A Study for Estimating Thermal Strain andThermal Stress in Optical Fiber Coatings
by Yasuo Nakajima *, Hiroki Tanaka *, Kouji Mochizuki *, Kazuyuki Fuse *,Yoshihiro Arashitani *, Takuya Nishimoto *, Atsuyoshi Seno * and Mitsunori Okada *In general, optical fibers are coated with UV-curable resins--a soft primarycoating and a hard secondary coating--to protect the glass. Under UV radiation
curing heat is produced and it is known that, since the coefficient of thermal expansion (CTE) of
the primary coating is greater than that of the secondary coating, a negative hydrostatic pressure
is produced in the primary coating during the cooling process, resulting in a force acting todelaminate the primary coating from the glass 1)~3). To achieve long-term reliability of optical fibers
it is necessary to analyze the thermal strain and thermal stress that arise in the coatings of thefiber, and accordingly, in this work, we discuss methods for measuring the CTEs of the coatings
and the modulus of elasticity of the secondary coating during the drawing process.

ABSTRACTINTRODUCTION

Optical fibers are drawn with resin coatings that protect
the glass. In general UV-curable resins are used for thecoatings, and in most single-mode (SM) fibers a dualcoating structure is adopted. Each coating layer has anindependent function in the protection of the glass. The
coating in direct contact with the glass is known as theprimary (P) coating, with the role of acting as a buffer
against the external forces that can cause microbending.
Accordingly the primary coating is designed to be soft,
with a Young’s modulus of 1 MPa or less, and in consideration of the conditions of use, the glass transition temperature Tg is lower than room temperature. The primarycoating is then covered by a hard secondary (S) coating
for protection against external forces, and generally
speaking a material having a Young’s modulus of 500
MPa or more and a Tg of 60℃ or above is used.
During the drawing process the optical fiber is heatedby an exothermic reaction as the UV-curable coatingcures and by heat irradiated by the UV lamp, so that thetemperature of the coatings rises above the Tg of the secondary coating. After UV lamp irradiation, the fiber is selfcooled to room temperature and then wound on aspool 1)~4).
During the cooling process following curing, the secondary coating, since its Tg is higher than room temperature, transforms from the rubbery state to the glassy state.
The primary coating, for its part, remains in the rubbery
state as it cools to room temperature. The CTE of a polymer changes significantly at its Tg 1). This means that at* FITEL-Photonics Lab., R&D Div.

temperatures below the Tg of the secondary coating. The
coefficient of thermal shrinkage of the primary coating isgreater than that of the secondary coating. This CTE mismatch gives rise to strain at the primary/secondary interface, resulting in a force acting to delaminate the primarycoating from the glass. Figure 1 is a schematic of CTE
mismatch between the primary and secondary coatings,
where β is cubic CTE, its subscript indicates the type of
coating, and ΔT is the difference between the Tg of thesecondary coating and room temperature.
Knowing the thermal strain of optical fiber coatings
would be of great importance in terms of fiber reliability.
The purpose of this study is to measure the CTEs of eachof the coatings from the coatings of actual optical fibers,
and further to determine the actual thermal strain produced in the coatings and further, the residual stress.
Accordingly, for the measurement of CTE we used a thermo-mechanical analyzer (TMA) and to estimate residual

Secondary coating
Volume change

1.

Primary coating（βp−βs）
Δ

Cooling

RT
Figure 1

Tg of secondary coating

Schematic of CTE mismatch between primary andsecondary coatings.

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A Study for Estimating Thermal Strain and Thermal Stress in Optical Fiber Coatings

METHOD FOR MEASURING CTE OF
OPTICAL FIBERS

2.1 Method for Preparing Samples
For the UV-curable resins used for the primary and secondary coatings, we used commercially available materials.
The samples had outer diameters of 125/195/245 μm forthe glass/primary coating/secondary coating respectively.
2.2 Preparing Samples for CTE Measurement
To measure the coefficients of thermal expansion of the
optical fiber coatings, two types of coating samples wereprepared. The first were standard dual-coated silica glass
fiber samples, and the other were tube samples consisting of the coatings only.
The tube samples were prepared by pulling out the silica glass from the coated fiber in liquid nitrogen.
2.3 CTE Measurement by TMA
For CTE measurement we used a thermo-mechanicalanalyzer (TMA-40 from Mettler Toledo). The instrument
was placed on a vibration isolation table and was cooledwith liquid nitrogen to effect measurement from below
room temperature,
Temperature conditions:cool from 25 to -100℃ at a rate of -10℃/min
hold at -100℃ for 10 minheat from -100 to 150℃ at a rate of 10℃/min
In order not to apply load to the samples, CTE measurement was carried out at zero-load, and in two directions: longitudinal and radial. Since measurement at zeroload is particularly sensitive to vibration, the vibration isolation table was essential.
CTE in the longitudinal direction of the fiber was measured in tensile mode. Samples with a measured lengthof 12.5 mm were held at both ends by copper wire andattached to the TMA instrument.
CTE in the radial direction of the fiber was measured incompression mode. The shape of the probe was a planecircle with a diameter of 3 mm, and the measured lengthwas 245 μm, approximately the same as the outer diameter of the fiber.

3.2 Relaxation Modulus Measurement by DMA
The relaxation modulus was measured by means of a
DMS6100 made by SII Nano Technology with the cured
film mounted on a tensile jig, using a time sweep of stress(at 1-sec intervals). In measuring, the film samples were
mounted with chuck intervals of 20 mm, held at a temperature of 140℃ for 40 min, and then, with strain applied tothe sample, the temperature was lowered to 30℃ at a rateof 1℃/min, and strain was applied until finally the strain
on the sample reached 2%. Then, they were held at astrain of 2% for 300 min. When the stress obtained was
divided by the cross-sectional area of the film, it was possible to determine the secondary coating modulus, modeling after the drawing process. Figure 2 shows the temperature-strain profile.
Using the same instrument and with a temperature
sweep at a frequency of 1 rad/sec, the storage modulus
of elasticity (E ’), loss modulus of elasticity (E ”) and tanδ
were measured in the range of 50~150℃. In this work theglass transition temperature Tg was taken as the peakvalue of tanδ 1).
3.3 Measuring Young’s Modulus
Young’s modulus was measured using a Tensilon-type tensile tester (RTC1310A from A&D). With film samples measuring 6(W) ×50(L)×0.03(t) mm, chuck intervals of 25 mm,pulled at room temperature with a strain rate of 1 mm/min,the Young’s modulus was determined from 2.5% strain.
Table 1 shows the results for Young’s modulus and Tg.

200
180
160
140
120
100
80
60
40
20
0
40

500
400
Temperature
Displacement

300
200
100

140

240

340

Displacement（µm）

2.

three commercially available materials having different values of Tg (A: high; B: middling; and C: low). The cured
films were prepared by application to a glass substrate witha depth of 100 μm, and irradiation in nitrogen by a UV lamp
2
(Fusion F450, D-bulb) with a UV dose of 1.0 J/cm . Sample
dimensions were 2(W)×20(L)×0.1(t) mm.

Temperature（℃）

stress we used a dynamic mechanical analyzer (DMA) tomeasure the modulus of elasticity of the secondary coating, modeling after the drawing process.

0
540

440

Time（min）

3.

METHOD FOR MEASURINGRELAXATION MODULUS

3.1 Preparing Cured Film
In this work, we adopted the term relaxation modulus forthe modulus of elasticity of the secondary coating that isdetermined modeling after the thermal history of the drawing process based on estimated residual stress.
In measuring the relaxation modulus, we used cured film.
The UV-cured resins used for the secondary coating were

Figure 2

Table 1

Conditions of measurement.

Properties of secondary coatings.

Young's Modulus

Glass Transition Temp.

A

690 MPa

110℃

B

760 MPa

84℃

C

453 MPa

63℃

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A Study for Estimating Thermal Strain and Thermal Stress in Optical Fiber Coatings

4.

RESULTS AND DISCUSSION

4.1 CTE Measurement by Tensile Mode
Figure 3 shows the results of CTE measurements by tensile mode. As can be seen, thermal shrinkage of the fiber
samples with glass is remarkably lower than that of the
tube samples consisting of coating resins only.
-6-1
The linear CTE of silica glass is a mere 0.5×10 K ,and since the primary coating adheres to the silica glass
fiber, it can readily be seen that the longitudinal thermal
expansion of the secondary coating will be restricted by
the silica glass.
The CTE of the samples was calculated for two separate temperature ranges. Since the CTE of a polymer
changes significantly at the Tg, we made the separation
at -50℃, the Tg of the primary coating. Table 2 shows theresults of CTE measurement by tensile mode.
4.2 CTE Measurement by Compression Mode
Figure 4 shows the results of CTE measurement by compression mode. As can be seen, radial thermal shrinkage ofthe fiber samples is greater than that of the tube samples.
The CTEs of the fiber samples and tube samples were
calculated for the same temperature ranges as in the tensile mode tests. Table 3 shows the results for CTE measured by compression mode.

βS = αSL＋2×αSR

With respect to the fiber samples, the primary coating
adheres to the silica glass, so that the secondary coating
cannot expand and contract freely and the thermal expansion of the coatings is restrained by the silica glass fiber.
Since the CTE of silica glass is remarkably lower than thatof the coatings, thermal expansion can be neglected.
Accordingly we may determine the cubic CTE of the primary coating fromβP
βP
D G＋（D P－D G）×（1＋ 2 ）＋（D S－D P）×（1＋ 2 ）（1＋αFR）
=D S×

0.2

0.0

0.0

-0.4
-0.6
-0.8
-1.0

Tube
Fiber

-1.2
-1.4
-100

-80

-60

-40

-20

0

20

40

-0.2
-0.4
-0.6
-0.8
Tube

-1.0

Fiber

-1.2
-1.4
-100

-80

Table 2
SampleFiber
Tube

Figure 4

CTE measurement by tensile mode.

Longitudinal CTE measurement by tensile mode.
Linear coefficient of thermal expansion-50 to -100 ℃

25 to -50℃
0.004×10
0.66×10

-4

-4

K

K

-1

-1

-60

-40

-20

0

20

40

Temperature（℃）

Temperature（℃）

Figure 3（2）

where: βP is the cubic CTE of the primary coating
βS is the cubic CTE of the secondary coating
αFR is the linear CTE of the primary coating in
the radial direction
DG is the outer diameter of the silica glass (125 μm)
DP is the outer diameter of the primary coating (195 μm)
DS is the outer diameter of the secondary coating(245 μm)

0.2

-0.2

（1）

where: βS is the cubic CTE of the secondary coating
αSL is the linear CTE of the secondary coating in
the longitudinal direction
αSR is the linear CTE of the secondary coating in
the radial direction

Diameter change rate（％）

Length change rate（%）

4.3 Estimation of CTE for Each Coating
The cubic CTEs of the primary coating and secondary
coating were estimated from the tensile-mode and compression-mode measurements of CTE for the fiber samples and the tube samples. The method of estimating
cubic CTE for each coating was as follows:
At temperatures ranging from 25℃ to -50℃, in the caseof the tube samples the primary coating is in the rubbery
state and the Young’s modulus is significantly smaller

than that of the secondary coating, so that the secondary
coating can expand and contract freely. Since the cubic
CTE of the secondary coating is two times the linear CTE
in the radial direction plus the linear CTE in the longitudinal direction, we may determine the cubic CTE of the secondary coating from

-0.10×10 -4 K -1
0.62×10-4

K-1

Table 3SampleFiber
Tube

CTE measurement by compression mode.

Radial CTE measurement by compression mode.
Linear coefficient of thermal expansion
25 to -50 ℃
1.17×10-4

0.86×10

-4

K

-1

K

-1

-50 to -100 ℃
0.77×10-4

K-1

0.56×10-4

K-1

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A Study for Estimating Thermal Strain and Thermal Stress in Optical Fiber Coatings

4.4 Internal Strain in Fiber Coating
Next we investigated internal thermal strain in the secondary coating by means of measurement of CTE. Figure 5
shows results for thermal expansion of tube samples bytensile mode in the -100~150℃ temperature range. In
the area inside the dotted circle in Figure 5, thermal
shrinkage of the tube samples occurred at approximately
90℃, a temperature that is close to the Tg of the secondary coating.
4.5 Verification of Internal Strain in Fiber Coatings
We verified that the thermal shrinkage observed in
Figure 5 is due to internal strain in the secondary coatingby means of the method described below.
In this method, tube samples were aged under zeroload conditions using the following program:

Table 4
SampleEstimated cubic CTE for each coating.

Temperature conditions:
heat from 25 to 150℃ at a rate of 10℃/min
cool from 150 to 25℃ at a rate of 10℃/min
The linear thermal expansion of tube samples subjectedto the above thermal profile was then measured under thesame conditions as in Section 4.4 above.
Figure 6 shows the results for the CTE of aged tube
samples. In contrast to the thermal shrinkage observed
around 90℃ in Figure 5, no thermal shrinkage wasobserved in the aged tube samples. Thermal shrinkage
was evidently eliminated through zero-load aging.
These results suggest that the secondary coating has
latent internal strain, and that internal strain is caused by
the curing process at the time of drawing. From the factthat internal strain gives rise to longitudinal shrinkage, it issuggested that the strain that has been extended in thelongitudinal direction accumulates in the secondary coating.
4.6 Relaxation Modulus in the Secondary Coating
Figure 7 shows results measured by the method
described in Section 3 above. For any of the resins examined, the modulus of elasticity increased with cooling from
140℃ to 30℃, and the slopes of the initial rises are substantially the same, though the maximum values differ.

3.0
2.5

Length change rate（%）

Table 4 shows the estimated values of cubic CTE foreach coating. One-third of the cubic CTE is the linear
CTE. At temperatures between -50℃ and 25℃, that is tosay where the primary coating is rubbery and the secondary coating is glassy, the CTE of the primary coating was
2.7 times higher than that of the secondary coating.
Further the CTE of the primary coating in the rubbery
state was 1.8 times higher than in the glassy state. It wasestimated that this would be approximately 3 times, but
further confirmation is required for the fact that it was
lower than predicted at temperatures below -50℃. In thisestimation, since the secondary coating is always glassy
at room temperature, we calculated the CTE of the primary coating taking the secondary coating CTE as-4-1
2.38×10 K .

Cubic coefficient of thermal expansion
25 to -50 ℃
6.34×10-4

K-1

3.54×10-4K-1Secondary

2.38×10-4K-1

2.38×10

-4

K

-1

1.5
1.0
0.5
0.0
-0.5
-1.0

-50 to -100 ℃

Primary

2.0

-1.5
-100

-50

0

50

100

150

Temperature（℃）

Figure 6

Thermal expansion of aged tube samples by tensile mode.

3.0

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-100

-50

0

50

100

150

Temperature（℃）

Figure 5

Thermal expansion of tube sample by tensile mode.

200
180
160
140
120
100
80
60
40
20
0
40

250
A

200

B

150

C

100

Temperature

50

Modulus（MPa）

2.0

Temperature（℃）

Length change rate（%）

2.5

Used to the estimation

140

240

340

440

0
540

Time（min）

Figure 7

Results for relaxation modulus.

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A Study for Estimating Thermal Strain and Thermal Stress in Optical Fiber Coatings

Secondary coating A was the highest and secondary
coating C the lowest. When subsequently held at 30℃
under an applied strain of 2%, the modulus of elasticity
decreased gradually over time. Even at the end of themeasured time, the modulus of elasticity still continued todecrease, but it is presumed that it is approaching a substantially equilibrium condition.
The moduli shown in Figure 7 suggest that there is acorrelation with the Tg of the secondary coatings shownin Table 1. Secondary coating Tg increases in sequence
for coatings A, B and C. This order is the same as that of
the moduli shown in Figure 7. On the other hand, it alsosuggests that there is no correlation between the Young’s
modulus of the cured films and the moduli in Figure 7.
Generally speaking, resins that are rubbery at temperatures above Tg are easily relaxed. The difference between
pre-aging temperature of 140℃ and secondary coating
Tg is 30℃ for material A, 53℃ for material B and 77℃ formaterial C, so that the temperature range for relaxation isbroader for resins with lower Tg. The results obtained
here corroborate this expectation, demonstrating that thedegree of relaxation is quantitative.
The samples are being cooled from a temperature
above Tg to room temperature under constant applied
strain, and this process models after the drawing of actual
fibers. In the actual drawing process, the glass surface iscovered with UV-curable resin coatings, which are thenirradiated under a UV lamp and heated by the exothermic
curing reaction and by the radiant heat. The optical fiber
is then cooled to room temperature and wound on aspool. In this condition the adhesiveness of the primarycoating binds it to the glass. For this reason the coating iscooled under conditions of constant strain.
The method used in this work does not, strictly speaking, reproduce the actual drawing process, but it holds
forth the promise of enabling a quantitative analysis
based on evaluation of residual stress in the optical fiber
coatings. Specifically, the measured values obtained bythis method have been effective in analyzing the stresses
caused by the coatings at the glass/primary interface 1), 2).

5.

CONCLUSIONS

5.1 Determining CTE for Each Coating
By conducting measurements on fiber samples with silica
glass and on tube samples, from both the longitudinal
direction and the radial direction, we were able to determine the cubic CTE of each coating. It was confirmed thata method using a thermal mechanical analyzer (TMA) wasan effective means for measuring the CTE of optical fiber
coatings.
According to Reference 1) the CTE of the primary isapproximately 3 times higher than that of the secondary.
(The original document is Reference 5)). In the method
described in this work we were able to determine theaccurate CTEs necessary to the calculation of accurate

thermally induced residual stresses in dual-coated opticalfibers.
5.2 Internal Strain in Optical Fiber Coatings
It became clear that the secondary coating had internalstrain. The fact that thermal shrinkage of tube samples
occurs at approximately 90℃, corresponding to the Tg of
the secondary material, means that this internal strain canbe released at temperatures above the Tg of the secondary coating.
It was also confirmed that for tube samples, thermal
contraction in the longitudinal direction disappears when
the secondary coating is aged under zero load at temperatures above Tg.
As described above, the internal strain in the secondary
coating is formed in the curing process during opticalfiber drawing. It is assumed that this is caused by the secondary coating being cured at temperatures above Tg,
internal stress in the secondary coating being caused by
the mismatch in CTE between the primary coating andsecondary coating during the cooling process.
5.3 Relaxation Modulus of the Secondary Coating
The modulus of a secondary coating that is determinedmodeling after the thermal history of the drawing process,based on estimated residual stress, is termed the relaxation modulus. The measuring method involves aging thesecondary coating above the Tg while strain is appliedand finding the stress when cooled to room temperature.
It became clear that the correlation of the relaxation modulus to Tg was high.
This method has not yet been able strictly speaking to
reproduce the actual drawing process, but since it makes
possible a quantitative analysis based on evaluating
residual stress in the optical fiber coatings, it is expected
to prove useful in analyzing the stress produced by thecoatings at the glass/primary interface.

REFERENCES
1) C. J. Aloisio, W. W. King, R. C. Moore: A viscoelastic analysis ofthermally induced residual stresses in dual coated optical fibers,
Proc. 44th IWCS, p. 139 (1995).
2) W. W. King, C. J. Aloisio: Thermomechanical Mechanism for
Delamination of Polymer Coatings From Optical Fibers, Journal of
Electronic Packaging, 119, p. 133 (1997).
3) Win-Jin Chang: Viscoelastic analysis of hydrostatic pressure induced
optical effects in double-coated optical fibers, J. Appl. Phys., Vol. 93,
No. 1, 1 January (2003).
4) Y. Arashitani, Y. Nakajima, Y. Gamoh, H. Tanaka, M. Okada: A
Method for Estimating the Contribution of Modulus and Tg on the
Residual Stress in Optical Fiber Coatings, Proc. 53rd IWCS, p. 285(2004).
5) J. D. Ferry: Viscoelastic Properties of Polymers, John Wiley & Sons
(1980).

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