing method is to predict the location and extent of damage within a composite laminate structure. In order to achieve this goal, the self-sensing method generally includes two interrelated techniques. One is the /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.compscitech

2 2514 L. Shen et al. / Composites Science and Technology 67 (2007) measurement of the electrical behavior of composite laminates (both intact and damaged), and the other is the development of a mathematical model, which relates the measured electrical behavior to the mechanical damage. Typical mathematical models include the artificial neural network [13] and the response surface [16,17] models. In these mathematical models first a system of functions, which relates the mechanical damages to the measured electrical data, is assumed with some unknown coefficients. These coefficients are then obtained by matching the well-defined damage patterns to the measured electrical data. Once the unknown coefficients are determined, the models can predict damage using the electrical data as input. The current techniques for the measurement of the electrical behavior of composite laminates are the two-probe and four-probe methods. The two-probe method is based on the definition of resistance according to Ohm s law. In this method two electrodes are used to measure the electrical resistance. However, contact resistance may be introduced due to the imperfect bonding between the electrodes and the composite laminates. Since the contact resistance is unknown and difficult to determined, and sometimes, can be even more profound than the real resistance of the sample due to poor contacts at the probe, in general the two-probe method is not recommended in self-sensing measurements. Alternatively, the four-probe (resistance) method was proposed, in which a pair of electrodes are used for the current input, and another pair of electrodes for the voltage output [6 12]. Based on the measured voltage and current, the resistance between the voltage contacts is then derived. However, the validity of this approach to obtain an accurate measurement of the resistance has not been investigated. In the mean time, the potential and voltage change methods were also introduced. Both potential and voltage change methods are based on the principle of the four-probe method with exception that the resistance is not calculated from the measured voltage and charged current. Instead, both methods use directly the measured potential and voltage change as the input in the mathematical models for the prediction of the mechanical damages. In this study, the basic problems in 2-D were investigated through numerical analysis, i.e., the validity range of the four-probe method and the relative magnitude of the voltage and resistance fractional changes due to damage. Two beam-type specimens with and without damage were designed, and numerically simulated using the finite element method (FEM). For the two-probe and four-probe methods, various resistances and voltage changes were simulated and compared. As a result, the validity and the applicability of the four-probe methods were discussed. 2. The two-probe and four-probe methods 2.1. The two-probe method Resistance measurement: Fig. 1a schematically shows a body, on which a pair of electrodes with conductive wires Fig. 1. Schematic diagrams of two-probe method; (a) point electrodes for resistance measurement and (b) plate electrodes for conductivity measurement. is attached. This is a common practice to measure the electrical resistance between the two electrodes of the body using the two-probe method. The two-probe method is based on Ohm s law, i.e., V = IR with V, I and R being voltage, current and resistance between the two electrodes respectively. When connecting an electrical meter to the two ends of the conductive wires, a circuit is formed, in which a current is produced by the power of the meter. Based on the current and voltage and using Ohm s law, a resistance is measured. However, the measured resistance should be carefully understood. In fact, in addition to the target resistance R 0 between the two electrodes of the specimen, the measured resistance R also includes the resistance R 1 of electrodes with wires, the resistance R 2 of the meter, and the contact resistance R 3 due to the imperfect bonding between the electrodes and the body. The measured resistance R can be approximated as the specimen s resistance R 0, only if the sum of the other three resistances is small compared with the target resistance R 0. Because the conductivities of the wires and electrodes such as silver paint paste are many orders of magnitude higher than that of the measured body, the resistance R 1 of the wire is relatively small. Also, the meter resistance R 2 can be controlled to be relatively small by using meters with higher resolution. But the contact resistance R 3 is not always controllable. For example, even though a perfect bonding may be achieved by careful treatment and preparation, some imperfect bonding may develop when the system is subjected to loading during service or experimental measurements. That is why the four-probe methods were proposed by Wang et al. [6 12]. However, the conditions under which the four-probe method can be effectively used for the resistance measurement of composite panels have

3 L. Shen et al. / Composites Science and Technology 67 (2007) not been studied comprehensively, and may result in significant errors. This will be analyzed later. Conductivity measurement: When measuring the conductivities of materials such as composite panels with continuous carbon fibers and polymer matrix, a rectangular or strip panel with plate electrodes is commonly used as shown in Fig. 1b. Such a specimen can lead to a uniform current density in the rectangular or strip panel. The silver paint paste was usually used as electrodes. If it was carefully prepared, the bonding between the electrodes and the panel can be assumed perfect. In this case, the measured resistance R can be approximated as the resistance R 0 of the panel between two plate electrodes. Then, the conductivity of the composite panel r can be determined as r = L/(RA), where, L and A are the length and crosssectional area of the panel, respectively. Since the composite panel is orthotropic, the conductivities in the other two directions will be different and can be measured similarly The four-probe methods Resistance method: The initial design of the four-probe method for a strip specimen by Wang et al. [6] is shown in Fig. 2a. The outer and inner pairs of electrodes were used as current and voltage contacts, respectively. If the current density between the pair of voltage contacts is uniform, the resistance of the segment between the voltage contacts can be calculated through Ohm s law: R ¼ V I ; where, V and I are the voltage and current from the voltage and current contacts, respectively. Because the two quantities of voltage and current are independent of the resistances caused by electrodes, wires and imperfect electrode a b c S S L Silver Paint Electrodes L A 1 A 2 A 3 A 4 B 1 B 2 Silver Paint Electrodes 2A 1A 2B 1B 2C 1C Fig. 2. Schematic diagrams of four-probe method for (a) volume resistance measurement, (b) surface and oblique resistance measurement, and (c) multi-prove method. 2D 1D 2E 1E B 3 B 4 ð1þ bonding, the measured resistance is accurate. Based on the measured resistance, the electrical conductivity can then be obtained. But one should keep in mind that the condition of uniform current density between the pair of voltage contacts must be met Eq. (1) to be valid. Otherwise, significant errors may occur. Therefore, sufficient spacing between the two voltage contacts and between the current and voltage contacts was suggested [6]. However, it appears that a detailed investigation on the validity of the fourprobe method has not been carried out. Furthermore, the four-probe method was used to measure the resistance change of a strip of composite panel due to damage such as the delamination induced by successive indentations or impacts [7 9]. Fig. 2b is a schematic diagram showing the application of the four-probe method. The resistances between the electrodes located on the same side and different sides of the panel are named as the surface and oblique resistance, respectively [10,11]. In order to measure the change of surface resistance R A2 A 3 between electrodes A 2 and A 3 due to the damage, electrodes A 1 and A 4 are used as current contacts, and the voltage between electrodes A 2 and A 3 before and after damage is measured. Then, the corresponding resistance before and after damage is obtained using Ohm s law, leading to the resistance change due to the damage. Similarly, the oblique resistance change between electrodes A 2 and B 3 due to the damage is measured with electrodes A 1 and B 4 used as current contacts. Potential and voltage change methods: As mentioned above in the introduction, the potential and voltage change methods have also been proposed by Wang et al. [11] in addition to the four-probe resistance method (referred to as the four-probe method throughout the paper). Instead of calculating resistance through Ohm s law, the measured potential and voltage are directly adopted in sensing the mechanical damage of the composite panels. The difference between the two methods is that in the potential method, the ground is used as one electrode for voltage contact. So, the measured voltage is the potential of the other electrode, thus the name potential method. However, since the ground is also one electrode of the current contacts, the contact resistance due to the electrode is involved in the measurement. The voltage change method avoids the contact resistances. But it depends on the structural configuration and relative locations between the current and voltage contacts. For example, different current contacts will lead to different voltage changes even though the fractional change in voltage can avoid the effect due to the current magnitude. Also, the voltage change depends on the panel size even though the local information around a pair of voltage contacts holds the same. As a result, the trained response surface or neural network can only be valid for the specific composite panel used. The four-probe resistance method does not involve the above mentioned problems caused by the potential and voltage methods because the resistance change between two voltage contacts depends only on the material

4 2516 L. Shen et al. / Composites Science and Technology 67 (2007) properties and geometry structures of the local composite panel, i.e., the panel material sufficiently far away from the voltage contacts has no or little effect on the resistance between the two voltage contacts. However, the existing method of using Eq. (1) to derive the resistance change between two voltage contacts cannot be valid for the highly orthotropic composite panel. This problem has not been addressed and will be investigated using numerical experiments in this study. Multi-probe method: Another application of the fourprobe method was carried out by Todoraki et al. [16] where it was called the multi-probe method, as shown in Fig. 2c. A constant electric current was charged from the left edge (1A and 2A) to the right edge (1E and 2E), and electric potential changes at each electrode were measured with electrodes 1E and 2E as the ground. So, the potential change in each electrode is actually the voltage change with respect to electrode 1E or 2E as a fixed contact in a pair of voltage contacts. 3. Numerical analysis 3.1. A specimen without damage A 2-D strip specimen without delaminations is used to carry out a numerical analysis, as shown in Fig. 3a. The dimensions are similar to the specimen used by Wang et al. [10,11], i.e., L 0 = 200 mm, L 1 = 10 mm, L 2 =30 mm, L 3 = 2 mm and H = 3.2 mm. The electrical conductivity in longitudinal direction is taken as r L =15X 1 mm 1 and the electrical conductivity in the through-thickness direction r T is used as a variable to carry out a parametric study. For a composite panel the through-thickness conductivity r T (in the order of 10 3 X 1 mm 1 ) is usually much smaller compared to the longitudinal conductivity r L. In order to measure the surface and oblique resistances according to the two- and four-probe methods, the electrodes A 0 to A 6 and B 0 to B 6 are mounted on both sides of the specimen (Fig. 3). The electrode width is L 3 = 2 mm and its conductivity is set at 10 8 X 1 mm 1 so that the electrode resistances can be assumed negligible. a L 3 L 0 L 1 L 2 A 0 A 1 A 2 A 3 A 4 A 5 A 6 B 0 B 1 B 2 B 3 B 4 B 5 B 6 b L 3 L 0 L 1 L 2 A 0 A 1 A 2 A 3 A 4 A 5 A 6 B 0 B 1 B 2 B 3 B 4 B 5 B 6 Fig D specimen and electrode locations (a) without delamination and (b) with delamination. H H The surface resistances between the pairs of electrodes A 1 A 5 and A 2 A 4 and the oblique resistances between electrode pairs A 1 B 5 and A 2 B 4, namely R A1 A 5, R A2 A 4, and R A1 B 5, R A2 B 4, respectively, will be investigated using the two- and four-probe methods. According to the two-probe method, a unit current I is applied as input to an electrode pair and the corresponding voltage output V is obtained from numerical simulation using the finite element method. Then, using Ohm s law, the resistance R between the electrode pair is derived as R = V/I. Because no contact resistance is involved in the numerical experiment, the corresponding value of resistance can be used as target resistance to investigate the validity of the four-probe method. Based on the four-probe method, a unit current I is applied as input to the electrode pair A 0 A 6 or A 1 A 5, and the voltage V between the electrode pair A 1 A 5 or A 2 A 4 as output is obtained from numerical experiments. Then, the surface resistance R between the electrode pairs A 1 A 5 or A 2 A 4 is derived as R = V/I according to Chung [18]. For the oblique resistance measurements, instead, a unit current I is applied as input to the electrode pair A 0 B 6 or A 1 B 5, and the voltage V between the electrode pair A 1 B 5 or A 2 B 4 as output is obtained from numerical experiments. Subsequently, the oblique resistance R between the electrode pairs A 1 B 5 or A 2 B 4 is derived as R = V/I. As mentioned previously, the four-probe method is valid for the resistance measurement if the current density between the voltage contacts is uniform. The numerical experiment is designed to investigate under what conditions this uniformity assumption can be met. For this purpose, various through-thickness conductivities such as from to 20 X 1 mm 1 are used. It will be seen that when the through-thickness conductivity is not small compared to the longitudinal one, as is the case for isotropic materials, the four-probe method works well. Otherwise, its accuracy is poor A specimen with a delamination Fig. 3b shows the same specimen as shown in Fig. 3a but with a delamination located at its center with a length of 25 mm. The longitudinal and through-thickness conductivities r L and r T are taken as r L =15X 1 mm 1 and r T = X 1 mm 1, respectively, which are close to the real values for the composite panel. The surface resistances R A1 A 5 and R A2 A 4, the oblique resistances R A1 B 5 and R A2 B 4, and the through thickness resistance R A3 B 3 are numerically obtained according to the two-probe method. Since no contact resistance is involved in the numerical calculation by the two-probe method, the resistances obtained by the two-probe method are exact and serve to check the accuracy of the four-probe method. The corresponding resistances are also obtained using the four-probe method, where the outside electrode pairs are used as the current contacts for the case of surface/oblique resistance. For example, to obtain R A1 A 5 or R A2 B 4, the electrode pair A 0

5 L. Shen et al. / Composites Science and Technology 67 (2007) Fig. 4. Finite element mesh for (a) specimen 1 (no delamination), and (b) specimen 2 (with delamination). A 6 or A 1 B 5 is used as the current contacts and the voltage between the electrode pair A 1 A 5 or A 2 B 4 needs to be obtained numerically. The resistance change for each case due to delamination is obtained by comparing it with the corresponding value of the specimen without delamination. For the case of the through thickness resistance R A3 B 3, two pairs of current contacts are used, i.e., A 2 B 2 and A 2 B 4. As voltage percentage change was used in the literature, another purpose of the numerical analysis is to check if the voltage and resistance percentage changes due to the delamination using the four-probe method are close to the accurate resistance percentage change FEM simulations The commercially available FEM code, ABAQUS, was chosen for this study. To ensure convergence, very fine meshes (9310 and 9598 linear quadrilateral elements) were used for specimens 1 and 2, respectively. The meshes around the electrodes A 3 and B 3 are shown in Fig. 4a and b for specimens 1 and Results and discussion 4.1. The validity range of the four-probe method Since the finite element method is used in this study, for the two-probe method, the numerical calculations do not involve any resistances caused by electrodes with wires R 1, the meter R 2, and the contacts R 3 in the calculation. Thus it can be used to represent the exact solution R 0 for the system. In reality, the measured resistance through the two-probe method in general involves the contact resistance R 3 and other resistances; it can not be used as accurate resistance of the sample, which is also the reason that the four-probe method was introduced. To be able to check the validity of the four-probe method, the resistance obtained from the definition, which is the same as the resistance from the two-probe method without contact, wire, and meter s resistances involved, is used as reference (two-probe), then the resistance from the four-probe method is calculated through the ratio of the measured voltage to the input current. The comparison of the resistances between the two is demonstrated below. The first specimen without delamination shown in Fig. 3a is designed to check the validity of the four-probe method numerically. Based on the accurate theoretical results, the resistances at various locations are calculated using the four-probe method. The surface and oblique resistances for various through-thickness conductivities are listed in Table 1, and also plotted in Figs. 5 and 6. From these comparisons, it is clearly seen that when the through-thickness conductivity is not too small compared to the longitudinal conductivity, the four-probe method can work well. For the present case, if the longitudinal conductivity is 15 X 1 mm 1, then the through-thickness conductivity should be larger than 1 X 1 mm 1 for the four-probe method to be applicable. However, for commonly used composite panels, the through-thickness conductivity is much smaller than the longitudinal one, say around X 1 mm 1. Thus, the four-probe method cannot be effectively used to measure the surface and oblique resistances for real composite panels. The underlying reason for this is that when the through-thickness conductivity is small, the voltage in the through-thickness direction exists due to the dominant electrical conduction in the longitudinal direction. Fig. 7 shows the contour plot of the current density vector, where the current density A/mm is applied between electrodes A 0 and A 6. Also, the potential at each electrode and the magnitude of the current density at the middle of two adjacent electrodes are displayed in Fig. 7. Voltage drop in the through-thickness direction was also reported based on measurements Table 1 Comparison of the electrical resistances between the accurate and four-probe methods (r L =15X 1 mm 1 ) r T (X 1 mm 1 ) R (X) A1A5 R (X) A2A4 R (X) A1B5 R (X) A2B4 Two-probe Four-probe Two-probe Four-probe Two-probe Four-probe Two-probe Four-probe

6 2518 L. Shen et al. / Composites Science and Technology 67 (2007) Surface resistance R A1A5 ( Ω ) probe method 4-probe method Oblique resistance R A1B5 ( Ω ) probe method 4-probe method Surface resistance R A2A4( Ω ) Conductivity in thickness direction σ Τ (Ω -1 mm -1 ) probe method 4-probe method Conductivity in thickness direction σ Ω mm -1 ) Τ Fig. 5. Comparisons of surface resistances between the accurate results and the four-probe method. for a plate-type specimen [16]. As a result, the uniform current condition, which is the basic assumption of the fourprobe method, cannot be reached for the case of highly anisotropic panels. In addition, the distances between the two voltage electrode contacts and between the voltage and current electrode contacts will affect the accuracy of the four-probe method. Currently 30 mm spacing has been chosen according to Chung s suggestion [18]. A detailed study on the effect of spacing should be carried out separately The voltage and resistance percentage change due to delamination According to the four-probe method, the voltage percentage change due to damage can be directly measured. It is plausible to use the voltage (or potential) percent change to replace the resistance percentage change. However, as discussed previously, the voltage percentage change is actually dependent on the selection of current contacts as well as the geometry of the specimen, while the latter is not. The numerical experiment using the second specimen is designed to Oblique resistance R A2B4 ( Ω ) investigate this problem. The voltage percentage changes V A 0A 6 A 1 A 5, V A 0A 6, V A 1A 5, V A 0B 6 A 1 B 5, V A 0B 6, V A 1B 5, V A 2B 2 A 3 B 3, and V A 2B 4 A 3 A 3 are numerically obtained and compared with the theoretical resistance percentage changes, where the superscripts correspond to current contacts and the subscripts to the voltage contacts in the four-probe method. For example, V A 0A 6 A 1 A 5 denotes voltage percentage change between the electrodes A 1 and A 5 under current input between electrodes A 0 and A 6. V A 0A 6 A 1 A Conductivity in thickness direction σ Ω mm -1 ) Τ probe method 4-probe method Conductivity in thickness direction σ Ω mm -1 ) Τ Fig. 6. Comparisons of oblique resistances between the accurate results and the four-probe method. Fig. 7. Contour plot of the current density vector, and the values of potential at each electrode and the magnitude of current density at the middle of two adjacent electrodes. is calculated using the ratio of the corresponding voltages for specimens 1 (without delamination) and 2 (with delamination) as follows:

7 L. Shen et al. / Composites Science and Technology 67 (2007) Table 2 Comparison between the voltage and resistance percentage changes and the dependence of voltage percentage changes on different current contacts Four-probe voltage V 1 (mv) V 2 (mv) (V 2 V 1 )/V 1 (%) Two-probe resistance R 1 (X) R 2 (X) (R 2 R 1 )/R 1 (%) A 1 A 5 [A 0 A 6 ] A 1 A A 2 A 4 [A 0 A 6 ] A 2 A A 2 A 4 [A 1 A 5 ] A 2 A 4 A 1 B 5 [A 0 B 6 ] A 1 B A 2 B 4 [A 0 B 6 ] A 2 B A 2 B 4 [A 1 B 5 ] A 2 B 4 A 3 B 3 [A 2 B 2 ] A 3 B A 3 B 3 [A 2 B 4 ] A 3 B 3 V ¼ V 2 V ð2þ V 1 where V 1, V 2 are voltages of specimen 1 and 2, respectively. The resistance percentage changes are calculated using the two-probe method for specimens 1 and 2, and are denoted as R A1 A 5, R A2 A 4, R A1 B 5, R A2 B 4 and R A3 B 3, respectively. Note that the difference between V A 0A 6 and V A 1A 5 will show the dependence of the voltage percentage change on the current contacts. The same is also valid for the differences between V A 0B 6 and V A 1B 5, and between V A 2B 2 A 3 B 3 and V A 2B 4 A 3 A 3. But the resistance percentage change is not affected by the current contacts because it only depends on the material properties and structural change such as delamination of the composite panel. The FEM results for the voltages, resistances and their percentage change are listed in Table 2, where the column and row values correspond to voltage/resistance and contacts, respectively. For example, V A 0A 6 A 1 A 5 and R A1 A 5 correspond to the values of and in Table 2, respectively. It can be seen from Table 2 that the voltage and resistance percentage changes are significantly different. Also, the voltage percentage changes depend on the current contacts used. For example, the surface voltage percent change between the electrodes A 2 and A 4 under the current contacts A 0 and A 6 and A 1 and A 5, i.e., V A 0A 6 and V A 1A 5 are and , respectively. On the other hand, the oblique voltage percent changes are not severely affected by the different current contacts, as shown by the values of V A 0B 6 ¼ 1:762 and V A 1B 5 ¼ 1:603, and by those of V A 2B 2 A 3 B 3 and V A 2B 4 A 3 A 3. Therefore, it is not reliable to use the voltage percentage changes to inversely predict damage inside composite panels because there are no consistent changes due to the different current contacts. 5. Conclusion Strip type specimens with and without delamination damage are used to carry out numerical analyses of the electrical resistance and voltage in a carbon fiber-reinforced composite panel. The purpose of the study is to determine the validity range of the four-probe method for resistance measurement, and the applicability of the voltage change method based on the four-probe method. The present study shows that the method is only valid when the through-thickness conductivity is comparable to or larger than the longitudinal conductivity. For example, if the longitudinal conductivity is 15 X 1 mm 1, the through-thickness conductivity should be larger than 1 X 1 mm 1. The present results show that the damage induced voltage change between a pair of voltage contacts is not consistent with the resistance change due to the same damage. The underlying reason for this is that the damage induced voltage change depends on the current contacts used, while the resistance change does not. Acknowledgements This work was supported by Global Contour Ltd. through NSF SBIR Phase IIA grant. The authors would like to thank Prof. Deborah Chung of the State University of New York/Buffalo for her valuable suggestions during the course of this project. References [1] Liang D. Fibre optic silicon impact sensor for application to smart skins. Electron Lett 1993;29(6): [2] Kuang KSC, Kenny R, Whelan MP, Cantwell WJ, Chalker PR. Residual strain measurement and impact response of optical fibre Bragg grating sensors in fibre metal laminates. Smart Mater Struct 2001;10(2): [3] Porfilio M, Graziani. ISIS: An in situ impact sensor for space debris monitoring. Adv Space Res 2004;34(5): [4] Imai S, Tokuyama M, Hirose S, Burger GJ, Lammerink TSJ, Fluitman JHJ. Thin-film piezoelectric impact sensor array fabricated on a Si slider for measuring head-disk interaction. IEEE Trans Magn 1995;31(6.1): [5] Haywood J, Coverley PT, Staszewski WI, Worden K. An automatic impact monitor for a composite panel employing smart sensor technology. Smart Mater Struct 2005;14(1): [6] Wang X, Chung DDL. Real-time monitoring of fatigue damage and dynamic strain in carbon fiber polymer matrix composite by electrical resistance measurement. Smart Mater Struct 1997;6: [7] Wang X, Wang S, Chung DDL. Sensing damage in carbon fiber and its polymer matrix and carbon-matrix composites by electrical resistance measurement. J Mater Sci 1999;34(11): [8] Wang S, Chung DDL. Mechanical damage in carbon fiber polymer matrix composites, studied by electrical resistance measurement. Compos Interf 2002;9(1): [9] Wang S, Mei Z, Chung DDL. Interlaminar damage in carbon fiber polymer matrix composites, studied by electrical resistance measurement. Int J Adhes Adhes 2001;21(ER6): [10] Wang S, Wang D, Chung DDL. Method of sensing impact damage in carbon fiber polymer matrix composite by electrical resistance measurement. J Mater Sci 2006;41(8):

8 2520 L. Shen et al. / Composites Science and Technology 67 (2007) [11] Wang S, Chung DDL. Self-sensing of damage in carbon fiber polymer matrix composite by measurement of the electrical resistance or potential away from the damage region. J Mater Sci 2005;40(24): [12] Wang S, Chung DDL, Chung J. Self-sensing of damage in carbon fiber polymer matrix composite cylinder by electrical resistance measurement. J Intell Mater Syst Struct 2006;17(1): [13] Anderson TA, Lemoine GI, Ambur DR. An artificial neural network based damage detection scheme for electrically conductive composite structures. In: Proc of 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conf 2003; 1997, p [14] Todoroki A, Tanaka Y, Shimamura Y. Measurement of orthotropic electric conductance of CFRP laminates and analysis of the effect on delamination monitoring with an electric resistance change method. Comput Sci Technol 2002;62: [15] Todoroki A, Tanaka Y. Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method. Comput Sci Technol 2002;62: [16] Todoroki A, Tanaka Y, Shimamura Y. Multi-probe electric potential change for delamination monitoring of graphite/epoxy composite plates using normalized response surfaces. Comput Sci Technol 2004;64: [17] Todoroki A, Tanaka Y, Shimamura Y. Electrical resistance change method for monitoring delaminations of CFRP laminates: effect of spacing between electrodes. Comput Sci Technol 2005;65: [18] Chung DDL. discussions.

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