Anthony N. Sinclair

Acoustic wave scattering from transversely isotropic cylinders

Mathematical expressions are derived for the far‐field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave. The normal‐mode solution is based on decoupling of the scalar potential representing the horizontally polarized shear wave from those of the compressional and vertically polarized waves. The solution degenerates to the well‐known simple model for isotropic cylinders in the case of very weak anisotropy. The solution is used to study the influence of each element of the stiffness matrix on the various resonant modes of vibration. Perturbations of the elements c33 and c44, which characterize the cylinder along the axis, significantly affect resonant frequencies corresponding to axially guided waves. Perturbations of c11 and c12, which characterize the material on the transverse plane, predominantly affect the Rayleigh and Whispering Gallery resonance frequencies. Perturbations of c13 affect all three ty...

Recovery of a sparse spike time series by L/sub 1/ norm deconvolution

An L/sub 1/ norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in CANDU nuclear reactors. For each problem, parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor. This performance factor is based on a quantified analysis of the transitions in estimates of h as the damping parameter is varied over a wide range of possible values. It is shown that for the examined cases in which the true impulse response is a sparsely filled spike strain, the L/sub 1/ norm provides significantly better results than the more commonly used L/sub 2/ norm minimization schemes. These results are shown to be consistent with theoretical predictions. >

Analysis of the Peel Test: Prediction of Adherend Plastic Dissipation and Extraction of Fracture Energy in Metal-to-Metal Adhesive Joints

The peel test has been widely used for the mechanical measurement of the adhesion phenomenon. However the proportion of the energy input dissipated plastically within the adherend is a major concern in analyzing peel test data. This paper presents an analytical approach to predict the adherend plastic dissipation in the peel test for metal-to-metal adhesive joints, thereby allowing the fracture energy to be extracted from the test data using an energy balance approach. Expressions are developed for the deflection of an elastic-plastic beam on an elastic foundation, which is then combined with known solutions for the deformation of an elastic-plastic strip under large displacement. The model takes into account both the adhesive and adherend compliance effects on the plastic dissipation. Numerical predictions of the model are presented to gain insight into the effects of adherend properties and peel angle on plastic dissipation in the peel test. It is demonstrated that experimental results with various adherend properties and peel angles are consistent with the predictions of the model. An important conclusion is that for typical structural adhesives, the effects of plastic dissipation may be kept small by using a relatively low yield strength alloy with a thickness much smaller than the critical thickness at which the plastic dissipation effect is a maximum. The extraction of the fracture energy from the test data is also discussed with regard to the mixed-mode nature of the peel test.

Nondestructive evaluation of cylindrical components by resonance acoustic spectroscopy

Examples of the applications of resonance acoustic spectroscopy (RAS) for the purposes of nondestructive evaluation (NDE) and on-line monitoring of the properties of various cylindrical components are presented in this paper. The mathematical equations for the scattering of a plane acoustic wave from isotropic and transversely isotropic cylinders and isotropic clad rods are reviewed. A new technique called material characterization by resonance acoustic spectroscopy (MCRAS), for the evaluation of the elastic constants of isotropic rods and wires, is introduced. This new technique is compared to the traditional time-of-flight measurement technique. Possible applications of RAS in NDE and on-line monitoring of clad rods are demonstrated using practical examples. The possibility of using RAS for evaluation of axial and transverse properties of fiber-reinforced composite wires and rods, which are transversely isotropic in nature, is discussed. The results indicate that RAS can be used as a tool for NDE and on-line monitoring of various properties of cylindrically-shaped components.

Comparison of three formulations for eddy-current and skin effect problems

Three finite-element formulations based on different definitions of current density are compared. Formulations I and II are based on incomplete equations for total and source current densities, respectively. Formulation III is based on a complete equation for source current density. To validate the third formulation, a one-dimensional test problem is solved analytically for the magnetic field intensity. The formulations are applied to a nondestructive testing example and a three-phase bus-bar example. Results show that errors due to the use of incomplete equations for current densities increase with frequency and conductor dimensions.

Improved finite element method for EMAT analysis and design

Electromagnetic acoustic transducers (EMATs) operating in transmitting mode are examined. Two different finite element formulations, derived for two different definitions of source current density, are compared in order to show the importance of skin and proximity effects. An EMAT consisting of six source conductors is modeled as an example. Results obtained with an earlier method are compared with new FEM results at two different frequencies. The effect of lift-off and distance between conductors is investigated.

Adhesive joint durability assessed using open-faced peel specimens

Abstract This paper presents an investigation of the durability of two aluminum-epoxy adhesive systems by means of open-faced peel specimens. A peel analysis model was used to determine the fracture energy from the peel data. Both wet and dry peel tests were conducted in order to distinguish between the reversible and the permanent effects of water. The effects of water on the cohesive properties of the adhesives were also assessed by tension tests. It was found that, for the two-part epoxy adhesive, which plasticized to a large extent, the peel testing should be carried out in a dry state to assess the interfacial weakening. It was also observed that the two-part adhesive was much stiffer in the dry, degraded state, and it was important to take account of such permanent changes in the cohesive properties associated with water uptake when determining the fracture energy from the peel data. In contrast, the one-part epoxy system did not suffer from appreciable cohesive changes, either reversible or permane...

On the Determination of Fracture Energy Using the Peel Test

This paper presents an improved model for the prediction of the adherend plastic dissipation in the peel test, thereby allowing the determination of the critical fracture eaergy. The model, which is based on earlier work, takes into account the effects of adhesive shear stresses, and a bilinear stress-strain response for the flexible adherend. Treating the flexible adherend as a beam-on-elastic foundation, expressions for the normal and shear foundation constants due to the compliance at the root of the adherend under elastic-plastic loading are derived using the deformation theory of plasticity. Application of the model to experimental peel data shows that it gives an improved estimate of the critical fracture energy.

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.

A calibrated finite element model of adhesive peeling

A finite element model of the flexible-rigid peel test was compared with experimental steady-state peel forces for nine configurations (three adherend thicknesses and three angles) in order to investigate the von Mises critical strain as a failure criterion. It was found that the critical von Mises strain was approximately constant for a given adherend thickness at the three peel angles, but that it increased significantly as the adherend thickness increased. Modification of the functional dependence of adhesive yield stress on hydrostatic stress did not correct for this thickness dependence. The steady-state peel geometry and loads were determined by executing the model incrementally through small load steps beginning with the initial undeformed shape of the adherend. This simulation of the transient stage of the peel test illustrated the large differences between the peel force and geometry at the onset of adhesive failure and at steady state.