GWW School of Mechanical Engineering Georgia Institute of Technology 801 Ferst Dr. Atlanta, GA 30332 and School of Civil and Environmental Engineering Georgia Institute of Technology 790 Atlantic Dr. Atlanta, GA 30332
Abstract: This paper reports on a method that uses nonlinear Lamb waves to detect material nonlinearity. Lamb waves are well-suited for the interrogation of thin metallic layers which act as waveguides, giving Lamb waves great potential in nondestructive evaluation applications. However, measuring nonlinear Lamb waves and extracting the information necessary for nondestructive evaluation is complicated by the inherent dispersive and multimode nature of Lamb waves. This paper presents a procedure that overcomes these difficulties and develops a reliable and robust measurement methodology. By using hybrid wedge generation and laser interferometric detection in combination with signal processing in the time-frequency domain, it is possible to make relative measurements of material nonlinearity parameters, which are an indicator of plasticity driven damage.
Abstract: This note presents a procedure to generate nonlinear Rayleigh surface waves without having to drive the transmitting piezoelectric transducer at high voltages; driving at low voltages limits the excitation of the intrinsic nonlinearity of the piezoelectric transducer element, and enables an efficient measurement procedure to isolate inherent material
nonlinearity. The capabilities of this proposed technique are demonstrated by measuring the material nonlinearity of aluminum alloy 2024 and 6061 plates with Rayleigh surface waves.
Abstract: This paper presents the successful application of a nonlinear ultrasonic technique, nonlinear wave modulation spectroscopy (NWMS)
to quantitatively track the evolution of microcracks in Portland cement mortar samples. The damage type considered in this study is
microcracking due to alkali–silica reaction (ASR), a deleterious reaction occurring in concrete structures around the world. Nonlinear
ultrasonic measurements are conducted on six different mortar specimens that are monitored from their initial, intact state up to their
fully damaged state. The objective of this research is to determine the sensitivity and suitability of NWMS to quantitatively track this
damage state throughout an entire life-cycle and to nondestructively identify the initiation time and the extent of microcracking in these
mortar specimens. The nonlinear ultrasonic measurements are made with standard laboratory equipment, and the inherent high
attenuation of cement-based materials is overcome with a procedure that uses the sideband energy instead of measuring peak amplitudes.
The results show that the NWMS method can track the progressive damage in mortar, demonstrating the feasibility of using this
nonlinear ultrasonic technique to quantitatively assess the deterioration of cement-based materials.
Abstract: The objective of this research is to develop an accurate and reliable procedure to measure the second order harmonic of a Lamb wave propagating in a metallic plate. There are two associated complications in measuring these nonlinear Lamb waves, namely their inherent dispersive and multi-mode natures. To overcome these, this research combines a time-frequency representation with a hybrid wedge generation and laser interferometric detection system. The effectiveness of the proposed procedure is demonstrated by characterizing the inherent material nonlinearity of two different aluminum plates whose absolute nonlinearity parameters are known from longitudinal wave measurements.
Abstract: A micromechanical model for an interface between two solids in elastoplastic contact is presented to predict the acoustical linear and nonlinear interfacial stiffnesses during loading-loading cycle. This interface is a representative model for apparently closed cracks and imperfect bonds that are interacting with ultrasonic waves sent for evaluating quality of their interfaces. For better physical description of the elastoplastic contact behavior of the interface, the previous model [Kim et al., J. Mech. Phys. Solids 52, 1911-1934 (2004)] is improved in two important aspects: the unloading model for unit contact element (asperity) and the geometrical and statistical parameters of the interface. The model is validated with experimental results. The interface parameters are obtained by fitting measured reflection coefficients during loading-unloading cycle with the theoretical model. Using so obtained parameters, the linear and second-order interfacial stiffness and the nonlinearity in transmitted longitudinal waves are calculated. Theoretical nonlinear transmission amplitude is in good comparison with the experimental result, demonstrating the capability of the present modeling framework in predicting both linear and nonlinear ultrasonic responses of imperfect interfaces. It is observed that the effect of adhesive force, which is not taken into account in the model, may be important in a certain stage of the unloading phase.
Abstract: This letter reports on the experimental observation of a direct correlation between the acoustic nonlinearity measured with Lamb waves and the level of plasticity in a metal specimen. This correlation implies that even though Lamb waves are multi-modal and dispersive, they will interact with a material’s plasticity in a manner similar to longitudinal and Rayleigh waves; there is a fundamental relationship between material plasticity and acoustic nonlinearity that is independent of wave type. As a result, Lamb waves can be used to quantitatively assess plasticity driven material damage using established higher harmonic generation techniques.
Abstract: A large number of fatigue experiments on standardized samples is required for the development of databases of the fatigue properties
of specific material systems. To facilitate such studies, different visual monitoring methods for surface fatigue cracks have been used;
however, the problem of monitoring internal fatigue crack initiating during cold dwell fatigue of Ti is much more complicated. This paper describes the development and integration of several nondestructive evaluation methods for monitoring and sizing microcracks in titanium fatigue samples. For in situ monitoring of crack initiation and evolution ultrasonic Lamb wave signals are excited and acquired in the sample continuously during fatigue tests at different levels of fatigue load using a high-speed data acquisition system. Localization of the secondary cracks is done by both the in situ ultrasonic method and an ultrasonic immersion scanning method here referred to as ‘‘vertical C-scan’’ (VC-scan). The VC-scan is developed for imaging small cracks aligned normal to the fatigue sample axis. Microradiography has been performed on fatigue samples to confirm the localization and sizing of the detected cracks with other ultrasonic NDE techniques. The fusion of data from different NDE techniques provides useful information on the initiation, location, shape, size and growth history of fatigue cracks.
Abstract: The effectiveness of advanced ultrasonic techniques to quantitatively characterize the capillary porosity and entrained air content in hardened cement paste is examined. Direct measurements of ultrasonic attenuation are used to measure the volume fraction and average size of entrained air voids and to assess variations in intrinsic porosity – as influenced by water-to-cement ratio (w/c) – in hardened cement paste samples. For the air entrained specimens, an inversion procedure based on a theoretical attenuation model is used to predict the average size and volume fraction of entrained air voids in each specimen, producing results in very good agreement with results obtained by standard petrographic methods and by gravimetric analysis. In addition, ultrasonic attenuation measurements are related to w/c to quantify the relationship between increasing porosity (with increasing w/c) and ultrasonic wave characteristics.
Abstract: This paper describes a surface acoustic wave method for the measurement of crack closure/opening stress during fatigue testing. The dependence of surface wave signature on fatigue load reveals the crack opening/closure characteristics displayed during the fatigue cycle, from which the crack-mouth-opening and fully-crack-opening stresses are determined as functions of the number of cycles. The change of crack closure loads during fatigue life is interpreted by a simple model describing crack growth inside the pit-induced plastic yield zone. The loading-unloading hysteresis is observed and related to the movement of the crack opening/closure front across the boundary of the plastic yield zone during the crack opening-closing process. Examples are given for fatigue tests on Al 2024-T3 and Inconel 718 samples in which the surface fatigue crack initiated from a surface pit.
Abstract: A surface acoustic wave method for in-situ monitoring of fatigue crack initiation and evolution from a pit-type surface flaw is described. The method is demonstrated for fatigue tests on Al 2024-T3 and Inconel 718 samples with different surface pit sizes. The surface acoustic wave signature is acquired continuously during the fatigue cycle without stopping the fatigue test. Crack initiation and propagation are identified clearly from the ultrasonic surface wave reflection signals. Crack initiation in the Inconel 718 sample is observed to occur in a much later stage of fatigue life than in the Al-2024-T3 sample. The ultrasonic results are supported by fractographs of fracture surfaces. Small crack sizing is performed from the ultrasonic signatures using the low frequency scattering model.
Abstract: A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In-situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.
Abstract: In this paper analytic expressions for effective elastic constants of anisotropic multilayers are presented. The present theory is applicable to multilayers with the general anisotropic layers and with arbitrary crystal orientation angle. An example of calculation is given for the titanium bi-crystal quasi-periodic layered medium. Based on the present result, the average elastic wave propagation in the long wavelength regime can be analyzed.
Abstract: Effects of fiber-matrix interfacial debonding on the attenuation and speed of antiplane shear wave propagating in fiber-reinforced composites are investigated. A probabilistic approach is proposed based on the scattering analysis of a single fiber that is representative of randomly distributed fibers with random interfacial cracks. The average total cross section of the representative fiber is obtained using assumed probability distributions, and then the causal differential method is applied to calculate the effective wave speed and attenuation. For a composite with low fiber volume fraction, the results are compared with those from the Waterman and Truell theory. When the mean crack size exceeds a certain subtending angle, the interfacial debonding alters significantly dynamic behaviors of the composites. While the attenuation varies mainly in low frequency region quite sensitively to the variance of the crack length, the change of wave speed takes place in the whole frequency range considered.
Abstract: Fatigue crack initiation and growth from artificial pits of different depths has been studied. To analyze the experimental results a simple three dimensional fracture-mechanical model has been developed. The model shows very good agreement with experiments, including for small cracks, in describing the initiation and growth of a fatigue crack emanating from a pit and in predicting the dependence of reduction of fatigue life on pit size. Based on experimental data an empirical relation between the depth of the corrosion pit and the fatigue life has been established. Also, a microradiographic method for pitting corrosion depth determination has been described.
Abstract: A dynamic self-consistent method previously proposed and validated for composites containing spherical inclusions is applied to the simplest two-dimensional problem: SH wave propagation in unidirectional fiber reinforced composites. The self-consistent conditions for SH waves are derived and the effective wave speed and coherent attenuation are calculated numerically for five different composites. For two composites showing very different dynamic behaviors, the results of the present theory are compared with those of multiple scattering theories and another self-consistent theory. At low volume fractions the present theoretical results coincide with those of the multiple scattering theory using exact pair-correlation functions, whereas the results based on another self-consistent theory deviate markedly from the others. As the volume fraction increases, the three theories give different results although they have qualitatively similar trends. The present theoretical results for composites considered in this article exhibit less dispersion and physically realizable attenuation. An important observation is that the multiple scattering theory predicts vanishingly small attenuation at low frequency when volume fraction is high. Experiments over wide ranges of frequency and volume fraction are needed in order to assess the accuracy and validity of the present theory.
Abstract: Elastic wave propagation in a discrete random medium is studied to predict dynamic effective properties of composite materials containing spherical inclusions. A self-consistent method is proposed which is analogous to the well-known coherent potential approximation in alloy physics. Three conditions are derived that should be satisfied by two effective elastic moduli and effective density. The derived self-consistency conditions have the physical meaning that the scattering of a coherent wave by the constituents in the effective medium vanishes, on the average. The frequency-dependent effective wave speed and coherent attenuation can be obtained by solving the self-consistency conditions numerically. At the lowest resonance frequency, the phase speed increases rapidly and the attenuation reaches the maximum in the composites having a large density mismatch. The lowest resonance is caused mainly by the density mismatch between matrix and particles and higher resonances by the stiffness mismatch. The dispersion and attenuation of longitudinal and shear waves are affected by the lowest resonance much more than by higher ones. The lowest resonance frequency of particles in the effective medium is found to be higher than that of a single particle embedded in the matrix material of composites due to the stiffcuing effect. The results obtained from the present theory are shown to be in good agreement with previous experimental observations of Kinra et al. [Int. J. Solid Struct. 16, 301-312 (1980)]. Part of the calculated results are compared with those computed by the Waterman and Truell theory. The present theory is in better agreement with the experiments for the examples dealt with.
Abstract: Dispersion and attenuation characteristics of elastic waves propagating in viscoelastic fiber-reinforced composites are studied. The present analysis is based on the multiple scattering formulation for randomly distributed scatterers in an absorbing medium. Frequency-dependent complex material properties of the matrix are estimated from the attenuation coefficients by using the causality relationship between their real and imaginary parts. Pair-correlation functions for finding the accurate average of the T matrix are obtained by Monte Carlo simulation to study the dense fiber system. Resultant effective phase speed and total attenuation
of longitudinal and shear waves are presented along the frequency varying the fiber volume fraction. In these results, fluctuations in dispersion and rapid increase in attenuation curves can be observed due to the resonance of fibers. Additionally, the shifts in resonance frequency from
the single scattering resonance to higher frequency can be noted as the fiber volume fraction increases. Because the scattering dispersion is not strong in the low-frequency region, the viscoelastic dispersion is dominant in that region. It is possible to determine the dominant range of viscoelastic or scattering dispersion mechanisms depending on the frequency. In conclusion, the effect of the matrix viscoelasticity is very important in multiple scattering formulation for solving practical problems.
