Analysis of the Resistance of an Electrical Conductor as a Function of the Parameters of the Work Hardening Process and its Deometry

In the current economic context, the electric cable industry is facing technical and economic challenges. Indeed, because of the globalization of world markets and the continuous rise in the price of raw materials necessary for the manufacture of electric cables, particularly copper, manufacturers must adapt their economic models in order to ensure the sustainability of their activities. They must therefore put in place a global strategy to improve the performance of manufacturing processes on the one hand and, on the other hand, to optimize the design parameters of electric cables. The objective is part of an approach to optimize the consumption of raw materials while respecting the framework of standard requirements for electric cables. However, this objective cannot be achieved without a detailed understanding of the electrical phenomena, which prevail in the structures of cables. For this, the study of manufacturing processes and design parameters is essential in order to identify and quantify their impacts on electrical behavior, and more precisely on the total electrical resistance of cables. The latter generally consist of a conductive core of copper or aluminium and one or more protective layers of dielectric and / or metallic materials. Research is mainly focused on the study of the conductive part of the cable. This consists of unit strands assembled in successive concentric layers. The shape of the strands can be circular, profiled, triangular, oval, etc. Generally, the conductive core is fabricated using cold deformation processes, such as wiring and compaction. During these operations, it undergoes plastic deformations so as to reach well-determined geometric specifications. These deformations result from the stress fields generated by the tensile, torsional, compressive and friction forces specific to manufacturing processes. It is accepted that these deformations influence the mechanical and electrical behavior of the conductive core. From a mechanical point of view, the plastic deformations of the unit strands lead to hardening by strain hardening of the material, thus modifying its overall mechanical properties. This results in an increase in the elastic limit of the material and a more pronounced mechanical rigidity in traction of the conductive core. It is understood that the modifications observed are not the same from one design to another. They are then dependent on design parameters, such as the number and shape of elementary strands, the number of layers, the wiring pitch, the wiring direction, the compaction rate (compression rate of the core), the shape and size of the inter-strand contact areas. From an electrical point of view, all these variations must be studied in order to quantify their impacts, at the same time on the electrical conductivity of the material, the distribution of the current and the total electrical resistance of the cable. The research focuses on the analysis of the electrical behavior of the conductive strands of electrical cables, and more specifically on their total electrical resistance.
The analysis will mainly concern the study of the electrical resistance in stationary mode (direct current). The industrial objectives revolve around the following points:
 Understand the electrical phenomena that reign in conductive souls,
 Size the conductive cores to obtain a specific electrical resistance,
 Reduce the consumption of raw materials, particularly copper.
In order to achieve these objectives, the use of calculation tools based on numerical models to predict the mechanical and electrical behavior of conductors.
First, the reproduction of the cabling and compacting processes will allow us to approximate the deformation fields of the conductive core and the real shape of the inter-strand contact areas. Secondly, the electrical analysis will determine their influences on current conduction and therefore on the total electrical resistance of the conductive core.
These models, based on the finite element method, will be used to quantify the influence of the parameters of the cabling and compacting processes on the electrical properties of conductive cores. The results of the simulations will be used to establish a set of design parameters in order to optimize the consumption of the raw material.
The conductive core undergoes plastic deformations by strain hardening of the material during manufacture; it will then be useful to analyze their influences on the electrical conductivity of the material.
From a crystallographic point of view, these plastic deformations are due to the formation, the multiplication and the displacement of mobile linear defects in the crystal lattice of the metal.
These defects are called dislocations. The increasing number of dislocations produced during plastic deformations and their interaction with each other (or with impurities, precipitates, etc.) leads to their mobility being reduced. This results in hardening of the metallurgical structure of the metal.
This phenomenon is called "hardening". This also causes a decrease in grain size thereby increasing the number of grain boundaries in the metal structure.
In addition, the defects and vacancies contained in the crystal lattice of the metal, constitute obstacles vis-à-vis the carriers of electric charges (electrons).
These variations cause a degradation of the electrical conductivity of the material, but also an uneven distribution thereof in the section of the conductive core.
The electrical contact resistance and the variation in electrical conductivity as a function of the strain hardening of the material will be characterized experimentally.
Then, the latter will be used in numerical models by defining a mechanicoelectric coupling strategy, thus making it possible to take into account the influence of contact resistance and strain hardening on the total electrical resistance of the cables.