An Investigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders

Transcription

1 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October An Investigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders L. Kumosa, D. Armentrout, B. Benedikt and M. Kumosa Center for Advanced Materials and Structures Department of Engineering, University of Denver 390 S. York St., Denver, CO 8008, USA ABSTRACT The applicability of using flat composite plates and hollow core composite cylinders for moisture absorption testing of unidirectional glassrpolymer composites used in high voltage composite ( non-ceramic) insulators was examined. Two main issues were addressed in this work. First, the effect of specimen geometry ( cylinders vs. plates) on moisture absorption by the composites was investigated both numerically and experimentally. Both classical Fickian and non-fickian diffusions were considered. Subsequently, hollow core cylinders made up of ECR ( low seed) - glass fibers and epoxy resin were tested for their high voltage properties under controlled moisture diffusion conditions. The specimens were exposed to warm, moist air and their high voltage properties were ascertained using a modified version of the ANSI test ( standard C9.11 Section 7.4.) for water diffusion electrical testing. It was found that the behavior of the hollow core cylinder and flat plate composite specimens subjected to moisture compared reasonably well experimentally and very well numerically. From the high voltage tests, a direct correlation was found between the amount of moisture that had been absorbed by the specimens and the amount of leakage current that was detected. It was shown that using the thin walled composite cylinders leakage currents could be predicted based on the amount of absorbed moisture in the insulator composites. The predictions can be made based on relatively short term moisture data even if the diffusion process in the composites is anomalous in nature with long times required for full saturation. After additional verifications, considering other composite systems, the hollow core cylinder testing under controlled moisture and high voltage conditions could become a screening test for selecting suitable glassrpolymer composites for insulator applications. Index Terms Composite, nonceramic insulators, GRP composites, moisture, moisture absorption, leakage current, modeling, hollow core rods. INTRODUCTION 1.1 COMPOSITE ( NON-CERAMIC) GRP ROD INSULATORS omposite Ž non-ceramic. insulators, based C on glass fiber reinforced polymer Ž GRP. rods, have been widely used in transmission and substation applications for several years worldwide. Their advantages over traditional porcelain insulators are numerous, however their strength-to-weight ratio and ease of installation are their defining characteristic. Yet, under certain in-service conditions, harsh environmental variables such as high moisture contents, elevated temperatures, electrical fields, and acidic conditions can cause severe damage to the in- Manuscript recei ed on 4 December 003, in final form 3 January 005. sulators and in particular to their GRP rods. For instance, brittle fracture of the GRP rods can occur w1-18 x, leading to the failure of the insulators if either water or nitric acid is allowed to penetrate inside the units. The ingress of water into the composite GRP rods can also alter the dielectrical properties of the insulators making them less suitable for high voltage insulation applications w1, 19 x. It has been recently shown that an increase in the amount of moisture inside unidirectional glassrpolymer composites leads to a higher leakage current w1, 19 x. The water diffusion electrical testing in w1, 19xwas performed on solid rod composite specimens using a modified verw0 x. In sion of the ANSI standard C9.11 Section 7.4. the modified tests w1, 19 x, amounts of moisture and leakage currents were measured only before and after mois r05r$ IEEE 1043

2 1044 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders ture exposure. No attempt was made however, in Refs. 1 and 19 to correlate the rates of moisture absorption to the rates of increase in leakage currents. The moisture absorption properties of E-glass and ECR-glassrpolymer resin composites used in composite insulators have been recently investigated both numerically and experimentally using flat plate specimen geomew1 x. The composites were ranked for their resistance tries to moisture absorption after exposure to humid air with a relative humidity of 80% at 50C. The effects of fiber and polymer types on moisture uptake by the composites were thoroughly investigated. The most important data and conclusions presented in w1xare further evaluated in the context of the high voltage testing performed in this research. The purpose of this research was to investigate the effects of varying levels of moisture on the dielectric properties of a unidirectional GRP composite. Rather than using flat composite plates as was done in previous moisture abw1 x, or solid rods following w19 x, hollow core sorption work cylinders were used in this research to investigate leakage current as a function of changing moisture content. Since thin walled composite cylinders have less mass than the solid rods previously used, they should be much more suitable for moisture absorption experiments, reaching saturations within relatively short periods of time. Also, the round geometry of the hollow core cylinder specimens, not possessed by the plates, makes them suitable for the electrical tests according to the ANSI standard w0 x. Both their cylindrical geometry and small mass make them appropriate for the moisture diffusion electrical testing. Since no systematic research on the applicability of thin walled composite cylinders to moisture testing of insulator composites has ever been performed, this specimen geometry had to be investigated and compared to the composw1 x. The comparison ite plates used in previous research between the two geometries had to be conducted both numerically, by simulating moisture absorption, and experimentally. This was one of the objectives of this research in addition to establishing the effect of the amounts of moisture on the magnitudes of leakage currents. 1. MOISTURE DIFFUSION ANALYSIS The moisture diffusion process for most unidirectional composites is assumed to be Fickian in nature w, 3 x. This means that the diffusion of moisture into the material follows Fick s second law, which is also the same law that governs heat conductivity w x. Fick s second law states: c c s Dx Ž 1. t x where c is the concentration of moisture, t is time, x is distance through the transverse direction of a specimen and D is the coefficient of diffusivity in the transverse x Figure 1. Schematic representation of the procedure for applying the Fickian diffusion numerical prediction to the moisture absorption data. direction. Using the appropriate boundary conditions, Shen and Springer w, 3xpresented a solution for Fick s second law and obtained a relationship between the moisture content at any time Ž M., the maximum moisture content Ž M. of a specimen, its thickness Ž h. MAX, and the diffusivity constant Ž D.. This relationship is given as: x 0.75 Dx t MAX ž ž h / / Ms M 1yexp y7.3 Ž. where both MMAX and Dx can be obtained from the moisture contentrweight gain vs. square root of time Ž ' t. plots as shown in Figure 1. This is done by using the following equation: h My M1 / ž / 4M MAX ' t y ' t 1 D s Ž 3. A ž assuming that the apparent diffusivity, D, is approxi- A mately equal to the transverse diffusivity, D. In equation x 3, MMAX is the average equilibrium value on the curve and the term ŽŽ M y M. rž t y t.. is equal to the slope ' ' 1 1 of the initial linear segment of the moisture contentrweight gain vs. ' t curves. For more detailed information on the application of the Fickian diffusion nuw3 x. The values for percent moisture content at any time can merical prediction, the reader is referred to be determined using: weight of moist specimenyweight of dry specimen Ms weight of dry specimen 100%. Ž 4. The behavior of materials in a moist environment dew3 x. Materials in an environment with constant humidity but pends greatly on the conditions of that environment varying temperatures show the same level of maximum

3 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October dissolution, micro-cracking, molecular binding, or structural relaxation. Figure c demonstrates these effects on the moisture absorption curves. These phenomena deviate from single-phase Fickian diffusion and therefore cannot be accurately analyzed using the numerical procedure presented. A multiple-phase model needs to be implew1 x. mented Figure. Behavioral relationships in the moisture diffusion tests. a, effect of temperature on moisture absorption; b, effect of the ambient relative humidity on moisture absorption; c, anomalous behavior of moisture absorption due to material instability. moisture absorption, but the rates of absorption differ. A specimen in a cooler environment will take more time to equilibrate than a specimen in a warmer environment. This principle is demonstrated in Figure a. In constant temperature, but with varying amounts of humidity, the rates of water absorption stay the same, but the total amount of moisture absorbed increases with an increase in ambient humidity. Figure b demonstrates this relationship. Not only do environmental variables impact the moisture absorption curves, but so do material properties like 1.3 EDGE EFFECT It has been shown that a unidirectional composite material takes moisture faster in the direction parallel to the fibers than in the direction perpendicular to the fibers w3 x. This is in part due to the quality of the resin-fiber interface. This can be better seen in the model presented by Shen and Springer for parallel Ž D. and perpendicular Ž D. diffusion in a unidirectional composite w3 x: H Ž. D s D 1y Ž 5a. R f ž ' / D s D 1y r Ž 5b. H R f where f is the volume fraction of fibers and DR is the diffusivity of the resin. This model assumes that the fibers do not absorb any moisture. Other models for DH have also been presented by Shirrell and Halpin w5, 6 x, Woo and Piggott w7x and Kondo and Taki w8 x. Shirrell and Halpin used equations for shear stiffness to define diffusivity, Woo and Piggot utilized a relationship between resistance and diffusivity. Some authors w9x have gone as far as adopting the work of Lord Rayleigh Ž ca regarding electrical conductivw8x devised a model using the fiber ity. Kondo and Taki arrangement as a variable. The work of Shen and Springer has been widely utilized with a high degree of success and acceptance w, 3, x. Shen and Springer w3x have devised a method of converting the apparent diffusivity of a composite to the diffusivity of its resin including a correction for the effects of the edges in a unidirectional composite specimen. The apparent diffusivity of a rectangular specimen can be related to the diffusivities in each direction. The relationship is as follows: ž ( / ( h Dy h Dz DAs Dx 1q q Ž 6. l D n D where D x, Dy and Dz are the diffusivities in each direc- tion, h is the specimen thickness, and l and n are the nominal lengths of both sides of the specimen. Using equations Ž 5a. and Ž 5b., D, D and D can be defined as: x x y z Dxs D cos q D H sin Ž 7a. Dys D cos q D H sin Ž 7b. D s D cos q D sin 7c Ž. z H x

4 1046 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders where, and are the angles between the Cartesian plane of a rectangular specimen and the direction of the fibers as defined in w3 x, and D and D H are the parallel and perpendicular diffusivities, respectively defined by equations Ž 5a. and Ž 5b.. Combining equations Ž.Ž. 5, 6 and Ž. 7 gives the model by which the diffusivity of the resin can be calculated: / f Ž. ( DRs DA 1yf cos q 1y sin ž / / f Ž. ( 1yf cos q 1y sin h ž 1q l f )1y Ž f. cos q 1y( sin ž / / f Ž. ( 1yf cos q 1y sin h ž q Ž 8. n f )1y Ž f. cos q 1y( sin ž To examine the effect of the edges of a specimen on the calculation of apparent diffusivity, the diffusivity of the resin Ž D. R needs to be calculated. By calculating D R, itis possible to compare the effect of the specimen edges for varying specimen geometries. In theory, the values obtained for the diffusivity of the resin by this method for any composite system based on the same resin and fiber should be all very similar, regardless of specimen geometry. 1.4 EDGE-EFFECT CORRECTION IN HOLLOW CORE CYLINDER SPECIMENS The assumption that diffusivity occurs only in one direction can be made for only extremely thin specimens where their thickness to length ratio approaches zero. However, real specimens used in moisture research exhibit significant diffusion from other directions along the other exposed surfaces. Shen and Springer w3xdevised a method for correcting this error in rectangular specimens, as was briefly described in Section 1.3. In this paper the method proposed by Shen and Springer has been altered to apply to hollow cylinders, instead of rectangular specimens. The mass of moisture, m m, in a purely one dimensional material of infinite thickness can be determined using the following equation w3 x: ( y1 Dt x mms AŽ cmaxycini. Ž 9. Figure 3. Schematics of a hollow cylinder and a flat plate. where A is the area of the specimen exposed to moisture, cmax is the maximum moisture concentration, cini is the initial concentration, Dx is the diffusivity constant along the x direction, and t is time. Similarly, the measure of moisture in a 3-dimensional rectangular specimen taking into account all possible surfaces is given by equation Ž 10. w3 x: Ž. ž ' ' m s c yc nl D qnh D m MAX INI x y t q hl Dz / Ž 10. ' ( where the term A in equation Ž. 9 is replaced by individual surfaces Ž nl, nh, hl., which are each affected by diffusivities in different directions Ž D, D, D. x y z. However, if we consider a hollow core cylinder of outer radius R, inner radius r and height H, and assume that the fibers are oriented down along the height of the cylinder Žsee Figure 3., then equation Ž 10. becomes: ž Ž. Ž. ' mms cmaxycini R y r D q RH D H ' t q rh DH / Ž 11. ' ( Ž where R y r.,rh and rh are the two end surfaces, the outer surface, and the inner surface of a hollow core cylinder, respectively. D and D H are the diffusivities parallel and perpendicular to the fibers, respectively. The term thickness that was used when referring to rectangular specimens is now the wall thickness of the hollow core cylinder, which is equal to the difference of the external radius Ž R. and the internal radius Ž r.. For a dry specimen the initial concentration cini is zero, and we can define the dry mass of the specimen md as w3 x: Ž. m s Ž R y r. H Ž 1. d where is the density of the material. Therefore, we can Ž. Ž. write equation 11 as a function of moisture content %

5 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October M instead of mass of moisture m: mm 4cm Ms 100s m Ž R y r. d R y r ž ' H ' H H / ' ( t D q R D q r D Ž 13. where cmscmaxycini. It should also be recognized that w3 x: Ž. Ž. mmqdy md mmaxr Ž R y r. H MMAXs 100s m m r Ž R y r. H d d c m 100s Ž 14. where MMAX is the maximum moisture content and mmq d is the mass of a moist specimen, and equation Ž 13. can be written as: ž / ' ( 4MMAX Ry r t Ms D q' D H Ž 15. Ry r H ' Ry r It can be seen that the term Ž D q' D H. repre- H sents the total diffusion into a specimen and can be replaced with the term ' D A, where D A is the apparent diffusivity measured experimentally: ( A 4MMAX t Ms ' D Ž 16a. Ry r ž / Ry r D H D s D q Ž 16b. H D A ( Equation Ž 16b. relates the apparent diffusivity to the parallel and perpendicular diffusivity measured in hollow core cylinder specimens. Using equations Ž 5a. and Ž 5b. for parw3xequation Ž 16b. can allel and perpendicular diffusivity be written as: ' 0 f Ry r 1y fr D s D Ž 1y. q Ž 17. H 1y A R f ) Using equation Ž 17. the measured apparent diffusivity Ž D. can be related to the diffusivity of the resin Ž D. A R and then using Shen and Springer s model for parallel Ž D. and perpendicular diffusion Ž D. H, the parallel and perpendicular diffusion can be calculated for a given material. Once these analyses have been performed, the apparent diffusivity can be compared to the perpendicular diffusivity Ž D. H and examined as to whether the assumption of thin specimens being affected only by 1-dimensional diffusion is appropriate. 1.5 ANOMALOUS DIFFUSION ANALYSIS The analysis presented in the previous sections deals with single phase diffusion where there is only one phase of moisture uptake followed by equilibrium. Anomalous diffusion implies numerous different phases of moisture absorption leading to a final equilibrium w3-36 x. The behavior of some of the composite materials investigated in this research has been previously found to be anomalous Ž non-fickian. w1 x. This type of diffusion cannot be readily analyzed using the single-phase methods presented above; a multi-phase diffusion model is needed which describes the physical behavior of the material. One such model was presented by Carter and Kibler w3 x. This model uses the assumption that moisture in materials with anomalous Ž two-phase. diffusion occurs in two distinct yet related phases. The first is the absorption of water molecules in the mobile phase into the material with a diffusion coefficient D. Next, the molecules are bound to the molecular structure of the resin with a probability and become unbound with a probability B. Using these assumptions, Carter and Kibler devised a model for the analysis of moisture absorption in materials with anomalous diffusion characteristics. A convenient approximation of this model is presented below w3 x: ž Ž odd. ykl t Max l s1 B 8 e y t Ms M e 1y Ý q B l B / ybt y t ybt q Ž e y e. qž 1y e. ;,B q B s DrŽ h. Ž 18. The value of D can be assumed from simple singlephase diffusion in equation Ž. 3. The necessary MMAX value used to calculate D is assumed to give the best possible fit for the initial slope and first knee in the moisture content vs. square root of time curves, up to the second phase of diffusion. FINITE ELEMENT MODELING ANALYSIS Moisture diffusion in materials can be simulated numerically using for example the finite element method Ž FEM.. FEM can be used to solve the diffusion equation, which is given by the following formula w37 x: ž / ž z / cž x, y, z, t. cž x, y, z, t. s D t x x xt ž / cž x, y, z, t. cž x, y, z, t. q Dy q D Ž 19. y y z z

6 1048 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders where cž x, y, z, t. denotes the moisture concentration, which depends upon position and time, D x, Dy and Dz are diffusivities along x, y and z directions, respectively. In the case of a unidirectional composite plate, it has been assumed that the fibers are aligned along the x direction; therefore diffusivity Dx is different than the diffusivities corresponding to the remaining two directions. A similar assumption can be made in the case of the composite cylinders. In order to determine the moisture distribution in a composite specimen, boundary conditions have to be specified in addition to equation Ž 19.. It can be assumed that at the initial time t 0, concentration c is equal to zero everywhere inside the plate or cylinder. However, on the surfaces, the moisture concentration is different than zero, which corresponds to the fact that these surfaces are subjected to diffusion from the surrounding environment. The magnitude of the initial concentration ci on the surfaces can only be determined from an experiment. However, if the magnitude of ci is known, the changes of concentra- tion c with time can be quite easily determined from equation Ž. 1. ANSYS 6.1 w37x with 3D 8-node elements Ž Solid 70. was used to generate finite element representations of isotropic and unidirectional composite plates and cylinders with different thicknesses. Due to symmetry conditions, one-eighth of each plate and cylinder was modeled. The FEM model of one of the considered plates and one of the considered cylinders are presented in Figures 4a and b, respectively. 3 MATERIALS AND SPECIMEN PREPARATION 3.1 PLATES In previous work, moisture absorption testing was performed on eight glassrpolymer composites used for high voltage insulator applications w1 x. These composites were based on three types of fiberse-glass, ECR Ž high seed. - glass and ECR Ž low seed. -glassand three different resinsmodified polyester, epoxy and vinyl ester. ECR Žlow seed. -glassrmodified polyester was not available from the manufacturer, and therefore was omitted. Glasforms, Inc. supplied the composite materials, which were made by pultrusion with no post curing being applied to the final products. The materials were machined into flat 5050 mm plates with three different thicknesses Ž 1, and 4 mm.. 3. CYLINDERS For the electrical testing performed in this work, only one of the eight materials tested previously was chosen. ECR Ž low seed. -epoxy was picked for its excellent resistance to stress corrosion cracking provided by the fibers, and its behavior in the presence of moisture w1 x. The epoxy resin does not absorb moisture too fast, as in the Figure 4. FEM representations. a, one-eighth of a hollow cylinder; b, one-eighth of a plate specimen. case of the modified polyester material, but it does have an interesting tendency to not fully equilibrate with its surroundings right away like the vinyl ester and modified polyester materials do. The rod specimens used for the ANSI water diffusion electrical test w0x are only defined by their length; the radius of the cylinder is left undefined. The stock material that was provided by the manufacturer for this research was in the form of long rods with an approximate diameter of 15.9 mm. Since the testing of the specimens was going to take place in humid air, such a large volume would require unrealistically long times of exposure for complete saturation. Therefore, a hollow cylinder specimen with the center core removed was agreed upon. The criteria for this specimen were that it had to have a very similar surw1 x. The hollow core cylinders were machined from 15.9 mm face area to volume ratio as the plates in diameter rods of various lengths obtained from Glasforms, Inc. Rods were cut to mm long pieces using a Buehler Slow-Cutting saw equipped with a diamond waffering blade. The pieces were cut in methanol.

7 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October Next, a 7.9 mm pilot hole was drilled out of the center. This produced nine hollow cylinders with 4 mm thick walls. Three of these were cleaned and set aside, while the other six were then placed in a lathe and the centers were bored out to the desired diameters. The cutting on the lathe was performed in two steps. First one side was cut, halfway through the specimen, and then the other side was also cut to match the first. This was done in an attempt to minimize the cracking of the composite, especially in the thin 1 mm thick walled specimens. As a result, nine specimens were prepared, with 1, and 4 mm wall thickness, three specimens for each wall thickness. 4 EXPERIMENTAL PROCEDURES 4.1 MOISTURE EXPERIMENTS Moisture experiments were performed pursuant to the recommendations made by ASTM Standard D59rD59M-9 w38 x. After machining, the specimens were thoroughly cleaned using methanol in conjunction with an ultrasonic bath. Once cleaned, the specimens were placed into an oven maintained at 60 C and dried. The mass of the specimens was recorded frequently to monitor the drying procedure. Once the specimen mass had stabilized, the initial mass after drying and the initial leakage currents of the specimens were recorded. The relative humidity in the drying oven was assumed to be negligent. At 1% ambient lab relative humidity, which has been previously measured, there would be a relative humidity of 1.7% in the oven. This would have very little effect on the moisture tests. The specimens were placed into an environmental chamber maintained at 50 C and 80% relative humidity. A Standard Environmental Systems, Inc. model SHBr4 environmental chamber was used, where the temperature was kept within 1C, and the humidity was kept within 3%. The mass of the specimens was measured using an analytical balance with a readability of 0.1 mg. The scale was auto-calibrated before every testing session, and each specimen was allowed to cool to room temperature before the mass was recorded so that the specimen s temperature would not affect the reading on the scale. To ensure that the specimens did not spend more than 30 minutes outside of the environmental chamber thus affecting moisture data, three specimens at a time were weighed. The specimens were weighed at increasing time intervals due to the considerable slow-down in moisture uptake for a period of approximately 4 months. After each weighing the specimens were tested for their electrical properties as described in the next section. The specimen preparation procedures and moisture testing performed on the composite cylinders was exactly the same as the procedures applied in the moisture testing on the composites plates of various thickness. The only Figure 5. High voltage test setup for measuring leakage currents. exception was the measurements of the leakage currents that were performed on the cylinders after drying for an initial leakage current value, and after each weighing of the specimen while exposed to moisture. 4. ELECTRICAL TESTING During high voltage testing, the composite cylinders were placed between two brass electrodes in a high voltage chamber as shown in Figure 5. A Hipotronics HD- 140-Auto was used for the voltage source of these tests. The ANSI standard w0x calls for the voltage to ramp at approximately 1 kvrs to 1 kv. The unit was set at the maximum voltage ramp rate and set to stop at 1 kv, yielding the initial voltage time curve shown in Figure 6. It can be seen in Figure 6 that the initial curve ramps up at about 1.3 kvrs to 8 kv, and then slowly approaches 1 kv at a rate of 00 Vrs. After a 60 s hold at 1 kv, the voltage decreases to zero at a rate of 1. kvrs. A Protek 608 digital multi-meter, with a 0.1 A resolution on the 5 ma scale, was used to record all ac leakage current values. For these tests, a max function was used that stores the maximum current value sampled at a rate of 10 samplesrs. The maximum value was held until the meter was reset. During testing, a dry standard specimen that was kept inside the Plexiglas high voltage chamber was tested for its ac leakage current at the beginning and at the end of each testing session to give us some indication of changes in ambient conditions for each testing session. These current changes shown through the standard specimen were then used to correct the data analysis presented later.

8 1050 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders Figure 6. Typical voltage vs. time response for a leakage current test. Figure 7. FEM comparison between moisture absorption curves for hollow cylinders and plates with 1,, and 4 mm thicknesses subjected to different diffusivities along Ž D. and perpendicular Ž D. I H to the fiber direction. 5 RESULTS AND DISCUSSION 5.1 FEM RESULTS FEM analysis of the plates and cylinders was performed in three stages. First, specimens were modeled with the diffusivity allowed only in the direction perpendicular to the fibers. Values for D, D H, and MMAX were used for illustration and were not directly taken from any experimental data. The second stage involved modeling a completely homogeneous plate and hollow core cylinder specimens with no differences in diffusivity along any of the directions. The same diffusivity was used perpendicular to the fibers Ž D., as was used along the fibers Ž D. H. Finally, plate and hollow core cylinder specimens were modeled where the diffusivity of moisture along the fibers was set to.75 times that of the diffusivity perpendicular to the fibers. The ratio of DrD H equal to.75 was experimentally determined in the previous moisture diffusivity research w1 x. Very slight differences were observed in the moisture absorption curves obtained in the three stages, indicating that the effect of specimen orthotropy was relatively small. For the third case for DrD H of.75 the numerical curves are presented in Figure 7. Very good agreement between the data for the plate and cylinder geometries can be seen in Figure 7, regardless of the chosen orthotropy, indicating very close numerical behavior of the plates and hollow core cylinders. 5. MOISTURE RESULTS FROM PLATES AND CYLINDERS The moisture content versus square root of time curves for the plate and cylinder specimens made out of ECR Ž low seed. -glassrepoxy are presented in Figure 8 for comparison. Most obvious is the clearly non-fickian behavior, which was observed for all the epoxy-based composites with E-glass and ECR-glass fibers w1 x. There was no distinct equilibrium in these specimens, but a second slower diffusion that took place after the initial surge of moisture uptake. This non-fickian behavior of the epoxy-based composites is further investigated in Section 5.4 of this work. Averaged moisture results for the mm thick plate specimens are presented in Table 1 w1 x. In addition, three typical moisture curves for the E-glass fiber based composites with modified polyester, epoxy and vinyl ester resins from the plate experiments are shown in Figure 9. The Fickian Ž modified polyester, vinyl ester. versus non- Fickian Ž epoxy. behavior of the composites can be clearly observed in Figure 9. In Figure 8 it can be noticed that the excellent agreement that was present in the numerical comparisons of plates and hollow core cylinders shown in Figure 7 is somewhat missing in the experimental data. During the initial uptake of moisture for specimens of the same thickness, the slopes match and therefore the curves are very close, however as the tests progress the cylinders start to deviate from the plates by taking on significantly more water. This is especially true for the and 4 mm thick specimens. However, it can also be observed in Figure 8 that none of the specimens Ž 1, and 4 mm thick. reached saturation, therefore, the maximum moisture contents in Figure 8. Comparison between plate and hollow core cylinder experimental results.

9 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October Table 1. Averaged moisture absorption results from three mm specimens for each of the eight tested composites w1 x. Rate of Water Absorption MMA X DA Ž y4 '. Ž. Ž y6 y1 10 % weight gainr 5 % 10 mm s. E-glassrmodified polyester E-glassrepoxy E-glassrvinyl ester ECR Ž high seed. -glassrmodified polyester ECR Ž high seed. -glassrepoxy ECR Ž high seed. -glassrvinyl ester ECR Ž low seed. -glassrepoxy ECR Ž low seed. -glassrvinyl ester fractions of fibers were slightly lower by 3-4% for the same composites. Since moisture absorption in glassrpolymer composites is dominated by the resin, this could be another explanation why the cylinders were absorbing moisture with slightly higher rates. Also, due to slightly different pultrusion conditions, the fiber orientation and distribution in the cylinder and plate specimens could be a little different, further affecting the moisture curves. Obviously, the above three material related factors could not be incorporated into the finite element computations, therefore they would not affect the data in Figure 7. Figure 9. E-glassrmodified polyester and E-glassrvinyl ester mm plate specimens showing single-phase Fickian behavior, and a mm E-glassrepoxy specimen showing slightly non-fickian behavior. the specimens could not be exactly determined. Certainly, the rates of moisture absorptions are affected by the specimen thickness and geometry but it is unclear if the same effects could also influence the maximum moisture contents in the composite if the data in Figure 8 are considered. It appears that the level of deviation of the plates and hollow core cylinders is related to the thickness of the specimens with the differences between the moisture absorption curves in Figure 8 for the plates and cylinders increasing with the specimen thickness. It is unclear why such a difference exists; however some possibilities are considered. First of all, a different form of machining was used for the plates Ž surface grinding. and for the hollow core rods Ž drilling, boring, lathe cutting.. These two different machining procedures could cause slightly different types of surface damage to the composite affecting the moisture absorption data. There is also the possibility that there are some slight differences in the volume fraction and distributions of fibers in the two geometries caused by the pultrusion process and the use of different shaped dies Ž circular vs. rectangular dies., or by varying fiber bundle sizes. The fact is that the volume fractions of fibers in the composite plates were found to be similar ranging from 53 to % with the exception of the ECR Ž high seed. - glassrvinyl ester composite for which the fraction of fibers was approximately 66% w1 x. For the cylinders, the volume There is also another fact that must be considered here. In general, the amount of absorbed moisture in the composite plates decreased with an increase in the specimen thickness w1 x. This was especially apparent in the case of the vinyl ester based composites. Since the thickness effect was observed for the same composites, both the machining and fiber volume fraction effects could not be used to explain this rather unexpected phenomenon. It appeared that the maximum moisture contents decreased with an increase in the specimen volume. Since the volumes of the plates and cylinders for the same specimen thickness are different, with the volumes of the mm thick cylinders and plates equal to 60 mm 3 and 5000 mm 3, respectively, the larger volume of the plates could absorb less moisture concentration than the smaller cylinders. Therefore, the effect observed in the data in Figure 8 could be of the same type as observed in the plate testing w1 x. However, since the ECR Ž low seed. -glassrepoxy specimens did not reach saturation Ž both plates and cylinders., the specimen volume effect on saturation in this case could not be clearly established based on the data shown in Figure 8. It should be pointed out that the maximum moisture contents were determined indirectly in section 5.5 using the Carter and Kibler approach. One could also point out that the difference in the moisture absorption between the plates and cylinders could be caused by the obvious difference in the geometries of the two specimens. For the mm plates, for example, the ratio between the surface areas perpendicular to the fibers to the total surface area of the specimen is about 3.7% whereas the same ratio for the mm thick cylinder is 6.3%. Since for our composites D is approximately.75

10 105 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders times larger than D H, this could indicate why the cylinders absorbed moisture faster than the plates. However, this effect, which was incorporated into the finite element model, does not influence the data in Figure 7. Moreover, the difference in the diffusion coefficients along and transverse to the fibers should affect the rates of moisture absorption but not the maximum moisture contents. It is clear from the data presented in Table 1 and in Figure 9 that the modified polyester based materials took on moisture much faster than either the epoxy-based or vinyl ester-based materials Ž see Figure 9 as an example.. Moreover, the modified polyester based composites took slightly higher total amounts of water. The results in Table 1 do not show some of the abnormal behavior encountered when performing moisture tests on glassrpolymer plate specimens w1 x. First, the 4-mm thick vinyl esterbased specimens did not reach the same equilibrium as the 1 and mm thick specimens. Next, all the epoxy-based materials did not reach a steady equilibrium, and after the first initial surge in moisture absorption, they continued to take on moisture with a second, slower rate as shown in Figures 8 for the ECR Ž low seed. -glassrepoxy composite, as an example. Last, the different materials with ECR Ž high seed. -glass fibers absorbed less moisture than other materials with the same resin and either E-glass or ECR Ž low seed. -glass fibers. 5.3 EXPERIMENTAL VERIFICATION OF FEM RESULTS FOR CYLINDERS AND PLATES To further investigate the validity of the numerical moisture models, a comparison of the FEM and experimental results is presented. This comparison is presented in Figures 10a and 10b for both the plates and the cylinders, respectively. Here very good agreement is seen between the experiment and the model for the initial phase of moisture uptake. However, the non-fickian behavior can be seen when the experimental data surpasses the numerical model, which assumes equilibrium. Very good agreements between the experiment and the model were observed in the data for the composite plates, which exhibited the classical Fickian diffusion w1-4, 30, 31 x. For the composites that achieved saturation, the vinyl and modified polyester based systems, the agreements were good within the initial uptake and saturation regions, especially for thin specimens. 5.4 EDGE-EFFECT CORRECTION To investigate the effect of the edges of the cylinders on the diffusion calculations, edge-correction was performed using equation Ž 17.. The values for apparent diffusivity Ž D. A were obtained from the single-phase Fickian equations and were inserted first into equation Ž 5b. Žun- corrected solution for D. and then into equation Ž 17. Ž R the corrected solution for D.. These values were then plot- R Figure 10. Comparisons between FEM predictions and experimental data for mass of moisture absorbed vs. square root of time. a, plates; b, cylinders. ted against wall thickness Ž Ry r. and are shown in Figure 11. Since, in theory, the diffusivity values of the resin should not be affected by specimen geometry, the results from equations Ž 5b. and Ž 17. should be the same. However, examining the data in Figure 11, it is clear that the uncorrected results are affected by geometry. This demonstrates the importance of addressing the edge-effect caused by varying specimen geometries. A similar in- Figure 11. Uncorrected Žequation Ž 5b.. and corrected Žequation Ž 17.. values of the diffusivity of the resin Ž D. r for the E-glassrepoxy hollow cylinders. Calculations performed using single-phase Fickian assumptions.

11 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October Table. Values from the single-phase Fickian model Žequation Ž 3.. of ECR Ž low seed. -glassrepoxy cylinders that are then used to fit the Carter and Kibler model w3x for anomalous diffusion. Wall Thickness DA s D M Ž MAX Assumed wmmx Specimen Ž y7. w 10 mm rs x Single-Phase. w% x Table 3a. Values obtained from fitting the ECR Ž low seed. - glassrepoxy cylinders experimental data to the Carter and Kibler model w3xusing the nonlinear regressionrleast squares method. Sum of Wall B MMAX Squares Ž y8. Ž y8 Thickness Specimen Ž Theoretical. Error w x w y1 x w y1x w x Ž y4 mm s s % vestigation was performed in previous work w1x on the experimental results from the plate specimens with different fibers and resins. Comparing the values of corrected D for ECR Ž low seed. R -glassrepoxy hollow cylinder specimens in Figure 11 and the corresponding values for plate specimens of the same material, the values were found to Ž y6 be almost identical.510 mm rs.. This indicates the very similar behavior of the same material in geometrically different specimens. 5.5 ANOMALOUS DIFFUSION ANALYSIS The Carter and Kibler model w3x was used to analyze the non-fickian moisture data shown in Figure 8. Values for, B and MMAX were calculated using the nonlinear regressionrleast squares method with reasonably low errors. The data for the 4 mm thick specimens were assumed to behave similarly to the 1 and mm thick specimens. However, this was not verified since the testing time did not allow the thickest specimens to reach either equilibrium or the second, slower rate of diffusion. The value of D was assumed from the single-phase Fickian model since this diffusivity only takes into account the initial rate of diffusion. For the cylinders, the values obtained from the single phase Fickian analysis of the data used in the Carter and Kibler model are presented in Table. The values for, B and MMAX for the cylinders obtained by using the nonlinear regressionrleast squares method are presented in Table 3a along with the error associated with that method. Evaluating the data in Table 3a, it can be seen that, at least for the 1 and mm thick specimens, there is a pattern for the values of and B, where is usually smaller than B. Also, the values of MMAX for three of the six specimens shown in Table 3a show values in the area of 0.34%. The 4 mm thick specimens could not be analyzed in this way due to the fact that the 4 mm thick specimens barely finished the first stage of diffusion when the test came to an end. Also, there was very little Ž if any. data from the second, slower diffusion phase. Therefore, the nonlinear regressionrleast squares fitting method could not be used for these specimens. The variables defining a pattern cannot be approximated from experimental data if the pattern is not present. Due to the scatter in the experimental moisture results presented in Figure 8, a certain degree of uncertainty exists in the predictions of M Ž theoretical. MAX. In some cases, the nonlinear regressionrleast squares fitting provided highly unlikely values in the ranges of several percent Ž see Table 3a.. If during the fastest initial diffusion phase the specimens take on moisture up to 0.5% at most, it is highly improbable that the specimens will take on an additional 810% of moisture during the second, slower diffusion phase while at the same time asymptotically reaching equilibrium. The number of necessary molecular binding sites for accommodating the bound phase of absorption to accomplish this feat would be extraordinarily high. Based on the assumption that the three specimens that provided MMAX values of approximately 0.35% were correct, the approach was modified by averaging those three realistic values of M MAX. The averaged value Ž 0.35%. was then inserted into the nonlinear regressionrleast squares analysis for each of the 1 and mm thick specimens and B and were re-calculated. Those results are presented in Table 3b. It can be seen from Tables 3a and 3b that by performing this modification, we were able to obtain much more consistent values of and B, while at the same time only minimally increasing the sum of squares error. This also indicates the extreme sensitivity of this analysis to the minimal scatter in the experimental moisture results. Table 3b. Modified nonlinear regressionrleast squares analysis where an averaged value of MMAX from specimens 1 and for the 1 mm thick cylinders and specimen from the mm thick cylinders in Table 3a is substituted in, solving for and B. Sum of Wall B MMAX Squares Ž y8. Ž y8 Thickness Specimen Ž Theoretical. Error w x w y1 x w y1x w x Ž y4 mm s s %

12 1054 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders Table 3c. Modified nonlinear regressionrleast squares analysis where averaged values of and B from 1 and mm thick cylinders in Table 3b are substituted in, solving for M MAX. Wall B MMAX Sum of Squares Ž y8. Ž y8 Thickness Specimen Ž Theoretical. Error w x w y1 x w y1x w x Ž y4 mm s s % and B values for the 4 mm thick specimens were calculated by taking the values of and B for the 1 mm thick specimens and dividing by the thickness in mm. Figure 1. Non-Fickian behavior of ECR plates and cylinders. Ž low seed. -glassrepoxy In the next step of the analysis, the values of and B for each of the three specimens for a given thickness shown in Table 3b were averaged and substituted in for each of the three specimens for a given thickness. Subsequently, the new maximum moisture contents and associated errors were re-calculated. By doing this, we could verify whether these averaged values of and B, in conjunction with the experimental data would yield values of M MAX similar to those found for the three specimens believed to show realistic data listed in Table 3a. Those results are presented in Table 3c. It can be seen that the averaged values of and B provided very similar values of M MAX. However, the sum of squares errors increased slightly. The difference in B and between the 1 and mm thick specimens shows that the model we are using is somewhat misguiding. Carter and Kibler claim that the values of and B are material properties not affected by specimen geometry, however the values of B and in Table 3c show that there is an effect of specimen geometry. Furthermore, the values of and B for the mm thick specimens are almost twice as small as for the 1 mm thick specimens. This can be explained if we consider the definitions of B and given by Carter and Kibler. They state molecules of the mobile phase diffuse with a concentration- and stress-independent diffusion coefficient D and are absorbed Ž become bound. with a probability per unit time at certain sites whose nature is unspecified. Molecules are emitted from the bound phase, thereby becoming mobile, with a probability per unit time B. Carter and Kibler assumed no difference in the thickness of the specimen, other than the single-phase part of the analysis used to find D. It stands to reason that if a specimen geometry is altered by increasing thickness, its volume increases much faster than its surface area. Therefore, the flow of moisture is considerably slowed in thicker specimens, decreasing proportionally the probabilities of binding and unbinding B of water molecules in the resin. Yet this is not accounted for in Carter and Kibler s model for anomalous diffusion Žsee equation Ž 18.. w3 x. It stands to reason that and B should be proportionally smaller as specimen thickness increases. Assuming this trend, the values of and B for the 4 mm thick specimens were approximated by taking the values for 1 mm thick specimens and dividing them by 4. This is only an approximation of the true values of B and for the 4 mm thick specimens, considering also the fact that the values for the 1 and mm thick specimens are also not completely accurate. The results for the 4 mm thick specimens are also presented in Table 3c. They show similar values of M MAX, albeit with again slightly higher errors than the thinner 1 and mm thick specimens. Since the values of B and were only approximated here, the predicted values of MMAX listed in Table 3c are most likely not exact, especially for the 4 mm thick specimens. Therefore, it is still unclear what is the actual effect of specimen thickness on the maximum moisture contents considering the data shown in Figure 8. The analysis performed on the ECR Ž low seed. - glassrepoxy cylinders was also performed on the plates tested in previous research w1 x. In Figure 1, examples of hollow cylinder and plate ECR Ž low seed. -glassrepoxy specimens are shown with both single-phase Fickian and non-fickian Ž Carter and Kibler. fits. The anomalous diffusion fits match the experimental data much better than the single-phase Fickian fits. 5.6 HIGH VOLTAGE TESTING OF COMPOSITE CYLINDERS WITH MOISTURE Three ac leakage current and moisture content vs. time plots for 1, and 4mm thick specimens are presented in Figures 13a- 13c, respectively as examples of the response of the three specimen geometries to moisture and high voltage. In these plots, the ac leakage current data has been standardized using the data from the test standard,

13 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October Figure 13. Leakage current and moisture content vs. square root of time plots. a, one 1 mm thick; b, one -mm thick; c, one 4 mm thick ECR Ž low seed. -glassrepoxy hollow cylinders along with the anomalous Ž non-fickian. diffusion fits and leakage current predictions. Figure 14. Averaged leakage current vs. moisture content curve with a linear trend fit and R value. a, all three 1 mm thick; b, all three mm thick; c, all three 4-mm thick ECR Ž low seed. -glassrepoxy hollow cylinders. which was kept in the ambient conditions of the testing setup. The plots in Figures 13a - 13c are quite representatives for the three specimen geometries. As was described earlier, the Protek meter used for measuring the results in Figures 13a - 13c has a resolution of 0.1 A. Since the change in leakage current was very small, the quantization error of the meter is large in com- parison. In order to reduce this error, the average values of the leakage currents versus the average moisture contents for the three specimen geometries are shown in Figures 14a - 14c. It can be seen that leakage currents increase with an increase in the amount of moisture, as can be expected. The average values were determined from three independently tested composite specimens for each cylinder thickness. The data in Figures 14a - 14c do ex-

14 1056 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders Table 4. Predicted values of maximum moisture content Ž M. MAX, Moisture-Leakage Current Factor Ž F. M y LC, Maximum Leakage Current Ž I. and time to 99% of saturation Ž t. L(AC)y MAX SAT. Sum of Wall Squares Thickness Specimen MMAX FMy LC IL(AC)y MAX tsat Error Ž mm. Ž %. Ž Ar%. Ž A. Ž years. Ž 10y The values of tsat are the same for each of the three specimens per thickness since this value seems to be governed by the values of B and. hibit some scatter, but the overall trends seem to be linear. Despite the scatter, the slopes of the curves slightly increase with the thickness of the specimens. It is also apparent in the data shown in Figures 14 that the amount of scatter decreases with an increase in the specimen wall thickness. Assuming that the moisture vs. leakage current relations are truly linear, the magnitudes of the leakage currents could be predicted as a function of the time of exposure to moisture for a given composite and moisture conditions. Using the data in Table 3c, for the best fits of the moisture curves, several issues can be addressed. First, the maximum moisture content and the corresponding maximum leakage current could be estimated based on the relatively short-term moisture data presented in this work. Second, the time for the maximum moisture content and for the maximum leakage current could also be predicted. Finally, a characteristic constant, which might directly relate leakage current to moisture for the composites tested under the same moisture conditions, could be established. Obviously, the predictions would be affected by the assumptions made in the approximations of and B described in the previous section. The predicted leakage current for the corresponding estimated maximum moisture content from Table 3c for each of the nine tests performed are shown in Table 4, with the times necessary for each to attain 99% of maximum moisture saturation and leakage current. Also presented are the corresponding sum of squares errors in the predictions of leakage currents. It should be noticed that the errors are greatly increased compared to the errors for anomalous diffusion analysis. This is due to the considerably increased scatter in the leakage current data as compared to the moisture results. The leakage current analysis was performed assuming linear relations between the moisture and leakage current data shown in Figures 14a- 14c, and that the moisture and leakage current curves shown in Figures 13a - 13c differ by a constant Žmoisture - leakage current factor, F. M-LC as shown in the following relationship: I Ž t. s F MŽ t. Ž 0. LŽ AC. MyLC where I is ac leakage current and Mt Ž. L( AC) is moisture as a function of time. In the case of the ECR Ž low seed. -glassrepoxy composite used in this research, which showed characteristically non-fickian diffusion, Mt, Ž. was evaluated using a model for anomalous diffusion shown in equation 18. However, in the case of other materials which behave in a purely Fickian manner, where there is a distinct equilibrium after an initial surge in moisture absorption, a single-phase Fickian equation can be substituted such as the one presented in equation Ž.. The factors for the ECR Žlow seed. -glassrepoxy hollow cylinder specimens tested in this research were calculated for all nine tests and are shown in Table 4. The data listed in Table 4 clearly indicate the importance of the non-fickian diffusion analysis performed in this research. This type of analysis is essential for the prediction of the maximum leakage current and moisture content using the relatively short-term moisture and leakage current data for the ECR-repoxy composite investigated in this study. An alternative approach would be to investigate the composite subjected to moisture for up to 8 years, which would be required to obtain 99% saturation of the 4 mm thick specimens. For the thinner specimens the required testing times would be shorter, however, the scatter in the leakage current data would be noticeably higher. For the ECR-glassrepoxy composite system investigated in this project the moisture-leakage current factor was found to be somewhere between 1.35 and.55, with the average of 1.97 Ž see Table 4.. It can also be seen that the factors slightly increase with the specimen wall thickness. The average factors for the 1, and 4 mm thick specimens were 1.7, 1.86 and.35 Ar%, respectively, which coincide well with the slopes in Figures 14a-14c. In the calculation of the factors, using equation Ž 0., moisture content in % was used. Obviously, for the same moisture content the three specimen geometries will absorb different amounts of moisture. In addition, the moisture distributions in the cylinders will be different depending on the specimen thickness. These effects can be seen in Figures 15, 16a and 16b where the moisture distributions in the cylinders with the 1, and 4 mm wall thickness for a moisture content of 0.% are shown using the finite element models developed in this study Žsee Figure 4a.. Both the distribution of moisture through the thickness in the middle of the cylinder walls Ž Figure 16a. and along the cylinders Ž Figure 16b. are very different depending on the thickness. Also, for the 0.% moisture

15 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 1, No. 5; October Figure 15. FEM moisture concentration contour plot of one-eighth a 4 mm thick hollow cylinder with 0.% moisture content Žmoisture concentration in units of grmm 3.. Figure 16. a, Moisture concentration vs. wall-thickness plots at the center planes; b, Moisture concentration vs. distance along height from center plots of the specimens for hollow cylinders with 1, and 4-mm wall thicknesses with 0.% moisture content Žsee dashed line A in Figure 15.. content the mass of moisture, ignoring the edge effect clearly seen in Figures 15 and 16b, is 0.65 x 10 y, 1. x 10 y and.1010 y g for the 1, and 4 mm wall thickness, respectively. The increase in leakage current due to moisture absorption was also calculated for each of the cylinders assuming that the dielectric constant of water does not change when it is absorbed in the composite. The increase in leakage current due to the capacitance increase caused by the absorption of 0.% moisture would be 0.01, 0.0 and 0.04 A for the 1,, and 4 mm thick cylinders, respectively. From the leakage current graphs in Figures 13 and 14, the increase in current with moisture is much higher than what can be accounted for by the change in capacitance. The additional increase in the leakage currents that was observed is due to variety of other moisture concentration-dependent and moisture mass-independent effects unknown at present to the authors. The small increase in the factors with the wall thickness could suggest that some effect of moisture mass and distribution is still present in the leakage current data. The increase in moisture content in unidirectional glassrpolymer composites when used for high voltage insulation will drastically decrease the insulation characteristics and increase the potential for electrical failures of the final product. Therefore, an investigation of the moisture-leakage current factors needs to be performed involving other composite materials used for high voltage Žnon- ceramic. insulator applications. It can be expected that the factors for other composite systems used in composite insulators will be different and could be significantly different than the factors for the composite system investigated here. This could be especially true in the case of glass fiber composites with high seed counts w19xand unw39 x. It can also be expected that even for the cured resins ECR-glassrepoxy composite system tested here the factor would drastically increase if the composite were subjected to long-term aging involving significant disintegration of the epoxy resin. Using the novel approach proposed in this work, such issues could be quite precisely investigated. 6 CONCLUSIONS Particular emphasis was placed in this research to investigate the response of a unidirectional ECR Žlow seed. -glassrepoxy composite to moist air at 50C using either flat plates or hollow core cylinders. A comparison between the plates, used in previous testing of unidirecw1 x, and the cylinders tional glassrpolymer composites used in this research illustrated the close characteristics of both geometries. In the numerical calculations, the two specimen geometries were virtually indiscernible with slight differences observed in the experimental data. Since moisture absorption by the ECR Ž low seed. - glassrepoxy composite was non-fickian in nature and could not be accurately described using single-phase models, an anomalous diffusion Ž double phase. model was applied to the experimental results with success. A methodology, based on Carter and Kibler s model for anomalous

16 1058 Kumosa et al. : An In estigation of Moisture and Leakage Currents in GRP Composite Hollow Cylinders diffusion, was suggested discussing how to handle non- Fickian diffusion in insulator composites for various specimen thicknesses. The effect of moisture on the measured leakage currents in the ECR Ž low seed. -glassrepoxy composite was also investigated using the hollow core cylinders. Despite some scatter observed in the experimental data, a linear relationship was noticed between the amount of moisture in the composite and the level of ac leakage current. Using Carter and Kibler s model the maximum moisture content, maximum leakage current and time-to-saturation for the composite were predicted. The analysis performed in this work provides groundwork for the comparative testing of various composite materials exposed to moisture in different geometries. The ability to perform an analysis of the leakage current as a function of the absorbed moisture levels of various insulator composites using the hollow core cylinder geometry could provide special significance for the composite insulator industry, allowing long-term predictions of electrical insulation properties of materials in moist environments. By measuring the moisture-leakage current factors, introduced in this study, different insulator core composites could be ranked for their electrical response under moisture as a function of in-service conditions. ACKNOWLEDGMENT This research was supported by the Electric Power Research Institute Ž EPRI. under contract EP-P971rC1399. The authors are grateful to Dr. John Stringer of EPRI and Mr. R. Stearns of the Bonneville Power Administration for their support of the research presented in this paper and, in general, for their support of the insulator research at the University of Denver. REFERENCES wx 1 M. J. Owen, S. J. Harris and B. 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