Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution

Damage Identification in Fiber Metal Laminates using Bayesian Analysis with Model Order Reduction

Fiber metal laminates (FML) are composite structures consisting of metals and fiber reinforced plastics (FRP) which have experienced an increasing interest as the choice of materials in aerospace and automobile industries. Due to a sophisticated built up of the material, not only the design and production of such structures is challenging but also its damage detection. This research work focuses on damage identification in FML with guided ultrasonic waves (GUW) through an inverse approach based on the Bayesian paradigm. As the Bayesian inference approach involves multiple queries of the underlying system, a parameterized reduced-order model (ROM) is used to closely approximate the solution with considerably less computational cost. The signals measured by the embedded sensors and the ROM forecasts are employed for the localization and characterization of damage in FML. In this paper, a Markov Chain Monte-Carlo (MCMC) based Metropolis-Hastings (MH) algorithm and an Ensemble Kalman filtering (EnKF) technique are deployed to identify the damage. Numerical tests illustrate the approaches and the results are compared in regard to accuracy and efficiency. It is found that both methods are successful in multivariate characterization of the damage with a high accuracy and were also able to quantify their associated uncertainties. The EnKF distinguishes itself with the MCMC-MH algorithm in the matter of computational efficiency. In this application of identifying the damage, the EnKF is approximately thrice faster than the MCMC-MH

Experimental determination of Lamb wave dispersion diagrams over large frequency ranges in fiber metal laminates

Fiber metal laminates (FML) are of high interest for lightweight structures as they combine the advantageous material properties of metals and fiber-reinforced polymers. However, low-velocity impacts can lead to complex internal damage. Therefore, structural health monitoring with guided ultrasonic waves (GUW) is a methodology to identify such damage. Numerical simulations form the basis for corresponding investigations, but experimental validation of dispersion diagrams over a wide frequency range is hardly found in the literature. In this work the dispersive relation of GUWs is experimentally determined for an FML made of carbon fiber-reinforced polymer and steel. For this purpose, multi-frequency excitation signals are used to generate GUWs and the resulting wave field is measured via laser scanning vibrometry. The data are processed by means of a non-uniform discrete 2d Fourier transform and analyzed in the frequency-wavenumber domain. The experimental data are in excellent agreement with data from a numerical solution of the analytical framework. In conclusion, this work presents a highly automatable method to experimentally determine dispersion diagrams of GUWs in FML over large frequency ranges with high accuracy

Numerical Simulation of the Elastic–Ideal Plastic Material Behavior of Short Fiber-Reinforced Composites Including Its Spatial Distribution with an Experimental Validation

For the numerical simulation of components made of short fiber-reinforced composites, the correct prediction of the deformation including the elastic and plastic behavior and its spatial distribution is essential. When using purely deterministic modeling approaches, the information of the probabilistic microstructure is not included in the simulation process. One possible approach for the integration of stochastic information is the use of random fields. In this study, numerical simulations of tensile test specimens were conducted utilizing a finite deformation elastic–ideal plastic material model. A selection of the material parameters covering the elastic and plastic domain are represented by cross-correlated second-order Gaussian random fields to incorporate the probabilistic nature of the material parameters. To validate the modeling approach, tensile tests until failure were carried out experimentally, which confirmed the assumption of the spatially distributed material behavior in both the elastic and plastic domain. Since the correlation lengths of the random fields cannot be determined by pure analytic treatments, additionally numerical simulations were performed for different values of the correlation length. The numerical simulations endorsed the influence of the correlation length on the overall behavior. For a correlation length of 5 mm, a good conformity with the experimental results was obtained. Therefore, it was concluded that the presented modeling approach was suitable to predict the elastic and plastic deformation of a set of tensile test specimens made of short fiber-reinforced composite sufficiently

Ermittlung des Maßes der Nichtlinearität einer Platte mittels experimenteller Untersuchungen linearer und nichtlinearer Ausbreitungseigenschaften von LAMB-Wellen

Wegen der enormen Steigerung der Betriebskosten in der Luftfahrt hat in den letzten Jahrzehnten eine sukzessiveWeiterentwicklung im Bereich der verwendeten Materialien stattgefunden. Dabei wird immer mehr auf faserverstärkte Kunststoffe zurückgegriffen. Diese weisen im Gegensatz zu den bisher verwendeten Aluminiumlegierungen eine deutlich bessere spezifische Steifigkeit und Festigkeit auf. Somit kann das Strukturgewicht bei gleichzeitiger Anpassung der Konstruktion deutlich gesenkt werden. Im Gegensatz zu den bis dahin weit verbreiteten Aluminiumlegierungen lassen sich Schädigungen der Struktur nicht mehr so leicht nachweisen. Um diesen neuartigen Werkstoffen Genüge zu tragen, müssen somit auch die Inspektionsmethoden angepasst werden. In der jüngsten Vergangenheit hat sich gezeigt, dass LAMB-Wellen eine geeignete Möglichkeit darstellen, Strukturen auf den aktuellen Grad der Nichtlinearität bzw. Materialdegradation hin zu analysieren. LAMB-Wellen sind dafür besonders gut geeignet, da sich diese über große Flächen ausbreiten und dabei die gesamte Bauteildicke durchdringen. In dieser Arbeit werden dazu sowohl lineare als auch nichtlineare Ausbreitungseigenschaften auf ihre Sensibilität gegenüber Schädigungen in Aluminium und CFK untersucht. Dazu wird zunächst eine Methode zur Bestimmung von Dispersionsdiagrammen für unidirektionale Faserverbunde entwickelt, die Dispersionsdiagramme für Aluminium und unidirektionales CFK erstellt und geeignete Anregungsfrequenzen zur Untersuchung höherharmonischer Moden bestimmt. Aus der Analyse der höherharmonischen Moden wird der relative akustische Nichtlinearitätsparameter 0 als Vertreter der nichtlinearen Ausbreitungseigenschaften ermittelt und die Veränderung mit der Entwicklung der Gruppengeschwindigkeit verglichen. Dazu werden die Messungen an Proben mit unterschiedlichen eingebrachten Schädigungen durchgeführt. Es kann gezeigt werden, dass der relative akustische Nichtlinearitätsparameter 0 von LAMB-Wellen geeignet ist, Schädigungen in Aluminium und CFK zu detektieren. Im Gegensatz dazu scheint die Gruppengeschwindigkeit nur bedingt geeignet. Die bisher nur für Aluminium erzielten Ergebnisse, dass die nichtlinearen Ausbreitungseigenschaften deutlich sensibler auf Schädigungen reagieren, kann somit auch für CFK nachgewiesen werden

The Guided Ultrasonic Wave Oscillation Phase Relation between the Surfaces of Plate-like Structures of Different Material Settings

Lamb waves occur in thin-walled structures in two wave modes—the symmetric and the antisymmetric mode. Their oscillation on the structures‘ surfaces is either in phase (symmetric) or shifted by a phase angle of π (antisymmetric). In this work, a method is developed by which to compare the surfaces’ oscillation phase relation to answer the question of whether fiber metal laminates show the same surface oscillation behavior as described for metals. The evaluation of time signals regarding the instantaneous phase angle is performed by using the continuous wavelet transformation and the short-time Fourier transformation. Numerical simulations utilizing the finite element method provide time signals from the top and bottom surface of different thin-walled structures of different material settings and configurations. The numerically obtained time signals are evaluated by the developed methods with respect to the oscillation phase. Subsequently, the oscillation phase is evaluated experimentally for the wave propagation in a fiber metal laminate. It is shown that the method based on the continuous wavelet transformation is suitable for the evaluation of oscillation phase relations in time signals. Additionally, it is proven that fiber metal laminates show only two phase relations, which indicates the occurrence of Lamb waves

The Guided Ultrasonic Wave Oscillation Phase Relation between the Surfaces of Plate-like Structures of Different Material Settings

Lamb waves occur in thin-walled structures in two wave modes—the symmetric and the antisymmetric mode. Their oscillation on the structures‘ surfaces is either in phase (symmetric) or shifted by a phase angle of π (antisymmetric). In this work, a method is developed by which to compare the surfaces’ oscillation phase relation to answer the question of whether fiber metal laminates show the same surface oscillation behavior as described for metals. The evaluation of time signals regarding the instantaneous phase angle is performed by using the continuous wavelet transformation and the short-time Fourier transformation. Numerical simulations utilizing the finite element method provide time signals from the top and bottom surface of different thin-walled structures of different material settings and configurations. The numerically obtained time signals are evaluated by the developed methods with respect to the oscillation phase. Subsequently, the oscillation phase is evaluated experimentally for the wave propagation in a fiber metal laminate. It is shown that the method based on the continuous wavelet transformation is suitable for the evaluation of oscillation phase relations in time signals. Additionally, it is proven that fiber metal laminates show only two phase relations, which indicates the occurrence of Lamb waves

Influence of a Flat Polyimide Inlay on the Propagation of Guided Ultrasonic Waves in a Narrow GFRP-Specimen

Structural health monitoring systems for composite laminates using guided ultrasonic waves become more versatile with the structural integration of sensors. However, the data generated within these sensors have to be transmitted from the laminate to the outside, where polyimide-based printed circuit boards play a major role. This study investigates, to what extent integrated polyimide inlays with applied sensor bodies influence the guided ultrasonic wave propagation in glass fiber-reinforced polymer specimens. For reasons of resource efficiency, narrow specimens are used. Numerical simulations of a damping-free specimen indicate reflections of the S0-mode at the integrated inlay. This is validated experimentally with an air-coupled ultrasonic technique and a 3D laser Doppler vibrometry measurement. The experimental data are evaluated with a method including temporal and spatial continuous wavelet transformations to clearly identify periodically occurring wave packages as edge reflections and distinguish them from possible inlay reflections. However, even when separating in-plane and out-of-plane movements using the 3D measurement, no reflections at the inlays are detected. This leads to the conclusion that polyimide inlays are well suited as substrates for printed circuit boards integrated into fiber-reinforced polymer structures for structural health monitoring, since they do not significantly influence the wave propagation