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Fatigue behavior of UV-cured silica optical fibers
Journal of Non-Crystalline Solids 52 (1982) 561 566 North-Holland Publishing Company
561
F A T I G U E B E H A V I O R OF UV-CURED SILICA O P T I C A L FIBERS W A N G Jianguo, Q I N Chen and LI Jiazhi Shanghai Institute of Ceramics. Academia Sinica, Shanghai, China
The fatigue behavior of UV-cured silica optical fibers was determined. The accelerated tests gave data in agreement with Charles' law.
1. Introduction
The long term mechanical reliability of optical fibers is necessary for the successful implementation of many optical communication systems. In general, glass materials display the characteristics of delayed failure, i.e. static fatigue. The nature of this phenomenon is due to the reaction between the hydroxyl ions and pre-existing flaws on the glass surface. Under stress, the reaction promotes flaw growth resulting in strength reduction. It is obvious that the static fatigue of optical fibers should be thoroughly understood. However, it would take a lot of time to perform such experiments in a normal environment. At low applied stress, fracture may be delayed for several months or even several years. Therefore, some methods of accelerating the test must be used. One of them is to carry out the test in a water bath at high temperature. Under these conditions, in view of the fact that the chemical reaction is accelerated and the surface energy is reduced, the testing time is shortened. Dynamic fatigue testing, i.e. the stressing rate technique, is another fast method. As is well known, the static fatigue of glass may be expressed by the following relation, namely Charles' static fatigue formula: lnt~ = - n In o~ + In K s,
(1)
where t S is the average failure time at constant applied stress os, n and K S are parameters depending on the material and environment. The parameter n is called the stress-corrosion susceptibility factor. For dynamic fatigue, there exists the following relation between the stress rate d and average rupture strength 6d: 1 1 In 6u = n +------i-In d + ~
in K a
(2)
thus
6d=dia,
lnt-d= --nln6a+lnK a.
(3)
F r o m eq. (3), we can see that dynamic fatigue and static fatigue have similar 0022-3093/82/0000-0000/$02.75 © 1982 North-Holland
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
562
expressions. In this paper, the results of the fatigue behavior investigation are described.
2. Experiment The optical fiber was drawn using a graphite resistance furnace from a CVD preform. The drawn fiber was coated in-line with a UV-cured epoxy-acrylate using a flexible applicator made from a silicone elastomer. The coating thickness on the 150 # m fiber was about 50 #m. The details of the fabrication have been described elsewhere [1]. The short-term tensile strength, for 500 mm lengths are plotted on a Weibull probability scale in fig. 1. It was noted that the distribution of strength was multimodal. The Weibull shape parameters m, from the higher to lower strength part, were about 9 and 4, respectively. In addition, after being aged for 10 months in a room environment, the strength distribution of this optical fiber did not display any change.
2.1. Static fatigue test The mandral method was adopted. The 500 mm long specimens were wound on metal rods with different diameters. The stress level subjected was calculated as follows: o = E ( d / D ) , where E is Young's modulus, d and D are the diameter of the fiber and rod respectively. The deadline of the test was 104 min. The stress applied to the fibers varied from 1.69 to 2.54 G N / m 2. The results of tests in water at 80°C are given in table 1. The characteristic lifetime
99 90 4% rain "1
70 5O 3O 20
/ 0.5
I
I
!
1
2
3
I
I
!
4fi6
O'GN/m 2
Fig. 1. The short-term tensile strength of the CVD silica optical fiber: ×, freshly drawn; 0, after having aged for 10 months.
Wang Jmnguo et al. / Fatigue behavior of UV-cured opticalfibers
563
Table 1 The results of static fatigue test Diam of rod (mm)
Applied stress (GN/m 2)
Slope S
Characteristic lifetime F = 63.2% (min)
4 4.5 5 5.5 6
2.54 2.25 2.03 1.83 1.69
3.59 1.99 0.78 0.60 0.38
2.1 383 595 5939 49150 a
a Extrapolation.
in the table is the failure time at F = 63.2% in Weibull statistics. F r o m table 1 it c a n be found, that with the increase of the applied stress, the failure time becomes rapidly shorter. The results were treated b y f o r m u l a (1) a n d a straight line fit, In oa = - 0 . 0 4 2 In t s + 0.991 was o b t a i n e d (fig. 2). The stress corrosion susceptibility factor n was estimated to be a b o u t 23.8.
2.2. Dynamic fatigue test The d y n a m i c fatigue test of a 125 m m long fiber was performed o n a model 1122 type I n s t r o n m a c h i n e at four different cross-head speeds V of 200, 20, 2 a n d 0.5 m m / m i n . The results of the test are given in table2, treated by f o r m u l a (2). A straight line fit In ~d = 0.039 In V + 1.187 was o b t a i n e d (fig. 3). Thus, the stress corrosion susceptibility factor n was estimated to be a b o u t 24.3. As stated above, the two tests showing the fatigue behavior of the optical fiber are in agreement with Charles' law. The value of the stress-corrosion susceptibility factor n o b t a i n e d b y the two methods was a b o u t 24.
0
1
2
3
4
5 6 7 Lnt {rnin)
8
9
10 11
Fig. 2. The dependence of the static applied stress on the characteristic lifetime for the CVD silica optical fiber.
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
564
Table 2 The results of dynamic fatigue test Cross head speed (mm/min)
Average strength ( G N / m 2)
Value of m ( F > 10%)
200 20 2 0.5
3.97 3.79 3.38 3.15
16.47 15.18 14.05 8.19
1.5 1.4 1.3 l 1.2 1.1 1.0 -2
I
I
I
I
n
m
I
-1
0
1
2
3
4
5
6
LnV
Fig. 3. The plot of the dynamic fatigue for the CVD silica optical fiber.
3. Calculation of the n value with the Weibull distribution Charles' flaw may be rewritten as: /l/t,2 = (O,aj/Oa ' )n.
(4)
This relation may also be deduced by fracture mechanics [2]. If the initial flaw size of the pre-existing flaws on the glass surface is a i, a c is the critical flaw size and the rate of the slow crack growth is v, then, the failure time t for an applied stress o, may be obtained by the integral fifo da/v. When n is large enough, t=Ao~-zo~ ", where A is a constant, and oc is the critical failure stress. If two sets of fibers tested have the same Weibull distribution, we would obtain the relation in formula (4). Therefore: n = l n ( t , / t 2 ) / l n ( o , 2 / o , ~ ).
(5)
But, in general, two sets of the fibers tested may not be similar. Their distribution curves of the failure time have different slopes S. Thus. at the
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
565
99 90 70 50
_~ 30 u_
10 5 I
1 O0
200
I
I
I
I
I
I
I
400 600 1000 2000 t (rain)
I
5000
Fig. 4. The plot of the static fatigue tested in an 80°C water bath for CVD silica optical fiber.
failure probability ~ , the failure time is calculated as follows: lnln( - - i l f ( s 2 - s , ) + s,6 ln( t],/t2i ) =
S, S 2
- s26,
'
(6)
where b I, b 2 a r e intercepts. At F, = 63.2%, the above-mentioned formula can be simplified: ln(t 1/t 2 ) : b 2 / S 2 - b , / S , .
(7)
Combining eqs. (6) and (7), we obtain: tl : ( 62/32 -- 6 1/81 ) / l n ( o a,/oa, ).
(8)
According to eq. (8), we obtained n = 24.6 under an applied stress of 1.83-2.03 G N / m 2 (see fig. 4).
4. Conclusion
The value of the stress-corrosion susceptibility factor n obtained by means of various methods for testing optical fiber was about 24. The minimum lifetime tmin after proof testing is given by tmi. = (Op/Oa)nB/o~. after Love et al. [3], let B--0.0036. To assume a minimum lifetime of 20 years of the optical fiber after 800 g proof testing the service stress would be less than 200 g. In the static fatigue test of the 80°C water bath, a very large change of slopes in the lifetime Weibull distribution curves was found (see table 1). This phenomenon could apparently not be attributed to different distributions of the flaws among the sample sets.
566
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
References [1] Qin Chen et al., J. Chinese Silicate Soc. 9 (1981) 149. [2] R.E. Love, Fibers and Integrated Optics, SPIE 77 (1976) 69. [3] R.E. Love et al., Opt. Engng. 17 (1978) 114.
561
F A T I G U E B E H A V I O R OF UV-CURED SILICA O P T I C A L FIBERS W A N G Jianguo, Q I N Chen and LI Jiazhi Shanghai Institute of Ceramics. Academia Sinica, Shanghai, China
The fatigue behavior of UV-cured silica optical fibers was determined. The accelerated tests gave data in agreement with Charles' law.
1. Introduction
The long term mechanical reliability of optical fibers is necessary for the successful implementation of many optical communication systems. In general, glass materials display the characteristics of delayed failure, i.e. static fatigue. The nature of this phenomenon is due to the reaction between the hydroxyl ions and pre-existing flaws on the glass surface. Under stress, the reaction promotes flaw growth resulting in strength reduction. It is obvious that the static fatigue of optical fibers should be thoroughly understood. However, it would take a lot of time to perform such experiments in a normal environment. At low applied stress, fracture may be delayed for several months or even several years. Therefore, some methods of accelerating the test must be used. One of them is to carry out the test in a water bath at high temperature. Under these conditions, in view of the fact that the chemical reaction is accelerated and the surface energy is reduced, the testing time is shortened. Dynamic fatigue testing, i.e. the stressing rate technique, is another fast method. As is well known, the static fatigue of glass may be expressed by the following relation, namely Charles' static fatigue formula: lnt~ = - n In o~ + In K s,
(1)
where t S is the average failure time at constant applied stress os, n and K S are parameters depending on the material and environment. The parameter n is called the stress-corrosion susceptibility factor. For dynamic fatigue, there exists the following relation between the stress rate d and average rupture strength 6d: 1 1 In 6u = n +------i-In d + ~
in K a
(2)
thus
6d=dia,
lnt-d= --nln6a+lnK a.
(3)
F r o m eq. (3), we can see that dynamic fatigue and static fatigue have similar 0022-3093/82/0000-0000/$02.75 © 1982 North-Holland
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
562
expressions. In this paper, the results of the fatigue behavior investigation are described.
2. Experiment The optical fiber was drawn using a graphite resistance furnace from a CVD preform. The drawn fiber was coated in-line with a UV-cured epoxy-acrylate using a flexible applicator made from a silicone elastomer. The coating thickness on the 150 # m fiber was about 50 #m. The details of the fabrication have been described elsewhere [1]. The short-term tensile strength, for 500 mm lengths are plotted on a Weibull probability scale in fig. 1. It was noted that the distribution of strength was multimodal. The Weibull shape parameters m, from the higher to lower strength part, were about 9 and 4, respectively. In addition, after being aged for 10 months in a room environment, the strength distribution of this optical fiber did not display any change.
2.1. Static fatigue test The mandral method was adopted. The 500 mm long specimens were wound on metal rods with different diameters. The stress level subjected was calculated as follows: o = E ( d / D ) , where E is Young's modulus, d and D are the diameter of the fiber and rod respectively. The deadline of the test was 104 min. The stress applied to the fibers varied from 1.69 to 2.54 G N / m 2. The results of tests in water at 80°C are given in table 1. The characteristic lifetime
99 90 4% rain "1
70 5O 3O 20
/ 0.5
I
I
!
1
2
3
I
I
!
4fi6
O'GN/m 2
Fig. 1. The short-term tensile strength of the CVD silica optical fiber: ×, freshly drawn; 0, after having aged for 10 months.
Wang Jmnguo et al. / Fatigue behavior of UV-cured opticalfibers
563
Table 1 The results of static fatigue test Diam of rod (mm)
Applied stress (GN/m 2)
Slope S
Characteristic lifetime F = 63.2% (min)
4 4.5 5 5.5 6
2.54 2.25 2.03 1.83 1.69
3.59 1.99 0.78 0.60 0.38
2.1 383 595 5939 49150 a
a Extrapolation.
in the table is the failure time at F = 63.2% in Weibull statistics. F r o m table 1 it c a n be found, that with the increase of the applied stress, the failure time becomes rapidly shorter. The results were treated b y f o r m u l a (1) a n d a straight line fit, In oa = - 0 . 0 4 2 In t s + 0.991 was o b t a i n e d (fig. 2). The stress corrosion susceptibility factor n was estimated to be a b o u t 23.8.
2.2. Dynamic fatigue test The d y n a m i c fatigue test of a 125 m m long fiber was performed o n a model 1122 type I n s t r o n m a c h i n e at four different cross-head speeds V of 200, 20, 2 a n d 0.5 m m / m i n . The results of the test are given in table2, treated by f o r m u l a (2). A straight line fit In ~d = 0.039 In V + 1.187 was o b t a i n e d (fig. 3). Thus, the stress corrosion susceptibility factor n was estimated to be a b o u t 24.3. As stated above, the two tests showing the fatigue behavior of the optical fiber are in agreement with Charles' law. The value of the stress-corrosion susceptibility factor n o b t a i n e d b y the two methods was a b o u t 24.
0
1
2
3
4
5 6 7 Lnt {rnin)
8
9
10 11
Fig. 2. The dependence of the static applied stress on the characteristic lifetime for the CVD silica optical fiber.
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
564
Table 2 The results of dynamic fatigue test Cross head speed (mm/min)
Average strength ( G N / m 2)
Value of m ( F > 10%)
200 20 2 0.5
3.97 3.79 3.38 3.15
16.47 15.18 14.05 8.19
1.5 1.4 1.3 l 1.2 1.1 1.0 -2
I
I
I
I
n
m
I
-1
0
1
2
3
4
5
6
LnV
Fig. 3. The plot of the dynamic fatigue for the CVD silica optical fiber.
3. Calculation of the n value with the Weibull distribution Charles' flaw may be rewritten as: /l/t,2 = (O,aj/Oa ' )n.
(4)
This relation may also be deduced by fracture mechanics [2]. If the initial flaw size of the pre-existing flaws on the glass surface is a i, a c is the critical flaw size and the rate of the slow crack growth is v, then, the failure time t for an applied stress o, may be obtained by the integral fifo da/v. When n is large enough, t=Ao~-zo~ ", where A is a constant, and oc is the critical failure stress. If two sets of fibers tested have the same Weibull distribution, we would obtain the relation in formula (4). Therefore: n = l n ( t , / t 2 ) / l n ( o , 2 / o , ~ ).
(5)
But, in general, two sets of the fibers tested may not be similar. Their distribution curves of the failure time have different slopes S. Thus. at the
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
565
99 90 70 50
_~ 30 u_
10 5 I
1 O0
200
I
I
I
I
I
I
I
400 600 1000 2000 t (rain)
I
5000
Fig. 4. The plot of the static fatigue tested in an 80°C water bath for CVD silica optical fiber.
failure probability ~ , the failure time is calculated as follows: lnln( - - i l f ( s 2 - s , ) + s,6 ln( t],/t2i ) =
S, S 2
- s26,
'
(6)
where b I, b 2 a r e intercepts. At F, = 63.2%, the above-mentioned formula can be simplified: ln(t 1/t 2 ) : b 2 / S 2 - b , / S , .
(7)
Combining eqs. (6) and (7), we obtain: tl : ( 62/32 -- 6 1/81 ) / l n ( o a,/oa, ).
(8)
According to eq. (8), we obtained n = 24.6 under an applied stress of 1.83-2.03 G N / m 2 (see fig. 4).
4. Conclusion
The value of the stress-corrosion susceptibility factor n obtained by means of various methods for testing optical fiber was about 24. The minimum lifetime tmin after proof testing is given by tmi. = (Op/Oa)nB/o~. after Love et al. [3], let B--0.0036. To assume a minimum lifetime of 20 years of the optical fiber after 800 g proof testing the service stress would be less than 200 g. In the static fatigue test of the 80°C water bath, a very large change of slopes in the lifetime Weibull distribution curves was found (see table 1). This phenomenon could apparently not be attributed to different distributions of the flaws among the sample sets.
566
Wang Jianguo et al. / Fatigue behavior of UV-cured optical fibers
References [1] Qin Chen et al., J. Chinese Silicate Soc. 9 (1981) 149. [2] R.E. Love, Fibers and Integrated Optics, SPIE 77 (1976) 69. [3] R.E. Love et al., Opt. Engng. 17 (1978) 114.