The Combined Effect of Temperature and Humidity on the Fatigue
Parameters and Reliability of Optical Fiber
Janet L. Mrotek*† and M. John Matthewson‡
Photonic Component Reliability Group, Department of Ceramic & Materials Engineering,
Rutgers University, 607 Taylor Road, Piscataway, NJ, USA 08854-8065
The lifetime of an optical fiber depends on its environment. Previous work extensively measured and characterized the
separate effects of humidity and temperature on the fatigue parameters using three different kinetics models, but the
combined effect has not been determined in detail. In this work, the details of how the fatigue parameters vary with
temperature in a humid environment were investigated. It was found that the kinetics model parameters were different
from values obtained elsewhere in liquid water. This may be the result of differences in the apparent activation energy
for fatigue in liquid and vapor environments.
Keywords: optical fiber reliability, lifetime models, humidity, temperature
Most models currently used for making lifetime predictions of optical fiber do not explicitly incorporate the details of
the service environment.1 Therefore there is an implicit assumption in such predictions that the environments relevant to
the lifetime prediction (i.e. service and proof test environments as well as the environment used to measure the fatigue
parameters) are all the same. In general these environments are not the same but some compensation for this can be
made by using “worst case” fatigue parameters (e.g., as in Ref. 2). However, clearly, if there are significant deviations
between the test and service environments reliability predictions will be erroneous. Specifically, environments more
aggressive (hotter and more humid) than typical laboratory test environments of ~25°C and 50% humidity will lead to
earlier failure while benign environments (e.g. space applications with extremely low water content) will result in much
longer lifetimes than the models predict. It is therefore clearly desirable to have lifetime models that explicitly
incorporate the character of the service environment. For this we need detailed information on how the fatigue
parameters vary with environmental factors such as temperature, humidity and pH; preferably over a broad range of
In earlier work3 the effect of humidity on the fatigue parameters of pristine fiber at 25°C was extensively studied and the
results were interpreted in terms of three kinetics models (the power law and two exponential forms). It was found that
the chemical kinetics model proposed by Wiederhorn and Bolz,4 which assumes that the stress at the crack tip modifies
the activation energy of the chemical reaction via an activation volume, provides the most consistent description of the
effect of humidity. Similar work that examined the effect of temperature in liquid aqueous environments5 did not favor
any one of the three kinetics models but did show that the interpretation of the results in terms of an activation barrier for
fatigue does depend on which form is used. However, a general result was found; the stress dependence of the activation
entropy is the dominant factor and that the activation enthalpy does not alone explain the observed temperature
dependence. The activation entropy increases with applied stress. A generalized chemical kinetics model for fatigue
suggested that the apparent activation parameters are not unique but will depend on the environment to some extent.6
This was later validated by comparing fatigue in pure water and in pH 7 buffered water.7 This therefore means that the
activation parameters will not be the same in liquid water and water vapor.
Up until this point, the effects of humidity and temperature have been studied independently of each other or have only
been studied in terms of their effect on strength rather than on the fatigue parameters. Duncan, France and Craig8
presented strength data which imply that the strength degradation can be solely described by the dew-point temperature,
* Formerly Armstrong; † email@example.com; ‡ firstname.lastname@example.org; 1 732 445-4534; fax 1 732 445-3258;
Reliability of Optical Fiber Components, Devices, Systems, and Networks II,
edited by Hans G. Limberger, M. John Matthewson, Proc. of SPIE Vol. 5465
(SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.582546
thus combining the effects of temperature and humidity into one variable. However, this suggests that strength is
dependent only on the thermodynamics of the equilibrium between the vapor and condensed phases of water and does
not depend on the kinetics of the reaction between water and silica, which is clearly wrong. Armstrong et al.9 examined
this question in detail and found that the dew point temperature was not the controlling parameter - therefore the kinetics
of the reaction between water and silica does indeed play a role.
In the work presented here, we examine the dependence of both the strength and the fatigue parameters on temperature
in water vapor which complements the earlier work of Shiue and Matthewson for liquid water.5,7 Since interpretation of
such results can depend on the mathematical model used to analyze the data, three different models will be used. The
models describe how the crack growth rate, dc/dt, depends on the applied stress intensity factor, KIC
which is designated the “power law”.10
which assumes the activation energy for fatigue is reduced by an amount proportional to applied stress intensity.4
which assumes the activation energy is reduced by an amount proportional to the strain energy release rate, i.e. is
proportional to the square of the stress intensity. This form may be found by simplifying10 a more general form
proposed by Lawn.11
While of different mathematical forms, the three models each involve two parameters which have the same meaning in
each model. The Ai (i = 1…3) are pre-exponential terms which represent the overall crack growth rate and the ni which
represent how sensitive the rate is to the applied stress. If fatigue is treated as a chemical reaction whose activation
energy is modified by the applied stress, then all three models can be incorporated into absolute rate theory to give a
general form for Ai:5,6
where c0 is the increase in crack length per breaking bond at the crack tip, kB is Boltzmann’s constant, T is absolute
temperature, h is Planck’s constant,
is some function of the concentration, C, of the reacting species, R is the gas
are the activation enthalpy and entropy for crack growth in the limit of zero applied stress. The
same theory shows that the ni parameters can be expressed as a linear function of reciprocal temperature:
where bH and bS represent how the activation barrier for the fatigue process is reduced by the effect of stress on the
enthalpy and entropy components of the barrier. In general, the function
depend on temperature (for example the partial pressure of water for a vapor environment or the concentration of
hydroxyl ions in liquid water) so that if an mth order reaction is assumed:
will depend on temperature since C can
then the apparent activation energy for fatigue is given by
∆H is the activation enthalpy for the concentration of the reacting species. This shows that the activation
enthalpy (and for similar reasons the activation entropy) depend on the nature of the environment.
Proc. of SPIE Vol. 5465 269
While bH and bS have been determined for liquid environments,5 they have not been determined for a humid
environment. The purpose of this work is to address this issue since it should not be assumed the values of these
parameters would be the same in all types of environment.
The specimen used in this study was a dual acrylate coated fiber. The fiber strength was measured at five different
faceplate velocities (1, 10, 100, 1000, 5000 µm/s) using a two-point bending apparatus.12 The strength was measured by
allowing the coated fiber to equilibrate in the appropriate environment, which was 50±1% humidity at temperatures
ranging from 5 to 55 ± ??1°C. Twenty samples were measured at each speed. At the lower speeds, up to ten specimens
could be broken simultaneously by supporting the fibers between multi-grooved faceplates. It has been shown
previously that if this fiber is properly equilibrated with the test environment the coating will not perturb the reaction
kinetics.3 Therefore, for convenience only coated fibers are studied here. The equilibration periods utilized depended
on the temperature of the test environment and ranged from overnight for the lower temperatures to one hour for the
higher temperatures. Numerical integration was used to calculate the fatigue parameters ni and Ai for each model from
the data at each temperature. The following parameter values were assumed for this analysis: critical stress intensity
factor KIC = 0.75 MPa.m1/2, crack shape parameter, Y = 1.16, and initial/inert strength σi = 12 GPa – while the numerical
results depend on these values, the trends are insensitive to them and changing these parameters would not change any of
3. RESULTS AND DISCUSSION
Figs. 1 and 2 show the calculated values of ni and Ai respectively as a function of reciprocal temperature. Table 1
presents the values of bH and bS calculated from the slope and intercepts of the best fit regression lines fitted to the data
of Fig. 1 using Eq. 5. For comparison purposes, the results from Ref. 5 for pure water and pH 7 buffer are also shown.
It may be shown that slope and intercept of linear fits to the results shown in Fig. 2 may be used to estimate values for
) lnln intercept
known) so the apparent activation entropy in the limit of zero stress can be defined:
is not known (or more particularly, the parameter α in Eq. 6 is not known even if the order, m, is
app , 0
which can be explicitly calculated from the intercept of the regression lines in Fig. 2.
To understand the implications of the current results it is useful to examine the earlier results in pure water and pH 7
buffer. The activation parameters shown in Tables 1 and 2 for these two environments are essentially the same within
experimental error. This is because these results were obtained for coated fiber which is an effective diffusion barrier to
the large ions in the buffer solution so the glass surface effectively sees the same environment in both cases.* Assuming
a temperature of around 300 K for the pure water and pH 7 results, the effect of stress is primarily felt through its
influence on the activation entropy since bH/T is small compared to bS (model 1) or negative which alone would impede
fatigue (models 2 and 3). Turning now to the results for the vapor environment, it is first noted that the confidence
intervals are quite large because of the narrower range of temperatures explored in the current work. However, it is clear
that the results are significantly different from the liquid environments. bH is of more importance whichever model is
used the interpret the data, because the values are larger than for the liquid environment. This difference in the
app , 0
are shown in
* Interestingly, when the coating is absent, stripped fibers do show different behavior in the two environments since the pH of water
varies with temperature while that of the buffer does not.7
270 Proc. of SPIE Vol. 5465
sensitivity to stress suggests that the nature of the reactions leading to fatigue are quite different and that the common
observation that the strength in liquid is not the same as the strength in humidity in the limit of 100% saturation is not
simply explained by a difference in overall fatigue rate, but is actually a different process.
Turning now to the values of the activation enthalpy and (apparent) activation entropy in the limit of zero stress, the
entropy plays a bigger role than in the liquid environment, at least for the exponential models. While the above
arguments suggest that there is no reason why these parameters should be the same since the reaction paths are different,
one expects further differences between
in liquid and vapor environments because the function
will be different in both cases.
Table 1: Parameters describing the sensitivity of the activation barrier to the applied stress, as defined by Eq. 5.
Results for liquid aqueous environments from Ref. 5 are also shown for comparison. The confidence intervals
represent a 95% range.
in Eq. 10
Environment Model 1 Model 2 Model 3
50% RH bH (kJ/mol)
84 ± 25 53 ± 29
−101 ± 87
bS (J/mol K)
−80 ± 80 250 ± 100 800 ± 280
7 ± 100
−130 ± 30
−350 ± 60
bS (J/mol K)
180 ± 30 870 ± 110 1700 ± 200
pH 7 buffer5
55 ± 91
−110 ± 40
−370 ± 60
bS (J/mol K)
160 ± 30 770 ± 120 1700 ± 200
1/T × 103 K-1
1/T × 103 K-1
Fig. 1: The fatigue parameter ni as a function of 1/T measured at
50% relative humidity.
Fig. 2: ln Ai as a function of 1/T measured at 50% relative
Proc. of SPIE Vol. 5465 271
Table 2: Activation barrier parameters for fatigue in the limit of zero applied stress. Results for liquid aqueous
environments from Ref. 5 are also shown for comparison. The confidence intervals represent a 95% range.
−9 ± 16
85 ± 10
39 ± 10
, 0 app
, 0 app
, 0 app
−80 ± 55
−91 ± 30
−150 ± 30
48 ± 8
−2 ± 14
−4 ± 9
50 ± 30
−460 ± 40
−380 ± 30
pH 7 buffer5
44 ± 8 5 ± 16
−12 ± 9
30 ± 20
−430 ± 50
−400 ± 30
Dynamic fatigue measurements on fused silica optical fiber as a function of temperature in a humid environment have
been used to characterize the nature of the activation barrier for the fatigue process and how the barrier height is reduced
by stress. The results have been found using three different forms for the fatigue kinetics model (the power law and two
exponential forms). The values of the parameters are significantly different for each model indicating that care should
be taken interpreting fatigue data since the interpretation might depend on the model used. It is therefore recommended
that when modeling fatigue and predicting lifetimes for critical applications a range of kinetics models should be
considered in order to distinguish general results from results that are merely artifacts of the assumed kinetics model.
The activation parameters in the humid environments are different from the values found in earlier work5 for liquid
aqueous environments. This suggests that the reaction paths in the two environments are different. It is well known that
the strength in liquid and high humidity are different – the current results show that this is not simply explained by
differences in water concentration/activity but that the fatigue reaction paths are different. It was found in liquid
environments that stress decreases the activation barrier primarily via entropic effects (independent of which kinetics
model is assumed) and that the effect of stress on the enthalpy component of the activation barrier is either negligible or
impedes fatigue. In contrast, we show that while entropy is still important in humid environments, enthalpy also plays a
role although the importance of that role depends on which kinetics model is assumed.
The results presented here were obtained for a polymer coated fiber. In other work this fiber was shown to have similar
fatigue behavior when stripped of the coating using hot sulfuric acid. In particular the reaction order with respect to
humidity was found to be two.3 However, other coatings may have a significant effect on the fatigue kinetics so caution
should be used before applying our results to other coating systems.
The results presented here use short lengths of fiber which have pristine strength and do not contain large defects. For
most, though not all, applications reliability is concerned with the behavior of a few large weak extrinsic defects. Since
extrinsic defects are different in character from the “defects” in the flaw-free material, the kinetics of fatigue for weak
defects should not be inferred from the results for high strength fiber but should be measured directly (see, for example,
the paper in this proceedings by Semjonov et al. which examines the fatigue behavior of large artificial flaws).
However, the approach used here does provide a methodology for interpreting the meaning of fatigue parameters for
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