1. Introduction

The strength of the splicing points between optical fibers not only directly measures whether or not the optical fiber fusion-splicing is successful, but also indirectly affects the service life and reliability of the whole optical fiber link [1,2]. Some classical references published have analyzed the root causes affecting strength of the fusion joints [3,4], applying the fiber strength theory [5–7] and reliability theory [8–10], and evaluated the service life of the fusion joints [11]. Many teams have also successfully prevented the strength degradation of the fusion joints by applying different methods and technologies [12,13] or directly improved the fusion strength [14–18]. Clearly, ameliorating the fusion strength has tremendous application value, such as manufacturing optical sensors with high stability and robustness [19,20] or designing long-lasting and durable heat shrinkable tubes [21] for protecting the optical fibers in the splicing section. However, the entire fiber fusion-splicing process is highly susceptible to ambient environment [22–24]. Some researchers have conducted many studies on the mechanism of environmental effects on the strength, reliability and service life of splicing joints [25–28] and practical applications including submarine fiber optic cables [29–31] and overhead optical cables [32–34]. Although the fracture mechanism and generic analytical model for fusion joints have been reviewed [4], they do not provide an in-depth analysis of how to enhance fusion strength. J.T.Krause has discussed the main factors affecting the silicon fiber original strength and outlined the intensity distribution and trend of its degradation in long fibers [3,6,7,15], but not delved into the specific details of these problems and provided a detailed derivation. M.Tachikura has realized the effect of contaminants on the fusion strength and succeeded in stopping the degradation of the fusion strength by using heating temperature dependence and heating time dependence [12–14], but not considered how to further enhance the fusion strength. The fusion strength has been increased by progressively optimizing the fusion parameters including fusion power, fusion duration, thermal advance and thermal compensation [16,17], but these methods all have great limitations. M.J.Matthewson has regarded strength and dynamic fatigue as a function of humidity and correlated crack growth rate with stress intensity, temperature and humidity in the form of function [25–28]. However, they do not consider the initial strength at the local fracture point and their models are only limited to specific service environments. O.Kawata has adopted a crack growth model to explain the reason for the increase in strength and raised the fusion strength by a factor of 3 by applying a hydrofluoric acid solution on the fiber surface in combination with validation testing [29–31]. However, they do not take into account the influences of fusion variables and environments. Y.Katsuyama has verified the long-term reliability of cable fibers in the overhead application environment by means of field experiments and performance evaluations [32,33], but it is difficult to complete these similar operations at high altitudes. When we first have applied directly these valuable experiences to on-site fusion splicing in the high-altitude environment, the expected results are not obtained, even far from the field measurement results. Fortunately, the altitude can be accurately measured [35,36]. Our team also has successfully carried out exploratory research on optical fiber fusion-splicing at high altitudes and clarified that the change of altitude can have a significant effect on the fusion loss [37–40]. However, these references all have not considered the influence of the high altitude environment on the fusion strength.

This paper does conduct an exploratory study of the fusion strength in high altitude environments. We firstly analyze the crack growth characteristics of the splicing points, concurrently introducing the environmental factors including temperature, humidity, oxygen content, atmospheric pressure, high wind and gravity, and then discuss the influence of fusion-splicing variables and parameters on the fusion strength due to the change of altitude, and then establish a mathematical model of the fusion strength under high altitude environment, and ultimately obtain the relationship between the tensile strength of the splicing points, the stress corrosion sensitivity factor and altitude. Especially, the optimal fusion conditions clarified by the published literature are directly applied to an exploratory experiment of on-site optical fiber fusion-splicing in high altitude areas for the first time. The experimental results show that the optical fiber splices are either very difficult to perform successfully, or even break outright directly; or the strength values of most of the successfully spliced fibers are overwhelmingly lower than 7.35kpsi, which can significantly increase the strength budget. To tackle this problem, we identify the main root cause of the degradation of the optical fiber fusion strength in high altitude environment and then propose a method to improve the optical fiber fusion strength under the high altitude environment by appropriately adjusting the axial offset and the fusion area length, which increases the strength of the fusion point by at least 13.2kpsi. Furthermore, we have conducted again several sets of field fusion experiments at different altitudes (53m, 2980m, 4000m, 4200m, 4300m, 5020m and 5200m). In particular, a large number of field experimental data have been obtained. Even more importantly, the majority of the fusion strength values are greater than 56.53kpsi and even the strength of some individual splice joints are increased to about 123.46kpsi. Ultimately, the method presented has been directly applied to the splicing engineering in the high altitude environment, achieving good results, greatly saving time cost and economic cost of constructing long-span and super-long-distance optical fiber communication link in high altitude area, which has certain implications for the future research on the fusion strength in the high altitude environment.

2. Theories

The optical fiber fusion splicing platform [41] is adopted here and the detailed part of the arc discharge heating and fiber end fusion docking shown in Fig. 1(a). The physical property of the fusion splice is not exactly the same as those of the original fiber being fused [2]. Then, we assume that the optical fiber fusion technology merges two different types of optical fibers into a hybrid optical fiber, which is furthermore assumed to be a "new" optical fiber. Notably, it can exhibit different forms because of the fusion variables, fusion parameters, fusion environments and manual operations, as shown in Fig. 1(b$\sim$h).

 

Fig. 1. Schematic diagram of single-mode fiber fusion-splicing, (a): optical fiber fusion splicing; (b): misalignment; (c): running-back; (d): bulging; (e): necking; (f): bubbles; (g): incomplete fusion-splicing; (h): normal fusion-splicing.

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The surfaces of the "new" fibers shown in Fig. 1(b$\sim$g) are not smooth or complete, which can severely weaken the tensile strength of the fusion splice. Specifically, although the fusion splice shown in Fig. 1(h) is very smooth and intact, the new cracks can also be introduced into [1,2,29] and thus reduce the tensile strength of the "new" fiber. These cracks gradually increase over time. Even worse, the crack growth trend can be accelerated and exacerbated in the presence of water molecules [2,4,6]. Fortunately, W.Griffioen has revealed that the patterns of cracks or defects of the fusion splice can be diverse, as shown in Fig. 2(a), and also illuminated that these cracks or defects can extend in multiple directions of the optical fiber over time.

 

Fig. 2. Crack model, (a): crack patterns; (b): crack propagation; (c): crack profile structure. a and 2b represent the crack depth and length respectively, and $\sigma$ represents the surface tensile stress of the optical fiber, perpendicular to the crack.

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The theoretical model and mathematical expression of fiber fracture in plain area have been obtained [1,2,42,43]. The fiber fracture is the result of crack growth reaching its limit. Namely, an optical fiber can fracture when the force exerted on it in use exceeds its ultimate tensile strength $\sigma _{f}$, which is also called failure stress or fracture strength and can be expressed by Eq.(1).

(2)

Fig. 2(b) provides a model of a tiny crack on the fiber surface. We assume that the minimum size of the crack that breaks the fiber is $a_{cri}$, also called the critical crack size, and the minimum tensile stress required to fracture the fiber is $\sigma _{cri}$ at this point. It can be reached from Eq.(1) that $a_{cri}$ is a function of the applied stress. Then, we assume that the local tensile load applied near the fiber crack is $\sigma _{lo}$, which is the fracture stress $\sigma _{f}$ multiplied by the effective contact area $A_{eff}$ of the fiber at that location and can be calculated by Eq.(3).

Then, the rate of crack growth can be obtained from the classical power-law model of crack and here set as $V_{crack}$, which is widely regarded as a generalized growth rate calculation equation for cracks or defects [1,2,42,43] and can be expressed by Eq.(4).

To keep the fusion splice from breaking, we make the maximum force acting on the fiber as much as possible less than $\sigma _{f}$ during the fusion process. In other words, we can minimize initial crack length at the fusion splice surface or minimize the chemical reaction of $SiO_{2}$ with the external environment to maximize the tensile strength of the "new" fiber. Then, we model the transient state of the fiber in the fusion zone, as shown in Fig. 3. The fiber endings in molten silica form are subjected to multiple forces such as applied force, surface tension, thermal expansion force and gravity during the whole fusion process affected by the surrounding environment. As shown in Fig. 1(a), the two fibers placed in the fusion splicer are heated by the discharge of the two electrodes to reach the corresponding softening temperature and thus fusion spliced together. During this whole process, the center of the fusion region is subjected to the greatest influence of the heat source, and then this effect gradually weakens along the axial direction of the corresponding fiber core, as shown by the parabola and arrow direction in Fig. 3(a).

 

Fig. 3. The molten state of the fusion region, (a): thermal and mechanical characteristics of the fiber fusion-splicing process. $L$, $l_{1}$ and $l_{2}$ represent the fusion region length, the suspension beam length of the left and right fiber respectively; (b): the fusion splice. Cracks can appear anywhere near the left or right of the splice point.

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According to the working mechanism of the fusion splicer, at the instant of fusion, the resultant force $F_{all}$ acting on the molten fiber in the fusion area can be expressed by Eq.(5).

The axial offset between the two fibers is influenced by the harsh high-altitude environment, which in turn has a great impact on the fusion process [37–40]. Hence, we make a bold assumption that reducing the axial offset can improve the fusion strength. Then, we establish the Cartesian coordinate system, as shown in the upper left corner of Fig. 1(a), where only the force state in the transverse direction on the fiber surface is considered. According to the circular axis symmetry property of single-mode optical fiber, the forces in the axial direction of the fiber cancel each other even though the axial position of the two fibers is changed by the high-altitude environment. Then, we rewrite Eq.(5) and obtain the stress state of the molten silicon fiber in the direction perpendicular to the fiber axis under the action of the propulsive force $F_{B}$, as shown by Eq.(6).

Under the action of surface stress $\sigma$, the fiber surface is subjected to a force $F_{A}$ that separates the two fibers and is parallel to the fiber end face. We assume that the fiber core moves $x$ distance in the cross-sectional direction of the optical fiber. Then, the surface tension $F_{A}$ at this time can be obtained in combination with the force analysis method and expressed by Eq.(9).

During the fusion bonding of the fiber by heat, a viscous force $F_{\eta }$ appears in the silica glass against surface tension. Similarly, we can assume that the fiber core moves $x$ distance in the cross-sectional direction of the optical fiber. Then, the viscous force $F_{\eta }$ at this very moment can be deduced by combining the force analysis method and finally calculated by Eq.(10).

Substituting Eq.(9) and Eq.(10) into Eq.(6), the instantaneous force equilibrium state equation of the molten silicon optical fiber under the influence of transverse offset between the two optical fiber cores can be obtained, as shown by Eq.(11).

Then, substituting Eq.(7) and Eq.(8) into Eq.(11) and then solving the first-order differential equation, we can obtain the transverse offset $s$ between the two optical fiber cores, which finally can be accurately calculated by Eq.(12).

A further analysis of Eq.(12) shows that the transverse offset $s$ between the two optical fiber axes in a high-altitude environment is related to not only the fusion splicer propulsion force, fusion temperature and fusion time, but also the melting zone length, the melting zone width and the effective contact area during the fusion-splicing process.

Back into the Fig. 3(a), we assume that the fusion splicer pushes the fiber endings on the left and right sides forward $l_{1}$ and $l_{2}$ respectively during the fusion process. Besides, we can continue to assume that the ends of the two optical fibers do overlap each other by $l_{3}$ distance during the fusion-splicing operation, obviously $0\leqslant l_{3}\leqslant min\left \{l_{1},l_{2}\right \}$, otherwise there is no meaning. Then, the length $L$ of the fusion zone at this moment can be obtained and expressed by Eq.(14).

In accordance with the geometric properties within the optical fiber fusion area, we can also obtain the fusion width $l_{B}$, which is calculated by Eq.(15).

As shown in Fig. 1 and Fig. 3, the circularly axis symmetric optical fiber is uniformly heated up and down by the fusion splicer during the fusion process. Then, we can treat the molten silicon fiber diameter 2$r_{f}$ in the fusion region as the fusion zone width $l_{B}$ in the subsequent analysis.

Back into the Fig. 3(a) again, we assume that the radii of the left and right fiber are $r_{1}$ and $r_{2}$ respectively. The axial offset between the two fused optical fibers often has three cases, as shown in Fig. 4. To highlight the focus of this paper, we assume $r_{1}=r_{2}=r$.

 

Fig. 4. Transverse offset between the two fiber cores, (a): $s<r$; (b): $s>r$; (c): $s=r$.

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Then, the effective contact area $A_{eff}$ of the two optical fibers during the fusion process can be obtained by using simple geometric operations. Interestingly, it is found that the state of the optical fiber axial offset is consistent for either of the cases in Fig. 4(a), Fig. 4(b) or Fig. 4(c) after careful comparison. Namely, $A_{eff}$ aforementioned all can be calculated by Eq.(16).

As previously described, the "new" fiber formed can have a "blunt" defect or crack when there is an axial offset during the fusion-splicing process. Then, we set this crack length to be $a_{0}$, which is the initial length of the fiber surface crack with the initial inert strength. It can be reached from Fig. 1 $\sim$ Fig. 4 that the initial crack length $a_{0}$ of the fusion joint can be calculated by Eq.(17).

Referring to the classical experience [2,22], we set the current density at any point $p(x,y,z)$ in the fusion region as $I_{e}$, which conforms to the radially symmetric Gaussian distribution in the transverse direction apparently and can be calculated by Eq.(19).

As shown in Fig. 3, the energy released by the fusion splicer is transmitted along the optical fiber and gradually weakens during the fusion process. Hence, the energy $\omega$ acquired by the optical fiber in the region during the duration $t_{f}$ can be calculated by Eq.(21).

In the meantime, we partition a fusion region of length $L$ into a finite number of microelements for analysis and treatment [22] and assume that the energy released by the fusion splicer during the fusion splicing process is utilized for fusion splicing without leakage. Then, it is obtained from the law of conservation of energy that the energy required to squeeze the ends of two fibers together is equal to that gained by the local fibers in the fusion area, as expressed by Eq.(22).

Then, the initial inert fusion strength $\sigma _{I}$ of the "new" optical fiber can be obtained by combining with Eq.(18), Eq.(21) and Eq.(22), and finally calculated by Eq.(23).

Ultimately, we obtain the tensile strength of the splicing points at high altitudes. However, it is very difficult to obtain an exact closed-form solution of Eq.(23). So in the subsequent part of this article, we describe it in detail by means of simulation and thus obtain its approximate values.

The tensile strength of the fusion splice mainly depends on its the surface condition, environmental factors, and the mechanical load that it is subjected to during the fusion-splicing process. Noteworthily, the close contact between the molten silicon optical fiber and the surrounding environment is unavoidable during the fusion-splicing process. When the fiber fusion-splicing is performed in the high altitude environment, the complex terrain topography and variable climate with the increasing altitude all can seriously affect the heat and force state of molten silicon fiber. Consequently, when the altitude is $Z$ meters with the pascal intensity of pressure $P_{Z}$ and the pressure $F_{P}$, the applied force $F_{B}$ that makes the two optical fibers be squeezed each other and connected together becomes $F_{B}-F_{P}$. Fortunately, the pascal intensity of pressure $P_{Z}$ has been obtained by our previous work [38] and can be expressed by Eq.(24).

Then, the atmospheric pressure $F_{P}$ acting on the end faces of the two optical fibers with a cross-sectional area of $A_{csa}$ can be calculated by Eq.(25) in the high-altitude environment.

Furthermore, combining with Eq.(12), Eq.(13), Eq.(24) and Eq.(25), the axial offset $s_{Z}$ affected by the change of altitude in the process of optical fiber fusion-splicing under the high altitude environment can be obtained and expressed by Eq.(26).

Then, the instantaneous theoretical value of the initial inert tensile strength $\sigma _{Z}$ of the fusion splice in the high-altitude environment can be obtained by combining with Eq.(16), Eq.(23), and Eq.(26), and finally expressed by Eq.(27).

The fracture of the fiber occurs when $K_{I}$ = $K_{IC}$. The local force on the molten fiber is greater than $\sigma _{Z}$ in the local range of the fusion process at this time. Thus, the ultimate tensile strength $\sigma _{f}$ near the fusion point can be obtained by rewriting Eq.(3) and expressed by Eq.(28). It should be noted that the effective radius of the fusion point can be approximately $r_{f}$ at this very moment.

Then, in combination with Eq.(1), Eq.(4), Eq.(27) and Eq.(28), the stress corrosion sensitivity factor $n_{Z}$ of the fusion splice in the high altitude environment can be calculated by Eq.(29).

Noteworthily, we assume that the robustness of the fiber fracture toughness is very strong during the fusion-splicing process in the high altitude environment. Then, the surface crack size $a_{C}$ of optical fiber can be treated as the initial crack length $a_{0}$ at the fusion splice at this time.

The instruments and meters are effortless to fail and the electrodes of the fusion splicer are also easy to be contaminated in the high altitude environment, the reasons for which are not the research focus of this paper and thus not be given unnecessary details here. However, these factors all can lead to some deviation of the actual fusion strength from the theoretical value, which here is denoted by $\sigma _{ad}$. For more accurate calculation, the final value of the fusion strength acquired at high altitudes can be expressed as $\sigma _{F}$, which is finally calculated by Eq.(30).

3. Experiments

Till now, no theoretical studies and field experiments have been reported on the optical fiber fusion strength in high-altitude environments. In our previous work [38], we have defined the high cold day, the high cold month, the high cold region, and the plateau. Here, we continue to use these concepts for ease of understanding. The Ultra-Low-Loss (ULL) optical fibers coming from the same manufacturer, the same batch and the same type are selected for the study in the course of the subsequent experiments. The material and geometric parameters of the ULL fibers are all taken as their average values respectively, as shown in 1. The length of each ULL fiber is 500 m. The SM G652 Std. fusion-splicing mode and the default parameters of the fusion splicer manual are selected in subsequent all fusion-splicing experiments.

Table 1. Characteristic parameters of the ULL optical fibers

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Then, the fusion-splicing experiments based on the "Tibet-Central" networking project in China have been conducted at seven different altitude points in the high altitude environment respectively. The environmental factors vary at different altitudes, as shown in 2. Noteworthily, the subsequent fusion experiments are repeated with the same number of experiments and the same steps. The ten samples are taken for each selected experiment object during the experiment, and the samples and their parameters are assumed to be all consistent in the same sample space. In addition, this paper assumes that all the tools, instruments and meters are clean and in good condition and that they are all also very ideal in the use process.

Table 2. The environmental information at different altitudes

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While the measurement period of fiber strength is very long, often up to several months or more, we are unable to stay at high altitudes for long to achieve this goal. Hence, the fusion points obtained successfully at high altitudes are sealed to avoid contact with the external environment and then brought back to the laboratory, assuming that they are in ideal condition throughout the operation. Then, the classical strength test device [2,16,17] is set up in the laboratory to measure the tensile strength of the splicing points, as shown in Fig. 5. In the meantime, the environmental parameters are continuously adjusted to imitate the field fusion-splicing environment at high altitudes. Finally, the strength test is performed on the fused section of optical fiber to obtain the measured values of the fusion strength.

 

Fig. 5. Testing device for the tensile strength of the fusion joints.

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4. Numerical analysis and discussion of results

During the fusion process, the fusion splicer discharges and heats the ends of the optical fibers, resulting in fibers being fused together and forming a very short "new" fiber, as shown in Fig. 1. The fiber endings are subjected to the joint action of various forces including $F_{A}$, $F_{B}$, $F_{C}$, $F_{P}$, $F_{g}$ and molten glass adhesion, as shown in Fig. 3(a). The axial alignment state between the fiber cores, as shown in Fig. 4, can affect the molding state of the "new" fiber and even introduce directly cracks to the splicing points, as shown in Fig. 2. Here, the applied force $F_{B}$ is in units of g$\cdot$m, whose range is still set from the lowest value to the critical value of 30g$\cdot$m, and increases in steps of 1g$\cdot$m. In addition, assuming that the properties of the fiber materials themselves are stable in the high-altitude environment, the change in the mode field radius $w_{u}$ of the ULL fiber is not affected by change in altitude. It is the axial offset between the optical fiber cores that plays a crucial role in the fusion process. Eq.(26) treats the axial offset $s$ as a function of the altitude $Z$. Particularly, the axial offset increases significantly with the increase of altitude [38].

To enhance the strength of splicing points or prevent the degradation of that in the high-altitude environment, the influence of axial offset between fiber cores on fusion strength has been studied for the first time. We have treated the tensile strength $\sigma _{f}$ of the splicing points as a function of the axial offset $s$ between the fiber cores. Then, we calculate and simulate Eq.(23) and find that the tensile strength $\sigma _{f}$ decreases significantly as the axial offset $s$ gradually increases, as shown in Fig. 6. Especially, the closer the axial offset $s$ is to the core diameter 2$r$, the more significantly the tensile strength $\sigma _{f}$ decreases. It is worth noting that when $s \geqslant 2r$, even a very successful fusion splice is meaningless. Then, the tensile strengths $\sigma _{f}$ obtained under the condition that the initial crack length $a_{0}$ is selected as 0.13 or 0.24$\mu m$ and the melt region length $L$ is selected as 0.3 or 0.7$mm$ respectively are selected for further comparison. Obviously, regardless of the values of $a_{0}$ or $L$, the tensile strength $\sigma _{f}$ decreases as the axial offset $s$ increases, as shown in Fig. 6. Noteworthily, the magnitude of $\sigma _{f}$ varying with $L$ is significantly larger than that of $\sigma _{f}$ varying with $a_{0}$. However, this trend becomes less and less pronounced with the gradual increase of $s$, even close to the same at $s \geqslant 2r$. In turn, we can improve the tensile strength of the splicing points by reducing the axial offset $s$ at high altitudes. The mechanical strength is usually in units of Kilopounds per Square Inch (kpsi), and 1kpsi $=6.9\times 10^{-3}$GPa.

 

Fig. 6. Tensile strength versus axial offset.

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Eq.(2) implies that surface crack growth shown in Fig. 2 is accelerated when water molecules are present in the molten region. The extremely harsh fusion environments at high altitudes can severely accelerate and exacerbate this change. Hence, we relate the fusion point surface crack size $a_{Z}$ with the altitude $Z$ in the form of a function and then find that $a_{Z}$ increases significantly with the gradual increase of altitude $Z$, as shown in Fig. 7. Then, the surface crack sizes $a_{Z}$ obtained under the condition that the fusion zone width $l_{B}$ is selected as 15 or 25$\mu m$ and the melt region length $L$ is selected as 0.3 or 0.7$mm$ respectively are selected for further comparison. Obviously, regardless of the values of $l_{B}$ and $L$, the surface crack size $a_{Z}$ increases significantly with the raise of altitude $Z$, as shown in Fig. 7. According to Eq.(1), this can severely reduce the tensile strength of the splicing points. In other words, the surface crack size of the fusion splice increases significantly with the gradual increase of altitude, which in turn seriously reduces the fusion strength. Besides, the magnitude of $a_{Z}$ varying with $L$ is close to the same as that of $a_{Z}$ varying with $l_{B}$. Consequently, we can minimize the surface crack size $a_{Z}$ of the fusion splice by controlling $l_{B}$ and $L$ as much as possible to improve the fusion strength at high altitudes.

 

Fig. 7. Surface crack size of the splicing points versus altitude.

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Here, the axial direction of the electrode is located in the Y-axis and the distribution of the heat source to which the optical fibers in the melting region are subjected is shown by the dotted line in Fig. 1. Based on the circumferential symmetry of the fiber, we assume that the heating lengths of the fiber on the left and right side of the Y-axis are the same, and both are $L/2$. Meanwhile, the heating widths on the upper and lower sides of the melting fiber are equally wide, and both are $r_{f}=l_{B}/2$. Then, the variation characteristic of the tensile strength $\sigma _{Z}$ of the splicing points in the high altitude environment can be precisely characterized by Eq.(27). Apparently, the tensile strength $\sigma _{Z}$ of the splicing points decreases exponentially with the gradual increase of altitude $Z$, as shown in Fig. 8. Furthermore, the tensile strengths $\sigma _{Z}$ obtained under the condition that the fusion zone width $l_{B}$ is selected as 15 or 25$\mu m$ and the melt region length $L$ is selected as 0.3 or 0.7$mm$ respectively are selected for further comparison. Obviously, regardless of the values of $l_{B}$ and $L$, the fusion strength $\sigma _{Z}$ decreases significantly with the raise of altitude $Z$, as shown in Fig. 8. It follows that the tensile strength of the splicing points decreases dramatically with gradual increase of altitude. In short, the higher the altitude is, the lower the fusion strength becomes. Particularly, the magnitude of $\sigma _{Z}$ varying with $L$ is evidently larger than that of $\sigma _{Z}$ varying with $l_{B}$. Therefore, we can enhance the tensile strength of the fusion point in the high altitude environment by controlling $l_{B}$ and $L$ as much as possible.

 

Fig. 8. Fusion strength $\sigma _{Z}$ versus altitude $Z$.

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Then, the surface crack size at the fusion point in the high altitude environment is researched for the first time. Measurements are made at seven different altitudes respectively and the simulation results are shown in Fig. 9. Obviously, the surface crack size of fusion joint increases significantly with the gradual increase of altitude, and the higher the altitude is, the more obvious this trend becomes. Especially, the variance is very small and smooth, which verifies the validity of the model proposed. Comparing it with Fig. 7, we find that the variation trend of both is basically the same, that is, the surface crack size $a_{Z}$ increases significantly with the gradual increase of altitude $Z$. Most strikingly, the fusion success rate shows a significant downward trend with the increasing altitude. Especially when the altitude is more than 5000$m$, the fusion failure rate reaches about 90$\%$ disappointingly. It is meaningless to measure the surface crack size of the failed fusion joint at this point. It is worth noting that in terms of the fiber surface crack size, there is such a case that the values of a few samples at high altitudes are smaller than those in plain areas. In other words, the surface crack sizes of fusion points obtained at high altitudes are not always larger than that obtained in plain areas. Fortunately, these are only a small number of exceptions and do not affect the overall trend.

 

Fig. 9. Surface crack size of the fusion splice versus altitude.

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To verify the validity of the model proposed, we compare the strength of the original fiber with that of the fusion-splicing fiber, and the simulation results are shown in Fig. 10. Obviously, the strength of the original fiber with the protective sleeve is significantly higher than that of the original fiber bared, so does the fusion-splicing fiber. Whether or not there is a protective sleeve, the strength of the original fiber is always higher than that of the fusion-splicing fiber. In addition, the tensile strength of both raw or splice fibers with protective sleeves and raw or splice fibers bared all can weaken significantly with the gradual increase of altitude. This weakening phenomenon is particularly prominent in the strength characteristics of splicing points, which verifies again that the fusion strength decreases significantly with the gradual increase of the altitude under the influence of the high altitude environment. Especially, the weakening trend becomes particularly obvious when the altitude is above 5000m.

 

Fig. 10. Ultimate tensile strength versus altitude.

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To further verify the validity of the model proposed, we compare the fusion strength at seven different altitudes, and the simulation results are shown in Fig. 11. Obviously, the fusion strength decline from altitude of 53 m to altitude of 5200m. Besides, the mean and variance of the fusion strength at altitudes of 53, 2980, 4000, 4200, 4300, 5020 and 5200m all decrease in turn. For example, the mean value 103.75, variance 118.04, and standard deviation 10.865 of the fusion strength at the altitude of 53m are significantly greater than the mean value 23.56, variance 68.306, and standard deviation 8.2647 of the fusion strength at the altitude of 5200m. In brief, the fusion strength has a very remarkable downward trend with the continuous increase of altitude. Moreover, the higher the altitude is, the more obvious this trend becomes. Noteworthily, when the altitude is above 5000m, either the fibers are difficult to be successfully fusion-spliced or even fractured directly, or the strength of most of the successfully joints is significantly lower than 4.35kpsi. Surprisingly, although the fusion strength decreases dramatically with the increase of altitude, this change does not occur with regularity at the same altitude point.

 

Fig. 11. Tensile strength of the fusion joints versus samples.

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To further verify the validity of the proposed model, we assume the fusion process is ideal and fix other parameters. Then, the average values of the fusion strength obtained when the melt area length $L$ is 0.05, 0.1, 0.2, 0.3, 0.5, 0.7 and 1mm respectively are selected for further comparison, and the simulation results are shown in Fig. 12. Obviously, no matter what the fusion length $L$ is, the fusion strength $\sigma _{Z}$ decreases significantly with the increasing altitude. Besides, the higher the altitude is, the more pronounced this phenomenon becomes, and the greater the degree of reduction becomes, which is basically consistent with the results presented in Fig. 8. Moreover, the longer the fusion region is, the lower the fusion strength becomes. This is because the longer the melt zone is, the larger the area of the molten fibers in contact with the surrounding environment becomes, which in turn prolongs the duration of the chemical reaction revealed by Eq.(2) and increases the probability of surface cracks being introduced into the splicing points.

 

Fig. 12. Fusion-splicing strength versus altitude.

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Fiber strain is an important indicator of optical fiber durability. To further verify the validity of the model proposed, we discuss the strain in the splicing points obtained at the seven different altitudes, and the simulation results are shown in Fig. 13. Obviously, the tensile strength of the splicing points and its strain both decrease significantly with the gradual increase of altitude. In particular, the variation of strain in the fusion splice is more pronounced compared to the change trend of the fracture stress at the fusion point. Besides, the higher the altitude is, the greater the variation of strain in the fusion splice becomes, that is, the more significant the strain reduction in the fusion splice becomes at this time. For example, compared with Fig. 8, the measured strength at an altitude of 53m is close to the theoretical strength, while the measured strength at an altitude of 4300m is significantly smaller than the theoretical strength. Moreover, the higher the altitude is, the more obvious this feature becomes.

 

Fig. 13. Strength and strain in the splicing points versus altitude.

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The stress corrosion sensitivity factor $n_{\sigma }$ obtained by applying valuable experiences [2,6] is far from the predicted and budgeted values in the high-altitude environment. This is because the high altitude fusion environment is very complex like a "black box", and includes not only relative humidity and absolute temperature, but also non-negligible environmental variables such as oxygen content, pressure, high wind and gravity. Here, we treat all these variables as elements of the "black box" and apply Eq.(29) to vividly describe the change characteristics of the stress corrosion sensitivity factor $n_{Z}$ in the high-altitude environment, as shown in Fig. 14. Obviously, $n_{Z}$ decreases significantly with the gradual increase of altitude, which means that the growth rate $V_{crack}$ of the surface crack in the splicing points at high altitudes becomes significantly larger and then the service life of the fusion splice serving the high altitude environment can be severely shortened. Especially, the higher the altitude is, the more obvious the characteristic that the actual value of the stress corrosion sensitivity factor $n_{Z}$ is smaller than the theoretical value of that becomes, and the larger the error between the actual value and theoretical value at the splicing points becomes. It means that the growth rate of the surface cracks in the splicing points at high altitudes is dramatically larger than that at plains.

 

Fig. 14. Stress corrosion sensitivity factor $n_{Z}$ versus altitude $Z$.

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Consequently, we can optimize the fusion strength $\sigma _{Z}$ by adjusting the melt zone width $l_{B}$, melt zone length $L$ and initial axial offset $s_{0}$ in the high altitude environment, and the simulation results are shown in Fig. 15. Obviously, the fusion strength obtained at $s_{0}=0\mu m$ is significantly greater than that obtained at $s_{0}=1\mu m$, while the fusion strength obtained at $s_{0}=1\mu m$ is significantly greater than that obtained at $s_{0}=4\mu m$. In addition, the measured values are basically consistent with the theoretical value when $s_{0}=1\mu m$ and $s_{0}=4\mu m$, while the measured value is basically smaller than the theoretical value when $s_{0}=0\mu m$, because it is impossible for the fiber cores alignment to achieve 100$\%$ [2,41]. It is notable that no matter what the value of $l_{B}$, $L$ or $s_{0}$ is, the error of the fusion strength obtained at high altitudes increases evidently with the increase of altitude. Moreover, the higher the altitude is, the larger the error becomes. In turn, we increase the fusion strength by 13.2kpsi by appropriately adjusting $l_{B}$, $L$ and $s_{0}$. It is worth noting that the strength value of the strengthened fusion points at high altitudes is still far below the average value of the tensile strength of the splicing points in plain areas. Besides, the number of samples with this fusion strength value obtained from the field experiments is much lower than the total number of samples. Fortunately, this effect has achieved the desired goal because the success rate of optical fiber fusion-splicing is extremely low in the high-altitude environment.

 

Fig. 15. Fusion strength versus altitude.

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5. Conclusion

In present work, we elaborate the main cause of tensile strength degradation of the fusion splice and discuss the influence of fusion variables on fusion strength in the high altitude environment. The exploratory experiment of field fusion-splicing is carried out at high altitudes for the first time. Then, we propose a mathematical model to improve the fiber fusion strength under the high altitude environment by combining factors of temperature, humidity, oxygen content, atmospheric pressure, high wind and gravity. Furthermore, based on the "Tibet-Central" networking project in China, the field fusion experiments are carried out at seven locations with different elevations respectively. Meanwhile, a large number of field experimental data have been obtained. It is found that the fusion strength of most fusion points achieved successfully has been promoted by at least 13.2kpsi. Besides, the majority of the fusion strength values are greater than 56.53kpsi and even the strength of some individual splice joints is increased to about 123.46kpsi. Notably, the essential reason behind the result that the change of altitude can have a significant influence on the strength of the optical fiber splice point is that the fiber endings are extremely sensitive to their surrounding environment during the entire fiber fusion process.

Although the first study of fusion strength in high altitude environments has many limitations, we have successfully identified the main causes of very low fusion strength in the high altitude environment, as well as the approach to achieve fiber fusion-splicing successfully and the method to increase fusion strength as much as possible. Ultimately, the method presented has been directly applied to the fiber splicing engineering in the high altitude environment, achieving good results, greatly saving time cost and economic cost of constructing long-span and super-long-distance optical fiber communication link in high altitude area, which has certain implications for future research on the fusion strength of different kinds of optical fibers in the high altitude environment. Besides, the experimental data obtained from field experiments at high altitudes have expanded data reserve of the fusion strength data library. It should also be noted that with the altitude of more than 3000m, the fusion strength decreases significantly and can be increased by properly adjusting the configuration of fusion parameters at this time. However, when the altitude reaches above 5000m, it is almost difficult to successfully fusion splice under general conditions. To achieve optical fiber fusion-splicing successfully at this very moment, we need to think of other methods, such as improving performance of the fusion splicer.