Determination of the Complex-Valued Elastic Moduli of Polymers by Electrical-Impedance Spectroscopy for Ultrasound Applications

Abstract

A method is presented for the determination of complex-valued compression and shear elastic moduli of polymers for ultrasound applications. The resulting values, which are scarcely reported in the literature, are found with uncertainties typically around 1% (real part) and 6% (imaginary part). The method involves a setup consisting of a cm-radius, mm-thick polymer ring glued concentrically to a disk-shaped piezoelectric transducer. The ultrasound electrical-impedance spectrum of the transducer is computed numerically and fitted to measured values as an inverse problem in a wide frequency range, typically from 500 Hz to 5 MHz, both on and off resonance. The method is validated experimentally by ultrasonic through transmission around 1.9 MHz. The method is low cost, not limited to specific geometries and crystal symmetries, and, given the developed software, easy to execute. The method has no obvious frequency limitations before severe attenuation sets in above 100 MHz.

Impact of Injection Molding Parameters on Material Acoustic Parameters

“…Before proceeding to the study's theoretical and experimental support, it is enlightening to consider an overview of why creating such a link between the two fields is essential, and to elaborate on the approach taken throughout this research to establish such a link. The present work aims to use the novel acoustic test developed by Bodé et al [26] to gather data on the acoustic parameters of polymethyl methacrylate (PMMA) chips manufactured with the help of a DOE, as a case study, and to analyze and identify correlations between the injection molding process parameters and the acoustic parameters of the material. The work follows the methodology depicted in Figure 1, comprising theoretical elements, simulations, experimental production, acoustic tests, and correlation analysis.…”

“…The work of Bodé et al [26] on ultrasound spectroscopy introduced an innovative approach to evaluating the complex-valued elastic moduli of polymers. Their method of ultrasound electrical-impedance spectroscopy (UEIS) employs a piezoelectric disk that induces vibrations in an attached polymer ring, facilitating the characterization of the ring's complex-valued elastic compressional and shear moduli.…”

“…This impedance spectrum enables determination of a polymer sample's four unknown material parameters using UEIS. This technique is described in detail in [26] and will be briefly explained in Section 3.3.…”

“…As explained in Section 3.3, one ring was cut from the center of each chip [26]. The position of the place where the disk was cut was kept the same for all the samples since the properties of an IM part could be affected differently depending on the distance from the gate [35].…”

“…Inspired by the same methodology, a recent study was undertaken by our group where the focus was on the IM simulation, production, and QA analysis of an LOC molded with PMMA LG IG 840, as this grade was available both for production and in the archive of MOLDEX3D ® software. This laid the groundwork for designing the experiments for the current study, where acoustic tests of the optimized IM parts were performed after QA and residual stress analysis using a novel test established by Bodé et al [26]. The incorporation of the acoustics of polymers in injection molding is an essential area of research due to its potential to improve the quality and consistency of parts produced through this manufacturing technique.…”