THE MEASUREMENT OF TRANSMISSION , ABSORPTION , EMISSION , AND REFLECTION

 

This is continuation from the previous tutorial - Optical Fibers for biomedical applications

 

 

1.  INTRODUCTION

Silica-based light-guide fibers have been produced and deployed with great success in spite of their well-known ‘‘brittleness.’’ For instance, techniques have been developed that allow long lengths (tens of kilometers) of such fibers to be drawn and coated in-line. The preform and draw processes allow production fiber that has a flaw-free surface with, essentially, the theoretical strength under the conditions of use/test \(\sim5.5\text{GPa}\) for most of its length.

The few manufacturing defects that occur are eliminated by a proof-testing procedure that allows the remaining length of fiber to attain almost any desired guaranteed strength. While the commonly specified proof stress is approximately 700 \(\text{MPa}\), by reducing the available continuous lengths and at some increase in cost, higher proof stresses are possible.

Success of this sort has not been achieved with all glass fibers, however. Multicomponent silicate fibers, hollow waveguides, and photonic crystal guides have been studied much less, and while their capabilities can be predicted to some extent, very few data are available. The mechanical properties of other specialty glass fibers, such as heavy-metal fluoride \(\text{(HMF)}\), telluride, and chalcogenide glasses, have also been studied with varying degrees of success.

Intensive study and modification of the processes used for manufacturing the fiber preforms and the resulting fiber have resulted in the very high quality fiber described earlier.

The use of very high quality raw materials for the core and cladding, control of the purity of the gases employed in the furnace, as well as control of the solid and gaseous impurities available to interact with the hot fiber in the draw environment proved very important in this regard.

Because it was known that contact of the pristine fiber surface with any hard material would easily cause surface damage and a precipitous reduction in strength, techniques were developed very early to enable a protective polymer coating to be applied in-line without itself causing damage to the fiber surface.

Because of the purity of all of the materials employed, there are rarely any solid impurity particles in the body of the fiber, so in almost all cases, the strength of the fiber is the strength of its surface.

Thus, the condition of the surface of the fiber determines its strength. Whatever the situation with regard to the ‘‘starting’’ strength of any given fiber or fiber type, several things must be kept in mind:

a. Fibers are normally coated in-line with a polymer, which provides protection from mechanical damage. The strength of bare fiber can be easily reduced precipitously by the development of such mechanical damage on the glass surface. The damage is the result of the contact of hard foreign particles on the glass surface, which produce strength reducing cracks or scratches. Such strengths show a very broad distribution and are unpredictable. 

b. Delayed failure or fatigue causes the initial strength to decrease with time under load in glasses of most compositions.

c. In some cases, strength decreases are noted with time under ‘‘severe’’ conditions, even in the absence of an applied stress; this is termed ‘‘zero stress aging.’’

d. Glasses are essentially ‘‘frozen’’ liquids with no regular lattice, but with a random structure and fluctuations characteristic of a liquid. They are in a metastable state with respect to the crystal and heating to a critical temperature where crystallization may occur at a reasonable rate will certainly lead to strength degradation.

Even if there is no crystallization, there may be relaxation of the glass structure and, therefore, changes in the glass properties that must be kept in mind when processing fibers for use in some applications.

 

 

2.  REVIEW OF GLASS PROPERTIES

In this section, we review some of the important parameters of glass systems that can affect their mechanical behavior and mechanical reliability.

 

Noncrystallinity, the Glass Transition (Tg), and Relaxation Processes 

Although there are several operational definitions of ‘‘glass,’’ for our purpose, we define a glass as a material that has been cooled from the melt without crystallizing. In the region from \(T_m\), the melting point and \(T_g\), the glass transition temperature (the temperature at which the viscosity, \(\eta\sim 10^{12.4}\text{Pa}/\text{sec})\), the material is called a ‘‘supercooled’’ liquid (Fig.1).

In this state, it has the structure of the liquid, and although the mobility of the structure is reduced as the temperature is reduced, structural rearrangements can occur in experimental times. Because of this, the coefficient of thermal expansion is substantially higher \((\sim 2-3\) times) than below \(T_g\).

As seen in Fig. 1, changes in cooling rate from Tg will result in changes in room temperature properties such as density and refractive index. To a very rough approximation, we may consider these materials to behave as maxwellian solids, with \(\eta=\text{G}\tau\), where \(\text G\) is the shear modulus and \(\tau\) the shear relaxation time; at \(T_g\), relaxation times of the order of minutes are found.

Thus, metastable equilibrium is achieved in reasonable experimental times. Below \(T_g\), relaxation increases with an activation energy of the order of 400–1000 \(\text{kJ}/\text{mol}\), and thus, major structural changes cannot usually occur in experimental times.

However, in the case of rather rapidly quenched materials, such as silica fibers, it has been found that substantial relaxations can occur below \(T_g\).

Below \(T_g\) the mobility is so small that structural rearrangements do not occur in experimental times. This material is considered to be in the amorphous or glassy state. 

 

 

On cooling from \(T_g\) to room temperature, the linear thermal expansion is the result of changes in bond lengths, whereas above \(T_g\), a thermal expansion coefficient, which is at least twice as great, is due to structural rearrangements and to bond length changes.

For materials such as silica, silicates, and some chalcogenides, upon reheating through \(T_g\) and up to the melting point, there is little probability of crystallization when heating at reasonable rates. Other glasses such as the \(\text{HMFs}\) may rather easily crystallize on either reheating or on the initial cooling.

Thus, in such glasses, care must be taken to ensure that no crystallization occurs. In particular, surface-nucleated crystallization may be a problem both mechanically and optically. 

Glasses differ from their crystalline counterparts in that their structure has no repeating lattice but is instead random. There may be both chemical and structural randomness, which may give rise to optical scattering.

Regions of chemical or structural fluctuations may lead to fluctuations in solution rate as well. We postulate that this may lead to the zero stress aging described later.

 

Brittleness, Hardness, and Cracking

Most of the inorganic glasses with which we are concerned fail in a brittle manner. That is, they will fail by fast fracture (i.e., cracks that grow unstably to produce rapid and complete failure without any significant ductile deformation). Brittle materials are sensitive to the presence of cracks and other stress-concentrating defects, and if mishandled, it is possible to introduce significant damage with corresponding weakening. 

As a result, glasses are frequently mistakenly described as ‘‘brittle’’ if they are weak and easily break on handling. However, this is incorrect because ‘‘brittle’’ refers to crack propagation without ductility; whereas brittle materials are often weak, they can also be extremely strong if severe strength-degrading defects are avoided or eliminated. Pure silica and silicate glasses have high intrinsic strengths that are higher than most ‘‘strong’’ ductile metals. 

However, their brittleness means they are easily damaged. Contact of the newly drawn perfect surface of a silica light-guide fiber with a sharp hard object will result in an instantaneous and serious reduction in strength, by a factor up to 100 or more. The susceptibility to surface damage (cracking) is not easily understood or predicted.

Although, as just stated, the glasses with which we are concerned are basically brittle, under the action of a complex state of applied stress such as found under a sharp indenter or scribe, they will flow at room temperature. This flow will result in the development of residual stresses and ultimately lead to the generation of cracks. Also, even blunt indenters, if subject to a high enough load, will result in the generation of cracks. Two investigations in the literature illustrate this nicely.

Baikova et al. studied the behavior of a glass plate when indented with a 2-\(\text{mm}\) diameter steel ball.

Their initial results showed a great deal of scatter in the load required to produce cracking and thus considerable variability in the strength reduction, certainly at loads in the range of 20–100 \(\text N\), and occasionally at substantially lower loads.

After cleaning the ball and the glass surface, they found the higher loads were required to cause fracture, and from this, they deduced that the presence of dust particles was the cause of the very much lower loads.

With a clean ball on a clean surface, the load necessary to cause cracking and thus lower the strength of a silica plate was found to be approximately 100 \(\text N\), in agreement with that predicted for this situation in which a ball is loaded on a flat substrate. In this case, the tensile stress that induces cracking is just outside the contact area, roughly the diameter of the ball.

One of the present authors has shown more quantitatively that the use of an indenter in the shape of the corner of a cube, rather than the much more blunt Vickers pyramid indenter with a 138-degree included angle, results in a reduction of the load to cause cracking by two orders of magnitude \((<2\;\text{mN}\) versus 2 \(\text N\) or more) (Fig. 2). In the case of the cube corner indenter, cracking is produced during loading and the appropriate equation to describe this effect is

\[\tag{1}P_r\sim P\left(\frac{E}{H}\right)^{1/2}\cot\psi^{2/3},\]

where \(P_r\) is the crack opening force due to the applied load \(\text P\), \(\text E\) is Young’s modulus, \(\text H\) the hardness, and \(\psi\) is the indenter angle. In the case of the

 

 

blunter Vickers pyramid indenter, cracking may occur on unloading and, therefore, is driven by the residual stresses developed during the plastic deformation associated with formation of the permanent impression. 

 

Composition Effects 

Table 1. lists a number of typical inorganic glasses that may be of use as light guides or in light-guide devices, together with some of their important properties. \(\text E\) is the Young’s modulus, \(\text{K}_{IC}\) is the fracture toughness, \(H_V\) is the Vickers hardness, \(T_g\) is the glass transition temperature, and a is the coefficient of thermal expansion. Columns five through eight list some strength values and are described later.

As indicated earlier, glasses are often referred to as brittle, whereas as can be seen here, they can have exceptionally high intrinsic strengths. 

 

Silicates 

The vast majority of commercial glasses are so-called multicomponent glasses \(\text{(MCGs)}\) that contain three to six oxide components. Early in the development of light-guide fibers, many workers attempted to employ these well-known and well-characterized glasses for long-length communications. 

It was found very difficult to purify them to the extent necessary for low optical loss. In addition, it was found quite early on that by using vapor-phase processes and extreme purity liquid precursors for the preparation of pure glass-former glass fibers, high purity could be maintained throughout the fiber production.

However, even so, it was not possible to produce \(\text{MCG}\) fibers because suitable liquid precursors were generally not available. In addition, simple two-component alkali silicates that were predicted to have ultimate scattering losses lower than silica could not be used because at the low alkali concentrations desired, phase separation was encountered.

Also, the addition of even small amounts of these oxides results in a glass with very different viscosity and thermal expansion, so processing of these with a silica cladding becomes difficult. Duncan et al. looked at alkali and alkaline earth borosilicate glasses (silica and NBS glass), but as indicated earlier, had problems with purity.

Figure 3 is a Weibull probability plot (see the later section on Weibull statistics) of the distributions of the strength of silica and an \(\text{NBS}\) glass and it is seen that reasonable strengths were obtained for such glasses, but their purity, and thus, optical transmission, was poor.

In the future, it may be desirable to employ such glasses, if extremely low losses are not required, because their mechanical properties may be suitable.

In Fig. 3, we present failure strain rather than failure stress/strength. The reason for this is that a common technique used for testing these fibers

Table 1. Mechanical properties of various glasses

 

 

Tellurite Glasses 

Although tellurium dioxide does not form a glass in its pure state, oxide glasses based on \(\text{TeO}_2\) have been found to have desirable light-emitting properties when doped with rare earth ions. In particular, the optical behavior of these glasses has been studied extensively for use as erbium-doped fiber amplifiers. To our knowledge, only one study of the mechanical strength of these glasses has been carried out. 

 

Nonoxide Glasses

Because of their atomic sizes, bond types and bond strengths, oxide glasses show very strong optical absorptions in the near infrared \(\text{(IR)}\). Although the near-IR band edge may be moved somewhat further into the IR by using large heavy atoms in a silicate glass or by going to a germanium-based glass, to shift the band edge substantially, glasses based on anions other than oxygen are required. For this purpose, chalcogenide and \(\text{HMF}\), non-silicate, nonoxide glasses have been studied intensively. 

 

Chalcogenides

Although chalcogenide glasses were studied as early as 1912, serious study of the individual chalcogens and chalcogenide glasses was not undertaken until the 1960s when interesting electronic properties were discovered. 

Chalcogenide glasses can be formed over a very wide range of composition. They contain one or more of the elements sulfur, selenium, or tellurium (chalcogens) with other elements from groups \(\text{IV}\), \(\text{V}\), and \(\text{VI}\) of the periodic table. For glasses having good transmission in the near \(\text{IR}\) (0.5–10 \(\mu m)\), most attention is now paid to glasses in the general composition ranges of \(\text{As-S}\), \(\text{As-Se}\), \(\text{Ge-As-S}\), and \(\text{Ge-Se-Te}\). Extrinsic absorption is most often caused by the presence of impurities of oxygen and hydrogen. 

 

Heavy-Metal Fluorides

In 1975, Poulain et al. unexpectedly discovered a fairly large range of glass-forming compositions based on HMFs; specifically zirconium fluoride. There followed a period of intense study because it had been shown theoretically that for highly pure glasses in these systems, there was the possibility of ultimate optical losses substantially lower than those for silica.

It has subsequently been found impossible to produce either bulk glass or fibers with impurity levels sufficiently low for these theoretical losses to be realized. In addition, the difficulties with crystallization during fiber drawing restrict the compositions that are practically useful.

However, they are still of some interest for certain applications. 

Compositions most studied are \(\text{ZBLAN}\) (fluorides of zirconium, barium, lanthanum, and sodium) and \(\text{ZBLAN}\) with additions of \(\text{AlF}_3\).

 

Photonic Crystal Fibers

Photonic crystal fibers or ‘‘holey’’ fibers are just that. They are fibers having holes distributed over their cross-section. Because they are normally a single material and normally silica, their material properties are the same as the materials listed in Table 1.

 

 

3.  MECHANICAL PROPERTIES 

In most of this section, we deal with general glass properties or with those of silica fibers. In the final portions of the section, we review nonsilica fiber properties. 

In Table 1, columns five through eight, some data on the strengths of a variety of glasses are given. In column 5, the highest reported measured strengths are given, with the measurement temperature indicated in parenthesis. For silica and the soda-lime–silica glass, these are strengths measured at 77\(\text K\) for what are thought to be flaw-free samples.

The value for silica is the same as that for a silica-clad light-guide fiber because in this case the strength-controlling surface is composed of silica. We designate these intrinsic inert strengths—strengths measured on samples with no flaws under conditions where no delayed failure or fatigue can occur (77\(\text K)\). Columns 6 and 7 give two approximations for the theoretical strengths.

The first (column 6) is an approximation based on the fact that the strength is expected to be a substantial fraction of the elastic (Young’s) modulus, in this case, we list \(\text{E}/5\). It is seen that this gives the value measured for silica. Column 7 is an estimate based on the proportionality of strength \((\sigma)\) and fracture toughness \(\text{(K}_{IC})\) for a given flaw size, \(\text c\), in Eq. (3).

Here, it is assumed that the effective ‘‘crack’’ size in all glasses is the same and the data are normalized to the value of 14 \(\text{GPa}\) for silica. Column 8 is the ratio of the highest measured strength (estimated at 77 \(\text K\) as twice the room temperature value) to the lowest estimated theoretical value.

As indicated, the value for silica is the theoretical value. For all other glasses except for \(\text{As}_2\text{S}_3\), the percentage is 30–40%. For \(\text{As}_2\text{S}_3\), it is possible that the fibers for which the measured strength at room temperature is 1.2 GPa may be very close to the inert, intrinsic, or theoretical ‘‘flaw-free’’ strength, approximately 2.4 \(\text{GPa}\) at 77 \(\text K\). 

 

Strength 

Inert, Intrinsic Strength: Tension and Two-Point Bend 

Figures 4 and 5—from the very important work of Proctor, Whitney, and Johnson in 1967—illustrate a number of significant points that we discuss later in this section. This work was carried out at Rolls Royce because of its interest in developing stronger aluminum aircraft parts by using silica fiber reinforcement. Figures 4 and 5 show the very significant temperature and 

 

 

 

time dependence of the tensile strength of silica fibers. These figures are of great significance and are critical to the understanding of silica and silicate fiber strength. They essentially show the effect of water vapor on the ‘‘instanta-neous’’ strength of a silica fiber. Two things should be noticed.

The large increase in strength as the temperature is lowered below room temperature, and the time dependence of the strength at room temperature are both manifestations of ‘‘fatigue’’ or delayed failure.

 

 

 

This is discussed in detail later. Here, we simply state that by testing under conditions in which the effects of moisture are eliminated (e.g., in a vacuum or at low temperature), there is no time dependence of strength; this is then termed the ‘‘inert’’ strength. Figure 3, from Duncan et al. shows the inert failure strain measured at 77\(\text K\) in two-point bending for fibers of silica and a sodium borosilicate glass (mentioned earlier).

These latter data are shown to illustrate two important points. First, these data are plotted on a Weibull probability scale, as described later. The high value of the slope of the lines indicates that the strength distribution is very narrow.

Second, many investigations of light-guide glass compositions, silicates, and the other glass types we discuss have employed the two-point bending technique for the study of the strength of these fibers. This technique has been described by a number of workers and has often been used in the study of light-guide fibers because of its ease and adaptability to many temperatures and environments.

However, this measurement method gives failure strain rather than failure stress/strength. It is known that the Young modulus \(\text{(E)}\) of silica and other silicate glasses are rather substantial functions of strain. While little is known about the details of this nonlinear behavior, it is known that silica is anomalous in this regard. Its Young modulus increases with strain to at least approximately 10% strain, whereupon it decreases in a more normal way. In the evaluation of strength from failure strain at room temperature where the strain is less than 5–6%, the following equation is valid: 

\[\tag{2}\sigma=E\varepsilon;\;E=E_0(1+a\varepsilon),\]

where \(E_0\) is the Young modulus in the limit of zero strain (72 \(\text{GPa})\) and a corrects for the strain dependence of modulus. The accepted value of \(a\) for fused silica is 3 for simple tensile stresses.

However, asymmetry in the elastic modulus for tensile and compressive strains leads to a shift in the neutral axis of bent fiber such that the effective value of \(a\) that should be used for converting between bending stress and bending strain is 2.125.

Thus, at room temperature where the initial failure strain in air is about 7%, the corresponding \(\text E\) is 83 \(\text{GPa}\) or about \(15\%\) higher for bending.

While \(E\) at greater strains is not known exactly, it appears that at about 20% strain, the value at 77 \(\text K\), the modulus has essentially returned to its zero-strain value of 70 \(\text{GPa}\) or so.

This can be seen by dividing the 12.5 \(\text{GPa}\) strength measured by Proctor et al. by the failure strain of 18% measured by France et al.  to give \(E_{\varepsilon=18\%}\) approximately 69.4 \(\text{GPa}\).

Another example is that of a standard window or bottle glass composition, so-called soda-lime–silica glass. Ernsberger has found a strength of approximately 7.7 \(\text{GPa}\) at 77 \(\text K\), while Lower has found a failure strain of approximately 17.7%.

Thus, \(E_{\varepsilon =17.7\%}\sim43.5\text{GPa}\) whereas \(E_0\sim72\text{GPa}\). Very little is known about the strain dependence of E for other common silicate glasses.

In the preceding examples, we have shown data for strengths when there is no fatigue. In these cases, we have also chosen data for glasses that by our criterion are flaw free.

Thus, these strengths are inert, because they are free from atmospheric corrosion effects. Also, because they are flaw free, these strengths are considered intrinsic, that is, they are representative of the material and are not affected by the presence of flaws.

A paper by one of the present authors has been concerned with a description and definition of intrinsic inert strength. It is suggested that the following criteria are necessary for intrinsic strength:

The strength should be high with an essentially infinite Weibull modulus (i.e., the strength is single-valued), and therefore, there will be no size dependence of this strength (either fiber length or diameter). Results from Duncan et al. show the room temperature and 77 \(\text K\) failure strains for silica, as well as for a borosilicate glass that had early been the subject of much study as a glass for possible light-guide use (Fig. 3). As can be seen, these failure strains are high and basically single valued.

In addition, these measurements were made at 77 \(\text K\). This has the effect of eliminating the effect of water in the ambient, so there is no delayed failure/fatigue. These measurements are thus ‘‘inert.’’

 

Flaws

As mentioned earlier, if there are no flaws, the strength is intrinsic. In practice there will be flaws of varying types, sizes, severity, distribution in length, and so on, as discussed later in the section on Weibull analysis.

Flaws may be the result of scratching, adherence of solid foreign particles, or a change in the geometry of the fiber surface (see later discussion on aging). Reduction in strength may not be the result of a stress enhancement per se, but simply the result of a residual stress, perhaps because of a change in composition of the glass because of an impurity or an indentation too small to produce a crack.

In the case of a residual compressive stress, it will simply be added to the applied stress in calculating failure stress. 

In most cases, flaws produced as described earlier will initially have a sharp tip and the strength reduction resulting from this is one of the following:

Sharp flaws:

\[\tag{3}\sigma=\frac{K_{IC}}{Yc^{1/2}},\]

where \(\sigma\) is the strength, \(K_{IC}\) is the critical stress intensity factor or toughness, and \(Y\) is the crack shape parameter (normally taken to be \(\sim1.24)\), and \(c\) is the crack length. 

Blunt flaws: 

In the preceding discussion, we have been concerned with cracks that have sharp tips and can thus be described by Eq. (3). In a later section, we deal with flaws that have a rounded tip. In this case, assuming an elliptically shaped flaw:

\[\tag{4}\sigma_a=\frac{\sigma_u}{1+2(c/b)},\]

where \(\sigma_u\) is the ultimate strength (i.e., the intrinsic strength of the material), \(\sigma_a\) is the applied stress, and the denominator represents the stress concentration factor at the ‘‘crack’’ tip, where \(c\) is the major and \(b\) the minor axis of the elliptical flaw. Such macroscopically blunt flaws were studied by Inniss et al. and are described in a later section on aging. 

 

Effect of Fiber Diameter

In spite of experimental studies showing no such effect, there is often still the perception that the strength of glass fibers increases as the diameter decreases in fiber diameter. This is primarily due to the classic paper of \(A.A.\) Griffith in 1920.

In this work, he showed that the strength of a common soda-lime silicate glass \(\text{(SLS)}\) was a strong function of the fiber diameter. While this idea persisted for some time and is often still believed today, this effect was shown to be false by Otto in 1955 for a similar glass, \(\text E\)-glass, and perhaps more completely and convincingly by Cameron in 1960.

For these \(\text{MCGs}\), it would appear that fibers must be drawn above \(T_l\), its liquidus temperature (the temperature at which the last crystal melts), in order for a high strength single-mode distribution to be obtained.

When drawn at lower temperatures, which would normally be the case when drawing thicker fibers, a lower strength mode appears. Thus, the mean or average strength of this fiber diameter will be lower than is expected for that diameter. Cameron showed clearly that the high strength mode was independent of diameter for these \(\text E\)-glass fibers. 

While this diameter independence has not been demonstrated unequivocally in silica, the outstanding evidence is such as to be convincing. First, the essential constancy of the strength results on silica over the years, apparently independent of drawing conditions, show closely similar results. The work of Proctor et al. shown in Figs. 4 and 5 was carried out on fibers of 20- to 80-\(\mu m\) diameter and they indicate no effect of diameter on strength.

Most high-quality studies of the strength of silica for light guides have been made on 125-\(\mu m\) diameter fibers and have shown essentially the value found by Kurkjian and Paek, namely approximately 5.5 \(\text{GPa}\) at room temperature, which is very similar to the value found by Proctor et al. at room temperature. There have been few other studies of the tensile strength of silica glass at 77 \(\text K\).

However, Smith and Michalske measured 35-\(\mu m\) silica fibers in tension at \(\text{UHV}\) \((<6.6\times10^{-6}\text{Pa})\) at room temperature and found strengths approximately 11–14 \(\text{GPa}\).

Because it may be assumed that measurements at this high vacuum condition would be essentially inert, as were those of Proctor et al. at 77 \(^\circ\text K\), this agreement is expected.

It is also interesting to note that Griffith himself showed that the strengths of silica rods of 2-mm diameter were about 7 \(\text{GPa}\) at room temperature. While this was a crude bending measurement, it was firm enough and to Griffith, essentially unexplainable, so that he exempted it from his consideration of the diameter effect.

The interest in nano materials has just produced some interesting results in this regard. The group of Mazur at Harvard has been studying the optical guiding behavior of silica fibers of diameters less than the wavelength of light (see this tutorial Silica Nanofibers and Subwavelength-Diameter Fibers for more details).

They have made initial efforts to measure the strength of these fibers in both tension and two-point bending. While the diameter control is very good (better than 0.1%) due to the clever ‘‘selfmodulating’’ technique used to draw these ‘‘nanowires,’’ both of these testing techniques are difficult with fibers of this size, so the scatter in the data is quite large (Weibull modulus \(\sim 5)\).

While their data seem to show a dependence of strength on diameter, within the statistics, there is no significant dependence and the mean value of the combined results of tension and bending is approximately 5 \(\text{GPa}\), not too different for that normally found for 125-\(\mu m\) light-guide fibers. Additional work on these fibers would appear to be warranted.

All of these data are in Fig. 6, together with results for optical fiber with diameters up to 1 \(\text{mm}\). We will consider there to be no effect of fiber diameter on strength.

 

 

 

Effect of Ambient Chemistry 

Later in this tutorial, we discuss in detail the effects of ambient chemistry on the time dependence of strength. Here we simply show how changes in two important environmental parameters affect the short time strength (i.e., the strength recorded in seconds at room temperature). Figure 7 shows the effect of ambient relative humidity, while Fig. 8 shows the effect of the \(\text{pH}\) of the solution in which the measurements were made. 

In the section on intrinsic strength, we showed the effect of water on the strength of silica fibers. In Fig. 7, we show in detail the effect of changes in water concentration or activity (relative humidity) on the strength measured on a time scale of approximately 10 seconds.

As shown earlier, during the time of measurement, the strength has actually decreased from its inert value of approximately 14 \(\text{GPa}\) (or \(\sim\)20% strain) to a value of the order of 5 \(\text{GPa}\). As the relative humidity is increased, the strength decreases continuously, from about 6 to 5 \(\text{GPa}\).

The behavior illustrated in Fig. 7 deals with the effect of relative humidity. In the case of aqueous solutions, there is also an effect of the \(\text{pH}\) of the solution and this is shown in Fig. 8. In aqueous environments, reaction with hydroxyl ion is rapid compared to reaction with molecular water, explaining the sensitivity to \(\text{pH}\).

 

Tension

Light-guide fibers that are manufactured today show very high and very consistent tensile strengths. Figure 9 shows a Weibull probability plot 

 

 

 

 

 

 

 

of the tensile strength of light-guide fibers tested in tension for a 20-m gage length representing the improvements in strength over the years. For simple uniaxial tension, 

\[\tag{5}\sigma=\frac{L}{\pi r^2},\] 

where \(\sigma\) is the tensile strength, \(\text L\) is the applied axial load, and \(\text r\) is the fiber radius. Therefore, in tension, the stress for a given load is higher when the fiber has a smaller diameter. Table 2 shows what axial loads are required to generate a range of values of stress for several fiber diameters in the range of practical interest. 

In Fig. 9, it can be seen that the curve is bimodal. It has been shown that the very narrow high-strength mode is the ‘‘intrinsic’’ strength of the fiber under the test conditions. That is, the lengths of fibers showing this high uniform strength are flaw free. If such breaking is accomplished in the absence of water (say in vacuum or at 77 \(\text K\)), the strength of such flaw-free fibers is approximately 14 \(\text{GPa}\).

Under normal ambient conditions, the measured strength is time dependent and is approximately 5.5 \(\text{GPa}\) at room temperature and tested in 10 seconds (Fig. 9). There should be no slope to this curve.

However, while very high values of the Weibull slope, \(\text m\) (which correspond to a narrow distribution, see later discussion), can be measured in short lengths, many experimental factors contribute to the more moderate value of \(\text m\) \(\sim 50\). The lower strength broader distribution reflects a variety of ‘‘manufacturing’’ defects or flaws. These flaws act to reduce the strength of the fiber by acting as stress-concentrators according to Eq. (3). 

The exact nature of the failure probability–strength curve obviously depends on a number of factors but is represented reasonably by the lowest curve in Fig. 9 for good current manufacturing practices. As is seen later, this probability curve depends on the gage length tested.

Table 2.  Axial loads (for tensile loading) and bending radii (for flexural loading) that result in a given stress for fiber diameters of 125 and 80 \(\mu m\)

 

Weibull Statistics 

As we have discussed, the strength of brittle materials is controlled by the presence of stress concentrating defects. Such defects are distributed in size/ severity, nature, position, and orientation. As a result, the average measured strength of a set of specimens depends on the specimen size because larger specimens are more likely to contain larger defects and so are expected to be weaker on average. Weibull’s weakest link theory for brittle fracture assumes that failure is caused by the most severe defect and provides the following result for how the cumulative probability of failure by an applied stress \(\sigma\), \(\text{F}(\sigma)\), is related to \(\sigma\) and the length of the fiber, \(\text L\), 

\[\tag{6}F(\sigma)=1-\text{exp}[-Lf(\sigma)]\]

or

\[\tag{7}1\text n\;1\text n\frac{1}{1-F}=1\text n\;\text L+1\text nf(\sigma)\]

where \(f(\sigma)\) is a monotonically increasing function of \(\sigma\).\(f(\sigma)\) is not known a priori, but an empirical power law is ubiquitously assumed, which corresponds to the Weibull distribution:

\[\tag{8}f(\sigma)=(\sigma/\sigma_0)^m,\]

where \(\text m\) is the Weibull shape parameter (an inverse measure of distribution width) and \(\sigma_0\) is the Weibull scale parameter, which is a measure of centrality of the strength distribution. This results in the well-known Weibull distribution. Equation (7) then becomes

\[\tag{9}1\text n\;1\text n\left(\frac{1}{1-F}\right)=1\text n\;L+m\;1\text n\;\sigma-m\;1\text n\;\sigma_0.\]

Considering the failure of specimens with two lengths, \(\text L_1\) and \(\text L_2\), the applied stresses that give the same probability of failure, \(\sigma_1\) and \(\sigma_2\), are related by

\[\tag{10}1\text n\frac{\sigma_1}{\sigma_2}=\frac{1}{m}1\text n\frac{L_2}{L_1}.\]

Equation (10) is valid for any value of \(\text F\), so it is valid for the mean strength, median strength, or indeed any other percentile. Therefore, as expected, longer specimens are weaker than short ones.

This formalism shows how the strength depends on specimen length.

However, it results in \(\sigma_0\) having the strange units of [stress]\(\times\)[length]\(^{1/m}\). \(\sigma_0\) can be given the expected units of stress in several ways, but the simplest is to drop the length dependence in Eq. (9) to give

\[\tag{11}1\text n\;1\text n\left(\frac{1}{1-F}\right)=m\;1\text n\;\sigma-m\;1\text n\;\sigma_0.\]

For a given set of specimens, the length dependence of strength is ignored and the strength data are interpreted in terms of Eq. (11); when other specimen lengths are considered, Eq. (10) is used. Equation (11) may be visualized using a ‘‘Weibull plot,’’ which is a graph of \(1\text n 1\text n\) \([1/(1/F)]\) versus \(1\text n\sigma\), which, if the strength data are described by a Weibull distribution, is a straight line of slope \(\text m\) and intercept on the horizontal \(1\text n\sigma\) axis of \(1\text n\sigma_0\). \(\sigma_0\) is the 63rd percentile.

If the strengths are measured of specimens of length \(\text L_1\), then the expected strengths for specimens of length \(\text L_2\) can be calculated using Eq. (10). Graphically, Eq. (10) represents a sideways shift on the Weibull plot by an amount \(1\text n(L_2/L_1)/\text m\) or equivalently a vertical shift along the probability axis of \(1\text n(L_2/L_1)\).

An example of a Weibull plot is shown in Fig.10. The right-hand axis is linear in \(1\text n\;1\text n\) \([1/(1-\text F)]\), while the left-hand axis is the actual failure probability and is nonlinear. The shift in the strengths with test length in Fig.10 is illustrated in Fig.11 where the mean strength is shown schematically as a function of gage/test length.

 

 

 

 

 

 

Fatigue

We have noted that many glasses are weaker when measured in ambient conditions compared to measurements in ‘‘inert’’ environments, such as liquid nitrogen (77 \(\text K)\). The phenomenon causing this effect is termed fatigue. Most inorganic glasses show a time-dependent strength or delayed failure. This effect is apparent either on testing dynamically, when the measured strength is lower for slower stressing rates, or statically by applying a fixed load (stress), which eventually leads to failure, with the time to failure decreasing with increasing stress.

At least in oxide glasses, the mechanism is the combined effect of stress and the hydrolysis of strained siloxane bonds at the ‘‘crack’’ tip by ambient moisture: 

\[\tag{13}\equiv \text{Si}-\text O-\text{Si}\equiv+\text H_2\text O\rightarrow\equiv\text{Si}-\text O-\text H+\text H-\text O-\text{Si}\equiv.\]

In nonoxide glasses, the mechanism is often not completely determined. Figure 12 shows results of fatigue measurements over a rather extended time range. This is the result of the combination of a number of studies using various techniques. The combined results form a single curve.

 

 

 

A rough rule of thumb is that the long time strength is approximately one-third of the short time strength. A more complete analysis of a given fiber/device is, of course, ultimately required. 

As indicated earlier, it is believed that the very strong short sections of light-guide fiber are flaw free. In spite of this, the generally applied model for fiber fatigue involves the slow propagation of cracks in the sample:

\[\tag{14}V=AK^\text n_I,\]

where \(\text V\) is the crack growth velocity, \(\text K_{\text I}\) is the stress intensity factor, and A and n are empirical fit parameters. This equation appears to be appropriate whether the high or low strength behavior is considered. n is the stress corrosion susceptibility parameter.

A higher value provides greater fiber reliability. It has been shown that because of the very severe dependence of the velocity on stress, it is difficult to tell whether the empirical power law or a physically more meaningful exponential form are more appropriate and thus the simpler power law is commonly used, primarily because of its mathematical convenience.

The power law does, however, provide more optimistic predictions of reliability than exponential models. 

Service conditions are usually assumed to have constant applied stress and under such ‘‘static fatigue’’ conditions the time to failure, \(t_f\) , is given by

\[\tag{15}t_f=\frac{2}{(n-2)AY^2}\left(\frac{\sigma_i}{\text K_{IC}}\right)^{n-2}\frac{1}{\sigma^n}=B\frac{\sigma^{n-2}_i}{\sigma^n},\]

Where

\[\tag{16}B=\frac{2}{AY^2(n-2)}\frac{1}{K^{n-2}_{IC}},\]

and where s is the service stress and si is the inert strength (i.e., the strength that would be measured when no fatigue occurs). This is effectively the strength of the fiber at 77 \(\text{K}\). This is rarely known, but for silica it is approximately twice the strength measured at room temperature in times of the order of seconds (i.e., the normally measured strength). Equation (15) shows how the failure times for two different applied stresses are related: 

\[\tag{17}(t_f\sigma^n)_1=(t_f\sigma^n)_2.\] 

For both high and low strength silica fibers, it is assumed with reasonable justification, that \(n\approx20\).

For strength measurement using a constant stress rate, \(\sigma\), the failure stress, \(\sigma_f\), is given by

\[\tag{18}\sigma^{n+1}_{f,\dot{\sigma}}=\frac{2(n+1)\dot{\sigma}}{AY^2(n-2)}\left(\frac{\sigma_i}{K_{IC}}\right)^{n-2}=(n+1)B\dot{\sigma}\sigma^{n-2}_i.\]

Laboratory testing that has been accelerated by using aggressive environments (high temperature, high water activity) has shown an additional strength reduction mechanism in addition to fatigue.

This ‘‘aging’’ phenomenon must be considered because of its potential negative impact on reliability. 

 

Aging

In the study of the strength and reliability of silica light guides, testing is often carried out under extreme conditions to accelerate the degradation and, thus, hopefully allow prediction out to longer times/lifetimes. When this was done early in the study of silica light-guide fibers, an effect that had not really been known earlier was discovered in both aging and fatigue.

If fiber is held for some time under no stress and subsequently strength tested, it is found that depending on the condition of holding, or aging, the strength may have degraded. This is now known as zero stress aging, or more simply aging. Figure 24.13 shows results of a rather long duration aging test of a polymer-coated silica fiber aged in distilled water at \(25^\circ\text C\) and a shorter time test in \(100^\circ\text C\) water.

As can be seen, for some prolonged period, no strength degradation occurs, but eventually rather precipitous strength degradation occurs. This effect has been shown to be present in fatigue as well and the time scale depends on the state of the water (Fig.14). The important fact to be learned from Fig. 13 is that the activation energy for the process responsible for this strength degradation is approximately 80 \(\text{kJ/mol}\), the activation energy for the reaction of silica with water. 

The model that has been used to describe this aging effect involves surface roughening. As we have discussed, glasses are essentially supercooled liquid glasses and, as such, contain both chemical and structural fluctuations. These fluctuations have different thermochemical properties, including water solubility and dissolution rate.

These differences lead to roughening of the glass surface as shown in the atomic force microscopy \(\text{(AFM)}\) images in Fig. 15 when the surface is exposed to an aggressive environment. This effect was studied in greater detail using a model system by \(\text{I}\)nniss et al.

A more pronounced effect was shown in the borosilicates studied by France et al. and is shown in Fig.16. In this case, not only are these glasses less durable, but they show composition fluctuations that will contribute to the unequal solution rate effects. Such fluctuations have been shown in optical scattering studies.

The preceding discussion relates to the aging behavior of the pristine fiber strength, rather than the behavior of the occasional defects. Evidence suggests that aging weak defects in aggressive environments can lead to strength recovery

 

 

in much the same way as etching in hydrofluoric acid (a discussion of which is presented later). However, strength loss of the strong sections of fiber might be more important because the fiber might become too weak to handle along its entire length. 

 

Nonsilicate Glasses

The measurement of the strength, fatigue, and aging of nonsilicate glasses has not been very extensive. The measurements have often been made in two-point bending and, therefore, usually not for long lengths of fiber. While this is valuable for the assessment of the measured strength relative to the theoretical strength, these are not necessarily practical or useful strengths. In this section, we discuss all of these properties in nonsilicate glasses. 

 

Heavy-Metal Fluoride Glasses

The mechanical properties of \(\text{HMF}\) glasses are quite sensitive to the presence of liquid water, but not as sensitive to water vapor. The highest strengths for HMF glass fibers whose surface had been etched are approximately 1.4 \(\text{GPa}\); because the measurement was made in bending, the calculation of the failure stress depends on knowledge of the Young modulus. Carter found 

 

 

 

similar values and attributed the less than theoretical strength to the presence of bubbles and crystals. Her results (Fig. 17) illustrate the differences that may be seen in testing different fiber lengths.

Perhaps the most detailed study on fatigue and aging in \(\text{HMF}\) glasses is that of Colaizzi and Matthewson who characterized glasses whose compositions included \(\text{AlF}_3\) (Fig.18).

 

 

 

Chalcogenide Glasses 

Studies of the two-point bend strength of arsenic sulfide glass fibers as seen in Table 1 show the apparent approach to that theoretically expected strength, namely 1.5–2.5 \(\text{GPa}\). Devyatkh et al. published a value for strength under ambient conditions of approximately 1.2 \(\text{GPa}\). Sanghera (Fig.19), measured about a half of that value (0.570 \(\text{GPa}\)) at room temperature, but a value of 0.854 \(\text{GPa}\) at 77 \(\text K\) (i.e., \(\sim1.5\) times greater than the room temperature strength).

Applying this ratio to the data of Devyatkh et al. would give an ‘‘inert’’ strength of approximately 2.4 \(\text{GPa}\) or \(E/\sigma\sim6\) for their fibers. In fact these data are presented as strength, although the measured values are actually failure strain. In the case of Devyatkh et al., estimated strengths at 77 \(\text{K}\) amount to a failure strain of approximately \(16\%\), very nearly that found for silica. 

While the situation with respect to the fatigue and aging of silica and silicabased glasses is clearly due to the presence of water, the situation for chalcogen-ide glasses is not as clear; there is no clear-cut experimental evidence for the critical chemistry. Dianov et al. give values of \(n\sim10\)–20, but the scatter in the data (Weibull modulus, \(m\sim10)\) leaves this in doubt.

The data of Sanghera (Fig.19) are interesting in this regard. Here, we see that the ratio of strengths at 77 \(\text K\) and room temperature is approximately 1.5, while the ratio of room temperature to metal-coated strength is approximately 5. One possibility we may suggest here is that the fatigue is due to the interaction of the glass with oxygen rather than water.

 

 

 

Photonic Crystal or ‘‘Holey Fibers’’ 

The only set of experimental results on photonic crystal \(\text{(PC)}\) fibers is that of Zhou et al. These workers have found that the two \(\text{PC}\) fibers they have studied, with respectively 90 and 6 holes, show breaking loads effectively 10 and 20% higher than that found for standard single mode fused silica clad fibers. When account is taken of the differences in cross-sectional area (3% and 0.4%, respectively), the strengths are 4.45, 5.0, and 5.4 \(\text{GPa}\), respectively, for the standard single-mode fiber, 90-hole fiber, and 6-hole fibers.

However, the experiments were not well controlled in that the three fibers had different polymer coatings, so the difference in strengths might not be significant.

 

 

 

 

 

Further, because the flaws causing failure are substantially smaller than the holes or the distance between the holes, the presence of the holes is not expected to have any effect on strength. 

 

 

4.  COATINGS

General Comments and Polymer Coatings 

Very early in the development of the light-guide technology, it was clear that the pristine surface of the as-drawn fibers would have to be protected from mechanical damage by applying a thin polymer coating to isolate the fiber surface from any hard sharp particles in the environment.

As their development progressed, dual coatings were developed; the inner compliant coating reduced the microbending losses, while the harder more abrasion resistant outer secondary coating made the assembly more robust.

Contrary to much early literature, polymer coatings were found to be quite permeable to water. It was found that penetration through typical coatings, which are approximately \(60\mu m\) thick is accomplished in times of the order of 1 hour or less.

Therefore, one must still expect strength degradation from both fatigue and aging. The details of the coating chemistry are apparently of importance to the aging behavior of the fiber and perhaps less so to the fatigue behavior, but no detailed explanation has yet been given. 

 

Metal Coatings

As indicated earlier, the polymer coatings that have been applied to light-guide fibers have been shown to be quite permeable to water, so once steady state has been attained, the fatigue and aging behavior of coated and bare fibers are similar.

It is natural, therefore, that a fair amount of early work was done on coatings that were hermetic (i.e., those that would isolate the fiber surface from water). Figure 20 shows that the use of a metal coating can result in a strength that is similar to that obtained at 77 \(\text K\), that is, the inert strength.

The results in Fig.20 are given as failure strength and should probably be corrected because they were taken in two-point bending and Eq. (2) was used to calculate failure stress with \(a=3\) instead of the value of \(a=2.125) appropriate for bending. However, Eq. (2) has only been verified for strains up to approximately 6% and is incorrect for the failure strains seen in Fig. 20. 

 

Inorganic Coatings

Many inorganic coatings have been tried, but the best has been found to be carbon, even though the behavior is complicated and variable. Figure 21 illustrates the effect of draw speed on the strength and fatigue parameter, \(\text n\). This is an effect connected primarily to the thickness of the coating.

However, it is known that the coating ‘‘composition,’’ thickness, and roughness influence the strength, fatigue (water permeability), and hydrogen permeability.

 

 

 

 

 

 

5.  HANDLING AND POST-DRAW PROCESSING 

In our earlier discussions, we considered short time fiber strength, long time fiber strength, fatigue and aging, all things that must be considered in the design of the system under consideration if some reasonable assumptions about the strength of the starting fiber are made.

On the other hand, some type of fiber handling and processing are very often required in the fabrication and assembly of any given device.

In this section, we describe some specific operations that may introduce unpredictable damage. By keeping in mind certain factors that can affect the strength of the fiber as a result of such processing, it should be possible to minimize both these strength reductions and reduce unexpected reliability consequences. 

 

Fiber Stripping

All-silica light-guide fibers have a coating (usually a polymer) applied in-line during drawing to protect the glass surface from mechanical damage. Use of fibers in practice very often necessitates the removal of this coating. Three general techniques can be used to accomplish this: mechanical, chemical, or thermal. 

While stripping in the field most commonly uses a tool similar to diagonal cutting wire strippers where the stripping hole is somewhat larger than the fiber diameter, this will inevitably lead to a strength reduction due to the sort of mechanical damage illustrated in Fig. 22.

While the strength reduction can be considerable in some cases, in general, there are still substantial lengths that have been left undamaged. Knowing this, it is possible to employ the very simple and quick mechanical stripping technique in conjunction with a proof-testing procedure to guarantee a desired strength. 

Other techniques have been employed that remove the coating with less surface damage and, therefore, with less strength reduction. The technique that has been found to produce the cleanest surface with no damage due to the process itself is chemical stripping using hot \((\sim200^\circ\text C)\) concentrated sulfuric acid. This process effectively removes most polymer coatings in a few seconds, producing a ‘‘clean’’ surface. It has been shown that by careful handling and stripping in this way, no strength reduction is observed.

In certain cases, soaking in acetone or methylene chloride may be used. These chemicals cause swelling of the coating, which may then be stripped off with no strength reduction.

There are also a number of thermal strippers available on the market, which can produce quite acceptable stripped fiber strengths.

 

 

Park et al.described an interesting and quite different approach. Their stripping technique makes use of the fact that the primary and secondary polymer coatings on dual-coated fiber have distinctly different properties.

By rapid local heating, the compliant primary coating will rapidly expand and effectively ‘‘explode’’ the more brittle primary coating with a resultant rather small decrease in fiber strength. 

 

Fiber Cleaving 

As discussed earlier, in the fracture of inorganic glasses, we are dealing with failure in a brittle manner. This results in a fracture surface that is generated by the propagation of a crack perpendicular to the axis of the applied stress.

If the applied stress is appropriate and the crack is of the right size and orientation, the crack will propagate such that a smooth ‘‘mirror’’ fracture surface is generated perpendicular to the fiber axis.

The details of this process are given in the section on fractography. Here, we simply illustrate the type of fracture surfaces that can be developed. Figure 23 shows micrographs of fracture surfaces.

In each case, the fracture was generated by a scratch at the bottom surface (i.e., the 6 o’clock position).

 

 

Figure 23a–f shows the fracture surface for increasingly large scratches, and consequently the fracture stress, as indicted by each micrograph, becomes less. It is seen that the smooth region/mirror becomes larger as the strength decreases. The objective of a good cleave is to have this mirror be the size of the entire fiber so that good mating is achieved.

The details of fractography are described later. Care must be taken that a simple cut is made and that there is not extensive damage to the fiber surface.

 

Splicing 

The joining of two sections of optical fiber can be done either mechanically or by fusion splicing. In mechanical splicing, the ends of the two fibers are joined by gluing them inside a sleeve or ferrule. While this technique is simple and rapid, it is bulky and not particularly robust.

For high-quality, high reliability work, especially for undersea use, fusion splicing is often employed. Figure 24 illustrates some very early splicing work. This shows the importance of avoiding damaging the fiber during stripping or subsequent handling. In the case of both splicing and tapering, some portion of the fiber is re-heated.

In the center region of either a splice or a taper, the fiber is completely melted and, thus, when cooled will be expected to have original perfect fiber strength. At intermediate positions along the fiber, the maximum temperature will be intermediate between the melting temperature and room temperature.

In some of these regions, the strength degradation due to the interaction of the fiber surface with water in the atmosphere will be rapid enough to cause strength degradation during the processing time.

 

 

Figure 25 shows later work by Krause. Here, it is shown that by careful stripping and by adhering to appropriately ‘‘clean’’ conditions, splices showing very little strength degradation can be obtained, while if in addition to ‘‘clean’’ conditions, the conditions are also ‘‘dry’’ (accomplished by the use of a \(\text H_2/\text{Cl}_2\) torch), essentially no strength degradation is suffered. While this is often not feasible in practice, strengths approaching those obtained under these ideal condition can be achieved. 

 

 

 

It should be kept in mind that the temperature gradient, which necessarily accompanies any such heating of a portion of the fiber, such as in tapering or thermal lensing, may lead to substantial strength degradation by the interaction of the hot surface with moisture described earlier. 

 

Polishing

Grinding and polishing of the ends of fibers involves many complicated and poorly understood processes. In the grinding process, sharp hard particles scratch the glass surface resulting in gouges and cracks. Some of these cracks cause chipping of the surface and thus removal of some of the glass. Grinding is used to rapidly approach the final desired size and shape.

The final shape and surface quality are produced by polishing. Polishing is similar to grinding except that much finer abrasive particles are used.

In each of these processes, a series of decreasing abrasive particle sizes is employed so that the damage created in one step is removed in the next step. It is important that the abrasive used in one step be removed before the next step.

Polishing has been shown to be a combination of mechanical and chemical processes, so the appropriate choice of both polishing material and size is important. 

 

Soldering/Pigtails

Fibers often need to be soldered into packages, many times to achieve hermeticity or to precisely maintain dimensional stability. It would seem that the use of the very strong melt-coated fibers described earlier would be the first choice. While this is sometimes the case, in most cases, more or less standard metallization processing is used using—for instance—reactive metals such as \(\text{Ti}\) or \(\text{Cr}\), which are evaporated or sputtered onto the glass surface and covered with a solderable and oxidation-resistant final layer.

While this process provides good adherence of metal to glass, the resulting assembly is usually rather weak, presumably due to the strength reduction accompanying the sputtering of the \(\text{Ti}\) or \(\text{Cr}\) layer. Little detailed work has been published regarding the mechanism of strength reduction is such systems; it would seem reasonable to attribute the weakening to the reaction of the sputtered metal with the perfect glass surface. In the case of a silica fiber coated with aluminum by the melt process, high fiber strength, good adherence of metal to glass, and good joint pull strength have been achieved (Fig. 26).

While not completely understood, although there is apparently interaction between the silica surface and the aluminum coating, the strength is recovered upon chemically stripping the aluminum. 

 

 

 

Recovery of Handling Damage: Etching 

The use of hydrofluoric acid \(\text{(HF)}\) for the etching of glass surfaces has been practiced commercially for many years. Proctor et al. found that etching of damaged commercial soda-lime–silica glass rods resulted in substantial recovery of strength.

In the case of silica rods, the recovery was not nearly as great; the maximum room temperature strength recorded was approximately 2.5 \(\text{GPa}\). Vitman et al. partially recovered strength of an abraded fiber. Miyama et al. etched silica light-guide splices and were able to increase the mean fiber strength from 0.8 \(\text{GPa}\) to approximately 2 \(\text{GPa}\).

Kurkjian et al. showed that etching of high-strength silica light-guide fibers resulted in a decrease in normal room temperature two-point bending strength from 5.5 \(\text{GPa}\) to a steady-state plateau value of approximately 3.5 \(\text{GPa}\) (Fig.27). It was suggested that the smooth perfect fiber becomes roughened by the acid etch and that the roughness acts as stress concentrators as described earlier in the section on aging.

Thus, although additional work is needed, we suggest that by appropriate etching of fibers damaged by handling abrasion or other mechanisms, strength increases to at least 3.5 \(\text{GPa}\) should be possible. Of particular practical importance, Kurkjian et al. found that the weakening of the perfect fiber was accomplished both with bare fibers and with coated fibers.

Thus, it would be expected that strengthening could also be accomplished by etching through the coating, which has been found.

 

 

 

 

6.  FRACTOGRAPHY 

A very useful practical tool is fractography. This is the microscopic study of fracture surfaces. Such studies can give valuable information about the stress level at which a fiber failed, the distribution of failure stress (tension/bending/ torsion), and can give an indication of the reason for failure. Figure 23 illustrates the features that may be seen on a typical fracture surface.

At the early stages of propagation, a crack will grow slowly and during this time will produce fracture surface that is quite smooth; this region is the ‘‘mirror.’’

The crack continuously increases in velocity, gradually approaching its limiting velocity (approximately one-third the longitudinal sound velocity) at which point the excess energy begins to be taken up by the creation of extra fracture surface; the surface roughens (the ‘‘mist’’ region) and at higher speeds produces steps in the surface (the ‘‘hackle’’ region). 

It has been empirically found that the radius of the mirror region, \(r_m\), is directly related to the stress at failure, \(\sigma\), by 

\[\tag{19}\sigma=\frac{A}{r^{1/2}_\text m},\]

where A, the mirror constant, is a parameter found empirically. It has been found that for all glasses considered here, the ratio of the mirror radius, \(r_m\) and the original flaw size, \(c\), is approximately 0.1. From Eq. (19), it can be seen that A has the units of stress intensity and is essentially proportional to KIC. If \(c\sim r_m/10\), then, \(\text K_{IC}\sim0.4\text A\). 

 

 

7.  PROOF-TESTING AND RELIABILITY 

As we have discussed earlier, the majority of the length of fiber has an extremely high strength, but occasional weak defects are encountered, which are introduced during manufacturer. These weak defects control the practical reliability of fiber that is of useful length (i.e., more than a few millimeters). Review of Eq. (9) for the Weibull strength distribution shows that even for very low applied stress, \(\sigma\), there is a small but finite probability of failure, \(\text F\).

Mechanical reliability can only be completely ensured if the applied stress is actually zero, which cannot be achieved in practice, especially for applications in which the fiber is bent.

The situation is greatly improved by ‘‘proof-testing’’— which involves applying a short pulse of stress to the entire fiber length—the weakest defects will fail under the proof stress and so are eliminated. If the fiber breaks, it can be discarded or spliced (followed by proof-testing of the splice, of course).

The resulting lengths of fiber will have a certain minimum assured strength after proof testing. Choice of the proof stress is a compromise: A high proof stress gives fiber with a high ensured strength but increases the frequency of proof failures and hence decreases yield. Lowering the proof stress improves yield but reduces the minimum strength. For silica fiber in telecommunications applications, the proof stress is typically 700 \(\text{MPa}\) (100 \(\text{kpsi}\)). 

Proof-testing of long lengths of fiber is normally performed using a continuous tester in which the fiber is fed around a pair of pulleys that apply a given tensile load to the section of fiber between them. While useful for long lengths of fiber, this technique is not suitable for short lengths.

In that case, the fiber is usually proof-tested by passing it through a series of rollers that bend the fiber in several directions so the entire surface of the fiber experiences a stress close to the maximum bending stress.

While the idea of proof-testing is simple, in practice it is complicated by fatigue. Firstly, proof-testing is conducted in ambient environment, so the surviving fiber has lost some strength during proof cycle.

This is a minor effect, and because the weakest fiber is removed, the average strength of the surviving fiber is increased by proof-testing. Secondly, proof-testing ensures a minimum strength, which is the strength immediately after proofing (i.e., the minimum inert strength, \(\sigma_i\), is the proof stress, \(\sigma_P\)).

As a result, if the strength of lengths of proof-tested fiber is measured, fatigue during the measurement means that some of the strengths are actually lower than the proof stress, although this occurrence is rare.

Thirdly, the proof stress cannot be removed instantaneously so that fatigue occurs during the unloading phase. As a result, the minimum ensured strength is a little lower than \(\sigma_P\). Crack growth during unloading is minor and is suppressed by unloading from the proof stress as quickly as possible.

These three effects have been studied in detail and reliability models have been developed.

 

Minimum Strength Design

The most common and conservative approach to reliability modeling is known as the ‘‘minimum strength design.’’ Here, the maximum applied stress is limited to some fraction of the minimum fiber strength, usually taken to be the proof stress. With this approach, one assumes that the length of fiber under stress is no weaker than the proof stress.

This is appropriate in applications in which many kilometers of fiber are stressed or where the fiber has been weakened by handling events where the protective coating has been removed, for example, fusion splicing. For silica-clad optical fiber with a value of the stress corrosion parameter, \(n\sim20\), the allowable applied stress is shown in Fig. 28 for three common stress events.

One is allowed to stress fiber to approximately one-fifth the proof stress for long-term events, one-third the proof stress for installation events lasting hours, and one-half the proof stress for short-term processing stresses.

These guidelines are shown in terms of bend radius in Fig. 29. Assuming the typical proof stress of 700 \(\text{MPa}\), the allowable bend radius for, say, fiber stranded about a central member in a cable is 32 \(\text{mm}\).

The maximum allowable tensile stress during installation of an aerial cable is 230 \(\text{MPa}\) for the same fiber. Pulleys used for guiding fiber during processing should be no greater than 25-\(\text{mm}\) diameter. 

 

Failure Probability Design

In splice enclosures and many photonic device applications, relatively short lengths of fiber are permanently coiled and stored. As shown earlier, the probability of encountering a flaw in a short length of today’s fiber is low.

Thus, a failure probability design methodology is appropriate in these situations. A general rule of thumb is that one can consider a failure probability design for deployed lengths of less than a kilometer. 

Failure probability is incorporated into Eq. (15) through the inert strength, \(\sigma_i\)

\[\tag{20}t_f=B(F\{\sigma_i\}^{n-2}\sigma^{-n}_a.\] 

 

 

 

 

 

The strength distributions, such as those shown in Fig. 9, can be directly substituted into Eq. (20), provided one accounts for the fatigue that naturally occurs when testing in air. When such modeling was being developed, it was recognized that one should account for fatigue during processing events like proof-testing and in-service life.

The Telecommunications Industry Association has captured these developments into a reliability guideline based on the power law crack velocity model. One of the most notable contributions is that of Mitsunaga et al. where field failure probability is estimated from knowledge of the proof-testing conditions and the proof test break rate, \(\text N_P\),

\[\tag{21}F=1-\text{exp}\left(-N_\text PL\frac{\text m}{\text n-2}\frac{\sigma^2_at_s}{\sigma^n_Pt_P}\right),\]

where \(\text L\) is the length of fiber, \(\sigma_a\) is the applied stress in service which is applied for a service life \(t_s\), \(\sigma_P\) is the proof stress which is applied for a time \(t_P\). The Weibull modulus, m, is that of the pre–proof-test strength distribution. This model assumes that the distribution of flaws surviving proof-testing can be estimated from those failing proof-testing.