Inverse ultrasonic determination of imperfect interfaces and bulk properties of a layer between two solids

Ultrasonic evaluation of ply and interleaf layer properties of interleaved composite laminates

An ultrasonic nondestructive evaluation procedure is presented for the ply and interleaf layer properties of carbon/epoxy composite laminates having interleaf resin layers at their interlaminar interfaces. It is shown that the material properties of plies (density, thickness, and transversely isotropic complex elastic moduli) and elastic interleaf layers (density, thickness, Young's modulus, and Poisson's ratio) can be identified by best fitting the theoretical energy transmission spectra of longitudinal waves through the laminate immersed in water to those obtained in ultrasonic measurement. It is also demonstrated that compared to the mass-less and null-thickness spring-type interlaminar interface model employed in the previous works, the present finite-thickness interleaf layer model can better reproduce the experimental transmission spectra of a unidirectional interleaved composite laminate containing ultrasonic bandgaps. Furthermore, the property characterization in the case where the plies and interleaf layers are assumed to be elastic and viscoelastic, respectively, is also examined. It is also shown that the ply and interleaf layer properties determined for the unidirectional laminate can be used to reproduce the transmission spectra measured for a quasi-isotropic laminate consisting of the same plies and interleaf layers.

Non-destructive testing of interfacial stiffness based on spring model for diffusion bonding interface of titanium alloy components with complex surface

Ultrasonic testing is an important non-destructive testing method, which is sensitive to the defects in the diffusion bonding interface. Ultrasonic testing of diffusion bonding interfaces in complex-surface components is a challenge due to the geometry and the weak echo signal of the diffusion bonding defects. This paper proposes an interfacial stiffness characterization method based on the spring model for the ultrasonic testing of the diffusion bonding interface of titanium alloy complex-surface component. Finite element models for ultrasonic field are established to analyze the diffusion bonding defects response, the effect of complex surface, and the inconsistency of the bonding interface depth in ultrasonic testing of the titanium alloy complex-surface component. 15 MHz is recommended as the testing frequency of the diffusion bonding interface. Ultrasonic C-scan experiments are conducted using specimens with embedded artificial defects and a titanium alloy complex-surface component. The simulation and experimental results show that the novel interfacial stiffness characterization method can be applied to ultrasonic testing of the diffusion bonding interface (inclination angle less than 14°) in complex-surface components, and the ability to test defects at the diffusion bonding interface can be improved.

Laser ultrasonics in a multilayer structure: Plane wave synthesis and inverse problem for nondestructive evaluation of adhesive bondings

A laser ultrasonic method is proposed for the nondestructive evaluation of bonded assemblies based on the analysis of elastic plane waves reflected from the bonding interface. Plane waves are numerically synthesized from experimentally detected cylindrical waves. Several angles of incidence with respect to the bonding interface are achieved by varying the delay in the synthesis step. An inverse problem using these plane waves is then solved to identify the normal and transverse interfacial stiffnesses that model the mechanical coupling between two bonded media. The semi-analytic model developed and detailed in Hodé et al. [J. Acoust. Soc. Am. 150, 2065 (2021)] is used to create the database that contains simulated laser-generated ultrasounds required to solve the inverse problem. The developed method is first validated with semi-analytic simulated input data where Gaussian noise has been added. Next, the method is applied using signals acquired on an aluminum alloy plate and on assemblies (with and without adhesion defects) made of two aluminum alloy plates bonded by an aeronautical structural epoxy adhesive film. Differences between the identified values of interfacial stiffnesses distinguish the three samples and obtain quantitative values to characterize the adhesive bonding.

Effect of interfacial adhesion on the ultrasonic interaction with adhesive joints: A theoretical study using spring-type interfaces

The effect of interfacial properties on the reflection and transmission characteristics of ultrasonic waves at adhesively bonded joints is theoretically investigated. An adhesive joint is modeled as a double-interface model, namely, a homogeneous layer coupled to adherends by two spring-type interfaces with different interfacial stiffnesses. For the normal incidence of a one-dimensional longitudinal wave, theoretical results are obtained and validated by finite element simulation. When the thickness of the adhesive layer is sufficiently small compared to the wavelength, the amplitude reflection and transmission coefficients show monotonic dependence on frequency, which can be explained by the theoretical relation of the double-interface model to a single spring-type interface model. The reflection and transmission behavior is invariant if the values of the two interfacial stiffnesses are interchanged. For a relatively thick adhesive layer, on the other hand, the reflection coefficient shows local minima at multiple frequencies. As one interfacial stiffness decreases, the local minimum frequencies decrease and the local minima increase. If the values of the two interfacial stiffnesses are interchanged, the reflection coefficient remains invariant but the reflection waveform shows different features. The obtained reflection and transmission characteristics are discussed in light of the characterization of the interfacial adhesion.

Swept-frequency ultrasonic phase evaluation of adhesive bonding in tri-layer structures

As modern aerospace and automotive designs continually strive for higher performance, and thus rely on advanced composite structures where adhesive bonding is a preferred method of joining, the need for a robust quantitative nondestructive bond strength measurement method has increased. As such, advanced nondestructive evaluation methods have been researched for increased sensitivity to weak interfacial bonding and ultimately to detect "kissing" bonds. In this work, a phase-based method for interrogating bonded joints and detecting weak adhesion is developed by using swept-frequency phase measurements of ultrasonic waves reflected from an adhesive joint and modeling adhesive interfaces as a distributed spring system. The method's sensitivity to bond strength is explored by ultrasonic phase evaluation of tri-layer joints with bond quality varied by controlling ultraviolet light exposure and extracting interfacial stiffness constants of the bonds. Mechanical tensile tests found each joint failed adhesively, allowing a linear correlation to be drawn between interfacial stiffness and tensile strength, consistent with previous theoretical research. The ultrasonic phase measurement method identifies intermediate bond strengths, rather than simply detecting good or bad bonds. This technique has the potential for the verification of bond quality in lightweight aerospace and automotive designs utilizing advanced composite structures with adhesive attachments.

Apparent anisotropy of adhesive bonds with weak adhesion and non-destructive evaluation of interfacial properties

The present research attempts to non-destructively characterize mechanical properties, which are representative of the interfacial adhesion and bond line cohesion of adhesively bonded assemblies, using an ultrasonic method. Eight bonded samples made of two aluminium substrates and of an epoxy-based adhesive layer were manufactured: four in which the adhesive is fully cured (100%) and four in which crosslinking is partial (80%). For each level of curing, four different surface treatments were applied to the aluminium substrates before assembling, in order to vary the quality of adhesion. Ultrasonic plane wave transmission coefficients (UPWTC) were either measured in a water tank, or simulated using the well-known stiffness matrix method that micmics the experiments, to produce input data for the inverse problem. This latest consists in the evaluation of the elastic properties of either the adhesive bond or the interphases between both substrates and the adhesive layer. If the interphases are of nominal quality, the values of the inferred properties of the adhesive bond match those previously measured on individual epoxy samples, whether the epoxy is fully or partially cured. However, when interphases are not of nominal quality level, the optimized bond moduli reveal an apparent anisotropy, although the epoxy layer is known to be isotropic. This apparent anisotropy is explained by an analytical rule of mixture, thus giving confidence in the proposed ultrasonic technique, which is then suggested as a potential way to detect weaknesses of interphases. Finally, the optimization of the interphases elastic properties is carried out. The measured normal and shear stiffnesses are shown to decrease as the interphases get degraded. All ultrasonically-measured parameters (apparent anisotropy of the bond and interfacial stiffnesses) vary monotonically with the bonds strength, which was measured via mechanical tests. The proposed UPWTC method was shown to have a strong potential to distinguish between adhesive and cohesive weaknesses of bonded joints, and to estimate corresponding mechanical properties.

Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity

Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.

SH ultrasonic guided waves for the evaluation of interfacial adhesion

Shear-Horizontally (SH) polarized, ultrasonic, guided wave modes are considered in order to infer changes in the adhesive properties at several interfaces located within an adhesive bond joining two metallic plates. Specific aluminium lap-joint samples were produced, with different adhesive properties at up to four interfaces when a glass-epoxy film is inserted into the adhesive bond. EMAT transducers were used to generate and detect the fundamental SH0 mode. This is launched from one plate and detected at the other plate, past the lap joint. Signals are picked up for different propagation paths along each sample, in order to check measurement reproducibility as well as the uniformity of the adhesively bonded zones. Signals measured for four samples are then compared, showing very good sensitivity of the SH0 mode to changes in the interfacial adhesive properties. In addition, a Finite Element-based model is used to simulate the experimental measurements. The model includes adhesive viscoelasticity, as well as spatial distributions of shear springs (with shear stiffness KT) at both metal-adhesive interfaces, and also at the adhesive-film interfaces when these are present. This model is solved in the frequency domain, but temporal excitation and inverse FFT procedure are implemented in order to simulate the measured time traces. Values of the interfacial adhesive parameters, KT, are determined by an optimization process so that best fit is obtained between both sets of measured and numerically predicted waveforms. Such agreement was also possible by adjusting the shear modulus of the adhesive component. This work suggests a promising use of SH-like guided modes for quantifying shear properties at adhesive interfaces, and shows that such waves can be used for inferring adhesive and cohesive properties of bonds separately. Finally, the paper considers improvements that could be made to the process, and its potential for testing the interfacial adhesion of adhesively bonded composite components.

Evaluation of interlayer interfacial stiffness and layer wave velocity of multilayered structures by ultrasonic spectroscopy

An ultrasonic evaluation procedure for the interlayer interfacial normal stiffness and the intralayer longitudinal wave velocity of multilayered plate-like structures is proposed. Based on the characteristics of the amplitude reflection spectrum of ultrasonic wave at normal incidence to a layered structure with spring-type interlayer interfaces, it is shown that the interfacial normal stiffness and the longitudinal wave velocity in the layers can be simultaneously evaluated from the frequencies of local maxima and minima of the spectrum provided that all interfaces and layers have the same properties. The effectiveness of the proposed procedure is investigated from the perspective of the sensitivity of local extremal frequencies of the reflection spectrum. The feasibility of the proposed procedure is also investigated when the stiffness of each interface is subjected to small random fluctuations about a certain average value. The proposed procedure is applied to a 16-layered cross-ply carbon-fiber-reinforced composite laminate. The normal stiffness of resin-rich interfaces and the longitudinal wave velocity of plies in the thickness direction evaluated from the experimental reflection spectrum are shown to be consistent with simple theoretical estimations.

Scattering of ultrasonic waves by heterogeneous interfaces: formulating the direct scattering problem as a least-squares problem

An analytic-numerical method to simulate the interaction of time-harmonic ultrasonic waves with imperfectly bonded layered structures is presented. In the proposed formulation, elastic layers may be either isotropic or anisotropic and adhesion interfaces are replaced by equivalent continuous distribution of normal and transversal springs. In addition, adhesion imperfections are allowed to be localized in space and are modeled by a corresponding local reduction in spring constants. The resulting direct scattering problem is formulated as a least-squares problem and solved accordingly. The formulation was extended for three different cases: Scattering from imperfectly bonded half-spaces, scattering from imperfectly bonded layered structures and scattering from imperfectly bonded layered plates immersed in acoustic fluid, and numerical simulations corresponding to each one of these cases are presented. The simulations indicate that the method is capable of capturing the scattering resulting from the interaction of ultrasonic waves with defective bonds as well as indicate that ultrasound has the potential of revealing the presence of defective bonds and interfacial heterogeneities.

Effective spring stiffness for a periodic array of interacting coplanar penny-shaped cracks at an interface between two dissimilar isotropic materials

An effective spring stiffness approximation is proposed for a hexagonal array of coplanar penny shaped cracks located at the interface between two dissimilar solids. The approximation is based on the factorization of the solution on the material dissimilarity factor, the crack interaction factor and the effective spring stiffness solution for non-interacting cracks in a homogeneous material. Such factorization is exact and was validated for 2D collinear cracks between two dissimilar solids. The crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material; also the material dissimilarity function recently obtained for non-interacting penny shaped crack at the interface between two dissimilar materials is employed. The obtained solution is useful for an assessment by ultrasonic measurements of the interface stiffness in bonded structures for monitoring the interfacial microdamage growth due to mechanical loading and environmental factors.

Some studies on evaluation of degradation in composite adhesive joints using ultrasonic techniques

Experimental and theoretical studies on degradation of composite-epoxy adhesive joints were carried out on samples having different interfacial and cohesive properties. Oblique incidence ultrasonic inspection of bonded joints revealed that degradation in the adhesive can be measured by significant variation in reflection amplitude as also by a shift in the minima of reflection spectrum. It was observed that severe degradation of the adhesive leads to failure dominated by interfacial mode. Through this investigation it is demonstrated that a correlation exists between the bond strength and a frequency shift in reflection minimum. The experimental data was validated using analytical models. Though both bulk adhesive degradation and interfacial degradation influences the shift in spectrum minimum, the contribution of the latter was found to be significant. An inversion algorithm was used to determine the interfacial transverse stiffness using the experimental oblique reflection spectrum. The spectrum shift was found to depend on the value of interfacial transverse stiffness using which a qualitative assessment can be made on the integrity of the joint.

Effective Spring Stiffness for a Planar Periodic Array of Collinear Cracks at an Interface between Two Dissimilar Isotropic Materials

Explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity (the well-known open interface crack model is employed for the solution). Since the interfacial spring stiffness can be experimentally determined from ultrasound reflection and transmission analysis, the proposed expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting (independent) cracks and the crack interaction factor. In order to avoid the effect of the crack surface interpenetration zones on the effective spring stiffness, the range of the tensile to transverse load ratios is obtained under the assumption of small-scale contact conditions. Since real cracks are often slightly open (due to prior loading history and plastic deformation), it is demonstrated that for ultrasound applications the results obtained are valid for most practical cases of small interfacial cracks as long as the mid-crack opening normalized by the crack length is at least in the order of 10^-5.

Shear horizontal guided wave modes to infer the shear stiffness of adhesive bond layers

This paper presents a non-destructive, ultrasonic technique to evaluate the quality of bonds between substrates. Shear-horizontally polarized (SH) wave modes are investigated to infer the shear stiffness of bonds, which is necessarily linked to the shear resistance that is a critical parameter for bonded structures. Numerical simulations are run for selecting the most appropriate SH wave modes, i.e., with higher sensitivity to the bond than to other components, and experiments are made for generating-detecting pre-selected SH wave modes and for measuring their phase velocities. An inverse problem is finally solved, consisting of the evaluation of the shear stiffness modulus of a bond layer at different curing times between a metallic plate and a composite patch, such assembly being investigated in the context of repair of aeronautical structures.

Determination of epoxy film parameters in a three-layer metal/adhesive/metal structure

The aim of this work is to propose a method to determine the elastic parameters and the thickness of a thin epoxy film located inside a 3-layer aluminum/epoxy/aluminum structure, based on ultrasonic measurements. This study is conducted at low frequencies, to allow the vibration of the whole structure. First, the direct problem is addressed. The sensitivity of the vibration modes to the parameters of interest is studied to select the most sensitive one for a given parameter to be determined. Second, the identification of the parameters with the selected modes is obtained by a minimization of the characteristic equation. This process is applied to experimental data: the longitudinal and shear wave velocities and the thickness of the epoxy film are obtained within a 3% error range.

Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.

Modulated angle beam ultrasonic spectroscopy for evaluation of imperfect interfaces and adhesive bonds

An experimental method incorporating high frequency pulsed angle beam ultrasonic measurements modulated by low frequency vibrations of a bonded structure is described. This method uses parametric/nonlinear mixing between high and low frequencies to characterize adhesive degradation. It is demonstrated that good quality (undamaged) bonds exhibit little dependence of ultrasonic signature on the overlay of low frequency vibration loads; however, environmentally degraded or imperfect bonds exhibit strong modulation of the resonance frequency of the ultrasonic signal reflected from the bond. The results are interpreted using a model for normal and oblique wave interaction with two nonlinear interfaces separated by an adhesive layer under quasi-static stress modulation.