Theoretical Analysis of the Thermally Induced Delamination of IPolymeric Coatings in Double-Coated Optical Fibers

SHAM-BONG SHIUE

Department of Materials Science Few Chia University

Taichung, Taiwan, Republic of China

To maintain its mechanical strength, the glass fiber of optical fibers is coated by polymwic materials during the fabrication process. However, when the thermally induced shear stress at the interface of the glass fiber and primary coating is larger than its adhesive stress, the adhesive bond between the glass fiber and primary coating will be broken. When the polymeric coatings are delaminated from the glass fiber, the optical fiber will lose its mechanical strength. In this article, the thermally induced delamination of polymeric coatings in double-coated optical fibers is inves- tigated. To minimize the coating’s delamination, the thermally induced shear stress at the interface of the glass fiber and primary coating should be reduced. The method to minimize such a shear stress is to select suitable polymeric coatings as follows: The thickness and Poisson’s ratio of the primary coating should be in- creased, but the Young’s modulus of the primary coating and the thickness, Young’s modulus, and thermal expansion coefficient of the secondary coating should be de- creased. Finally, the optimal design of commercialized double-coated optical fibers to minimize the thermally induced coating’s delamination is also discussed.

1. INTRODUCTION

ptical fibers with lclw transmission loss and wide 0 bandwidth have been developed, and many prac- tical transmission systems use these optical fibers. Long-term stability is im important requirement for optical transmission, so optical fiber must maintain stable performance in the most severe condition (1). In order to maintain the mechanical strength of optical fibers, the glass fibers are coated by polymeric mate- rials during the fabrication process (2). However, be- cause the physical properties of the glass fiber and polymeric coatings are different, thermal stresses will be built up in optical fibers after temperature drop. Many researchers (3-9) have studied this problem and found that thermal stresses resulted in an added transmission loss in opticA fibers at low temperatures.

On the other hand, thermally induced shear stress exists at the interface O F the glass fiber and primary coating. If this shear strws is larger than its adhesive stress, the adhesive bond between the glass fiber and primary coating will be broken and the polymeric coat- ings will be delaminated from the glass fiber. When the polymeric coatings are delaminated from the glass fiber, the optical fiber will lose its mechanical strength. Therefore, a good adhesion between the glass fiber and primary coating is important for the reliable per- formance of the fibers. However, large numbers of optical fibers are assemtiled in electro-optical devices

for communication systems. Before connection of the fibers to a device elements, the polymeric coatings must be removed from the glass fibers. If the adhesive stress between the glass fiber and primary coating is too high, it becomes very difficult to strip the coating materials from the glass fiber. Hence, a moderate ad- hesive stress between the glass fiber and primary coating are designed for most of the fibers, and it be- comes an important problem to minimize the thermally induced coating’s delamination in the optical fiber’s applications. In this article, the thermally induced coating’s delamination in double-coated optical fibers is investigated. The shear stress at the interface of glass fiber and primary coating is derived first, and then the optimal design of polymeric coatings to mini- mize the thermally induced coating’s delamination is considered.

2. ANALYSIS

The problem is depicted in RLJ. 1 . An optical fiber is constructed of a glass fiber coated by two polymer lay- ers. The r, E, a, and v represent the radius, Young’s modulus, thermal expansion coefficient, and Poisson’s ratio of materials, respectively. The subscripts “0,” “1,” and ’2” denote the glass fiber, primary coating and secondary coating, respectively. Here x and r repre- sent the axial and radial coordinates, respectively. The half length of optical fiber is L. In real applications,

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Sham-Tsong Shiue

Glass Fiber C 1 Primary Coating

3Cl;UI lual y bualll ly

I

I . t I t I

1

T2 ( X) . L L - c- '1

Fig. I. Schematic diagram of a double-coated optical-.

the primary coating and secondary coating of optical fibers are soft and hard polymeric materials, respec- tively. Because the physical properties of the glass fiber and polymeric coatings are different and we as- sume that no stress is in the system in the initial tem- perature, stress will be built up after temperature drop AT. For simplification, the primary coating is assumed to experience shear only. This is justified by the fact that the Young's modulus of the primary coating is sigmficantly smaIler than Young's moduli of the glass fiber and secondary coating. This assumption means that shear stress T ~ ( x ) at the interface between the glass fiber and primary coating and shear stress T~(x) at the interface between the primary coating and sec- ondary coating are inversely proportional to the corre- sponding radii:

(1)

Indeed, since no external forces act on the primary coating, this coating has to be in equilibrium under the action of the interfacial shear stresses only; there- fore, the following condition should be W e d :

T O W - '1 71(x) ro

2mro 1-L T o ( 8 d s - 2ari T 1 ( 0 d s = 0 (2) 1: The differentiation of this equation with respect to the axial coordinate x results in Eq 1.

The shear stress T ~ ( x ) can be determined from the following condition of the compatibility for the axial interfacial displacements:

UO(4 = U Z ( 4 - KTO(X) (3) Here %(x) represents the axial displacements of the points located at the glass fiber surface, and UJX) de- notes the axial displacements of the points located on the inner boundary of the secondary coating. The K T ~ ( X ) is determined from the shear strain T ( x ) / G

where T ( X ) and G are the shear stress and shear mod- ulus of the primary coating.

If the stresses T ~ ( x ) and T ~ ( x ) were known, then the displacements %(XI and ~ J x ) could be approximately evaluated on the basis of Hooke's law as follows:

where

and

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Theoretical Analysis of the ThermalLy Induced Delamination

is the axial force in the secondary coating. Introducing Eqs 5 and 7b into the compatibility condition (Eq 3), we obtain the following equation for the shear stress function T ~ ( x ) :

KdX) + qox TO(S)ds = (a0 - a,)ATx (8)

where

X = X, + A, (9)

Differentiating Eq 8 with respect to the axial coordi-

(10)

nate x, we obtain:

K T ~ ‘ ( x ) + ATo(x) = (ao - &,)AT

T$(x) - k2To(x) = 0

The next differentiation yields:

(1 1)

where the constant

k = V-K (12)

Equation 11 has the solution:

T ~ ( x ) = C , cosh(kx) + C, sinh(kx) (13)

where the constants C , and C, of integration can be determined from the boundary conditions for the force To (XI :

T,,(-L) = 0 (144

?&) = 0 (14b)

As evident from Eq 10, the conditions of Eqs 1 4 a and 14b are equivalent to the following conditions for the function T ~ ( x ) :

KT~’(-L:I = (ao- a,)AT

KT~’(L) = (ao- a,)AT

( 154

( 15b)

Substituting Eq 13 into these conditions, we obtain:

c, = 0 (164

and

(ao - )AT c - - Kk cosh(kl)

Then the solution (Eq 13) can be written as:

(17)

The shear stress T ~ ( x ) is an odd function with respect to the axial coordinate .Y. The minimum shear stress of T ~ ( x ) is zero at x = 0, and the maximal value of shear stress T,,(x) is:

which occurs at x = ir L. If the shear stress ro(x) is larger than the adhesive shear stress T , between the glass fiber and primary coating, then the polymeric coatings will be broken at the interface of the glass fiber and primary coating. It is noted that if kL is large enough (i.e., kL>3.5), tanh(kl) is equal to unity. In

POLYMER ENGINEERING AND SCIENCE, JUNE 1998, Vol. 38, No.

this case, T , = (az - a&T/Kk, which is independent on the fiber’s length.

From Eq 17, we know that the shear stress T ~ ( x ) is a function of material‘s properties of polymeric coatings and their thicknesses; therefore we could minimize such a shear stress by a suitable selection of polymeric coatings and their thicknesses. Since we assume that the primary coating is only subjected to shear stress and the effects of lateral forces on the axial displace- ments are not considered, al. uo, and u, disappear in Eq 17.

3. RESULTS In order to understand the effects of polymeric coat-

ings and their thicknesses on the shear stress T ~ ( x ) ,

the relations between the maximum shear stress T, and the thicknesses and Young’s moduli of the primary coating and secondary coating are shown in Figs. 2 and 3, respectively. The parameters of optical fibers are assumed as: ro = 62.5/pm, r1 = 100pm. r2 = 125pm. Eo= 72.5GPa. El = lOMPa, E, = 1.2GPa. a. = 5.6 X

10-7/0C, a2 = 2 X 10-4/0C and u1 = 0.495, with the ex- ception of the specified parameters, and L = 50 mm and AT = 100°C. I t is noted that if the maximum shear stress T , decreases, all the other shear stress T ~ ( x ) also decreases. Hence, we only consider the effect of polymeric coatings on the maximum shear stress T-. Figure 2 depicts that r , decreases with increas- ing r l , but T , decreases with decreasing r,. FYgure 3 shows that T, decreases with decreasing El and 4. On the other hand, the effect of a2 and Y, on the T,,

is shown in Fig. 4. The parameters are the same as those shown in Fig. 2 with the exception of the speci- fied parameters. Figure 4 shows that T , decreases with increasing vl, but T , decreases with decreasing a,. From the above evaluation, we know that the T,,

value could be minimized by a suitable selection of polymeric coatings and their thicknesses. In order to minimize such a shear stress in a double-coated opti- cal fiber, the thickness and Poisson’s ratio of the pri- mary coating should be increased, but the Young’s modulus of the primary coating and the thickness, Young’s modulus, and thermal expansion coefficient of the secondary coating should be decreased.

4. DISCUSSION

From the above evaluation, it is known that we can minimize the delamination of polymeric coatings by the suitable selection of the physical properties of polymeric coatings and their thicknesses. For com- mercialized double-coated optical fibers, the radius of the glass fiber is typically 62.5 pm; and the primary coating is a soft polymer used as a strain buffer to minimize the microbending loss, and the secondary coating is a hard polymer used to sustain the external mechanical force. It is noted that the secondary coat- ing must sustain the mechanical force, so it must have sufficient thickness and higher Young’s modulus. Based on the strength consideration, the best design

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Sham-Tsong Shiue

Fig. 2. The effects of the thick- nesses of the primary coating and secondary coating on the maximum shear stress 7-

Flg. 3. The effects of the Young’s modulioftheprimarycoatingand secondary coating on the maximum shear stress r,,

1026

El (MPo)

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Theoretical Analysis of the Thermally Induced Delamination

Fg. 4 . The effects of the Poisson’s ratio of the primary coating and thermal expansion coqmcient of

mum shear stress T- the secondary coatulg on the maxi- x z

of a double-coated optical fiber is to decide the thick- ness (i.e., r2-r1) and the Young’s modulus E, of the secondary coating first. Then, to minimize the ther- mally induced delamination of polymeric coatings, the Young’s modulus of the primary coating and thermal expansion coefficient of the secondary coating should be decreased and the Poisson’s ratio of the primary coating should be increased.

The adhesive stress at the interface of the primary coating and glass fiber can be estimated from the me- chanical strip force in the stripping process. An exam- ple is shown by Shiue and Chen (10). The strip forces Fa of two commercialized double-coated optical fibers illustrated (10) are 1.33 and 1.52 N, respectively, and the corresponding adhesive stresses T, are 6.6 and 7.2 MPa, respectively. Figures 2 to 4 show that if the selection of physical pxoperties of polymeric coatings is not in a good manner, T,, will be larger than 7,.

Therefore, it is important to minimize the thermally induced delamination of polymeric coatings by appro- priately selecting polyrmric coatings.

5. C0;NCLUSIONS

The thermally induced delamination of polymeric coatings in double-coated optical fibers is investigated. Some important results are summarized as following:

1) Because the physical properties of the glass fiber and polymeric coatings are different, a shear stress T ~ ( X ) exists ai: the interface of the glass fiber

and primary coating after temperature drop. The shear stress T ~ ( x ) is zero at the middle of the fiber, and has a maximum value at both ends of the fiber.

2) If the shear stress T ~ ( x ) is larger than the adhe- sive shear stress T , between the glass fiber and primary coating, the adhesive bond at the inter- face of the glass fiber and primary coating will be broken: therefore, in order to minimize the coat- ing’s delamination, such a shear stress should be minimized.

3) The shear stress T ~ ( x ) could be minimized by a suitable selection of polymeric coatings and their thicknesses. To minimize such a shear stress in a double-coated optical fiber, the thickness and Poisson’s ratio of the primary coating should be increased, but the Young’s modulus of the pri- mary coating and the thickness, Young’s modu- lus, and thermal expansion coefficient of the sec- ondary coating should be decreased.

4) Based on the strength consideration, the thick- ness and Young’s modulus of the secondary coat- ing should be decided first. Then, to minimize the thermally induced coating’s delamination, the Young’s modulus of the primary coating and ther- mal expansion coefficient of the secondary coat- ing should be decreased and the Poisson’s ratio of the primary coating should be increased.

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Sham-Tsong Shim

ACICNOWLEDGMENT a, thermal expansion coefficient of the secondary coating

K material's parameter A material's parameter A, material's parameter A, material's parameter

u, Poisson's ratio of the glass fiber

This work was supported by the National Science Council, Taiwan, Republic of China, under grant num- ber NSC 86-2215-E-035-001; and the Telecommuni- cation Laboratories, Chung-Hwa Telecommunication Corporation, Republic of China, under grant number v Poisson's ratio NSC-86-420 1.

NOMENCLATURE

C, constant of integration C, constant of integration

E, Young's modulus of the glass fiber El Young's modulus of the primary coating E, Young's modulus of the secondary coating G shear modulus of the primary coating k material's parameter L half length of the optical fiber r radial coordinate

ro radius of the glass fiber r, radius of the primary coating r, radius of the secondary coating

AT temperature drop To axial force in the glass fiber T2 axial force in the secondary coating

u, the axial displacements of the points located at the glass fiber surface

u, the axial displacements of the points located on the inner boundary of the secondary coating

E Young's modulus

x axialcoordinate

OreskLetten a thermal expansion coefficient a, thermal expansion coefficient of the glass fiber a1 thermal expansion coefficient of the primary

coating

u, Poisson's ratio of the primary coating v2 Poisson's ratio of the secondary coating

T, shear stress at the interface of the glass fiber and primary coating

T~ shear stress at the interface of the primary coating and secondary coating

T, adhesive shear stress at the interface of the glass fiber and primary coating

T, the maximum shear stress at the interface of the glass fiber and primary coating

T shearstress

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Receiued M a y I, 1997 Revised November 1997

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