Advancement of long-gauge carbon fiber line sensors for strain measurements in structures

Abstract

This article proposes a new technique that advances long-gauge carbon fiber line sensor technology, with and without post-tensioning of the sensor, to measure changes in strain levels in structural areas. Carbon fiber line sensors were fabricated to produce a slim high-strength sensor with a diameter of less than 1.4 mm using a carbon fiber tow with a width of 6 mm. A theoretical analysis of these sensors as well as several series of experiments was conducted to investigate the effect of fiber arrangement on the error compensation of the carbon fiber line sensors. The results revealed that using two sets of carbon fiber line sensors, one as an active sensor and the other to compensate the errors of the first, is an effective method when both sensors have a convergent fiber arrangement and change in resistance. A post-tensioning method was implemented to enhance the overall behavior of the sensor. The results showed that the post-tensioning method yields significant improvement in the linearity and cyclic ability up to 6000 microstrains and reduces the fluctuation errors in the change in resistance from ±0.031% to ±0.007%. Finally, the possibility of repairing damaged carbon fiber line sensors is also discussed.

Keywords

Carbon fibers sensors resistivity post-tension strain measurements

Introduction

In recent decades, carbon fiber–reinforced plastics (CFRP) have been widely investigated and applied in the aerospace, civil engineering, and auto industries because of their superior strength, stiffness-to-weight ratios, low density, long-term durability, and high resistance to chemical corrosion. In addition to these advantageous properties, another important characteristic of CFRPs is their favorable electrical conductivity and piezoresistivity (Schueler et al., 2001; Wu and Yang, 2006; Yang et al., 2006). In general, the resistivity of CFRPs increases linearly with applied tension and decreases linearly under compression, demonstrating piezoresistive effects. These electrical properties produce resistance variations in CFRPs undergoing changes in their mechanical, chemical, and thermal environments and thus render CFRPs potentially applicable as sensors of strain, stress, bio-feedback, damage, chemical exposure, and temperature (Ogi and Takao, 2005; Park et al., 2005; Shui and Chung, 1996; Wang and Chung, 2006; Wu et al., 2005, 2007).

Sensors can be separated into two types based on their gauge length: point sensors and long-gauge sensors. Point sensors are typically mounted near key parameters, as they have high sensitivity and precision. However, these sensors are expensive and are not suitable for detecting parameters in a large area or global sensing. In contrast, long-gauge sensors can be used for global sensing, which is useful for providing a comprehensive evaluation of the integrity of a structure (Huang and Wu, 2010).

Huang et al. (2010, 2012) studied the electrical sensing properties of CFRP strips to produce a CFRP strip long-gauge sensor for measuring low strain levels. It was found that the effective sensing behavior of a CFRP strip is related to its effective gauge length, and the transverse connection in a CFRP strip affects the linear strain response, especially when sensing is in a low strain range. The strain response properties of CFRP strips became more linear when the width-to-length ratio decreased. Moreover, when the gauge length of a CFRP strip was 500 mm or longer, its strain response exhibited a good linear relationship with the applied strain even at the low strain level of 200 microstrains. The strain response of a 500-mm-long CFRP strip maintained stable linearity throughout exposure to long-term cyclic tensile strain.

The change in resistance ΔR/R of a carbon fiber (CF) sensor is inversely proportional to the change in temperature because of the negative temperature resistivity of micro-CF. The measured signal from the CF sensors is related to the change in strain on the structural object but is also impacted by undesired effects from conditions such as temperature and humidity. CFs used continuously as the strain sensing elements in CF sensors clearly exhibit thermoelectric effects, reducing the reliability of the results calculated from these measurement signals (Huang et al., 2011; Huang and Wu, 2010). For carbon fiber line (CFL) sensors, the relationship between the change in resistance (ΔR/R), the applied strain ε, and the external errors (e) can be expressed as follows, where G_f is the gauge factor

\frac{Δ R}{R} = G_{f} \times (ε + e)

(1)

This problem of dual sensitivity to strain and other effects has plagued CFL sensors, and compensation for this error is necessary to advance a CFL sensor that yields effective and reliable strain measurements. Selecting and applying an appropriate compensating CF sensor is crucial to achieve improvement in the accuracy of results. The compensation sensor must be fabricated from the same material and have the same physical properties and gauge length as the active sensor and must only be subjected to interference effects and never to any quantity of applied strain (ε).

Huang and Wu (2012) also developed a signal processing method used to treat the structural strain responses of long-gauge CF sensors for static and dynamic strain measurements. This static denoising method is based on measuring the error range of CF sensors, as determined over long-term continuous loading and unloading experiments. For the experiment involving one-measure-time each second, the influence of noise on CF sensors followed a normal distribution, with a standard deviation of ±50 microstrains. For the experiment involving 25-measure-time each second, the signals were concentrated in a smaller range, and the probability density showed a clear increase. For signal selection based on multiple measuring times, the measured error range of CF sensors was consolidated from ±50 to ±10 microstrains.

This article presents a new approach for obtaining a long-gauge CFL sensor. The theoretical and experimental investigations discussed here clarified the effect of fiber arrangement on the error compensation of CFL sensors. Furthermore, a post-tensioning method was implemented to enhance the sensing behavior and cyclic ability of the CFL sensor under conditions of low and high strain. Finally, the possibility of repairing damaged CFL sensors is also discussed.

Theoretical background on the measuring circuit

The principle behind the operation of CFL sensors is based on establishing a relationship between the change in resistance ΔR/R and the strain ε. The resistance of a CFL sensor can be expressed as

R = ρ \times (\frac{L}{A})

(2)

where ρ is the resistivity, L is the effective gauge length of the sensor, and A is the cross-sectional area of the sensor. ΔR/R can be expressed as

\frac{Δ R}{R} = f (\frac{Δ ρ}{ρ}, \frac{Δ L}{L}, \frac{Δ A}{A})

(3)

According to the piezoresistive effect of semiconductor materials, the change in resistivity has a much greater effect than simple changes in geometry on ΔR/R (Huang and Wu, 2010). The ΔR/R of the sensor can therefore be expressed as

\frac{Δ R}{R} ≅ \frac{Δ ρ}{ρ}

(4)

Equation (4) represents the ideal condition, in which all the micro-CFs are ideally aligned and separated by epoxy resin, and the transverse electrical contact’s contribution to the sensor’s conductivity can be neglected. Then, the electrical resistance can be obtained by the parallel circuit approach from (Yang and Wu, 2003)

R_{0} = \frac{R_{f}}{n_{f}}

(5)

where R₀ is the initial resistance of the CFL sensor, R_f is the resistance of one microfiber, and n_f is the number of fibers in the sensor. In fact, owing to manufacturing defects inherent in CFL production, the arrangement of the microfibers in each sensor is different. To reflect practical conditions, ΔR/R can be written as

\frac{Δ R}{R} = (1 - η) \frac{Δ ρ}{ρ}

(6)

where η is a coefficient that reflects the transverse electrical contact’s contribution to the sensor’s conductivity. Thus, for any given strain level, ΔR/R differs from one sensor to another, as does the gauge factor.

By applying the Wheatstone bridge circuit to measure the total output signal of the active and compensation sensors, the change in resistance can be expressed as

\frac{Δ R}{R} = G_{fw} \times (ε_{w} + e_{w}) - G_{fc} e_{c}

(7)

where $G_{fw}$ , $ε_{w}$ , and $e_{w}$ are the gauge factor, applied strain, and external effects errors of the active sensor, respectively; and $G_{fc}$ and $e_{c}$ are the gauge factor and external effect errors of the compensation sensor, respectively. Under ideal conditions, when (1) the compensation sensor is subjected to only external effects, (2) both sensors have the same gauge factor $G_{f}$ , and (3) both sensors undergo the same external effects, the errors due to external effects will be effectively eliminated, and the output signal will be related to the applied strain only.

As described in this section, the two sensors will not be identical because of differences in their fiber arrangements, resulting in differences in their ΔR/R and gauge factors. Thus, errors caused by external effects will not be entirely removed; however, these errors can be reduced by choosing a compensation sensor with a gauge factor that converges on the gauge factor of the active sensor.

Experimental procedure and materials

The CF’s transverse connection, or tow, consists of numerous continuous microcarbon fibers. Each fiber can be considered as a sensing cell, such that the CF sensor’s output signal is the integrated response from all of the sensing cells. Under ideal conditions, a CF tow can be considered a parallel circuit that is composed of large numbers of micro-CFs. Under actual conditions, the microfibers are not completely straightened or arranged in parallel due to manufacturing defects, such as misalignment and breakage of fibers. Because the fiber distribution in this transverse connection introduces variability, the CFs of the samples in this study were pre-tensioned for 24 h under 500 microstrains to make the fibers as straight as possible.

Subsequently, to produce a CFL sensor with a gauge length of 500 mm, both ends were fully filled with conductive resins to improve the electrical contacts to each of the CFs in the cross section and to avoid the errors from contact resistance between CFs and the electrodes (Park et al., 2005), and then, the electrodes were connected to the conductive resin at both ends of the CFs with tin solder and copper cables. The CFs were then impregnated with epoxy resins and collected together manually to form a CFL sensor with a diameter of approximately 1.4 mm. Furthermore, the ends of the fixture used to hold the CFs in place were made of basalt fiber–reinforced polymer (BFRP) sheets and were bigger than the ends of the measurement sensor, thus providing enough bonding force to form the CFL sensor. The impregnated CFL sensor was cured at a temperature of approximately 45°C for 3 days, maintaining the sensor under tension until it was completely hardened. Finally, the tensile stress was released and the CFL sensor was ready to be installed at its measurement location, as shown in Figure 1. For all of the experiments in this study, the CFL sensors were installed on homogenous elastic glass fiber plates.

The CF tow used in this study was T700SC, produced by Toray Industries, Inc. The epoxy resin used was FR-E3P, produced by Nippon Steel Composite Co., Ltd, a bonding material approved by the Japan Society of Civil Engineers. The properties of these materials are shown in Table 1.

Table 1.

Properties of carbon fiber tow and epoxy resin.

Material	Thickness (mm)	Tensile strength	Tensile modulus (GPa)	Tensile elongation (%)	Volume resistivity (Ω cm)
Carbon fiber T700SC	0.136	4.9 GPa	230	2.1	1.6 × 10⁻³
Epoxy resin FR-E3P		51.9 MPa	3.43	1.513	1010–1020

To measure and monitor electrical strain, a CFL sensor must be connected to an electrical circuit that is capable of measuring changes in resistance corresponding to strain. A data measurement system was constructed with a Wheatstone measuring bridge connecting the active and compensation sensors, as shown in Figure 2.

Discussions

The effect of gauge factor on the compensation method

To study the effect of the change in the gauge factor on the compensation method, three sensors CFL₁, CFL₂, and CFL₃ were tensioned individually under 750 microstrains, and their measured ΔR/R signals were compared with the strain gauge as a reference strain. Figure 3 shows the behavior of the three sensors tested, and it is clear from the results that CFL₁ and CFL₂ had convergent ΔR/R, whereas ΔR/R for both of these sensors diverged from that of CFL₃.

In these experiments, the same CFL₁ was tested three times under a cyclic loading–unloading tension test from 0 to 750 µε with a loading rate of 1 kN/min (strain rate of 185 µε/min) under a stable laboratory conditions (18°C–20°C and 25%–30% relative humidity). The first test (group S₁) did not include a compensation sensor. For the second and third tests (groups S₂ and S₃), the same sensor used in group S₁ was connected with CFL₂ and CFL₃ as compensation sensors, respectively.

From Figure 4(a) to (d), the cyclic behavior of CFL₁ exhibited some error, which can be considered to be due to the external effects discussed in section “Introduction.” To reduce these errors, a compensation sensor was connected with the active sensor in groups S₂ and S₃. Strain signal measurements of group S₂ showed good stability, and the ΔR/R error was reduced from 0.022% to 0.007%, a reduction percentage of 68.2%. On the other hand, for group S₃, the ΔR/R error was reduced by a small value: from 0.022% to 0.015%, a reduction percentage of 31.8%. From the comparison of the three groups S₁, S₂, and S₃ shown in Figure 4(d), it can be concluded that use of a compensation sensor with a gauge factor closer to that of the active sensor can reduce the ΔR/R error significantly. These results are consistent with the theoretical approach in section “Theoretical background on the measuring circuit.”

Performance of CFL sensors under different strain levels

The behavior of group S₂ was studied under different strains to define the sensor’s error in the full range of strain levels. Thus, a cyclic tension test was applied in seven strain ranges to determine the cyclic behavior of the sensor. The tension loading–unloading cycle was repeated 30 times under each strain level: 300, 500, 750, 1000, 2000, 3000, and 4000 microstrains. All ranges were tested under approximately the same environmental conditions and load rating.

Figure 5(a) shows the relationship between the average ΔR/R_s over 30 loading cycles for each of the strain levels, relative to the reference strain. It is clear from Figure 5 that under higher applied strain, the measured signal exhibits poor linearity, showing instead a curvature that increases as the strain reaches maximum levels. Furthermore, the slope of the curvature increases with the increase in the strain value, and then, it gradually stabilizes in strain levels higher than 3000 microstrains, and it seems to be constant which has approximately average value of about 0.00049. To examine the relationship between signal fluctuation and maximum strain level from low to high strain levels, Figure 5(b) shows the distribution of the measured signal’s fluctuation through the 30 loading–unloading cycles for each of the seven experimental strain ranges. The errors of the signals under the different strain levels follow a normal distribution curve; this normal distribution lies entirely within the range of random extended signal fluctuation. Figure 5 shows that there is no significant change in signal fluctuation for the first three strain levels (300, 500, and 750 microstrains); the errors then increase with increasing strain until an upper limit of 3000 microstrains, after which the error appears to stay approximately constant. Table 2 illustrates the fitted equations and errors at each of the strain ranges; the errors were calculated to represent a 95% of the normal distribution, as calculated by standard deviations.

Table 2.

The results of tests of the CFL sensor under different strain levels.

Maximum strain (µε)	Maximum ΔR/R (%)	Fitted equations	Errors ΔR/R (%)
300	0.091	ΔR/R = 0.0003 × ε − 0.0065	±0.0057
500	0.152	ΔR/R = 0.0003 × ε − 0.0076	±0.0063
750	0.224	ΔR/R = 0.0003 × ε − 0.0124	±0.0072
1000	0.33	ΔR/R = 0.0004 × ε − 0.0007	±0.011
2000	0.75	ΔR/R = 0.0004 × ε − 0.0782	±0.0214
3000	1.195	ΔR/R = 0.0004 × ε − 0.126	±0.0289
4000	1.61	ΔR/R = 0.0004 × ε − 0.1693	±0.031

CFL: carbon fiber line.

During the fabrication of the CFL sensors, the CFs were pre-tensioned so that all of the microfibers were as straight as possible; in fact, however, not all of the microfibers could be completely straightened and would therefore not be pre-tensioned. As a result, at the beginning of the tests, the tension force F was not evenly distributed to all of the microfibers. Each fiber received a different magnitude of the force (F₁, F₂, …, F_n), and some fibers did not receive any force (F = 0) because of the winding of the fibers upon themselves. As the force of applied tension increased, some of the wound fibers also began to receive force, becoming active microfibers. Thus, the gauge factor of the active sensor differed from the compensation sensor, causing additional errors in the measured signal. These errors increased with increased applied strain, until reaching a limit at which the most of microfibers were active fibers. The incremental increase in error therefore has an upper limit above which it will not increase.

Regarding the curvature trend that appeared in the measured ΔR/R of the signals under high levels of applied strain, this phenomenon is considered to be caused by creep deformation from the resin, relaxation of the polymer matrix resin which is a viscoelastic material, and a slight elongation of the microfibers themselves. Inasmuch as the sensor was fixed from both ends on the glass fiber test plate, the slight elongation that occurred prevented full tensioning of the sensor on the plate, resulting in poor sensor sensitivity to low strains.

Post-tensioning method to enhance the behavior of CFL sensor

The tensioned fibers of fiber-reinforced plastic (FRP) composites did not exhibit creep, whereas significant creep occurred in the resin; therefore, the creep strain in the entire FRP material can be very limited if the fibers in the FRP are sufficiently straight (Everett, 1996). However, limitations of the production technology result in unevenness from fiber movements, such as local bending and skewedness, which are unavoidable. The elimination of creep deformation in the resin would allow stress to be uniformly transferred through the resin (Soudki, 1998). Therefore, it was considered that the unevenness of the fibers could be adjusted by post-tensioning along the axial direction of the longitudinal fibers. The resin in the CFL sensor continues to undergo creep deformation when it is subjected to a sustained load, allowing the possibility that the fibers could interact in the resin. During this post-tensioning process, the fibers tend to straighten because of resin creep, and their previously occurring unevenness can be adjusted, as shown in Figure 6.

To achieve this purpose, the CFL active and compensation sensors were post-tensioned after hardening using a tensile testing machine under a stress level of 0.60 f_u for 3 h. Subsequently, the sensors were installed on a glass fiber test plate, as before. The results of the post-tensioning test are shown in Figure 7, in which it can be seen that the creep in the CFL sensor increased with increased loading time until 2 h, after which the creep remained constant. Therefore, 2 h of loading eliminated errors from resin creep.

Tests of the sensor under the same seven strain levels were repeated to verify the enhancement percentage of the post-tensioning method. Figure 8 shows the performance of the sensors under the different strain levels, and the high degree of linearity of the post-tensioned CFL sensor is evident from Figure 8 for all strain levels from low to high. In addition to the enhanced linearity, the errors in ΔR/R were decreased, becoming constant at all strain levels, as apparent from Figure 8 and Table 3.

Table 3.

Results of tests of the post-tensioned CFL sensor under different strain levels.

Maximum strain (µε)	Maximum ΔR/R (%)	Fitted equations	Errors ΔR/R (%)
300	0.152	ΔR/R = 0.0005 × ε − 0.0092	±0.0069
500	0.248	ΔR/R = 0.0005 × ε − 0.0098	±0.007
750	0.36	ΔR/R = 0.0005 × ε − 0.0167	±0.0071
1000	0.484	ΔR/R = 0.0005 × ε − 0.0271	±0.0068
2000	1.006	ΔR/R = 0.0005 × ε − 0.0364	±0.0068
3000	1.51	ΔR/R = 0.0005 × ε − 0.0432	±0.007
4000	2.02	ΔR/R = 0.0005 × ε − 0.0575	±0.0072

CFL: carbon fiber line.

As a result of the post-tensioning of the CFL sensor, most of the microfibers were sufficiently straightened because of resin creep, and the previous unevenness of fibers was adjusted, resulting in a more uniform load carrying capacity. Moreover, the gauge factor of the active and compensation sensors will be constant and stable at any strain level; consequently, the errors in the measured signal can be limited and stabilized. From the fitted equations in Table 3, the gauge factor at any strain level has a constant value of 5, and 95% of the errors are within approximately ±0.007% (approximately ±14 microstrains). Finally, Figure 9 shows a comparison between the errors of the measured signal of the standard and post-tensioned CFL sensors under each strain level.

The measuring error of a CFL sensor generally includes a systematic error and a random error. The systematic error is a basic measure of sensor performance; on the other hand, the random error is generally caused by unstable external conditions, and it is difficult to forecast but can easily be reduced using the multi-measuring method in Huang and Wu (2012). By increasing the number of measurements taken in 1 s from 1 to 25, the total error can be reduced to ±5 microstrains, as shown in Figure 10.

Efficiency of the post-tensioned CFL sensor under high strains

Two specimens of post-tensioned CFL sensors were utilized to clarify the efficiency of the post-tensioning method in measuring high strain levels and elucidate the effects of post-tensioning on the gauge factor. The first specimen was tested under cyclic loading–unloading tensile strain, after having already been tested up to 4000 microstrains in the investigation discussed in section “Post-tensioning method to enhance the behavior of CFL sensor.” The rate of loading increased gradually by increments of 1000 microstrains to evaluate the limits of the sensor’s cyclic ability and the linearity of its signals. As is evident from Figures 11(a) to (d) and 12, the post-tensioned CFL sensor functioned well until 6000 microstrains, above which the sensor signal exhibited poor linearity relative to the reference strain, and the error clearly increased at the higher levels. It is evident from Figures 11 and 12 that the loading trend converged with the unloading trend until 6000 microstrains, above which the unloading trend neutralized and began to change its slope. This phenomenon can be considered a result of the initiation of microfracture to some of the microfibers. By means of loading–unloading tension cycles, the damage increases gradually resulting in stiffness reduction and some residual increase in the electrical resistance, which caused a small amount of random variation in the resistivity of the sensor during loading and unloading.

The second post-tensioned specimen was tensioned directly to an adequate strain of approximately 10,000 microstrains to investigate the overall behavior and changes in the gauge factor values relative to the reference strain gauge. The result clarified that the value of the gauge factor deviated substantially between 6000 and 7000 microstrains, as is apparent from Figure 13. The results from this second specimen’s limits of linearity and gauge factor are compatible with the first specimen, at 6000 microstrains and 5, respectively.

For the second specimen, some cracks and separation between the microfibers occurred when the specimen was loaded with 10,000 microstrains, as shown in Figure 14. This specimen was tested again under 30 cycles of loading under approximately 5000 microstrains, 50% of the maximum strain. Because of the separation between the fibers, the stress transferred into the fibers irregularly, affecting the stability of the measured signal. Therefore, a method of repairing the sensor is needed to control the regularity of stress transferring into the fibers. For this purpose, the sensor was repaired by re-impregnating the collected microfibers with epoxy resin. The cyclic behavior of the repaired sensor was then determined. Figure 15 shows that the signal from the repaired sensor exhibited good linearity until 3000 microstrains, after which the sensor lost stability and linearity and fluctuation errors increased.

Figure 16 shows a comparison of the post-tensioned CFL sensor before and after the repair, demonstrating that the sensor exhibited excellent linearity before any damage but showed poor linearity after damage, relative to the reference strain, with fluctuation errors in ΔR/R increased to a high value of 0.0255%. Figure 16 also shows that the repaired sensor had the same gauge factor as the normal mode of the post-tensioned sensor until 3000 microstrains. Moreover, the errors were reduced to 0.0105%. In general, it can be said that it is possible to repair the CFL sensor if its fibers are microdamaged by stress or external effects.

Conclusion

This article presents a new technique for measuring strain levels with a CFL sensor. The CFL sensor was fabricated manually to produce a long-gauge line sensor with a small diameter of less than 1.4 mm. The sensing errors of the CFL sensors were studied theoretically and experimentally. Some important conclusions can be drawn as follows:

The output signal of CF sensors needs to be compensated with an associated compensation sensor to reduce the undesired effects from external conditions. It has been demonstrated that a compensation sensor with a fiber arrangement and gauge factor that converges on those of the active sensor effectively reduces error.

The CFL sensor signal demonstrates good linearity with the applied strain under low strain levels; however, some curvature appeared and increased under higher strain levels. The signal fluctuation errors increased with increased applied strain levels up to 3000 microstrains, and then, the signal fluctuation error appears to remain constant.

A method of post-tensioning to control the initial creep of the CFL sensor was applied by tensioning the CFL sensor for 3 h under sustained stress of 0.60 f_u. The results showed that the post-tensioning method can significantly enhance the linearity of the measured signals and can eliminate or reduce errors.

The post-tensioned CFL sensor exhibits a good cyclic ability and stable gauge factor up to 6000 microstrains and can reduce the fluctuation errors in the ΔR/R from ±0.031% to ±0.007%. Beyond 6000 microstrains, the sensor exhibits poor linearity relative to the reference strain.

Further results showed that the sensor can be repaired if some damage to the microfibers has occurred; the repaired CFL sensor can be reused for strain measurements up to 3000 microstrains with acceptable errors.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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