Chun H. Wang

A synthetic time-reversal imaging method for structural health monitoring

This paper presents an experimental and theoretical investigation of the applicability of the time-reversal concept to guided waves in plate-like structures, where the stress waves are dispersive and of multi-modes. It is shown that temporal and spatial focusing can be achieved through time reversal, although the dispersive behaviour of the flexural waves renders it impossible to exactly reconstruct the waveform of the original excitation. Based on the principle of the time-reversal concept, a digital imaging method suitable for distributed sensor/actuator networks has been developed. This new method, which overcomes the limitation of the conventional phased array method that operates under pulse-echo mode, provides an efficient imaging method for locating and approximate sizing of structural damages. In addition, it has been shown that signal strengths can be considerably enhanced by applying the present synthetic time-reversal method, thus reducing the number of sensors and actuators required to achieve a given signal-to-noise ratio.

Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue—Part 1: Theories

Fatigue life prediction under multiaxis random loading is an extremely complex and intractable topic ; only a few methods have been proposed in the literature. In addition, experimental results under multiaxis random loading are also scarce. In part one of this two-part paper, a multiaxial non-proportional cycle counting method and fatigue damage calculation procedure are proposed, which is compared with one published damage-searching method. Both theories are based on critical plane concepts, one being an extension of the local strain approach for uniaxial variable amplitude loading and the other employing a new counting algorithm for multiaxis random loading. In principle, these two methods can be considered as bounding solutions for fatigue damage accumulation under multiaxis random loading.

Three-dimensional stress constraint in an elastic plate with a notch

Abstract This paper presents analytical solutions for the three-dimensional stress distribution around typical stress concentrators in an isotropic plate of arbitrary thickness. Based on the assumption of a generalised plane-strain theory, which assumes that the through-the-thickness extensional strain is uniform in the thickness direction, an exact three-dimensional solution has been obtained for an annulus subjected to arbitrary loading along its edges. Emphasis has been placed on the through-the-thickness stress constraint, which is a pre-requisite to analysing the effect of plate thickness on the elastic–plastic deformation at a notch root. Important results are presented on the effects of the plate thickness and Poissons ratio on the in-plane stress concentration factor and the out-of-plane stress constraint factor. By extending the theoretical method to a plate with a non-circular notch, an approximate solution has been obtained for the through-the-thickness constraint factor in a plate with a V-shaped notch having a circular tip. The present solutions have been shown to correlate well with numerical results obtained using the finite element method.

Wave reflection and transmission in beams containing delamination and inhomogeneity

This paper presents an analytical approach using higher order plate theories to determine wave reflections from and transmissions through a damaged region in a beam. The damaged region is either treated as two split beams or as an inhomogeneity. The reflection ratios and transmission ratios are found to depend strongly on the frequency of the incident flexural waves, as well as the size of the damage, which gives rise to strong stop/pass band behaviour. Using the spectral analysis method, the transient wave propagation in a beam with a part-through delamination is predicted and compared with experimental results, indicating a good agreement in the phases and amplitudes of both the reflected and transmitted waves.

Plastic yielding of a film adhesive under multiaxial stresses

Abstract This article presents a study of the plastic yielding behaviour of a rubber-toughened film adhesive (FM73) subjected to triaxial stresses. Experiments were carried out using a bonded joint specimen similar to the Iosipescu specimens originally designed for use with fibre composite materials. The experimental results reveal that the plastic yielding of the FM73 adhesive exhibits a complex dependence on the hydrostatic stress, especially in the compression regime. It is found that the conventional yield criteria widely employed to model adhesives, such as the modified Tresca criterion, the modified von Mises criterion, and the linear Drucker–Prager criterion, are unable to characterise the yield locus. To overcome this difficulty, the modified Drucker–Prager/cap plasticity model that is commonly associated with geological materials is adopted in the present study, which provides a good correlation with the experimental data.

Mindlin plate theory for damage detection: Source solutions

A consideration of the relevant length scales and time scales suggests that Mindlin plate theory provides a judicious model for damage detection. A systematic investigation of this theory is presented that emphasizes its mixed vector-scalar character and analogies with 3D elasticity. These analogies lead to the use of Helmholtz potentials, and to compact statements of the reciprocal theorem and the representation theorem. The plate response for a point moment is derived using a direct source specification, rather than an indirect specification through boundary conditions. Solutions are presented for combinations of such point moments (doublets) that represent, respectively, a center of bending, a center of twist and a center of inplane twist. The flexural response due to finite sources, such as piezoelectric actuators, can be modeled by distributions of centers of bending. Detailed results are presented for a circular, and for a narrow rectangular actuator. The far-field radiation pattern for an array of equally spaced actuators parallel to a straight boundary is derived. The solutions presented for the point moment and the point force constitute the components of a dyadic Green’s function which is required, along with its spatial derivatives, for a representation of plate-wave scattering by flexural inhomogeneities.

Fatigue crack growth in adhesively bonded composite-metal double-lap joints

Abstract This paper presents experimental and numerical investigations of the fatigue crack initiation and growth mechanism in metal-to-composite bonded double-lap joints. Fatigue tests were conducted under tension dominated loading, with crack lengths being measured optically. Examination of the fracture surface using scanning electron microscope revealed that fatigue cracks were near the interface between the co-cured adhesive and the first ply of the composite adherend. The finite element method has been used to determine the strain-energy release rate of a fatigue crack growing along the first ply of the composite. The effects of spew fillet size and crack initiation modes have also been studied by the finite element method. Comparison of the present experimental crack growth results with those measured using double-overlap joints, where the fatigue cracks were driven by pure mode II loading, indicate that the tensile mode loading has a overwhelming effect on the fatigue crack growth rates. The present results suggest that fatigue failure of metal-composite double-lap joints is mainly driven by tensile mode loading due to the peel stress.

Prediction of natural frequencies of finite length circular cylindrical shells

Abstract Analysis of the vibration characteristics of finite circular cylindrical shells is more complex than for beams and plates. This is because the coupling of vibration of shells between the three directions can no longer be neglected. A literature review of the subject reveals that in traditional analysis, assumptions are made to simplify the equations of motion so that they can be solved directly with the appropriate boundary conditions. Consequently, the results obtained could be in error under certain conditions. Based on the Loves equations and an infinite length model, a novel wave approach is introduced to predict the natural frequencies of finite length circular cylindrical shells with different boundary conditions without simplifying the equations of motion. Results obtained compare favourably with those obtained using the finite element method.

Compact solutions for the corner singularity in bonded lap joints

This paper presents compact solutions of the corner singularity at the adhesive/adherend interface in a bonded lap joint. Two configurations of special importance to evaluating joint strength are considered: corners pertaining, respectively, to a square edge and a spew fillet. The stress intensity factors are determined for the limiting case of rigid substrates by means of a numerical matched asymptotic expansion method. The non-dimensional stress intensity factor depends only on the Poissons ratio of the adhesive, and this variation is characterised in a convenient analytical form by polynomial expressions. Comparison with finite-element results of a bonded joint obtained using fine mesh near the corner points confirms that the present analytical solutions provide very good representations of the singular stress fields at adhesive/substrate corners.

Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue—Part 2: Comparison With Experimental Results

An extensive multiaxial random fatigue test program was conducted at room temperature using tubular specimens. Experiments were performed under combined tension/torsion and triaxial loading, covering proportional and nonproportional variable amplitude loading cases. The two proposed life prediction methods discussed in Part 1 are evaluated using the experimental results, demonstrating that these two methods provide satisfactory predictions.