April_AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | A P R I L 2 0 2 0 1 8 To design a conductor to resist damage from a strike, the electric fields, ohmic heating, heat flow, expansion, and mechanical effects from the strike must be simultaneously simulated on the conductor, the resin in which it is embedded, the composite structure on which it sets, and any coating systems. These analysis have been the subject of many papers, some of which are found in the first four references, and will not be repeated here; however, this is a pri- mary objective for most applications of these conductors, so the reader is en- couraged to seek and review their con- tent for suggested methods. To design a conductor or conduc- tor prepreg system for robust handling and conformability, an assessment is conducted of the elasticity, plasticity, and ultimate tensile properties of the perforated foil as it is fabricated and applied, including any veils or fabrics present in the product form. Such an as- sessment relies predominantly on me- chanical physics, which is not covered in this article. The conductive behavior of a chosen foil at or near a strike site, or elsewhere under a current load high enough to significantly alter the tem- perature of the conductor, is strong- ly impacted by the thermal effects. It is firmly suggested to include the ther- mal changes, and the impact of those changes on the properties of the con- ductor for an accurate simulation. Stan- dard laboratory measurement devices are generally used to determine the ba- sic conductance or resistance values of a foil. It is useful to predict the expected value obtained by such standard labo- ratory measurements. For this purpose, a simple simulation of the electrical properties alone at room temperature is a useful simplification. This simplifi- cation is used for the simulation exam- ples described below. CONDUCTOR DESIGN Freed from the constraints of a pierce-and-stretch process, many pat- terns are possible for the perforation of foils. Circular shapes, ovals, parabo- las, and other variations with predom- inantly rounded features are possible. Geometric shapes having few or many straight equal sides are feasible as well as modifications of these shapes that are axially elongated. Shapes having straight sides combined with rounded features can be imagined, as can shapes that appear without pattern, without symmetry, and possibly of random ap- pearance. These perforations can be or- ganized in several classical geometric special arrangements, such as square close packing or hexagonal close pack- ing, or they can be modifications of classical arrangements to advantage one direction over another, and they could be oriented to benefit the appli- cation. They could be random arrange- ments if it is beneficial. See Fig. 1 and Fig. 2 for two examples of such patterns. SOLID MODELING Foils having each candidate per- foration shape were modeled in Solid- works. Within each shape family (circles, parallelograms, hexagons, etc.) the models were parameterized to fa- cilitate rapid adjustments in shape and thickness. The model can be built to repre- sent an entire section of foil, having hundreds or thousands of perforations such as depicted in Fig. 3. This format consumes more memory and process- ing power and requires more time to create than smaller models. These ef- fects are non-linear. Patterns that are highly repetitious and symmetrical are represented by a unitary repeat- ing cell such as depicted in Fig. 4. For all patterns examined, a solid mod- el of a macro-cell that includes several (3 to 15) unitary cells in each direction was most useful to analyze large area conductors with sufficient voltage drop across the model without con- suming large amounts of mem- ory and processing power. See Fig. 5 for an example of this re- peating multi-cell model. To calculate the final engi- neering properties of the perfo- rated foil, such as basis weight and sheet resistance, it is conve- nient to use rectangular shaped models having a length L M and width W M as shown in Fig. 5. MESHING AND ANALYSIS PARAMETERS After the solid model is built, it is transferred to Comsol for analysis. The mesh was built of free tetrahedral ele- ments with the following parameters: Maximum element size = 2.52 mm Minimum element size = 0.454 mm Maximum growth rate = 1.5 Curvature factor = 0.6 Resolution factor = 0.5 Analysis of copper foil is discussed here, but aluminum, bronze, or oth- er metals or non-metals can be sub- stituted by using material properties appropriate to the material. Many of these properties are available as inter- nal standards in Comsol. The following material properties were used in the model: [7-8] Resistivity = 1.72x10 -8 Ω*m at reference temperature = 298 K Resistivity thermal coefficient = 0.0039 1/K Relative Permeability = 1 Coefficient of thermal expansion = 17x10 -6 1/K Heat capacity at constant temp = 385 J/kg/K Relative Permittivity = 1 Density = 8960 kg/m 3 Thermal conductivity = 400 W/m/K Young’s Modulus = 110x10 9 Pa Poisson’s Ratio = 0.35 The stationary study option was chosen. Equation (1) describes the cur- rent sources. Equation (2) describes the current density in a conductive medium and equation (3) describes the electric field in a floating potential surrounded by an insulating medium. The relation- ships of Equations (1), (2), and (3) are Fig. 1 — Example round/oval pattern.