Estimating the Mechanical Reliability of Optical Fiber

Transcription

1 Estimating the Mechanical Reliability of Optical Fiber Author: Ashutosh Goel Abstract The scientific background for the mechanical reliability of optical fibers and methodology followed at STL based on which the reliability of optical fiber under a constant stress has been estimated is described in this report. It should be noted that the reliability is expressed as an expected lifetime or as an expected failure rate. The results cannot be used for specifications or for the comparison of the quality of different fibers. Keywords Optical fibers, Mechanical Reliability, Power Law Theory, Lifetime estimation, Fatigue testing, Proof testing, Long length tensile testing I. INTRODUCTION According to Power law theory, optical fibers manufactured from vitreous silica, are sensitive to static fatigue: the duration of the application of the loading has an effect on the strength of glass. Classically, the static fatigue of glass is interpreted as the sub-critical growth of cracks. As the strength of glass is controlled by the size of flaws, the fatigue effect in glass fibers is related to the crack growth (stress corrosion) during aging in the given environment, under load [1]. Figure1: K I -V curve for silicate glasses, in general [2]. Figure 1 shows the typical general features of the velocity V of a running crack as a function of the stress intensity factor (K I = Y a 1/2 ; Y is the crack geometrical factor, is the applied stress and a is the crack depth) in a silica/silicate glass. In general, the K I -V curve is divided into three regions (Figure 1): In region I, the crack velocity increases with applied stress and humidity. The crack growth rate in this region is closely related to the mechanical fatigue of glasses; In region II, crack velocity is independent of applied stress but depends on humidity; In region III (i.e. around and above K IC (critical stress-intensity factor)), crack growth is independent of humidity but changes sharply with applied stress. However, it levels off at some characteristic speed (for example: around 1500 m/s for soda-lime glass) [2]. In a narrow range around K IC the crack velocity ranges between 10 3 and 1 m/s (region III). The slope of the curve is very steep. In absence of any water, this curve would extrapolate linearly to lower crack speed. The value of K IC for silica glass is 0.79 MN m -3/2 [3]. In region I, starting from very low velocity ( m/s; usual for optical fibers in deployment scenario), V is generally represented by Power law model (equation 1)...(1) where A is the environmental parameter and the slope of the curve in region I gives the value of stress-corrosion parameter, n, also known as fatigue parameter [2]. The value of n for region I vary between 10 and 40 such that smaller n refers to larger susceptibility to fatigue.

2 The technical report IEC/TR entitled, Optical fibers-reliability-power law theory by International Electrotechnical Commission (IEC) recommends the power law theory to estimate the reliability of optical fibers. Further it is noteworthy that in the case of high strength fibers (example: optical fibers), reliable study of the region II (Fig. 1) is practically unfeasible because this region is observed only for very high speed testing (>10 4 GPa/s) [4]. However, results from specially damaged fibers (for example: abraded fibers) are available because this region is shifted to lower testing speed ( GPa/s) [5]. II. IN-SERVICE LIFETIME OF THE OPTICAL FIBER UNDER CONSTANT STRESS Formula for estimating lifetime: According to the technical report of International Electrotechnical Commission-IEC/TR [6], the formula for calculating the in-service lifetime of an optical fiber based on power law theory is presented in equation (2)....(2) Where, t f is the lifetime (time to failure) under constant stress or static fatigue testing; m s is the Weibull modulus under static fatigue; is the Weibull -value; a is the applied stress under static fatigue and lifetime; a is the proof-test stress; t p is the effective proof time; L is the fiber effective length under uniform stress, or equivalent tensile length; n is the stress-corrosion parameter; P is the fiber survival probability. The lifetime model proposed in IEC/TR (Equation 2) is equivalent to that proposed by Griffioen et al. [7, 8] for long-length proof-tested fiber as given in equation (3):...(3) Where, s is the in-service stress, t s is the fiber lifetime, p is the proof stress, t p is the time during which each point of the fiber experiences proof stress, F is the failure probability, L is the fiber length, N P is the mean number of breaks per length during proof testing, m is the Weibull parameter obtained for extrinsic flaw distribution. The value of m is difficult to determine because of its correlation with the initial inert strength distribution of the fiber [9]. Therefore, Mitsunaga et al. [9] have recommended the use of repeated proof testing in order to estimate the value of m. At STL, we obtain the m value from the distribution of data for low strength region as obtained from the long length tensile strength tests on proof tested fiber as described in IEC [10] and will be discussed in section 3.4. Figure 2: Stress-Strain curve obtained for an optical fiber during axial tension test. Figure 3a

3 Tensile strength (GPa) Strain Min. Max. Median 0 m (mm/min) Figure 3b Figure 3 (a&b): Fracture probability v/s uniaxial tensile strength Fracture mechanics of optical fibres - Dynamic fatigue testing: In the deployment scenario, the optical fiber is under constant in-service stress (static fatigue) and is expected to be in service for excess of 25 years. However, it is not practical to conduct experiments to assess the reliability of fibres on such time scales. Therefore, in order to quantify the reliability of the system it is necessary to perform accelerated experiments in the laboratory and extrapolate these results to less severe in-service conditions. Thus, under such circumstances, the value of n for optical fibers is usually calculated by evaluating their dynamic fatigue behaviour via axial tension tests and two-point bending tests in accordance with TIA/EIA standards: TIA-EIA and TSB62-13, respectively. In dynamic fatigue testing, specimens are subjected to either tensile testing or bending loads, which increase in magnitude linearly with time until fracture occurs. Dynamic fatigue testing was first proposed by Charles [11] and further developed by Evans and Weiderhorn [12]. The data presented on dynamic fatigue testing in this report has been obtained on single mode optical fibers manufactured at STL with diameter of 250 m and is representative of our production process. The Young s modulus of the optical fiber as calculated from the slope of stress-strain curve (Figure 2) varies between 15 and 20 GPa. This is consistent with published reports, see for example Ref. [13]. Further, the Weibull distribution of fracture probability (in accordance with equation 4) versus uniaxial tensile strength at different strain rates is shown in Figure (4a)...(4b) Where, P f is the fracture or failure probability; f is the tensile strength of fibre; 0 is the characteristic strength (the stress at which 63.2% of failure will occur); m is the Weibull modulus. Table 1: Tensile strength data of STL optical fibers

4 Figure 4: Dynamic fatigue of optical fiber The value of stress corrosion parameter, n, is calculated from the slope of the curve between tensile stress v/s stress-rate as shown in Figure 4. In general, the value of n for STL fiber varies between 21 and 25 as obtained from axial tension data. It should be noted that the n values obtained from two-point bending test data are usually higher in comparison to those obtained from axial tension tests due to the smaller fiber gauge length used in former [3, 14] which consequentially results in predicting higher in-service lifetime of the fiber in comparison to that calculated by using axial tension tests [15]. In order to overcome this discrepancy in the lifetime estimates, IEC [16] suggests the use of axial tension data to resolve this dispute. Proof testing: The purpose of proof test is to ensure that the tensile strength of the fiber is good enough. The fibers are loaded with certain force depending on the desired final strength, to test for tensile strength and cracks or other mechanical faults. The mean number of breaks per unit length (N P ) is an important parameter used in equation (3) to estimate the lifetime of fiber. The faults can be caused by impurities on the fiber surface or in the perform or possibly by high drawing tension. The most commonly used minimum strength (also used at STL) is 0.70 GPa (or 100 kpsi). At STL, proof test of fiber is accomplished in accordance with the standard IEC [17]. The proof testing is divided into three phases. The first phase is loading during which the stress increases to proof stress level. Then the fiber goes to the proof testing region where it is subjected to the proof testing tension, during dwell time. After that the stress is unloaded during the unloading time. The fiber can break in every phase of proof testing. The proof-test time, t p, plays a crucial role in estimating the in-service lifetime of optical fiber as is evident from equation (3). The effective proof-test time is given by equation (5):...(5) where, t d is the dwell time, t l is the loading time, t u is the unloading time n is the stress-corrosion parameter. In equation 5, the t l and t u contribute little to the effective proof-test time. As an example, if n 20, and neither the t l nor t u exceeds 10% of the dwell time, the fraction in equation (5) constitutes less than 1% of the effective proof time. This shows that the dwell time should be kept small so as to minimize the fatigue of the surviving cracks [17]. Proof Test Stress =0.72Gpa Probability Plot of LLT Yearly Data in Gpa Weibull - 95% CI Sh ap e Scale N AD P- Valu e <0.010 Percent Truncation region 1 LLT Yearly Data in Gpa 10 Figure 5: Bimodal tensile strength Weibull plot for a 20 m gauge length test set-up at 5% min strain rate. Long length tensile testing: The long-length tensile tests on optical fibers are made in accordance with IEC [10]. The test is designed to measure the characteristics of the extrinsic region and therefore, large sample sizes (hundreds of specimens) and gauge lengths (20 m) are employed. The result of testing is a statistical distribution of failure stress values. Hence all the reported parameters are statistical in nature, with inherent variability that is a function

5 of the sample size and the variability of flaw size within the sample. The weakest site, or largest flaw, within a specimen will fail, and the typical failure stress decreases as gauge length increases. Figure 5 presents a typical example of bi-modal aggregate distribution as shown in Weibull plot for the 20 m gauge length set-up. Two modes are observed based on the tensile strength of fiber: a high strength mode which is very narrow and a lmuch broader low strength tail. The low strength tail can be controlled by proof testing the fiber which truncates the distribution [18]. The value of Weibull modulus, m, used in equation (3) to estimate the lifetime of the optical fiber is usually derived from the low strength (extrinsic region) of the curve obtained in Fig. 5 and its value generally varies between 2 5 [9]. III. CONCLUSION This document provides a detailed overview and insight into the theory and practice of estimating the mechanical reliability of optical fibers at Sterlite Technologies Ltd. Sterlite has a strong commitment to understand the strength and reliability of optical fiber across a diverse application scenario of interest to its customers. Our reliability modelling and testing complies with all applicable international standards, thereby assuring lifetimes well in excess of industry requirements. Author Ashutosh Goel Deputy Manager-R&D (Centre of Excellence) Sterlite Technologies Ltd. E-1, E-2, E-3, MIDC Waluj Aurangabad , Maharashtra, India Phone: ashutosh.goel@sterlite.com References 1.Wiederhorn, S.M. and L.H. Bolz, Stress Corrosion and Static Fatigue of Glass. Journal of the American Ceramic Society, (10): p Gy, R., Stress corrosion of silicate glass: a review. Journal of Non-Crystalline Solids, (1): p Chen, C.P. and T.H. Chang, Fracture mechanics evaluation of optical fibers. Materials Chemistry and Physics, (1): p Gougeon, N., M. Poulain, and R. El Abdi, Evolution of strength silica optical fibers under various moisture conditions. Optical Materials, (1): p Gavey, P.T., et al., Mechanical reliability predictions: An attempt at measuring the initial strength of draw-abraded optical fiber using high stressing rates, in 46th International Wire and Cable Symposium1997. p Optical fibres-reliability-power law theory, IEC/TR 62048; 2011, International Electrotechnical Comission, Switzerland. 7.Griffioen, W., et al., COST 218 evaluation of optical fibre lifetime models, in Optical Materials Reliability and Testing: Benign and Adverse Environments, R.A. Greenwel and D.K. Paul, Editors. 1992, SPIE. p Griffioen, W.W., Evaluation of optical fiber lifetime models based on the power law Optical Engineering, (02): p Mitsunaga, Y., et al., Failure prediction for long length optical fiber based on proof testing. Journal of Applied Physics, (7): p Optical fibres-part 1-31: Measurement methods and test procedures-tensile strength, IEC ; 2010, International Electrotechnical Comission, Switzerland. 11.Charles, R.J., Dynamic Fatigue of Glass. Journal of Applied Physics, (12): p Evans, A.G., Slow crack growth in brittle materials under dynamic loading conditions. International Journal of Fracture, (2): p Chean, V., et al., Study of the mechanical behavior of the optical fiber by a mark-tracking method. EPJ Web of Conferences, : p Han, L., et al., Characterization of tensile properties of optical fibers coated with new generation coating system and the comparison of fatigue behavior by tensile test and two-point bending technique, in 59th IWCS Matthijsse, P. and W. Griffioen, Matching optical fiber lifetime and bend-loss limits for optimized local loop fiber storage. Optical Fiber Technology, (1): p Optical fibres - Part 1-33: Measurement methods and test procedures - Stress corrosion susceptibility, IEC ed. 1.0; 2001, International Electrotechnical Commission: Switzerland.

6 17.Optical fibres-part 1-30: Measuurement methods and test procedures - Fiber proof test, IEC , 2010, International Electrotechnical Commission, Switzerland. 18.Matthewson, M.J., Optical fiber reliability models. SPIE Critical Reviews of Optical Science and Technology, CR50: p About Sterlite Technologies Limited Sterlite Technologies is a leading global provider of transmission solutions for the power and telecom industries. Equipped with a product portfolio that includes power conductors, optical fibers, telecommunication cables and a comprehensive telecom systems / solutions portfolio, Sterlite's vision is to 'Connect every home on the planet'. Sterlite is also executing multi-million dollar power transmission system projects, pan-india.