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Journal ArticleDOI

Ultrasonic scattering from imperfect interfaces: A quasi-static model

01 Dec 1984-Journal of Nondestructive Evaluation (Kluwer Academic Publishers-Plenum Publishers)-Vol. 4, Iss: 3, pp 177-196
TL;DR: In this article, a quasi-static model for ultrasonic transmission and reflection at imperfect interfaces is developed, where the interface is represented by a distributed spring determined by the change in static compliance of the medium with respect to one with a perfect interface, and a distributed mass, representing excess mass at the interface.
Abstract: A quasi-static model for the ultrasonic transmission and reflection at imperfect interfaces is developed. The interface is represented by a distributed spring, determined by the change in static compliance of the medium with respect to one with a perfect interface, and a distributed mass, representing excess mass at the interface. Comparison of the model predictions to exact solutions for two simple cases illustrates its accuracy at low frequencies. The spring stiffnesses can be derived from existing solutions for the elastic displacement of materials containing cracks and inclusions under static load. Results for a variety of cases are reviewed. Applications of the model to study the characteristics of partially contacting surfaces in several problem areas of current interest are discussed.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors derived the complete solutions for seismic wave reflection, conversion, and transmission across a displacement and velocity discontinuity between two half-spaces with different densities and elastic properties for all angles of the incident wave.
Abstract: Fractures and other nonwelded contacts are important mechanical and hydrological features of rock masses. Their effects on seismic wave propagation can be modeled as a boundary condition in the seismic wave equation. Seismic stress is continuous across such a boundary, but seismic particle displacement and seismic particle velocity are not. The complete solutions for seismic wave reflection, conversion, and transmission across a displacement and velocity discontinuity between two half-spaces with different densities and elastic properties are derived for all angles of the incident wave. The ratio between the seismic stress across this boundary and the seismic particle displacement and velocity are described by a specific stiffness and a specific viscosity, respectively. A displacement discontinuity results in frequency-dependent reflection and transmission coefficients and a frequency-dependent group time delay. The velocity discontinuity results in frequency-independent coefficients and zero delay. Results of laboratory experiments on compressional and shear wave transmission across three different natural fractures in a quartz monzonite are described. Measurements were made at different effective stresses under dry and saturated conditions at room temperature. It is shown that the effect of these fractures on the spectral amplitudes for compressional and shear pulses transmitted across these fractures are described well by a displacement discontinuity for compressional pulses under dry and saturated conditions and by a combined displacement and velocity discontinuity for shear wave pulses under dry and saturated conditions. Values of specific stiffness and specific viscosity vary between fractures and increase with increasing effective stress, as does the static specific stiffness of these fractures. Changes in the spectral amplitudes of transmitted pulses are also analyzed in terms of attenuation using the seismic quality factor Q, which is found to be a function of frequency.

592 citations

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the overall progress in nonlinear ultrasonic technique with the brief introduction of basic principle in the application of each nonlinear Ultrasonic phenomenon, including higher harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response.
Abstract: The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.

581 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the ratio between the normal and transverse interfacial stiffnesses can be used to classify the interface imperfections, e.g., kissing, partial, and slip bonds.
Abstract: Ultrasonic reflection measurements from material interfaces are commonly used to detect and quantitatively characterize boundary imperfections of different kinds. Either shear or longitudinal waves can be used to assess the degree of the interface imperfection in acoustical terms. On the other hand, the evaluation of this data in terms of strength-related mechanical properties requiresa priori knowledge of the physical nature of the imperfection. It is shown in this paper that the ratio between the normal and transverse interfacial stiffnesses can be used to classify the interface imperfection. This ratio is readily measured, e.g., by comparing the longitudinal and shear reflection coefficients at normal incidence. Both theoretical and experimental results indicate that different types of imperfections, such as kissing, partial, and slip bonds, can be distinguished by this simple technique.

256 citations

Journal ArticleDOI
TL;DR: In this article, the authors measured the reflection of ultrasonic waves from partially contacting aluminium-aluminium interfaces, performed in the low frequency regime where the wavelength of the ultrasound is large compared to the size of the gaps.
Abstract: The measurement of the reflection of ultrasonic waves from a partially contacting solid--solid interface can be used to study the contact conditions at that interface. This paper describes measurements and predictions of the reflection of ultrasonic waves from partially contacting aluminium--aluminium interfaces, performed in the low frequency regime where the wavelength of the ultrasound is large compared to the size of the gaps. The proportion of the incident wave which is reflected at the interface (the reflection coefficient) was measured as a function of frequency with a single wideband ultrasonic transducer. When load was applied across the interface three regions of contact can be seen; no contact, partial contact and perfect contact. In the no contact region the measured reflection coefficient was unity at all frequencies. In the partial contact region the measured reflection coefficient increased with frequency. No measurements were taken in the perfect contact region in which the reflection coefficient is known to be zero at all frequencies as this state is the same as a continuous piece of aluminium. The reflection coefficient variation with frequency was modelled using a spring model, good agreement between experiments and predictions being achieved. Reflection coefficient measurements were then used to study the contact between two aluminium surfaces under repeated loading and unloading cycles. Plastic flow on first loading was evident while subsequent loading cycles revealed largely elastic behaviour. Both elastic and plastic statistical contact models, as well as a numerical contact model, were used to predict the variation of interfacial stiffness with pressure. These models agreed qualitatively with the experimentally determined stiffness variations and the predicted stiffness was within an order of magnitude of the measured value in all cases.

242 citations

Journal ArticleDOI
TL;DR: In this article, the effect of interfacial stiffness is isolated by considering the ultrasonic wave interaction with a solid layer compressed between two substrates of the same material, and it is shown that in the high-interfacial-stiffness limit the resonance minima positions are given by the condition h=λ/4+nλ/2, n=0,1,2,…
Abstract: Ultrasonic waves reflected from the front and back surfaces of a thin layer are often not separated in the time domain, and interfere. The spectrum of the resulting interference signal depends on (a) the thickness of the layer and the elastic moduli and density of the layer and the surrounding material (substrates), and (b) properties of the layer/substrate interface which can be described in terms of the interfacial stiffness. In this paper the effect of interfacial stiffness is isolated by considering the ultrasonic wave interaction with a solid layer compressed between two substrates of the same material. Since the layer and the substrate have identical properties the effect of impedance difference on the layer reflection vanishes. An aluminum system is selected for the experiment; the contacting surfaces are roughened and varying pressure is applied to model imperfect interface changes. It is shown both theoretically and experimentally that the contact pressure increase results in increase of the interfacial stiffness and spectral minima shift to higher frequency. A simple analytical expression relating the reflection minimum position to the interfacial stiffness is derived and shows good agreement with experimental results. It is shown that in the high-interfacial-stiffness limit the resonance minima positions are given by the condition h=λ/4+nλ/2, n=0,1,2,… . In the limit of low interfacial stiffness the first minimum shifts to zero and higher order resonances are given by h=nλ/2. Since the resonance minima measurements can be done with high precision it is proposed to use the frequency minimum shift for determination of interfacial stiffness and, consequently, the quality of the interfacial contact.

187 citations

References
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Book
01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain

20,724 citations

Book
01 Jan 2000
TL;DR: The Stress Analysis of Cracks Handbook as mentioned in this paper provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations, along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more.
Abstract: Nearly double the size of the previous edition, the third edition of this classic reference provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations. For each configuration, The Stress Analysis of Cracks Handbook present crack tip stress intensity formulas along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more. Throughout, it stresses formulas for application to test configurations. The introductory section details the methods of developing the informatio A series of appendices represents special methods and special applications. Now in a hardbound format, the current Handbook offers a number of new features including: * Ne Stress Solutions * Cracked Configurations * Plates with Pinching Loads * Dislocations and Cracks Solutions * Plastic Zone Instability (Expanding a Potentially Interceding "Elastic" Failure Mechanism) * Estimation Methods for Stress Intensity Formulas * J-Integral Methods * Pure Shear Plasticity Solutions. The authors provide 30 new solution pages, plus modifications of older solutions. Contents Include: * Introductory Information Stress Analysis Results for Common Test Specimen Configurations with Cracks * Cracks Along a Single Line * Parallel Cracks * Cracks and Holes or Notches * Curved, Angled, Branched, or Radiating Cracks * Cracks in Reinforced Plates * Three-Dimensional Cracked Configurations * Crack(s) in a Rod or a Plate by Energy Rate Analysis * Strip Yield Model Solutions * Cracks(s) in a Shell * Appendices.

5,374 citations

Book
01 Jan 1982
TL;DR: In this paper, the authors present numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals using double kink mechanisms for discrete dislocations in BCCs.
Abstract: Preface Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals Microstructure and stray electric fields at surface cracks in ferroelectrics Double kink mechanisms for discrete dislocations in BCC crystals The expanding spherical inhomogeneity with transformation strain A new model of damage: a moving thick layer approach On configurational forces at boundaries in fracture mechanics HotQC simulation of nanovoid growth under tension in copper Coupled phase transformations and plasticity as a field theory of deformation incompatibility Continuum strain-gradient elasticity from discrete valence force field theory for diamond-like crystals

4,951 citations