Optical fibers produced with synthetic fused silica have remarkable strength. Based on the Si-O bond strength, the fiber has a theoretical strength of ~2,000kpsi, which is stronger than steel! In practice the observed strength is considerably lower (typically 700kpsi) due to the presence of small flaws in the bulk and on the surface of the silica. In order to produce a reliable fiber these flaws must be minimized or eliminated. The size of the flaw determines the stress level needed to fracture the fiber, a larger flaw causing a lower strength fiber.

The dynamic strength of an optical fiber refers to the force required for an instantaneous break (as opposed to a delayed failure). Since failure in brittle materials, like glass, is a statistical process, many samples must be measured in order to adequately represent the distribution of flaws (and strength) throughout the fiber. This distribution is commonly presented as a Weibull plot. The Weibull function is represented by:

Where F is the fractional failure probability, m is the Weibull slope, S is the failure stress, S_o is the Weibull characteristic stress (stress at F~0.632), L is the gage length, and L_o is the unit gage length. In a Weibull plot, a near vertical slope (m) with high stress values represents a tight strength distribution and a consistently strong product. This is demonstrated in the presented Weibull plot of Polymicro’s FVP050055065 high -OH fiber type (Figure 2-23). It is a 50mm core, 55mm clad OD with a 65mm OD polyimide buffer coating.

Figure 2-23 Wiebull Plot for 50m Core High -OH Optical Fiber

The mechanical strength of glass optical fibers will also degrade over time. This effect is known as static fatigue or stress corrosion. The mechanism in silica based optical fiber is the propagation of surface flaws due primarily to a combination of stress, moisture, temperature, and time. With a fiber under stress a surface flaw acts as a stress concentrator with the maximum stress being at the tip of the flaw. Water attacks and breaks the silica bonds preferentially at the high stress area at this type. This causes the flaw, and consequently the stress, to increases in magnitude until the fiber catastrophically fails. Temperature, of course, speeds up the reaction.

This mechanism is well described by Charles⁴ and can be represented by:

log(time-to-failure) = n x [log(1 sec failure-stress) – log(failure-stress)] (Eq. 2-19)

Where time to failure is in seconds and failure stress in kpsi. The static fatigue parameter, n, is an important constant that is very dependent on the specific manufacturer’s fiber and the materials used to produce it. In most analyses, the safest failure stress to use is the proof test of the fiber since the fiber has been confirmed to be at least that strong.

Static fatigue results are typically plotted on a log time to failure vs. log stress curve. In this case the fatigue curve will be straight with the slope being equal to n. Values for n range on the low end of ~10 for borosilicates up to >100 for hermetic fibers. Typical n values for polymer coated synthetic fused silica fibers range from 20 to 28.

An effective method to assure fiber strength is to perform a proof test on the fiber. The proof test is used to filter out flaws of a given size or larger. This assures the fiber will meet a minimum strength requirement, typically 100kpsi for most optical fibers. This proof test value can be adjusted higher or lower to meet the strength and lifetime requirements of the application. Proof testing can be performed either by applying either a bend or a tensile force on the fiber. Polymicro proof tests 100% of their optical fibers and capillary to insure strong, high quality product.

Stress on an optical fiber can be generated by tension, bending, or torsion. The calculation of the stress and the proof test method is typically based on either tensile force or bending stress. In tension the stress is simply the force divided by the cross sectional area of the glass. Note that the fiber coatings have Young’s moduli that are typically several orders of magnitude lower than the glass, and therefore do not bear a significant portion of the tensile load. Although the coatings do not add strength, they have the important function of protecting the glass surface from abrasion and chemical damage, which in turn would degrade fiber strength.

Bending stress can be determined through the following equations. These equations are used to determine the bend stress imposed on a fiber during use as well as the wheel radius needed to perform a specific level proof test. If we define the applied stress, s_a, as the strain, e, times Young’s Modulus, E, we can derive the relationship:

Where r is the fiber radius, R is bending radius, and C_th is the coating thickness. Thus, R is given by the following:

Figure 2-24 Bending Stress