CHAPTER 2: Literature review
2.5 Mechanical behaviour of flexural stressed composite insulators
25
26
ultimate tensile stresses of insulators increase with the diameter of the rod, being the crimped length. The analytical model of the suspension insulator gives an overview mainly on the strength of the FRP rod and the end fittings which have to withstand to the minimum requirement of the specified mechanical loads (SML) and limit load (2.13).
The maximum shear stress of the FRP rod must be approximately 40 N/mm2; the SML may be found by this formula:
= (2.24)
In order to establish whether the end fitting will withstand the SML specified, the transition zone between the connection part of the fitting and the crimped part, and the cross-sectional area of the end fitting are identified as the critical zone in which the failure may occur.
Figure 2-13: Critical cross-sections when dimensioning an end fitting [5]
The tensile stress in the cross-sectional area of the fitting as shown in Figure 2-13 is:
= ( − )/4< (2.25)
with the tensile strength of the fitting, the outer diameter, and the inner diameter of the end fitting.
The transition areas are subjected to shear stress which should withstand the SML
= < (2.26)
with the maximum shear stress.
Di Da
27 2.5.2 Line post insulator
2.5.2.1 Damage limit load
An evolution of deflection is observed when a constant stress is applied to the material.
It has been observed that deflection is formed from a family of the straight linear equation = . in a semi-logarithm diagram. This is illustrated by Figure 2-14.
Figure 2-14: Deflection variation versus time and variation of the creepage rate coefficient A versus the stress in the embedded cross-section
The creepage rate at the given moment is equal to / . is the time (moment) and A is a coefficient found experimentally. In the case of a line post insulator there is a ductile behaviour similar to metallic materials, with an elastic deformation at low stress levels and a quasi-plastic deformation at high stress levels. During the strain behaviour, there is an intermediate area separating both phases, called the “damage limit” [40].
Stress
Time With
stand C urve
Figure 2-15: Damage limit Figure 2-16: Load-time curve for composite insulators stressed under
cantilever load.
28 2.5.2.2 Long-term mechanical behaviour
Figure (2-15) shows that the stresses applied to a composite line post insulator must be maintained below the “damage-limit” stress. The first sign of failure or fatigue depends on the loading time and the load applied.
The “damage limit” was established by the CIGRE Working Group 22.3 after many series of tests of the insulator without weather sheds. This was inspired by the variation of deflection over time, with a visual inspection for cracks of the surface of the rod. The conclusion of these tests was that the damage limit of short insulators is smaller (between 325 and 425 MPa for a 45mm rod diameter), while for longer insulators with the same insulator diameter, the damage limit is greater (between 475 and 600 MPa).
The nominal bending stress may be determined by [5]:
= /32
(2.27)
with the external load (bending), the bending length, and the diameter of the rod.
The damage limit load is approximately 25% higher than the MDCL, and 20-40%
smaller than the SCL.
2.5.2.3 Load application curves obtained with the analytical formula
In order to plot the loading curves, some analytical formulas are used for small deflections (10% of the insulator length). The general formula of the moment comes from the “Theory of Elasticity of Timoshenko” [40]. For compression loads:
= ( + )
tanh
(2.28)
and tension loads :
= ( + )
tanh
(2.29)
with the vertical load, the longitudinal load, and Z the compression and tensile loads, :Young’s Modulus, : Moment of Inertia of the FRP rod, with = ; the diameter of the FRP rod; finally the stress on the FRP rod may be calculated by :
29
= / (2.30)
with = 32
Figure (2-17) shows the load curves which may be produced by the analytical formula for a horizontal line post insulator.
Tension loads Compression load Longitudinal load Withstand domain
0
Figure 2-17: Model of combined load curves for the line post composite insulator [40]
2.5.2.4 Line post insulators with an angle to the horizontal
By considering =15° the angle to the horizontal, the following modification is considered [5]:
= sin( ) + cos( )
= sin( ) + cos( )
= sin( ) + cos( )
(2.31)
, and are the loads applied to the free end of the insulator inclined at . The deflection may be calculated by the following formula:
= 3
(2.32)
with =
30
It is not easy to predict the life expectancy of composite material because failure modes and mechanisms are complex and react differently according to the fatigue behaviour and the environment in which the material will be used. Because the composite insulators for transmission and distribution lines have been designed for a long service life, the materials required for the insulators should be free from damage which is a consequence of the degradation of material during operation. The durability criterion of the composite materials shows the relationship between the material strength and the loading time. The long-term loading of the composite material will accumulate damage which is induced by accelerated stress. The material damaged will be intensified by the environment service condition such as temperature, moisture etc. This will lead to the studying of endurance limits. Figures 2-15 and 2-16 present different curves to give an interpretation of the long-term strength behaviour of the composite material. The material strength is intensely affected by the time of loading. Once the composite material is unloaded, the material should recover its initial static strength that was before the long-term loading.
Figure 2-18: Cyclic loading of the dynamic tests [5]