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When a longitudinal wave passes through a contact interface, second harmonic components are generated due to contact acoustic nonlinearity (CAN). The magnitude of the generated second harmonic is related to the contact state of the interface, of which a model has been developed using linear and nonlinear interfacial stiffness. However, this model has not been sufficiently verified experimentally for the case where the interface has a rough surface. The present study verifies this model through experiments using rough interfaces. To do this, four sets of specimens with different interface roughness values (Ra = 0.179 to 4.524 μm) were tested; one set consists of two Al6061-T6 blocks facing each other. The second harmonic component of the transmitted signal was analyzed while pressing on both sides of the specimen set to change the contact state of the interface. The experimental results showed good agreement with the theoretical prediction on the rough interface. The magnitude of the second harmonic was maximized at a specific contact pressure. As the roughness of the contact surface increased, the second harmonic was maximized at a higher contact pressure. The location of this maximal point was consistent between experiments and theory. In this study, an FEM simulation was conducted in parallel and showed good agreement with the theoretical results. Thus, the developed FEM model allows parametric studies on various states of contact interfaces.

The ultrasonic transmission spectrum in a double-layered bonded structure is related closely to its interfacial stiffness. Consequently, researching the regularity of the transmission spectrum is of significant interest in evaluating the integrity of the bonded structure. Based on the spring model and the potential function theory, a theoretical model is developed by the transfer matrix method to predict the transmission spectrum in a double-layered bonded structure. Some shift rules of the transmission peaks are obtained by numerical calculation of this model with different substrates. The results show that the resonant transmission peaks move towards a higher frequency with the increase of the normal interfacial stiffness, and each of them has different movement distances with the increasing interfacial stiffness. Indeed, it is also observed that the movement starting points of these peaks are at the specific frequency at which the thickness of either substrate plate equals an integral multiple of half a wavelength. The results from measuring the bonding specimens, which have different interfacial properties and different substrates in this experiment, are utilized to verify the theoretical analysis. Though the theory of “starting points” is not demonstrated effectively, the shift direction and distance exactly match with the result from the theoretical algorithm.

In this article, we study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge–Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38: 313, 2010 ) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding an (i) internal viscosity, (ii) interfacial stiffness and (iii) initial tangential force distribution at the interface, we manage to (i) avoid the model’s unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.

When two rough surfaces are loaded together contact occurs at asperity peaks. An interface of solid contact regions and air gaps is formed that is less stiff than the bulk material. The stiffness of a structure thus depends on the interface conditions; this is particularly critical when high stiffness is required, for example in precision systems such as machine tool spindles. The rough surface interface can be modelled as a distributed spring. For small deformation, the spring can be assumed to be linear; whilst for large deformations the spring gets stiffer as the amount of solid contact increases. One method to measure the spring stiffness, both the linear and nonlinear aspect, is by the reflection of ultrasound. An ultrasonic wave causes a perturbation of the contact and the reflection depends on the stiffness of the interface. In most conventional applications, the ultrasonic wave is low power, deformation is small and entirely elastic, and the linear stiffness is measured. However, if a high-powered ultrasonic wave is used, this changes the geometry of the contact and induces nonlinear response. In previous studies through transmission methods were used to measure the nonlinear interfacial stiffness. This approach is inconvenient for the study of machine elements where only one side of the interface is accessible. In this study a reflection method is undertaken, and the results are compared to existing experimental work with through transmission. The variation of both linear and nonlinear interfacial stiffnesses was measured as the nominal contact pressure was increased. In both cases interfacial stiffness was expressed as nonlinear differential equations and solved to deduce the contact pressure-relative surface approach relationships. The relationships derived from linear and nonlinear measurements were similar, indicating the validity of the presented methods.

This paper reveals the role of interfacial rigidity in a fiber reinforced polymer (FRP) composite to crack propagation path and its reinforcement, investigated by simulating a plane-strain model – containing the matrix with a fiber inclusion – loaded transversely. Two fibers, i.e. carbon fiber and glass fiber, were examined. The interface between fiber and matrix was pre-defined using the spring model characterized by a stiffness parameter. A range of interfacial stiffness values from infinity (rigid bonding) to low stiffness were carefully investigated. The results suggested that direction of crack propagations inclined to approach the fiber when the interfacial stiffness was low, even if the fiber had much higher elastic modulus than the matrix – this finding is in contrast to the inclusion theory that merely considers rigid bonding interface. It also suggests that there existed a transition region in which the crack propagation path was altered, from approaching to avoiding the fiber. The region occurred when the interfacial stiffness was in the range between 105 and 106 MPa/mm, within which mechanical properties of the model were recorded to vary notably

The elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area; 2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads; and 3) average gap shows an exponential relationship with load only in moderate load range.

Positioning and force control of an ultrasonic probe with soft contact against an object surface are important manipulation tasks for measurements in manual nondestructive contact ultrasonic testing. The use of a semispherical probe with soft contact allows a controlled increase of the contact force and energy transmission. However, successful application of contact ultrasonic testing depends on the control of the sensor’s pose and applied force at the mechanical contact between the probe and the surface of the inspected object. In this work we study the use of frequency signal information to control the alignment and force of the probe using a robotic arm to perform measurements on a rigid object assuming limited information of the surface orientation. A methodology of signal conditioning using a fast Fourier transform is implemented. The experimental results show that the proposed methodology based on frequency analysis allows a fine tuning of the probe pose with high sensitivity to load and misalignment, improving ultrasonic measurements.

This paper studies the early mechanical properties of fiber-reinforced cemented tailings backfill (CTB) and discuss its modification mechanism. The effects of fiber types and addition (polypropylene fiber, basalt fiber and glass fiber) on unconfined compressive strength of CTB were studied by unconfined compressive strength test (UCS). Scanning electron microscopy (SEM) was used to investigate the microstructure of fiber-reinforced CTB. Based on the theory of interface mechanics and the contact mechanism of fiber interface, the evolution mechanism of fiber-reinforced CTB interface characteristic stiffness was further explored. The results show that the fiber type and content have a significant effect on the strength of CTB, and the optimum addition of fibers is 0.4%. The strength of fiber-reinforced CTB samples increased first and then decreased with the increase of fiber content. The stress of CTB sample without fibers reaches the maximum value when the strain is 1.01%, while introduction of basalt fiber increases that value to 3.74%. In addition, the microstructure characteristics show that the hydration products around the fiber make the CTB sample have better compactness, and fibers can effectively inhibit the crack development of the CTB samples. Finally, using the theory of interface mechanics, it is found that the interface stiffness of CTB sample with basalt fibers is the largest, but the interface contact stiffness increases first and then decreases with the increase of fiber content, which is consistent with the law of macroscopic strength change.

The adoption of diffusion bonding in fracture critical titanium components has been limited by the complications that macroscopic anisotropy introduces to typical ultrasonic inspections. Previous attempts to overcome these limitations by using signal phase to extract otherwise hidden interface information showed promise but were susceptible to measurement error and proved impractical for typical aerospace component geometries. In the work presented here, significant improvements to the existing phase measurement approach are proposed alongside adaptations that permit its broader practical implementation. The principal parameters that affect the phase analysis of ultrasonic signals were investigated and their optimisation resulted in up to an order of magnitude improvement in phase measurement reliability, even at low signal-to-noise ratios. The application of these optimised parameters without a priori knowledge of the signal arrival time in an otherwise noisy waveform is illustrated, and the sensitivity of the approach to ambient temperature and annealing effects is also explored.

Diffusion bonds offer several advantages over alternative welding methods, including the ability to produce near-net shapes and achieve almost parent metal strength. However, voids remnant from the joining process can be tens of microns in their lateral dimension, making them difficult to detect with conventional pulse-echo immersion inspection at any significant metal depth. In titanium the inspection is particularly challenging; the anisotropic microstructure is highly scattering and the diffusion bond itself forms an interface between regions of preferred crystallographic orientation (macrozones), which can act as a weak spatially coherent reflector. A simple interfacial spring model predicts that, for partial bonds (sub-wavelength voids distributed on the bond line) and at certain frequencies, the phase of the signal can be used to separate the component of the signal due to the change in texture at the interface and the component due to the flaw. Here it is shown that the phase of the signal from an interface is also affected by the anisotropic microtexture of Ti–6Al–4V. Good separation between well-bonded and partially bonded samples was achieved using a symmetric inspection, where the magnitude and phase of the reflection coefficient were calculated for normal incidence from opposite sides of the diffusion bond.