Numerical Approximation of Maxwell Equations in Low-Frequency Regime

2021

The heat generated within thermoplastic carbon composite laminates during induction welding can be attributed to one, or a combination of the three heating mechanisms discussed in the literature: (i) Joule heating of fibers; (ii) Joule and/or dielectric heating of polymer; and (iii) fiber-to-fiber contact resistance heating. The answer to the question, which of the three heating mechanisms is most dominant, remains open. This research aims to provide an answer to this question through finite element simulations using both an in-house developed numerical Whitney-elements based toolbox for induction welding simulations (WelDone), and the commercially available software, ANSYS Maxwell. The simulations are done at two levels; first, using WelDone laminate-level simulations are performed to see in which direction: fiber-, transverse to the fiber-, or thickness direction, most of the heat was generated; and second, ANSYS Maxwell was used to simulate the solid loss on a microscopic, inside fiber and resin, level with and without the presence of resin. In the latter series of simulations, contact between fibers in different layers was explicitly modeled. The numerical simulations revealed that on the laminate-level most heat is generated in the fiber- and thickness directions. The former coincides with Joule heating of fibers, while the latter can be attributed to either Joule heating of polymer and fiber-to-fiber contact resistance heating, or both. The fiber level simulations, however, revealed that both fiber-to-fiber contact and no-fiber-to-fiber contact conditions have a significantly small effect on the solid loss compared to presence of resin. Based on the latter, the heat generation in the thickness direction was attributed to a second heating mechanism; Joule heating of polymer. It must be noted that the dielectric heating of polymer was ignored due to the relatively low operating frequency at which induction welding takes place.

Section: Numerical Simulations On the Laminate-levelmentioning

confidence: 99%

Heating mechanisms in induction welding of thermoplastic composites

2021

“…Next to neglecting capacitive effects, the second simplification is to introduce the time harmonic notation for all alternating field quantities (p. 63). 7 It applies to all quantities which vary periodically in time and follow a sinusoidal function. This is the case if the source current of the exciting coil is an alternating current, which is true for induction welding.…”

Section: Maxwell's Equations In Contextmentioning

confidence: 99%

“…P maps a Dirichlet condition F S of the elliptical problem to an equivalent Neumann condition @F @n S on a surface S. Utilizing the properties of P, the integral over the nonconductive domain O in equation ( 28) can be reduced to an integral over the boundary surface S, resulting in the final weak formulation (p. 229) 7 i!…”

Section: Weak Formmentioning

confidence: 99%

Modeling of induction heating of thermoplastic composites

Holland

et al. 2020

In this article, a hybrid finite element model is presented for the simulation of induction heating of layered composite plates. Modeling includes the alternating electromagnetic field generated by an alternating current running through a coil, the current densities in the composite plate resulting from the electromagnetic field, the heat generation resulting from the current density distribution, and the heat transfer resulting from the nonuniform heat generation in the plate and the temperature distribution in the plate. The different elements of the model are shown to capture the time-dependent temperature distribution resulting from a coil moving over the surface of a composite laminate.

“…The space between fibers is filled with polymer. This polymer acts as a dielectric, but at the very small dimensions of the polymer volume between the fibers, the polymer also acts as a conductor of high but finite resistance 8 (Figure 2(b)). When an alternating magnetic field is applied to the laminate, an alternating potential difference or E-field is created between the differently oriented fibers in adjacent layers and Joule and dielectric losses may occur in the polymer.…”

Section: Introductionmentioning

confidence: 99%

“…at the fiber junctions, temperature and pressure dependent resistance will arise, which can generate heat. 8 Based on the literature, two heating mechanisms have a significant contribution to the generated heat. [9][10][11][12][13][14] designate contact resistance between fibers as the most dominant heating mechanism in the laminate.…”

Section: Introductionmentioning

confidence: 99%

Microscopic level modeling of induction welding heating mechanisms in thermoplastic composites

Ali

2021

Simulation and analysis of electromagnetic induction heating of continuous conductive fiber-based composite materials is used to (in)validate a series of hypotheses on the physics dominating the heating process. The behavior of carbon fibers with and without surrounding polymer in an alternating electromagnetic field is studied at a microscopic level in ANSYS Maxwell using the solid loss to quantify heat generation in the composite material. To limit the number of elements, the fibers are modeled with a polyhedron cross-section instead of a circular cross-section. In addition, each layer is modeled as an layer of fibers, e.g. 20 fibers placed next to each other. The simulations indicate that samples with fibers oriented in 0 and 90 orientation yield a substantial higher solid loss than fibers oriented in the 0 orientation only. The solid loss in both cases is however not enough to explain the level of heating observed in practice. Filling the volumes between fibers with polymer results in greater solid loss than samples with no polymer between the fibers, at equal fiber volume fraction. Note, no contact between fibers is modeled. The conductivity of the polymer is experimentally determined. The lab tests show relatively low finite resistance values in the transverse direction, indicating that the polymer in a composite should not be considered an isolator. The simulations seem to justify the conclusion that heating of thermoplastic composites in an alternating magnetic field rely on currents through the polymer. Without the polymer and subsequently no polymer conductivity, even if the electrical fields are strong there is almost no heat generated. The carbon fibers are required to be in proximity of each other to create the electrical fields that induce the current through the polymer. The heating is determined by the product of current density squared times the resistivity of the polymer.