Chemical Kinetics Models for the Fatigue Behavior of Fused Silica Optical Fiber

Abstract

There have been numerous studies of the fatigue and strength behavior of fused silica optical fibers. However, no coherent model has emerged that self-consistently describes the simultaneous effects of stress, temperature and activity of the corroding species (e.g. water). A power law degradation kinetics model (relating the crack growth rate to the applied stress intensity factor, K I ) is widely used although various exponential forms based on chemical rate theory have also been proposed. The dependence of fatigue on parameters such as humidity, pH and temperature, has usually been treated in an empirical manner. Sometimes it is even ignoredfor example, the service environment is often assumed to be the same as the proof test environment when making lifetime predictions, thus avoiding the need for understanding the humidity dependence; this assumption is often unjustified. This paper reviews the dependence of fatigue on environmental factors and highlights some of the inconsistencies in published data. It is then attempted to present a coherent kinetics model that simultaneously accounts for stress temperature, humidity, etc. Several possible forms of the model are compared to a range of experimental data of several different types. The comparison is made using fitting techniques that account for correlation between fit parameters. It is found that a simple exponential form of the degradation kinetics model gives the best overall description of the temperature, humidity and pH effects on static and dynamic fatigue. It should be noted that the exponential form predicts shorter lifetimes than the ubiquitous power law model. Therefore, under some circumstances, the predictions of "worst case" models based on power law kinetics are unduly optimistic.

Humidity Dependence of the Fatigue of High‐Strength Fused Silica Optical Fibers

“…A key feature of the fitting program that distinguishes it from earlier work 3 is that the shape of the minimum in the residue is used to estimate the confidence limits for the fit parameters together with their correlation. 21,26 Throughout this work, reasonable values for key parameters were assumed: K IC ϭ 0.75 MPa⅐m 1/2 , Y ϭ 1.16, 27 and i ϭ 12 GPa. 9 The values of the n i are sensibly independent of these parameters; the values of the A i are not independent, but while their magnitudes do depend on the values chosen, the trends observed with humidity do not change.…”

<title>Cyclic fatigue of high-strength optical fibers in bending</title>

“…It is important to know which form is most appropriate since lifetime predictions are sensitive to this form. In particular, the empirical power law predicts longer lifetimes than the exponential forms 13,12 and is therefore not as conservative.…”

Strength-probability-time diagrams using power law and exponential kinetics models for fatigue

“…4). But, this is only the case if it is possible to use the approximations of equations (5) and (10). If any measurement under static or dynamic conditions exposes the fiber to a stress close to the initial/inert strength, i σ , those approximations are invalid and so equation (12) is also invalid.…”

“…All three models can be interpreted in terms of absolute rate theory for the stress corrosion process in which case the n i represent how the activation barrier for the reaction is reduced by stress [9]. The n i are not constants but depend on temperature [10].…”