There has been an increase in the use of ultrasonic arrays for the detection of defects in composite structures used in the aerospace industry. The response of a defect embedded in such a medium is influenced by the inherent anisotropy of the bounding medium and the layering of the bounding medium and hence poses challenges for the interpretation of the full matrix capture (FMC) results. Modeling techniques can be used to understand and simulate the effect of the structure and the defect on the received signals. Existing modeling techniques, such as finite element methods (FEM), finite difference time domain (FDTD), and analytical solutions, are computationally inefficient or are singularly used for structures with complex geometries. In this paper, we develop a novel model based on the Gaussian-based recursive stiffness matrix approach to model the scattering from a side-drilled hole embedded in an anisotropic layered medium. The paper provides a novel method to calculate the transmission and reflection coefficients of plane waves traveling from a layered anisotropic medium into a semi-infinite anisotropic medium by combining the transfer matrix and stiffness matrix methods. The novelty of the paper is the developed model using Gaussian beams to simulate the scattering from a Side Drilled Hole (SDH) embedded in a multilayered composite laminate, which can be used in both immersion and contact setups. We describe a method to combine the scattering from defects with the model to simulate the response of a layered structure and to simulate the full matrix capture (FMC) signals that are received from an SDH embedded in a layered medium. The model-assisted correction total focusing method (MAC-TFM) imaging is used to image both the simulated and experimental results. The proposed method has been vali-dated for both isotropic and anisotropic media by a qualitative and quantitative comparison with experimentally determined signals. The method proposed in this paper is modular, computationally inexpensive, and is in good agreement with experimentally determined signals, and it enables us to understand the effects of various parameters on the scattering of a defect embedded in a layered anisotropic medium.

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There has been a steady increase of composites and anisotropic materials in primary aircraft structures over the years. This increase is driven by the high strength to weight ratio of such materials leading to lighter and more efficient aircraft. As the uptake of such materials keeps increasing so does the complexity in geometry and manufacture of the parts which use these materials. As in the case of any structural component, these structures suffer from defects during manufacture and from damage inservice and have to be tested using nondestructive methods regularly. A plethora of NDT techniques exist for testing aircraft structures with ultrasonic NDT being a staple in the industry. Testing using single element transducers is being replaced by phased arrays as phased arrays can be used in different testing configurations such as beam steering or using phased arrays to capture the signals and then post process the data to form an image. Phased array testing of isotropic materials has been carried out for a number of years with a lot of research being devoted to the testing of such materials. The testing of isotropic materials is relatively less complicated than for anisotropic materials due to the constant material properties throughout the material, the types of defects or failures which such structures suffer and the effect of the material properties on the ultrasonic beam propagating through it or on the output signals. This leads to a simpler interpretation and easier understanding of results when such structures are tested. On the other hand testing of anisotropic materials is complicated by the fact that the material properties are not the same in every direction. The anisotropic nature of such materials has an effect on the ultrasonic beam propagation and output signals which makes the interpretation and understanding of the output more difficult. The layered structure of the composite materials also leads to multiple reflections and reverberations of the layers during inspection which are properties of the laminate, array parameters etc. leading to noise in the output signals and noise in the image. Due to this ultrasonic NDT remains a bottleneck in the further implementation of composites in aircraft structures. Understanding the effect of these various parameters experimentally would require dozens of experiments with different isolated parameters. To overcome the need for this enormous experimental campaign, modelling and simulations can be carried out to help understand these effects. There has been progress in the NDT community on the adoption of modelling methodologies to simulate the predict the response of the inspected material to the wave passing through it and the output signals which are generated. The numerical models already developed have been applied to a variety of scenarios and to different complex geometries but become quite computationally expensive as the material and inspection procedure complexity increases and take hours of runtime when run on personal computers. Some analytical and semi-analytical models which have been applied are restricted either in geometry, require the numerical evaluation of multiple integrals, are computationally expensive or do not take into consideration the array parameters or are singular when interacting with different geometries. @en

Phased array ultrasonic testing is widely used to test structures for flaws due to its ability to produce steered and focused beams. The inherent anisotropic nature of some materials, however, leads to skewing and distortion of the phased array beam and consequently measurement errors. To overcome this, a quantitative model of phased array beam propagation in such materials is required, so as to accurately model the skew and the distortion. The existing phased array beam models which are based on exact methods or numerical methods are computationally expensive or time consuming. This article proposes a modeling approach based on developing the linear phased multi-Gaussian beam (MGB) approach to model beam steering in anisotropic media. MGBs have the advantages of being computationally inexpensive and remaining non-singular. This article provides a comparison of the beam propagation modeled by the developed ordinary Gaussian beam and linear phased Gaussian beam models through transversely isotropic austenitic steel for different steering angles. It is shown that the linear phased Gaussian beam model outperforms the ordinary one, especially at steering angles higher than 20° in anisotropic solids. The proposed model allows us to model the beam propagation from phased arrays in both isotropic and anisotropic media in a way that is computationally inexpensive. As a further step, the developed model has been validated against a finite element model (FEM) computed using COMSOL Multiphysics.

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Ultrasonic testing using arrays is becoming widely used to test composite structures in the Aerospace industry. In recent years, the Full Matrix Capture (FMC) technique has been implemented to extract the signals for post-processing to form an image. The inherent anisotropy and the layering of the structure pose challenges for the interpretation of this FMC data. To overcome this challenge, modeling techniques are required that take into account the diffraction caused by finite-size transducers and the response of the structure to these bounded beams. Existing models either homogenize the entire structure, use computationally expensive finite difference time domain (FDTD) methods, or do not consider the shape of the bounded beam, which is used to test such structures. This paper proposes a modeling technique based on combining the Multi-Gaussian beam model with the recursive stiffness matrix method to simulate the FMC signals for layered anisotropic media. The paper provides the steps required for the modeling technique, the extraction of the system efficiency factor, and validation of the model with experimentally determined signals for aluminum as an isotropic material such as aluminum and Carbon Fiber Reinforced Plastic (CFRP) laminate as a layered material. The proposed method is computationally inexpensive, shows good agreement with the experimentally determined FMC data, and enables us to understand the effects of various transducer and material parameters on the extracted FMC signals.@en

In this paper we ultrasonic signals from array transducers are simulated using the Thompson and Gray measurement model. The measurement model consists of a beam model, a system efficiency factor which characterizes the response of the electro-mechanical and electrical components of the system, and a flaw scattering model. To inspect layered composite structures with complex geometries such as curvature, a beam model which is non-singular is required. Hence a multi Gaussian beam model for an ultrasonic array which includes the slowness surface parameters for unidirectional CFRP is investigated. The system functions of the ultrasonic array are modelled using a system efficiency model for a rectangular array. The Kirchoff approximation and separation of variables method for far field scattering in anisotropic materials is used to model the far field response of scatterers such as side drilled holes (SDH) in unidirectional CFRP. In summary the ultrasonic measurement model developed is able to predict the signals from scatterers such as side drilled holes (SDH) in transversely isotropic CFRP.

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Weight reduction is an important driver of the aerospace industry, which encourages the development of lightweight joining techniques to substitute rivet joints. Friction stir welding (FSW) is a solid-state process that enables the production of lighter joints with a small performance reduction compared to the base material properties. Increasing the FSW lap joint performance is an important concern. Friction stir weld bonding is a hybrid joining technology that combines FSW and adhesive bonding in order to increase the mechanical properties of FSW lap joints. FSW and hybrid lap joints were produced, using 2-mm-thick AA6082-T6 plates and a 0.2-mm-thick adhesive layer. Defect detection using the non-destructive test, phased array ultrasonic testing (PAUT), has been made. Microscopic observations were performed in order to validate the phased array ultrasonic testing results. Lap shear strength tests were carried out to quantify the joint’s quality. PAUT inspection successfully detected non-welded specimens but was not able to distinguish specimens with major hook defects from specimens correctly weld bonded with small hook defects.

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Ultrasonic arrays are used for non-destructive evaluation of structures for aerospace and other applications. With the increase in the usage of fibre-reinforced composites in aerospace structures, this evaluation becomes complex due to the effects of attenuation and reflection from the layer boundaries in composite laminates. Hence there is considerable interest in developing beam models for accurate evaluation in such anisotropic media. In anisotropic media, the phase velocity varies with direction of propagation of the ultrasonic beam. Hence, the slowness surface and its properties play an important role in the beam models which are based on the paraxial approximation. The beam from a single element transducer is well collimated. However the beam from individual array elements is not well collimated and may affect the beam propagation through the composite structure. In this paper, Multi modular Gaussian beam (MMGB) model based on the paraxial approximation is applied to study the propagation of beam from an ultrasonic array in transversely isotropic fibre-reinforced composites. The effect of the slowness surface properties on the beam diffraction and skew through the composite structure are studied along with the influence of array parameters on the beam propagation through the structure. This work has demonstrated that the overall beam profile for quasi longitudinal beam from an ultrasonic array propagating in transversely isotropic fibre reinforced composites can be modelled as multi Gaussian beams. Simulation results are presented which illustrate the effects of? slowness properties on beam propagation in unidirectional CFRP in the symmetric planes.@en