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ANALYSES OF COMPOSITE INSULATORS WITH CRIMPED END-FITTINGS: PART I - NON LINEAR FINITE ELEMENT COMPUTATIONS

M. Kumosa, Y. Han and L. Kumosa

Center for Advanced Materials and Structures Department of Engineering

University of Denver 2450 S. Gaylord St., Denver, Colorado 80208

Abstract The purpose of this research has been to design an advanced numerical model that can be used to evaluate the mechanical behavior of composite insulators with crimped end-fittings subjected to axial tensile loads. Two issues have been addressed in this study. First, examples of insulator failures due to improper crimping have been shown and discussed. Second, comprehensive non-linear two- and three-dimensional finite element simulations of crimped insulator ends have been performed. The effects of uniformly and linearly distributed crimping deformations as well as external tensile loads on mechanical stress in the insulator end have been examined. Numerical results have been compared with the experimental data obtained by performing tensile strength tests on crimped insulators supplied by NGK. It has been shown in this research that the type of crimping can significantly affect the mechanical strength of crimped composite insulators. For the same magnitude of crimping and the friction coefficient at the rod/fitting interface the load/displacement diagrams are strongly dependent on the crimping profiles generated during the manufacturing process. The highest radial and tangential stress concentrations in the composite rods exist due to crimping. However, the stresses are reduced if a crimped composite insulator is subjected to axial tension. At the same time, the normal stresses along the rod are significantly increased when the rod is being pulled out of the fitting. The concentration of the normal stress along the rod is significantly affected by the magnitudes of applied compression and axial tensile loads as well as the type of compression profile on the rod surface generated during manufacturing. It has been clearly shown in this research that the mechanical behavior of crimped composite insulators can be evaluated by performing finite element computations considering the actual crimping deformations and the geometrical and physical properties of the insulator end. Introduction 1.1 Composite Suspension Insulators with Crimped End-Fittings Composite suspension insulators are used in overhead transmission lines with line voltages in the range 69 kV to 735 kV. The insulators consist of a unidirectional E-glass reinforced polymer (GRP) rod with two metal end-fittings attached to the rod during assembly. In order to prevent electrical degradation of the GRP rod and the electrical leakage currents, the entire surface of the GRP rod is protected by a layer of rubber alloy with multiple weathersheds (see Figure 1). The rubber also protects the rod against

Published version can be found in Composites Science & Technology, Vol. 62, No. 9 (2002) pp. 1191-1207.

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corrosive environments which can be present in-service. The primary function of the end-fittings is to provide a mechanical link and to transfer loads from the high voltage conductor to the GRP-rod (at the line end), and from the GRP rod to the tower (at the tower end). In previous designs the fittings were attached to the GRP rod either by an epoxy adhesive (epoxy cone design) [1] or by metal wedges inserted into the rods inside the fittings (wedge design) [2]. However, due to a lower cost of assembly, most insulator manufacturers have adopted the crimped end-fitting design. In the crimped design, the end-fittings are radially compressed onto to the ends of the rod [3-6]. This results in a purely mechanical bond caused by residual compressive stresses at the interface between the GRP-rod and the end-fitting. Since composite insulators are a relatively new product, few published studies have examined their mechanical performance and design [1-16]. In this research, non-linear finite element computations have been performed to examine the effect of various crimping conditions on the mechanical strength of crimped composite insulators. Internal stresses in the insulator ends have been determined for various crimping conditions, external applied loads as well as elastic and elasto-plastic properties of the fitting material. 1.2 Crimping Procedure The bonding between the GRP rod and the metal end-fitting in the insulators with crimped end-fittings is purely mechanical in nature and is strongly dependent on the magnitude of compression applied during crimping and the friction coefficient between the fitting and the rod, as well as the geometry of the fitting [3-6,13-16]. Low crimping deformations will not provide a strong bonding between the GRP rod and the end-fitting especially if the friction coefficient at the interface is low. On the other hand, excessive crimping deformations might cause severe rod crushing. Since the transverse strength properties of unidirectional fiber reinforced polymer composites are significantly lower in comparison with their longitudinal strengths, severe cracking of the GRP rod can occur if excessive crimping deformations are applied during manufacturing (see Figure 2) [5]. These cracks might gradually grow in-service due to the complex mechanical (static and cyclic) stresses as well as the chemical and electrical environments associated with high voltage applications. In particular, humidity and corona discharges could have a severe effect on the in-service performance of overcrimped composite insulators. The combined effect of the mechanical, electrical and environmental stresses can cause brittle fracture failures of high voltage composite suspension insulators in-service [17-23]. 1.3. Strength of Composite Insulators with Crimped End-Fittings Since the GRP rod can slide inside the end-fitting during crimping, internal stresses in the rod can be estimated using the following simple plane stress model: σrr

rod = σθθrod = Ur

rod E22rod / rrod( 1− ν23

rod ) (1)

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where σrrrod and σθθ

rod are the radial and tangential stress components in the rod, rrod is the radius of the rod, Ur

rod is the radial displacement on the surface of the crimped rod, E22rod

is the Young’s modulus of the rod transverse to the fibers, and ν23rod is the Poisson’s ratio

in the cross-section of the rod. The mechanical strength of a composite insulator with crimped end-fittings can be determined by pulling the GRP rod out of the end-fittings [3-6, 14-16]. The insulator strength will depend on the amount of compression applied during manufacturing, the frictional properties of the rod/fitting interface and the geometry of the fitting. There are three important factors related to the fitting geometry which strongly influence the insulator strength. The first factor is the length of the fitting. Obviously, long fittings provide higher insulator strength than short ones. The second important factor is the size of a gap between the internal surface of the fitting and the rod surface before crimping is applied. The third factor is the internal surface of the fitting. Smooth surfaces will require larger compression deformations applied to the fitting and the rod surface in comparison with rough surfaces (for example threaded surfaces) for the same strength properties of the insulators. The other factor which also can have a significant affect on the insulator strength is the material of the fitting. Since the mechanical bonding between the GRP rod and fitting in crimped composite insulators is achieved due to the plastic deformation of the fitting material during crimping, the effect of plasticity of the fitting on the insulator strength could be significant. Different elasto-plastic properties of the fitting materials can noticeably influence the internal stress distributions in the GRP rod and thus the insulator strength for the same amount of compression applied to the fitting. 2. Analysis of Field-Failed Suspension Insulators due to Improper Crimping Improper crimping procedures can have serious effects on the short- and long-term strengths of composite suspension insulators. Two examples of damage caused by improper crimping procedures will be shown and discussed in this section. If crimping deformations in the GRP rods generated during manufacturing are excessive, the composite rod can be significantly damaged inside the hardware. Multiple cracks can be generated inside the rod (inside the fitting) near the rod/hardware interface. An example of this type of damage is illustrated in Figure 2. Another example of insulator damage due to improper manufacturing is illustrated in Figures 3a and 3b. A 115 kV suspension composite insulator that failed in service by rod fracture was examined. The insulator failed under relatively low tensile stresses, much lower than the tensile strength of the GRP rod in longitudinal tension. The damage zones presented in Figure 3a and 3b consists of numerous large transverse and longitudinal cracks in the GRP rod. The mechanical failure of the rod occurred just above the top surface of the end-fitting. Most importantly, the transverse cracks in the rod are planar in nature (see Figure 4) and closely resemble the brittle fracture cracks previously reported [1,18,19,21], if examined macroscopically. However, under higher magnifications significant differences were observed between the surface fracture morphologies of the

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insulators failed by brittle fracture and the damage in the insulator shown in Figure 3a and 3b. Under higher magnification (see Figure 4) the fracture surfaces are still planar without however flat fracture surfaces of the individual fibers (see Figures 5a and 5b). It should be pointed out here that when suspension insulators fail in service by brittle fracture, the fracture surfaces of glass fibers are also planar, however, consisting of clearly defined mirror and hackle zones. It can be clearly seen in Figures 5a and 5b that the fracture surfaces of the glass fibers are certainly not planar, and are highly irregular. This effect can be even better observed by examining the SEM micrographs presented in Figures 6 and 7. In Figures 7a and 7b the most typical surface fracture morphologies of individual fibers from the insulator in Figures 3a and 3b are illustrated. Not only the fracture surfaces are highly irregular but very often they consist of longitudinal cracks in the glass fibers (see Figure 7a). If compare with a typical fiber fracture caused by stress corrosion (brittle fracture, see Figure 7c [21]) the differences between these two fracture modes are apparent. In order to determine a potential cause of failure of the insulator shown in Figures 3-7 a unidirectional E-glass/epoxy specimen was mechanically damaged by applying large tensile and bending forces. Subsequently, the fracture surface of the specimens was examined by SEM. An SEM micrograph of this fracture surface is shown in Figure 8. Clearly, the microscopic features of the surfaces presented in Figures 5-8 are very similar. In particular, the micrographs shown in Figure 5b, 6b and 8 appear to be almost identical. Therefore, it was concluded that the damage to the rod in the insulator shown in Figure 3a and 3b was caused by a combination of manufacturing crimping stresses and mechanical tensile stresses concentrated in the rod near the fitting in service. The mechanically damaged insulators illustrated in Figures 2 and 3 were provided to this research by US electrical utilities as examples of mechanical failures of suspension composite insulators. These types of failures have not been detected in insulators manufactured by NGK. 3. Finite Element Computations In order to explain mechanical failures of crimped composite insulators a detailed analysis of internal stresses in their crimped ends is required. Therefore, a crimped composite suspension insulator was modeled in this study using ANSYS 5.2 [24]. Two- and three-dimensional axisymmetric models of the insulator end were generated, as illustrated in Figures 9 and 10. The 3-D model was composed of 8-node brick elements. The 2-D axisymmetric model used 8-node isoparametric elements. The point-to-surface contact elements were placed between the rod surface and the internal surface of the fitting. The finite element computations were performed assuming geometric non-linearity as well as elastic and elasto-plastic properties of the fitting material. The composite rod was assumed to be linear-elastic. The geometry of the finite element model follows the dimensions shown in Figure 9. The following elastic properties of the GRP rod were assumed:

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E11 = 49 GPa, E22= 13 GPa, G12 = 4.8 GPa, G23 = 4.3 GPa, ν12 = 0.34, ν23 = 0.5. where E11 is the longitudinal Young’s modulus, E22 is the transverse Young’s modulus, G12 and G23 are the shear moduli and ν12 and ν23 are the Poisson ratios of the GRP rod material. The end fitting was assumed to be made out of steel with the following properties: E = 213600 MPa, ν = 0.3, σY = 300 MPa, σU = 400 MPa and εU = 0.2. where E is the Young’s modulus and v is the Poisson ratio of the steel as provided by NGK whereas σY, σU and εU are the yield strength, tensile strength and elongation at failure, respectively. The plastic and strength properties of the fitting were estimated from the open literature for this particular steel. The analysis was divided into two steps, that is, crimping and pulling. In the first step, crimping was simulated on the surface of the end-fitting. In the second step, the rod was gradually pulled out of the end-fitting. The stresses in the GRP rod caused only by crimping as well as crimping and pull-out can be derived from the two-step finite element simulations. In addition, the load/displacement curves from the numerical pull-out can be determined. The actual crimping deformations applied during manufacturing were measured on the surface of the fitting of an insulator with the standard stress conditions from NGK [14,16] by comparing the diameters of the fitting in the compressed (plastically deformed) and uncompressed areas (third method described in Section 1.3). The measurements were performed in 24 locations on the surface of the fitting and then the average compression was determined. The crimping appeared to be uniform around the circumference of the end-fitting, and was almost uniform along the longitudinal direction with a small reduction close to the top surface of the fitting. At first, a perfectly uniform crimping profile was assumed (see Figure 9(a)) and the crimping was simulated via prescribed displacements applied onto the external surface of the fitting. The value of the friction coefficient at the rod/fitting interface was taken as 0.3 (measured and provided by NGK). The plastic deformation of the fitting during crimping was modeled assuming an elasto-plastic model with work-hardening presented in Figure 11. Secondly, the crimping conditions in the finite element analysis were modified to simulate linearly distributed crimping deformations along the length of the fitting. 4. Results and Discussion 4.1. Load-Displacement Diagrams The numerical and experimental load-displacement diagrams are shown in Figure 12. The experimental curve was obtained by subjecting the insulator manufactured by NGK with the standard crimping conditions to axial tension on an MTS testing machine [14,16]. The insulator failed by rod pull-out. After the mechanical test, the GRP rod was carefully

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examined. No damage of any kind was detected on the surface of the rod. It can be seen in Figure 12 that the numerically determined load-displacement diagram from the fully non-linear finite element computations is very close to the experimental curve for this particular insulator. The difference between the maximum loads, obtained experimentally and numerically, is only 2.9%. The frictional forces between the rod and the end-fitting increase as the pulling force is increased. The highest load takes place right before the entire rod slides inside the end-fitting. It can be seen in Figure 12 that there is a small drop on the experimental curve at the highest point. This might be caused by the fact that the friction coefficient during the pull-out experiment is not constant. Most likely, the drop in the load on the experimental curve coincides with the transition from static to dynamic friction. In the finite element model, a constant friction coefficient was assumed therefore the numerical curve does not exhibit a similar load drop. When the rod starts sliding out of the fitting, the contact area between the fitting and the rod decreases. Thus, lower pulling forces are required to pull the rod out of the fitting after the maximum load is achieved. The numerical and experimental load-displacement curves shown in Figure 12 are very close to each other. It can therefore be concluded that the numerical computations of the rod-pull out experiment closely simulate the actual experimental conditions. Thus, the internal stress distributions in the insulator end can be determined from the finite element analysis with a high degree of accuracy. 4.2. Internal Stresses and Strains in the Insulator The strain and stress distributions in the insulator end after crimping, calculated using the 3-D model, are presented in Figure 13(a-c). The plasticity of the metal end-fitting was included. The equivalent stress criterion was used as the criterion of plasticity. If the equivalent stress in an element exceeds the yield strength of the metal (which was assumed to be 300 MPa) the element is considered to be plastically deformed. The accumulated effective plastic strains, as defined in reference [24], are shown in Figure 13(a) whereas the stress components σrr and σθθ are plotted in Figure 13(b-c). The stress components of σrθ, σz, σzθ and σzr caused by crimping are significantly smaller than σrr and σθθ and therefore are not shown. The same strains and stresses calculated using the 2-D axisymmetric model are presented in Figure 14(a-c), where the coordinate system is the same as in Figure 10(b). The results from the 2-D calculations are very similar to those obtained from the 3-D model. For the axisymmetric geometry of the insulator and the assumed loading conditions, the two dimensional axisymmetric computations are accurate and much faster. As shown in Figures 13(a) and 14(a) a plastic zone develops through the thickness of the metal end-fitting. The plastic deformation is very uniform along the z direction (along the fitting) due to the uniform crimping simulated on the surface of the fitting. There is no plastic deformation of the composite rod, because the GRP rod is considered to be

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perfectly elastic. The stress contours of the σrr and σθθ in the rod are the same, because the rod is under uniform compression as the end-fitting is crimped. Moreover, the stresses in the crimped sections are almost uniform along the end-fitting and the rod (see Figures 13 and 14). The stresses and strains in the insulator change significantly when a tensile axial load is applied along the GRP rod. Figure 15 presents the contours of σz, σrr and σθθ at the highest pull-out load on the numerical curve shown in Figure 12. As illustrated in Figure 15, the stress components σrr, σθθ and σz are no longer uniformly distributed along the z direction. The tensile stress σz along the rod inside the fitting increases along z, and is proportional to the integration of σrz, which represents the friction along the interface between the rod and the end-fitting:

σz = 2

0r rod

z

� σrz dz (2)

The stresses in the fitting are not a major concern, whereas the stresses in the GRP rod are critical for this research. One apparent phenomenon is that the stresses in the rod are almost constant in the radial direction. The stresses on the rod surface are plotted in Figure 16. As shown in Figure 16(a), σrr and σθθ are evenly distributed when the rod is crimped with small σz and σrz stress components. During the rod pull-out process, the stress components σrr and σθθ decrease substantially as shown in Figure 16(b). At the same time, the stress along the z direction increases significantly and is especially high near the top surface of the fitting. The above observations clearly demonstrate that the most dangerous state of stress, as far as the possibility of internal intralaminar cracking in the rod is concerned (see Figure 2), is generated in the rod during the crimping process. During pull-out, the radial and tangential stresses are substantially reduced. However, the normal stress along the fibers is very high and can exceed the longitudinal tensile strength of the rod. The tensile stress concentration shown in Figure 16 near the top surface of the fitting can cause fracture of the rod during pull out. It is clear from the results presented in Figures 16a and 16b that crimping procedure must be optimized by keeping the radial and tangential stresses in the rod small (during crimping) and at the same time reducing the tensile stresses along the rod near the top of the hardware (during pull-out). This will create conditions in the rod such that the possibility of internal cracking by radial and tangential compressive stresses will be low and the rod will not fracture due to tension if subjected to excessive tensile loads. 4.3. Effect of Plasticity of the Fitting The above discussion of the internal stresses and load-displacement curves for the insulator with uniform crimping is based on the results obtained from the non-linear FEM simulations which included plasticity of the fitting material. Plasticity of the fitting is very important for two reasons. First, a singular stress region [4,5] can be generated at the bimaterial corner marked in Figure 9 by A, because both geometric and material

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discontinuities are present at the interface/wedge corner. These singular stress fields will be particularly strong if a crimped insulator is modeled without considering the frictional effects between the internal surface of the fitting and the external surface of the GRP rod. Even, if contact elements are used along the rod/fitting interface, singular stress fields will be present at the corner, however not as strong as in the fully linear case when the rod is fully bonded to the fitting. The plastic deformation of the end-fitting reduces the stress concentration in this region. As a result, the curves in Figure 16 are quite smooth, though the stresses increase slightly at the wedge corner. Secondly, the mechanical link between the fitting and the GRP rod is achieved through the residual plastic deformation of the end-fitting. After the plastic deformation is generated and the crimping forces are removed, the GRP rod is still compressed by the residual stresses in the end-fitting. The plastic deformation in the end-fitting, once crimped, changes little after the crimping forces are released. If plasticity is not considered, the 2-D model gives the stresses on the surface of the rod after it is crimped (see Figure 17). Compared with Figure 16 where plasticity was taken into account, Figure 17 presents similar stress distributions except at the terminus of the interface due to the presence of a weak singular field in this region. 4.4. Effect of Different Crimping Profiles In the next part of this study, the effect of linearly distributed crimping deformations along the fitting on the mechanical behavior of a crimped composite insulator was examined. In Figure 18 five experimental and numerical load-displacement curves are shown. Two numerical curves obtained with uniform crimping, with and without plasticity, are compared with the experimental load-displacement diagram from the NGK insulator with the standard crimping conditions. In addition, two other curves are also shown in this figure from the linear -elastic models with the linear crimping profiles (type 1 and type 2) shown in Figures 9(b) and 9(c). It can be noticed that the difference between the curves for the insulators modeled with uniform crimping, with and without plasticity is not large. However, the models with the linear crimping profiles generated significantly different load-displacement curves with much higher maximum loads in comparison with the previous two models. It can therefore be concluded that the non-linear model with uniform crimping, without considering plasticity, quite accurately simulates the experimental load-displacement diagram. The effect of the plastic deformation of the fitting for the insulators from NGK seems to be small and can be neglected in the computation of the numerical load displacement diagram. Since large computation times are required to model the insulators with the plastic deformation of the fitting this observation is important. Still, the curves modeled with plasticity provides a better approximation of the experimental load/displacement curve. The results presented in Figure 18 clearly demonstrate that the linear crimping models generate significantly different load/displacement diagrams in comparison with the models with uniform crimping. In the models with linear crimping the largest deformation of 0.324 mm was applied at the top of the end-fitting for type 1 linear

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crimping, and at the bottom of the end-fitting for type 2 linear crimping. The average crimping deformation was still the same as for the uniform crimping models. The effective crimping on the rod surface can be estimated knowing the crimping deformations applied during manufacturing on the surface of the fitting and the dimensions of a gap between the surface of the rod and the internal surface of the fitting using equation (3) presented below Ur

rod = Ure − G (3)

where Ur

e is the applied crimping on the end-fitting, Urrod is the effective crimping on the

rod surface, and G is the gap between the rod and the internal surface of the fitting. Taking the dimensions shown in Figure 9(a) and using equation (3), the average crimping on the rod surface was estimated to be 0.082 mm for the uniform crimping deformations, and 0.092 mm for the linearly distributed crimping profiles. The maximum crimping deformation on the rod surface for the linear crimping was estimated to be 0.244 mm (again using equation (3)). The average crimping on the rod surface for the linear crimping deformations applied to the fitting was found to be higher than the average compression of the rod surface for the uniform crimping, despite the fact that the same magnitudes of crimping were considered. In the next stage of this research, the analytically estimated compression values on the rod surface inside the fitting (from equation 3) were compared to the numerically determined compression data from the finite element analyses. Figures 19(a-c) show the effective crimping on the rod for the uniform and the two linear crimping profiles. The rod deformations presented in Figure 19 were obtained from the finite element simulations without considering plasticity. The agreement between the analytical and numerical predictions of the rod surface compression was especially good for the case of the uniform crimping. For the case of uniform crimping, the average rod compressions from the analytical and numerical predictions were found to be 0.082 and 0.080, respectively. For the linear cases, the analytical and numerical values of the maximum compression are 0.244 and 0.213 (type 1) and 0.244 and 0.216 (type 2), respectively. Because the magnitude of crimping on the GRP rod is higher for the cases with the linear crimping profiles than for the case of the uniform crimping, the numerical load-displacement curves for the linear crimping profiles exhibit higher maximum loads than that for the uniform crimping profile. It can also be concluded from the results presented in Figure 18 that the linear crimping conditions in the insulators could result in significantly improved mechanical strength properties of the insulators in comparison with the uniform crimping case provided that the GRP rod does not fracture during pull-out. Subsequently, the effect of the linear profiles on the stress distributions in the GRP rods was investigated. The stresses along the rod surface inside and just outside the fitting for type 1 and 2 linear crimping profiles calculated using the 2-D finite element model are

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presented in Figure 20 and Figure 21, respectively. The stresses in these two figures were obtained for the highest loads on the load/displacement curves shown in Figure 18. The stresses were determined from the models without considering plasticity of the fittings. After the rod is crimped, the values of the highest radial and tangential stresses along the rod for the linear crimping profiles are much higher than that for the uniform crimping shown in Figures 16 and 17. According to equation (1), the stresses in the rod are proportional to the radial deformation of the rod surface. Because of the significant difference in the effective crimping on the rod shown in Figure 19, the non-uniform crimping profiles generate significantly higher transverse stresses in the GRP rod during the crimping process. Obviously, if the transverse stresses are too high, the composite rod can be damaged during manufacturing. For type 1 linear crimping, the section of the rod surface with the highest crimping is also under the highest tensile stress when the rod is pulled out of the end-fitting. At the same time, the radial and tangential stresses are reduced during the pull-out process, as shown in figure 20(b) similar to the case with uniform crimping. The stresses in this figure were obtained for the highest applied load during numerical pull-out. The highest crimping deformation on the rod surface is at the bottom of the end-fitting for type 2 linear crimping. Similar to type 1 the radial and tangential stresses are reduced during pull-out. However, the tensile stresses along the rod (σz) are not concentrated near the top surface of the fitting like in the type 1 case. The maximum tensile stress along the rod occurs deep inside the hardware and is lower than in the case of type 1 at the onset of pull-out. A finite element model of crimping has been recently suggested by Bansal et al. [3-6]. In their model, crimping deformations were prescribed on the surface of the fitting similar to the analysis performed in this research. In the previous crimping analysis, however, the deformation on the rod surface was measured using an ultrasonic technique. Then, crimping was simulated by applying prescribed displacements on the surface of the fitting with their magnitude and distributions exactly the same as the displacements of the rod surface inside the fitting. Moreover, the presence of the gap between the internal surface of the fitting and the rod surface was not considered. It can be seen that there is a fundamental difference between the previous and current approaches. The previous model assumes that the displacements on the rod surface and the surface of the fitting are exactly the same. The present model of crimping is more advanced since it does not require measuring the deformation of the rod surface which can be very difficult. However, the exact dimensions of the fitting before crimping must be known, which in some cases might not be possible. Taking the above into account, the following recommendations can be provided regarding the finite element simulations of crimped composite insulators: 1. If the exact dimensions of the fitting before crimping are unknown and the gap between the rod and the fitting cannot be incorporated into a finite element model, the deformation of the rod surface inside the fitting due to crimping should be determined first using the ultrasonic technique. This obviously will require the high accuracy of the

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ultrasonic measurements. Then, crimping can be numerically simulated following the approaches described in Refs. 3-6. 2. If the gap between the fitting and the rod can be modeled, the crimping problem can be investigated using the approach suggested in this paper. In both cases, however, the friction coefficient at the rod/fitting interface and the elastic properties of the rod and fitting materials must be known. 4.5 Insulator failure due to improper crimping It can be seen in Figures 16(b), 17(b), 20(b) and 21(b) that large tensile stresses σz in the rod along the fibers develop when the rod is pulled out of the fitting. These tensile stresses can be responsible for the failure of the GRP rod in tension if large axial loads are applied even if the magnitude of crimping is low. The maximum tensile stresses in the GRP-rod generated during pull-out, for the insulators with the linear crimping profiles, are certainly higher than the tensile strength of most unidirectional glass/polymer composite rods. The tensile longitudinal strength of unidirectional glass/polymer composites used in GRP rods is of the order of 1000 MPa [14]. If this stress is not exceeded the rod will pull out without fracture. However, if the tensile stress concentration in the GRP rod near the top surface of the fitting is greater than the longitudinal tensile strength of the rod the rod will fracture in the direction perpendicular to the fibers 14,16]. However, the effect of other stress components on the failure process cannot be ignored since the stress distributions in the rod inside the fitting are triaxial. Despite the fact the shear stress components in the rod near the top surface of the fitting are small as shown in Figures 16(b), 17(b), 20(b) and 21(b) (for small crimping deformations) they can affect the failure process if large compression is applied. For the insulator with uniform crimping modeled in this study the shear stress components near the top surface of the fitting during pull-out were not significant. In addition, the radial and tangential stresses were also very small in this location. Moreover, the normal tensile stresses in the rod along the fibers were only slightly concentrated in the rod, near the top of the fitting. Therefore, the failure process in this case would be predominantly determined by the magnitude of the tensile stress σz in the rod. If this stress exceeds the longitudinal tensile strength of the rod material, the insulator will fail by rod fracture. However, if this stress is lower than the tensile strength of the rod the insulator should fail by rod pull-out. This might change however, if the crimping deformations on the composite rod are significantly increased in comparison with the amount of crimping assumed in this research. An increase in the magnitude of uniform crimping will dramatically increase the normal stress in the rod near the top surface of the fitting resulting in a significant reduction in the critical tensile loads at rod fracture. Considering all the numerical results presented in this study the failure of the crimped insulator shown in Figures 4-7 can now be explained. Since this particular insulator failed in service under low tensile loads the failure was most likely caused by large tensile stresses in the GRP rod at the top of the fitting. Either the magnitude of crimping was too

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high (if uniform crimping was applied) or the crimping profile was linear (close to type 1) or a combination of uniform and type 1 crimping profiles. The combination of type 1 linear crimping with the high crimping magnitude and low tensile loads would make the situation even worse since the normal stress would be concentrated even more. There is also another possibility. The rod could have been crimped off axis inside the fitting due to an incorrect manufacturing process and improper design of the fitting. In this case, the normal stresses in the rod caused by pulling and bending would be even higher exceeding the tensile strength of the rod material at relatively low applied loads. A combination of all the above factors (magnitude of crimping, shape of the crimping profile, design of the fitting and the position of the rod inside the fitting) caused the mechanical failure of the insulator presented in Figure 3. Conclusions The mechanical behavior of crimped composite insulators subjected to tensile axial loads can be predicted using non-linear finite element techniques. It has been clearly shown in this research that uniform crimping generated during manufacturing provides the most optimum stress conditions in the GRP rod as far as the possibility of internal cracking in the rod due to crimping is concerned. Non-uniform crimping conditions on the rod surface inside the fittings generate significantly higher tangential and radial stresses in the rod in comparison with the uniform crimping case. Under axial tension, crimped composite insulators develop large tensile stresses in the rod at the top of the fitting. It has also been shown in this research that crimped insulators with either uniform or type 1 crimping profiles can fail mechanically by rod fracture under relatively low axial tensile loads if crimping deformations are too high. References 1. M. Kumosa, H. Shankara Narayan, Q. Qiu and A. Bansal, Brittle Fracture of Non-

Ceramic Suspension Insulators with Epoxy Cone End-Fittings, Composites Science and Technology, Vol. 57 (1997) pp. 739-751.

2. M. Kumosa and Q. Qiu, Failure Analysis of Composite Insulators, Final Report to

the Pacific Gas & Electric Company, Department Of Engineering, University of Denver, Denver, Colorado (1996).

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Report to the Bonneville Power Administration, Oregon Graduate Institute of Science & Technology, Portland, Oregon, 1994.

4. A. Bansal, A. Schubert, M. V. Balakrishnan and M. Kumosa, Finite Element

Analysis of Substation Composite Insulators, Composites Science and Technology, Vol. 55 (1995) pp. 375-389.

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5. A. Bansal, Finite Element Simulation and Mechanical Characterization of Composite Insulators, Ph.D. Dissertation, Oregon Graduate Institute of Science & Technology, Portland, Oregon, 1996.

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Insulators with Crimped End-Fittings, Journal of Composite Materials, Vol. 31, No 20 (1997) pp. 2074-2104 .

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Insulators with Fiberglass Rod Submitted to Mechanical Loads, IEEE Trans. Power Apparatus and Systems (1983), pp. 3123-3129.

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12. L. Paris, L. Pargamin, D. Dumora and R. Parraud, Rating of Composite

Suspension Insulators Related to the Long Term Mechanical Strength of Rods, in Proceedings of the 1994 IEEE/PES Winter Power Meeting, New York, NY, February 1994.

13. J. Lanteigne, S. Lalonde, and C. De Tourreil, Optimization of Stresses in the End-

Fittings of Composite Insulators for Distribution and Transmission Lines, Journal of Reinforced Plastics and Composites, Vol. 15 (1996) pp. 467 - 478.

14. M. Kumosa, Y. Han, S.H. Carpenter, D. Armentrout and L. Kumosa, Suitable

Crimping Conditions in Composite Suspension High Voltage Insulators, Final Report to NGK Insulators, Ltd, 1998.

15. M. Kumosa et al, Fracture Analysis of Composite Insulators, Final Report to the

Electric Power Research Institute, Department of Engineering, University of Denver, Denver, 1998.

14

16. M. Kumosa, D. Armentrout, L. Kumosa and S.H. Carpenter, Analyses of Composite Insulators with Crimped End-Fittings: Part II - Suitable Crimping Conditions, submitted for publication to Composites Science and Technology.

17. M. Kumosa, Q. Qiu, E. Bennett, C. Ek, T.S. McQuarrie, and J.M. Braun, Brittle

Fracture of Non-Ceramic Insulators, Proc. Fracture Mechanics for Hydroelectric Power Systems, G.S. Bhuyan and J. Kibblewhite Eds.Vancouver, BC, Canada, September 1994, pp. 235-254.

18. M. Kumosa et al., Micro-Fracture Mechanisms in Glass/Polymer Insulator

Materials under Combined Effects of Electrical, Mechanical, and Environmental Stresses, Final Report to the Bonneville Power Administration, Western Area Power Administration and the Electric Power Research Institute, Oregon Graduate Institute of Science and Technology, Portland, Oregon, 1994.

19. Q. Qiu, Brittle Fracture Mechanisms of Glass-Fiber Reinforced Polymer

Insulators, Ph.D. Thesis, Oregon Graduate Institute of Science & Technology, October 1995.

20. A. R. Chughtai, D. M. Smith and M. Kumosa, Chemical Analysis of a Field

Failed Composite Suspension Insulator, Composites Science and Technology, Vol. 58 (1998) pp. 1641-1647.

21. T. Ely and M. Kumosa, The Stress Corrosion Experiments on an E-Glass/Epoxy

Unidirectional Composite, Vol. 34, No. 10 (2000) pp. 841-878. 22. S. H. Carpenter and M. Kumosa, An Investigation of Brittle Fracture of

Composite Insulator Rods in an Acid Environment with Either Static or Cyclic Loading, J. Materials Science, Vol. 35, Issue 17 (2000) pp. 4465-4476.

23. T. Ely, D. Armentrout and M. Kumosa, Evaluation of Stress Corrosion Properties

of Pultruded Glass Fiber/Polymer Composite Materials, Composites Science and Technology (2001) in press.

24. ANSYS Engineering System, User’s Manual for Version 5.2, Swanson Analysis

System Inc. (1995) 25. S. Ding and M. Kumosa, Singular Stress Behavior at an Adhesive Interface

Corner, Engineering Fracture Mechanics, Vol. 47 (1994) pp. 503-519. Acknowledgments

This research was supported by the Electric Power Research Institute under contracts #W08019-21 and EP-P2971/C1399 and NGK Insulators, Ltd. The authors are grateful to Dr. John Stringer of EPRI and Mr. M. Ishiwari of NGK for their support of this study.

15

Figure 1. Schematic of a non-ceramic (composite) insulator.

16

Figure 2. Network of circumferential cracks in a GRP rod caused by improper crimping detected in a suspension composite insulator.

17

Figure 3a. Damage zone in the GRP rod near the top surface of the fitting in a field failed 115 kV suspension insulator.

18

Figure 3b. Damage zone in the GRP rod near the top surface of the fitting in a field failed 115kV suspension insulator.

19

Figure 4. Fracture surfaces in the GRP rod (low magnification).

20

Figure 5a. Example of the fracture surface in the GRP rod shown in Fig. 4.

21

Figure 5b. Example of the fracture surface in the GRP rod shown in Fig. 4.

22

Figure 6a. Fracture surface at higher magnification.

23

Figure 6b. Fracture surface at higher magnification.

24

Figure 7a. Fracture surface in glass fibers due to mechanical damage.

25

Figure 7b. Fracture surface in glass fibers due to mechanical damage.

26

Figure 7c. Fracture surface in glass fibers due to stress corrosion failure.

27

Figure 8. Fracture surfaces in an E-glass/epoxy unidirectional composite failed mechanically under multiaxial loading conditions.

28

~8

X

14.13

70

2.5

2.5

0.162

tensile load

Uniformcrimping

GRP rod

end-fitting

r

z

A

Figure 9a. Crimped end fitting with uniform crimping condition.

X = proprietary information, (all dimensions in millimeters)

29

2.5

2.5

tensile load

GRP rod

end-fitting

r

z

A

0.324

crimping

Figure 9b. Crimped end fitting with type 1 linearly distributed crimping condition.

30

2.5

2.5

tensile load

GRP rod

end-fitting

r

z

A

0.324

crimping

Figure 9c. Crimped end fitting with type 2 linearly distributed crimping condition.

31

Figure 10a. Finite element representation of the insulator end;

3-D model.

Figure 10b. Finite element representation of the insulator end;

2-D axisymetric model.

32

σY

εY

Strain ε

Stress σ

Figure 11. Elasto-plastic finite element model for the end-fitting material.

33

0

50000

100000

150000

200000

0 2 4 6 8 10 12

Displacement (mm)

Tens

ile L

oad

(N)

ExperimentalFEM

Figure 12. Experimental and numerical load-displacement diagrams from rod pull-out with uniform crimping.

34

( a ) ( b ) ( c )

Figure 13. Strains and stresses in the end fitting after crimping for the 3-D model; (a) accumulative effective plastic strain, (b) σrr and

(c) σθθ.

35

Figure 14: Strains and stresses in the insulator after crimping for the 2-D model; (a) accumulated effective plastic strain, (b) σrr and (c) σθθ.

A = -450 MPa B = -350 MPa C = -250 MPa D = -150 MPa E = -100 MPa F = -50 MPa G = 0 H = 100 MPa ( c )

A = -450 MPa B = -350 MPa C = -250 MPa D = -150 MPa E = -100 MPa F = -50 MPa G = 0 H = 100 MPa ( b )

A = 0.001 B = 0.002 C = 0.004 D = 0.006 E = 0.008 F = 0.012 G = 0.016 H = 0.020 ( a )

36

Figure 15: Axial σz, radial σrr and tangential σθθ stresses for the 2-D model at the highest load during pull-out; (a) σz, (b) σrr and (c) σθθ

A = -450 MPa B = -350 MPa C = -250 MPa D = -150 MPa E = -100 MPa F = -50 MPa G = 0 H = 100 MPa ( c )

A = -450 MPa B = -350 MPa C = -250 MPa D = -150 MPa E = -100 MPa F = -50 MPa G = 0 H = 100 MPa ( b )

A = 50 MPa B = 100 MPa C = 200 MPa D = 300 MPa E = 500 MPa F = 700 MPa G = 1000 MPa H = 1400 MPa ( a )

37

-300

-200

-100

00 20 40 60 80 100

z (mm)

(MPa)

( a )

-400

-200

0

200

400

600

800

1000

0 20 40 60 80 100

z (mm)

(MPa)

( b )

Figure 16. Stresses on the rod surface (a) after uniform crimping and (b) at the highest load during pull-out with plasticity

σz

σrr = σθθ

σrr = σθθ

σz ≅ 0 σrz ≅ 0 σθz = σrθ = 0

σrz

σθz = σrθ = 0

Fitting GRP Rod

38

-300

-200

-100

00 20 40 60 80 100

z (mm)

(MPa)

( a )

-400

-200

0

200

400

600

800

1000

0 20 40 60 80 100

z (mm)

(MPa)

( b )

Figure 17. Stresses on the rod surface (a) after uniform crimping and (b) at the highest load during pull-out without plasticity

σz

σrr = σθθ

σrr = σθθ

σrz

σθz = σrθ = 0

Fitting GRP Rod

σz ≅ 0 σrz ≅ 0 σθz = σrθ = 0

39

0

50000

100000

150000

200000

250000

300000

0 2 4 6 8 10 12Displacement (mm)

Tens

ile L

oad

(N)

Experimental: standard stress conditionFEM: uniform crimping with plasticityFEM: uniform crimping, no plasticityFEM: type 1 linear crimping, no plasticityFEM: type 2 linear crimping, no plasticity

Figure 18. Experimental and numerical load-displacement diagrams during rod pull-out for the end fittings with different crimping profiles.

40

Figure 19a. Deformation of the rod surface after uniform crimping.

41

Figure 19c. Deformation of the rod surface after type 2 linear crimping.

42

Figure 19b. Deformation of the rod surface after type 1 linear crimping.

43

-1000

-800

-600

-400

-200

00 20 40 60 80 100

z (mm)

(MPa)

( a )

-800

-400

0

400

800

1200

1600

0 20 40 60 80 100

z (mm)

(MPa)

( b )

Figure 20: Stresses on the rod surface (a) after type 1 liner crimping and (b) at the highest load during pull-out without plasticity.

σz

σrr = σθθ

σrr = σθθ

σz ≅ 0 σrz ≅ 0 σθz = σrθ = 0

σrz

σθz = σrθ = 0

Fitting GRP Rod

44

-800

-600

-400

-200

00 20 40 60 80 100

z (mm)

(MPa)

( a )

-800

-400

0

400

800

1200

0 20 40 60 80 100

z (mm)

(MPa)

( b )

Figure 21: Stresses on the rod surface (a) after type 2 liner crimping and (b) at the highest load during pull-out without plasticity.

σz

σrr = σθθ

σrr = σθθ

σz ≅ 0 σrz ≅ 0 σθz = σrθ = 0

σrz

σθz = σrθ = 0

Fitting GRP Rod