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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this study, power losses in polymer optical fiber (POF) subjected to cyclic tensile loadings are studied experimentally. The parameters discussed are the cyclic load level and the number of cycles. The results indicate that the power loss in POF specimens increases with increasing load level or number of cycles. The power loss can reach as high as 18.3% after 100 cyclic loadings. Based on the experimental results, a linear equation is proposed to estimate the relationship between the power loss and the number of cycles. The difference between the estimated results and the experimental results is found to be less than 3%.

Compared with conventional glass fibers, polymer optical fiber (POF) offers a larger core diameter, higher numerical aperture, greater flexibility, lighter weight, easy coupling and lower cost [

In recent years, many researchers have investigated the power attenuation (

Up to now, little information regarding the sensitivity of POFs subjected to cyclic tensile loading has been revealed in the published literature. The aim of this study was thus to discover the power attenuation characteristics of POF fibers subjected to cyclic tensile loading. A series of experimental tests were performed to evaluate the power losses induced in cyclic elongated POFs with various load levels. One of the possible applications of this research may be development of a sensor which is buried in a structure to measure a small displacement at certain spots or in small regions, e.g., the contact points between a bridge and its piers.

The polymer material is viscoelastic. For the most general case of a linear viscoelastic material, the total creep strain ɛ(t) is given by Burgers’ model, which is a combination of the Maxwell and Kelvin models [_{1} is the instantaneous elastic strain, ɛ_{2} is the delayed elastic strain [_{3} is the Newtonian flow viscoelastic strain, which is identical to the strain of a viscous liquid following Newton’s law of viscosity. E_{1} and E_{2} are the elastic moduli, η_{2} and η_{3} are viscosities, σ is the applied stress, and t is the creep time. The strain-time relationship of Burgers’ model [

The POF specimen is a step index type SH-4001 fiber (Mitsubishi Rayon Company Ltd.) with a coating diameter of 2.2 mm, a cladding diameter of 1 mm, a core diameter of 0.98 mm, and a numerical aperture (NA) of 0.5. The refractive index of the core and cladding are 1.492 and 1.402, respectively. The core, cladding and coating of these POFs are fabricated from polymethyl methacrylate (PMMA), fluorinated polymer and low-density polyethylene (LDPE), respectively. In experiments, a length of 700 mm of POF is cut off from a scroll. The middle of the POF line is carefully measured to have a length of exact 100 mm and then clamped vertically on the test kit as the test section. Two ends of the POF line are connected to the optical power meter. One is connected to the light source (a light emitting diode with a wavelength of 660 nm), and the other is connected to the power detector. The launch NA of the LED used is 0.5. The power delivered to a POF specimen before elongating is measured in advance and denoted as P_{in}. The output power measured during fiber being elongated is denoted as P_{out}. The test result shows that the power P_{in} from the LED to the optical fiber is about 65 μW and this value is used for power normalization. In this study, the power losses in the POF specimens subjected to cyclic tensile loading are explored. In accordance with the JIS C6861 standard for plastic optical fibers test, the elongation rate is V = 100 mm/min in experiments. Here, one cycle of tensile loading is defined as the test section of the specimen is elongated with a load level varies from 0 N to P N at an elongation rate of V, and then is released to 0 N at the reverse rate of elongation. The cyclic tensile tests are performed with four different load levels, _{y}) is 100.

According to Burgers’ model, it can be seen from

In the following discussions, the lowest load in the unloading process and the highest load in the elongation test process are denoted as L-Load and H-Load. The lowest load is 0 N in the elongation test process and the highest load in unloading process is defined as the load level in experiments.

The corresponding variations of the power ratio P_{out}/P_{in} with the number of cycles are shown in _{out}/P_{in} decreases with the increasing number of cycles or the increasing load level. The results shown in _{out}/P_{out} obtained from the L-Load decreases about 3.7, 4.1, 10.4 and 13.8% at the load levels of P = 70, 80 90 and 100 N, respectively. The corresponding power ratio P_{out}/P_{in} obtained from the H-Load decreases about 3.7, 4.5, 12.6 and 18.3 %, respectively. It also can be found that the maximum power loss occurs at the first cyclic test, _{V} = 1. The results shown in _{V} = 1. It can be observed from the experimental cyclic load-displacement curves, as shown in

Additionally, it is observed from experiments that the fiber profile becomes linearly tapered as the POF is elongated. The reduction of the core diameter near the necked portions of the fiber changes ray paths and therefore introduces a power loss as rays propagate through the linearly tapered regions. From the experimental results, it can be seen that the core diameter in the middle region of the POF specimen decreases as the elongation increases. In a previous study [_{o} and used as a reference to normalize the ones obtained from the other tests. The normalized power ratio is defined as η̄ and can be expressed as:

The power ratios η_{o} for various load levels are listed in

Applying a linear least squares fitting technique to the data plotted in

The power ratio related to the number of cycles can be expressed as the following expression:

The predicted results obtained using

This study has investigated the effects of the cyclic load level and number of cycles on the power loss in polymer optical fibers deformed at load levels between 70 and 100 N. The results show that the POF specimen is significantly affected by the number of cycles and the load level. The power ratio reduces significantly as the number of cycles or the load level increases. The power loss can reach as high as 18.3% after 100 cyclic loadings. Based on the experimental results, an empirical expression is formulated to relate the power loss with the number of cycles. The maximum deviation between the predicted power loss obtained from the proposed equation and the experimental result is found to be less than 3%. Thus, the suitability of the relative displacement as a means of predicting the power loss in deformed POF sensors is confirmed. The potential applications of the developed cyclic tensile-POF sensing element can be found in measuring small displacements in certain areas or landslide alarming for its high sensitivity under cyclic loading deformation.

The strain-time relationship of Burgers’ model.

Experimental setup used to measure power loss in cyclic tensile test POF specimen.

The load-elongation curve of the POF specimen.

The cyclic load-displacement curve at load level P = 80 N.

Variation of the displacement with the cycles at various load levels. (

Variation of the power ratio with number of rollers. (

Variation of the normalized power ratio with the cycles at various load level. (

The power ratio η_{o} at C_{y} = 1 for various load levels.

70 N | 0.995 | 0.995 |

80 N | 0.992 | 0.992 |

90 N | 0.943 | 0.912 |

100 N | 0.911 | 0.864 |