3.1. Characterization and Analysis of Interface Region
A large number of cracks are recognized being parallel to interface extension plane in interface region, as shown in
Figure 3 of the morphology photos taken from transparent observations by the optical microscope. The background oblique traces in
Figure 3 represent the knife marks (slants) remained after the cutting process, which extend along the vertical direction through the sample as illustrated by
Figure 1b. Accordingly, the cracks indicated in
Figure 3 just develop along the parabolic interface as referenced in
Figure 1b. The cracks with a width of about tens of micrometers extend to several millimeters. It is indicated that these cracks only exist in interface area without any cracks arising in the cable body or recovery insulation with a uniform and continuous morphology. These cracks identify the locations of mechanical weakness, which will contribute to and even dominate the discharging channels of dielectric failures. Subsequently, we further use scanning electron microscopy (SEM) to obtain detailed structural information of interface region in EMJ.
The liquid-nitrogen brittle-fractured cross-sections in cable body, recovery insulation, and interface region are individually characterized by SEM with low magnification (×150) and small ratio scanning scale in a scanning range of 700 µm × 700 µm, as shown in
Figure 4. The cable body and recovery insulation exhibit a uniform and smooth texture. In contrast, the cracks in interface region, which have been roughly observed by optical microscopy, display as the strings of voids about 100 µm in size, which just identifies the width of cracks. Structural defects in interface region, which have been inevitably introduced in EMJ fabrication processes, are attributed to the inefficient interpenetration between cable body and recovery insulation. These defects are shown by the cracks on fractured surfaces in millimeter scale as observed by the optical microscope, while being particularly elaborated as the strings of voids in micrometer-resolution SEM characterizations.
3.2. SEM Characterization of Crystal Morphology
The microstructure of XLPE consists of crystalline and amorphous regions at room temperature. In crystalline region, XLPE molecules condensate into spherical polycrystals (spherulites) with a diameter in tens of micrometers. The spherulites are formed by the closely stacked lamellae being parallel to the radial directions and centering around spherulites nucleus. In the process of XLPE crystallization, in order to reduce the surface energy, the XLPE molecular chains are regularly and repeatedly folded into a crystal lattice with an unchanged chain length and bond angle, thereby forming a crystal lamella in a thickness of about 10 nm [
13]. The areas outside the spherulites are fulfilled by amorphous XLPE condensations. Although the semi-crystalline micro-structure of polymers is too complicated to be legibly comprehended, the random coil model proposed by Flory has been widely approved that the amorphous polymer molecules are engaged in a random coil conformation with the molecule chains being randomly entangled and arbitrarily penetrated [
14]. During the injection of melt polyethylene, melt fronts are blended with the cable insulation layer which although in a cross-linked structure shows a certain viscoelastic state at the temperature range of 110–125 °C. Thus, the macromolecules of injected molten PE are capable of being fused with the molten XLPE of cable body to realize entanglement and penetration [
15]. Nevertheless, the cross-linking network structure would highly restrict the movement of macro-molecular chains of cable XLPE, resulting in different structures from both sides of the interface area due to the imperfect entanglement fusion between the cable body and recovery insulation layers. Therefore, the residual interface stresses produced in crystallization process lead to the micro-cracks in interface region. It is reasonably suggested that the voids originate from the destruction of amorphous regions. The previous studies showed the thermal, mechanical, and dielectric properties of XLPE are closely related to these microstructures, as reported by Andjelkovic that the tensile strength and elongation-at-break of XLPE insulation cables are positively correlated with crystallinity [
16].
As shown in
Figure 5, the crystalline textures of cable and recovery XLPE are relatively smooth without any significant conformation defect. The typical lamella structure and the spherulites with a diameter of about 10 µm are shown after corroding the amorphous domain, while the ridge-like uneven micro-textures appearing on fractured surface indicate the fracture routes through cracks. The restriction of the cross-linking structure in cable body on the entangled movement and even crystallization process of the macromolecular chains is an elaborated manifestation of micro-cracks shown in macroscopic morphology. After surface has been corroded, the considerable disordered arrangements of lamellae are found to demonstrate the poor crystallinity of interface region.
We have dedicated to molecular dynamics simulations of calculating the interaction and force between the polymer chains connected by cross-linking bonds in the XLPE macromolecule structure with a PE-cross-linked network, in comparison to the Van der Waals force between low density polyethylene molecules. The theoretical results show significant mechanical contributions of cross-linking bonds to the interaction between XLPE macromolecular chains. The prospective calculation analyses are in progress and expected to be published in subsequent articles.
3.3. Electric Tree Inception and Propagation
Electrical-tree inception voltages fitted with two-parameter Weibull distribution for the three regions in XLPE EMJ are shown in
Figure 6, with the shape parameters and the characteristic tree inception voltage being accordingly listed in
Table 1. The inception voltage of cable body is 7.8 kV, while recovery insulation and interface region show 11.5% and 30.8% lower inception voltages of 6.9 kV and 5.4 kV respectively. The evident reduction in electric tree inception voltage of interface region is attributed to the micro-cracks in interface region [
17]. Charge carriers (electrons or holes emitted from the tip of needle electrode) can accelerate and gain much higher energy under concentrated electric field in the free spaces of voids in cracks, so as to destroy molecular bonds and develop carbonized discharging channels (tree like damages) under a lower inception voltage [
18].
Electrical-tree propagation experiments are carried out by applying 7.8 kV voltage to the needle electrode for a time interval of 6000 s. As the propagation characteristics shown in
Figure 7, the electrical-trees are initiated into a sparse dendrite geometry with a smaller diameter of tree channels and a significantly longer tree length in interface region than that in cable body and recovery insulation. With the prolongation of applying voltage, the density and diameter of tree channels in cable body and recovery insulation increase gradually as the geometry altering from a sparse branch to a dense and concentrated structure. In contrast, the electrical-trees in interface region persist in the dendritic structure from the initiation to the late stage of growth with an accelerated growth rate. The tree grows not only in the electric field direction, but especially along the direction of interface extension, as it is noted from the sample geometry. The lateral (direction of interface extension) development of tree branches is obviously faster than the vertical (electric field direction) development. As shown in
Figure 8, a substantial part of tree branches coincides with the cracks, implying the higher probability of tree propagation along cracks with a faster growth rate, which leads to the remarkable anisotropy of growth characteristics.
3.4. Growth Kinetics of Electric Trees
Electrical-trees usually start at the microscopic structural defects, where the structure deterioration zones with micro-cracks are caused by stress concentrations and thermodynamic drives under electric field and expand to submicroscopic trees, which will finally develop into electrical-tree aging area with macroscopic fractal structures [
19]. According to the growth kinetics of the electrically induced micro-cracks in non-crystalline polymer materials, the probability of forming submicroscopic trees can be determined by calculating the breaking rate of polymeric bonds [
20]. The growth rate of submicroscopic trees can be predicted from its length
LB (m) as following:
where
Y (m) denotes submicroscopic tree growth quantity, ω/2π (Hz) is intrinsic frequency of atomic vibrations, which indicates the performances associated with molecular vibrations in polymer materials,
Ue, and
U0 (Joule) symbolize the released electrostatic energy and the required activation energy respectively during micro-crack expansions,
ε (F/m) is dielectric permittivity,
E (V/m) is local electric filed, α represents the performance parameter associated with molecular vibrations in polymer materials,
l (m) signifies the linear dimension of micro-cracks,
k is Boltzmann constant, and
T (K) is thermodynamic temperature. A dynamic model for time-dependent growth rate of electrical-trees is given by integrating Equation (3) on time
t of applying electric voltage to obtain the growth quantity of all submicroscopic trees:
The electrical-tree characteristics described in Equation (4) are directly related to the density of micro-cracks in XLPE with a semi-crystalline structure. The exacerbation in molecular polarization and carrier transports for structure defects manifests as the distinctive electric field in cracks.
According to the material dielectric characteristics (relative dielectric constant, electrical conductivity and dielectric loss factor) in different regions of cable joint, the local electric field distributions near cracks are simulated by the finite element method as implemented in COMSOL multi-physics software, with the results being shown in
Figure 9. The white triangular region represents the tip electrode inserted into specimen, the circular regions indicate the void (air) micropores in defect cracks, and the intervals between the circles are identical to XLPE matrix. The electric fields in the air micropores of cracks are remarkably higher than that of XLPE matrix, with an obvious concentration of electric fields at the interval (XLPE) between the two adjacent micropores. The dielectric breakdown strength (DBS) and dielectric constant of air micropores in cracks are significantly lower than that of XLPE matrix. Thus, the electric field inside micropores will exceed DBS of air when the tip electrode is located in cracks or the electrical-trees develop to the surface of micropores under electric field. Consequently, the micro-pore surface is carbonized by the instantaneous electric breakdown of air in micropores, causing a considerable enhancement of electric field in XLPE interval between the adjacent micropores and lead to a preferred trend of electric-tree propagation along the string of micropores. Therefore, the electrical-tree will grow consecutively along the crack (a string of micropores) through a subsequent form of internal-breakdown, surface inception and inter-pore crossing. In addition, it is noted from the electric field distributions that the location of tip electrode (tree front) on micro-pore surface or in interval XLPE will not affect the trend of electrical-tree propagation through the string of micropores in an almost identical process of electric field enhancements, as illustrated by the comparison of left and right panels in
Figure 9.
The discharge avalanche theory and fractal geometry indicate that the electrical-tree growth should be considered as a random growth process of fractal clusters consisting of discontinuous micro-cracks [
21,
22]. Therefore, the growth quantity of electric trees can be defined as the sum of all-part clusters. Based on the fractal structure of electrical-trees, the growth quantity
Y and tree length
LB varying with the growing time can be evaluated from the growth length
L along electric field and the fractal dimension
Df of electrical-trees as follows:
The growth length
LB increases and decreases exponentially with the increase of local electric field and activation energy respectively. Furthermore, electric field distribution could be approximately calculated as following:
where
U = 7 kV is the applied voltage to the tree-initiation tip electrode,
r = 3 µm indicates the curvature radius of tip electrode,
R = 3 mm identifies the distance between tip and plate, by which the
αl is derived from activation volume Δ
V (m
3) under electric field [
23]:
The tree length versus the fractal dimension of the recovery insulation XLPE in cable joint is calculated from Equations (5)–(7) [
24]. The activation volume of interface region in cable joint is fitted from the experimental results of the fractal dimension of electrical-trees, as the results being shown in
Figure 10. The fractal dimension of electrical-trees in macroscopic scale implies a longer growth along electric field, as shown by the consistent experimental and theoretical results for cable body or recovery insulation in cable joint. In comparison, the variation slope (absolute value) of electrical-tree length as a function of fractal dimension is appreciably smaller for the interface region, implying that the electrical-tree growth length with the same fractal dimension is significantly reduced along the direction of electric field due to the insulation failure caused by the dielectric breakdown of air micropores in cracks, resulting in the expedited electrical-tree growth along multiple cracks with more circuitous trajectories and a larger activation volume (Equation (7)) in a dispersed geometry, as manifested by the increased fractal dimension of electric trees. Based on the experimental fractal dimension of electrical-trees in the XLPE matrix of cable body, the fractal graphic trees are drawn though a string of polygons in which the fractal dimension is set as 2 to simulate the breakdown process of air micropores in electrical-tree growth, as shown in
Figure 10b, which concisely elucidates the propagation mechanism of electrical-trees passing cracks in interface region of factory cable joints. Calculation and experimental results coordinately demonstrate the significant increase of activation energy volume in interface region of cable joints, suggesting that the micro-pore defects produced in the melt access process lead to the rapid growth of electrical-trees in interface region with a propagation rate greatly higher than that in the XLPE matrix of cable body and recovery regions.