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It is noted that certain common linear wave operators have the property that linear variation of the initial data gives rise to one-dimensional evolution in a plane defined by time and some direction in space. The analysis is given For operators arising in acoustics, electromagnetics, elastodynamics, and an abstract system.
Ultrasonic techniques, such as the use of guided waves, can be ideal for finding damage in the plate and pipe-like structures used in aerospace applications. However, the interaction of waves with real flaw types and geometries can lead to experimental signals that are difficult to interpret. 3-dimensional (3D) elastic wave simulations can be a powerful tool in understanding the complicated wave scattering involved in flaw detection and for optimizing experimental techniques. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate Lamb wave scattering from realistic flaws. This paper discusses simulation results for an aluminum-aluminum diffusion disbond and an aluminum-epoxy disbond and compares results from the disbond case to the common artificial flaw type of a flat-bottom hole. The paper also discusses the potential for extending the 3D EFIT equations to incorporate physics-based weak bond models for simulating wave scattering from weak adhesive bonds.
Structural health monitoring (SHM) for the detection of damage in aerospace materials is an important area of research at NASA. Ultrasonic guided Lamb waves are a promising SHM damage detection technique since the waves can propagate long distances. For complicated flaw geometries experimental signals can be difficult to interpret. High performance computing can now handle full 3-dimensional (3D) simulations of elastic wave propagation in materials. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate ultrasound scattering from flaws in materials. EFIT results have been compared to experimental data and the simulations provide unique insight into details of the wave behavior. This type of insight is useful for developing optimized experimental SHM techniques. 3D EFIT can also be expanded to model wave propagation and scattering in anisotropic composite materials.
The size and shape of a delamination in a multi-layered structure can be estimated in various ways from an ultrasonic pulse/echo image. For example the -6dB contours of measured response provide one simple estimate of the boundary. More sophisticated approaches can be imagined where one adjusts the proposed boundary to bring measured and predicted UT images into optimal agreement. Such approaches require suitable models of the inspection process. In this paper we explore issues pertaining to model-based size estimation for delaminations in carbon fiber reinforced laminates. In particular we consider the influence on sizing when the delamination is non-planar or partially transmitting in certain regions. Two models for predicting broadband sonic time-domain responses are considered: (1) a fast "simple" model using paraxial beam expansions and Kirchhoff and phase-screen approximations; and (2) the more exact (but computationally intensive) 3D elastodynamic finite integration technique (EFIT). Model-to-model and model-to experiment comparisons are made for delaminations in uniaxial composite plates, and the simple model is then used to critique the -6dB rule for delamination sizing.
Microcracking in composite laminates is a known precursor to the growth of inter-ply delaminations and larger scale damage. Microcracking can lead to the attenuation of ultrasonic waves due to the crack-induced scattering. 3D elastodynamic finite integration technique (EFIT) has been implemented to explore the scattering of ultrasonic waves due to microcracks in anisotropic composite laminates. X-ray microfocus computed tomography data was directly input into the EFIT simulation for these purposes. The validated anisotropic 3D EFIT code is shown to be a useful tool for exploring the complex multiple-scattering which arises from extensive microcracking.
The CMTB Thwacker hardware operates as a testbed analogue for the Flight Thwacker and Sieve components of CHIMRA, a device on the Curiosity Rover. The sieve separates particles with a diameter smaller than 150 microns for delivery to onboard science instruments. The sieving behavior of the testbed hardware should be similar to the Flight hardware for the results to be meaningful. The elastodynamic behavior of both sieves was studied analytically using the Rayleigh Ritz method in conjunction with classical plate theory. Finite element models were used to determine the mode shapes of both designs, and comparisons between the natural frequencies and mode shapes were made. The analysis predicts that the performance of the CMTB Thwacker will closely resemble the performance of the Flight Thwacker within the expected steady state operating regime. Excitations of the testbed hardware that will mimic the flight hardware were recommended, as were those that will improve the efficiency of the sieving process.
In this work, we present our study of Lamb wave crack detection using wavenumber analysis. The aim is to demonstrate the application of wavenumber analysis to 3D Lamb wave data to enable damage detection. The 3D wavefields (including vx, vy and vz components) in time-space domain contain a wealth of information regarding the propagating waves in a damaged plate. For crack detection, three wavenumber analysis techniques are used: (i) two dimensional Fourier transform (2D-FT) which can transform the time-space wavefield into frequency-wavenumber representation while losing the spatial information; (ii) short space 2D-FT which can obtain the frequency-wavenumber spectra at various spatial locations, resulting in a space-frequency-wavenumber representation; (iii) local wavenumber analysis which can provide the distribution of the effective wavenumbers at different locations. All of these concepts are demonstrated through a numerical simulation example of an aluminum plate with a crack. The 3D elastodynamic finite integration technique (EFIT) was used to obtain the 3D wavefields, of which the vz (out-of-plane) wave component is compared with the experimental measurement obtained from a scanning laser Doppler vibrometer (SLDV) for verification purposes. The experimental and simulated results are found to be in close agreement. The application of wavenumber analysis on 3D EFIT simulation data shows the effectiveness of the analysis for crack detection. Keywords: : Lamb wave, crack detection, wavenumber analysis, EFIT modeling
Guided wave (GW) based damage detection methods have shown promise in structural health monitoring (SHM) and hybrid SHM-nondestructive evaluation (NDE) techniques. Much previous GW work in the aerospace field has been primarily focused on metallic materials, with a growing focus on composite materials. The work presented in this paper demonstrates how realistic three-dimensional (3D) GW simulations can aid in the development of GW based damage characterization techniques for aerospace composites. 3D elastodynamic finite integration technique is implemented to model GW interaction with realistic delamination damage. A local wavenumber technique is applied to simulation data in order to investigate the detectability of hidden delamination damage to enable accurate characterization of damage extent.
Ultrasonic guided waves have proved useful for structural health monitoring (SHM) and nondestructive evaluation (NDE) due to their ability to propagate long distances with less energy loss compared to bulk waves and due to their sensitivity to small defects in the structure. Analysis of actively transmitted ultrasonic signals has long been used to detect and assess damage. However, there remain many challenging tasks for guided wave based SHM due to the complexity involved with propagating guided waves, especially in the case of composite materials. The multimodal nature of the ultrasonic guided waves complicates the related damage analysis. This paper presents results from parallel 3D elastodynamic finite integration technique (EFIT) simulations used to acquire 3D wave motion in the subject laminated carbon fiber reinforced polymer composites. The acquired 3D wave motion is then analyzed by frequency-wavenumber analysis to study the wave propagation and interaction in the composite laminate. The frequency-wavenumber analysis enables the study of individual modes and visualization of mode conversion. Delamination damage has been incorporated into the EFIT model to generate "damaged" data. The potential for damage detection in laminated composites is discussed in the end.
Guided ultrasonic waves (GUW) have the potential to be an efficient and cost-effective method for rapid damage detection and quantification of large structures. Attractive features include sensitivity to a variety of damage types and the capability of traveling relatively long distances. They have proven to be an efficient approach for crack detection and localization in isotropic materials. However, techniques must be pushed beyond isotropic materials in order to be valid for composite aircraft components. This paper presents our study on GUW propagation and interaction with delamination damage in composite structures using wavenumber array data processing, together with advanced wave propagation simulations. Parallel elastodynamic finite integration technique (EFIT) is used for the example simulations. Multi-dimensional Fourier transform is used to convert time-space wavefield data into frequency-wavenumber domain. Wave propagation in the wavenumber-frequency domain shows clear distinction among the guided wave modes that are present. This allows for extracting a guided wave mode through filtering and reconstruction techniques. Presence of delamination causes spectral change accordingly. Results from 3D CFRP guided wave simulations with delamination damage in flat-plate specimens are used for wave interaction with structural defect study.
Toward the goal of delamination detection and quantification in laminated composites, this paper examines guided wave propagation and wave interaction with delamination damage in laminated carbon fiber reinforced polymer (CFRP) composites using frequency-wavenumber (f-kappa) analysis. Three-dimensional elastodynamic finite integration technique (EFIT) is used to acquire simulated time-space wavefields for a CFRP composite. The time-space wavefields show trapped waves in the delamination region. To unveil the wave propagation physics, the time-space wavefields are further analyzed by using two-dimensional (2D) Fourier transforms (FT). In the analysis results, new f-k components are observed when the incident guided waves interact with the delamination damage. These new f-kappa components in the simulations are experimentally verified through data obtained from scanning laser Doppler vibrometer (SLDV) tests. By filtering the new f-kappa components, delamination damage is detected and quantified.
Ultrasound-based nondestructive evaluation (NDE) is a common technique for damage detection in composite materials. There is a need for advanced NDE that goes beyond damage detection to damage quantification and characterization in order to enable data driven prognostics. The damage types that exist in carbon fiber-reinforced polymer (CFRP) composites include microcracking and delaminations, and can be initiated and grown via impact forces (due to ground vehicles, tool drops, bird strikes, etc), fatigue, and extreme environmental changes. X-ray microfocus computed tomography data, among other methods, have shown that these damage types often result in voids/discontinuities of a complex volumetric shape. The specific damage geometry and location within ply layers affect damage growth. Realistic threedimensional NDE and structural health monitoring (SHM) simulations can aid in the development and optimization of damage quantification and characterization techniques. This paper is an overview of ongoing work towards realistic NDE and SHM simulation tools for composites, and also discusses NASA's need for such simulation tools in aeronautics and spaceflight. The paper describes the development and implementation of a custom ultrasound simulation tool that is used to model ultrasonic wave interaction with realistic 3-dimensional damage in CFRP composites. The custom code uses elastodynamic finite integration technique and is parallelized to run efficiently on computing cluster or multicore machines.
Ultrasonic wave phenomena constitute the leading physical mechanism for nondestructive evaluation (NDE) and structural health monitoring (SHM) of solid composite materials such as carbon-fiber-reinforced polymer (CFRP) laminates. Computational models of ultrasonic guided-wave excitation, propagation, scattering, and detection in quasi-isotropic laminates can be extremely valuable in designing practically realizable NDE and SHM hardware and software with desired accuracy, reliability, efficiency, and coverage. This paper presents comparisons of guided-wave simulations for CFRP composites implemented using three different simulation codes: two commercial finite-element analysis packages, COMSOL and ABAQUS, and a custom code implementing the Elastodynamic Finite Integration Technique (EFIT). Comparisons are also made to experimental laser Doppler vibrometry data and theoretical dispersion curves.
Reducing the timeline for certification of composite materials and enabling the expanded use of advanced composite materials for aerospace applications are two primary goals of NASA's Advanced Composites Project (ACP). A key a technical challenge area for accomplishing these goals is the development of rapid composite inspection methods with improved defect characterization capabilities. Ongoing work at NASA Langley is focused on expanding ultrasonic simulation capabilities for composite materials. Simulation tools can be used to guide the development of optimal inspection methods. Custom code based on elastodynamic finite integration technique is currently being developed and implemented to study ultrasonic wave interaction with manufacturing defects, such as in-plane fiber waviness (marcelling). This paper describes details of validation comparisons performed to enable simulation of guided wave propagation in composites containing fiber waviness. Simulation results for guided wave interaction with in-plane fiber waviness are also discussed. The results show that the wavefield is affected by the presence of waviness on both the surface containing fiber waviness, as well as the opposite surface to the location of waviness.
This chapter describes a new intelligent platform for learning optimal designs of morphing wings based on Variable Camber Continuous Trailing Edge Flaps (VCCTEF) in conjunction with a leading edge flap called the Variable Camber Krueger (VCK). The new platform consists of a Computational Fluid Dynamics (CFD) methodology coupled with a semi-supervised learning methodology. The CFD component of the intelligent platform comprises of a full Navier-Stokes solution capability (NASA OVERFLOW solver with Spalart-Allmaras turbulence model) that computes flow over a tri-element inboard NASA Generic Transport Model (GTM) wing section. Various VCCTEF/VCK settings and configurations were considered to explore optimal design for high-lift flight during take-off and landing. To determine globally optimal design of such a system, an extremely large set of CFD simulations is needed. This is not feasible to achieve in practice. To alleviate this problem, a recourse was taken to a semi-supervised learning (SSL) methodology, which is based on manifold regularization techniques. A reasonable space of CFD solutions was populated and then the SSL methodology was used to fit this manifold in its entirety, including the gaps in the manifold where there were no CFD solutions available. The SSL methodology in conjunction with an elastodynamic solver (FiDDLE) was demonstrated in an earlier study involving structural health monitoring. These CFD-SSL methodologies define the new intelligent platform that forms the basis for our search for optimal design of wings. Although the present platform can be used in various other design and operational problems in engineering, this chapter focuses on the high-lift study of the VCK-VCCTEF system. Top few candidate design configurations were identified by solving the CFD problem in a small subset of the design space. The SSL component was trained on the design space, and was then used in a predictive mode to populate a selected set of test points outside of the given design space. The new design test space thus populated was evaluated by using the CFD component by determining the error between the SSL predictions and the true (CFD) solutions, which was found to be small. This demonstrates the proposed CFD-SSL methodologies for isolating the best design of the VCK-VCCTEF system, and it holds promise for quantitatively identifying best designs of flight systems, in general.
Ultrasonic wave methods constitute the leading physical mechanism for nondestructive evaluation (NDE) and structural health monitoring (SHM) of solid composite materials, such as carbon fiber reinforced polymer (CFRP) laminates. Computational models of ultrasonic wave excitation, propagation, and scattering in CFRP composites can be extremely valuable in designing practicable NDE and SHM hardware, software, and methodologies that accomplish the desired accuracy, reliability, efficiency, and coverage. The development and application of ultrasonic simulation approaches for composite materials is an active area of research in the field of NDE. This paper presents comparisons of guided wave simulations for CFRP composites implemented using four different simulation codes: the commercial finite element modeling (FEM) packages ABAQUS, ANSYS, and COMSOL, and a custom code executing the Elastodynamic Finite Integration Technique (EFIT). Benchmark comparisons are made between the simulation tools and both experimental laser Doppler vibrometry data and theoretical dispersion curves. A pristine and a delamination type case (Teflon insert in the experimental specimen) is studied. A summary is given of the accuracy of simulation results and the respective computational performance of the four different simulation tools.
A method for adapting least squares reverse time migration (LSRTM) for ultrasonic guided wave imaging of composite laminates is proposed in this paper. As composites become more widely used in fields such as the aerospace industry, the need for high-resolution imaging in structural health monitoring (SHM) and nondestructive evaluation (NDE) is also growing. For instance, delamination is a common problem in composite laminates, which has led to a certain degree of apprehension in the use of composite materials for load-bearing structures. Although the solver-based imaging techniques using conventional reverse time migration (RTM) methods illuminate damage with a wide range of damage-scattering effects, the resulting images do not fully define the damage regions due to the limited data acquisition aperture, sensor density, frequencies/wavelengths, and incompleteness of adjoint reconstruction. Previously, the LSRTM theory was derived by incorporating a least squares migration (LSM) algorithm into RTM, and benchmarked its high-resolution damage imaging performance for isotropic plates. To improve damage imaging in composite laminates, a process to create an ultrasonic guided wave-based LSRTM method for anisotropic materials is proposed in this paper. The derivation of the forward modeling operator and the adjoint operator is presented. Numerical case studies were conducted to show the improvement of LSRTM over RTM in mapping damage in composite plates. Multiple damage sites or damage with a complex shape were created in the numerical studies based on 1) Born approximation-based modeling or 2) reduction of the plate stiffness-based modeling. LSRTM begins by using a forward modeling process. The forward modeling accuracy for the flexural wave solver used in this study for LSRTM was also compared with the results from a three-dimensional rotated staggered grid (RSG) elastodynamic finite difference solver, previously open-sourced by NASA Langley Research Center. These benchmarking studies have shown that the LSRTM method is more effective in reducing artifacts, improving resolution, and enhancing damage model reconstruction compared to RTM in composite laminates.
Dynamic stiffness of pneumatic tire model - response of rotating cylindrical shell to stationary point load