Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Elastic properties of lead phosphomolybdate glassess

Elastic properties of lead phosphomolybdate [PbO-1bMoO3-1bP2O5] glasses have been investigated using ultrasonic velocity measurements at 10MHz. The composition dependence of elastic moduli, Poisson's ratio and the Debye temperature are found to be consistent with a structural model proposed earlier. According to this model lead acts both as a network former and as a network modifier in different composition regimes. It is suggested that the incorporation of lead into the network is accompanied by the conversion of three-connected [Image ] tetrahedra into four-connected Image tetrahedra in the network. lead; phosphorus; molybdenum

Elastic Constants of Sodium Nitrate from 77 to 300 K

The six independent elastic constants of sodium nitrate are determined using 10 MHz ultrasonic pulse echo superposition technique over the temperature interval 77 to 300 K. The values obtained at 300 K are C11 = 5.71, C12 = 2.16, C33 = 3.3, C13 = 1.66, C44 = 1.24, C14 = 0.82, and at 77 K C11 = 6.63, C12 = 2.07, C33 = 3.99, C13 = 1.67, C44 = 1.69, C14 = 1.16 all expressed in units of 1011 dyn/cm2.

Elastic constants of galena down to liquid helium temperatures

The elastic constants of single crystal galena have been determined from the measured ultrasonic velocities down to liquid helium temperature. A cryostat incorporating an arrangement to inject the liquid bonding material at low temperature is described. At 5 K, the values of elastic constants are C11=14.90, C12=3.51 and C44=2.92×1010 N/m2.

The elastic constants of isomorphous sodium bromate and sodium chlorate from 77 to 350 K

The elastic constants of NaBrO3 and NaClO3 are evaluated from ultrasonic velocity measurements using pulse superposition techniques. The values of C11, C12 and C44 for NaBrO3 at 298°K are 5.578, 1.705, 1.510 (x 1010 N/m2) and for NaClO3 the values are 4.897, 1.389, 1.174. The values at 77°K are respectively 6.35, 1.98 and 1.65 for NaBrO3 and 6.15, 2.16 and 1.32 for NaClO3.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC 11,C 12 and C 44 of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values are C 11=4.90,C 12=1.39,C 44=1.17 (× 1010 N/m 2) at 298 K and 6.15, 2.16, 1.32 (×1010 N/m 2) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.

Characterization of Failure Modes in CFRP Composites - An ANN Approach

Carbon fiber reinforced polymer (CFRP) composite specimens with different thickness, geometry, and stacking sequences were subjected to fatigue spectrum loading in stages. Another set of specimens was subjected to static compression load. On-line acoustic Emission (AE) monitoring was carried out during these tests. Two artificial neural networks, Kohonen-self organizing feature map (KSOM), and multi-layer perceptron (MLP) have been developed for AE signal analysis. AE signals from specimens were clustered using the unsupervised learning KSOM. These clusters were correlated to the failure modes using available a priori information such as AE signal amplitude distributions, time of occurrence of signals, ultrasonic imaging, design of the laminates (stacking sequences, orientation of fibers), and AE parametric plots. Thereafter, AE signals generated from the rest of the specimens were classified by supervised learning MLP. The network developed is made suitable for on-line monitoring of AE signals in the presence of noise, which can be used for detection and identification of failure modes and their growth. The results indicate that the characteristics of AE signals from different failure modes in CFRP remain largely unaffected by the type of load, fiber orientation, and stacking sequences, they being representatives of the type of failure phenomena. The type of loading can have effect only on the extent of damage allowed before the specimens fail and hence on the number of AE signals during the test. The artificial neural networks (ANN) developed and the methods and procedures adopted show significant success in AE signal characterization under noisy environment (detection and identification of failure modes and their growth).

Embedded PZT wafer sensors for structural health monitoring

Recent advances in structural integrity evaluation have led to the development. of PZT wafer sensors (PWAS) which can be embedded or surface mounted for both acoustic emission (AE) and ultrasonic (UT) modes, which forms an integrated approach for Structural Health Monitoring (SHM) of aerospace structures. For the fabrication of PWAS wafers, soft PZT formulation (SP-5H Grade containing dopants like BA, SM, CA, ZN, Y and HF) were used. The piezoelectric charge constant (d(33)) was measured by a d(33) meter. As a first step towards the final objective of developing Health monitoring methods with embedded PWAS, experiments were conducted on aluminum and composite plates of finite dimensions using PWAS sensors. The AE source was simulated by breaking 0.5mm pencil lead on the surface of a thin plate. Experiments were also conducted with surface mounted PZT films and conventional AE sensors in order to establish the sensitivity of PWAS. A comparison of results of theoretical and experimental work shows good agreement.

Elastic constants of triclinic copper sulphate pentahydrate crystals

Using an iterative technique to obtain the exact solutions of the cubic Christoffel equation, the 21 elastic constants of copper sulphate pentahydrate have been determined at 25°C by the ultrasonic pulse echo method. The elastic constants, referred to the IRE recommended system of axes, are c11=5·65, c12=2·65, c13=3·21, c14=−0·33, c15=−0·08, c16=−0·39, c22=4·33, c23=3·47, c24=−0·07, c25=−0·21, c26=0·02, c33=5·69, c34=−0·44, c35=−0·21, c36=−0·16, c44=1·73, c45=0·09, c46=0·03, c55=1·22, c56=−0·26 and c66=1·00 in units of 1010 N m−2.

Compressibilities of some electrolyte solutions in relation to their stepwise dissociation

The compressibilities of some electrolytic solutions at low concentrations have been determined by employing Carstensen's phase-comparison pulse method for measuring the ultrasonic velocity differences and by simultaneously measuring their densities with a Weld-type pyknometer. The apparent molal compressibilities φ(χ̄2) of NaHSO4, KHSO 4, NaP2PO4 and Na-HPO4 have been plotted against the square root of the molarities c. The observations are explained in terms of incomplete dissociation.

Compressibility of dilute solutions of sulphuric acid

By employing Carstensen's phase-comparison pulse method for measuring ultrasonic velocity-differences, the compressibility of sulphuric acid has been studied anew, the special interest being in the low concentration region. Sulphuric acid is found to show at first a decrease in velocity with increasing concentration and then an increase. The curve representing the apparent molal compressibility Φ(κ̄2) against the square root of the molar concentration c, shows a maximum and a minimum. This anomalous behaviour is interesting in view of the extreme anomalies in other colligative properties of sulphuric acid. A qualitative explanation of the observed maximum and minimum has been suggested.

Elastic Properties of Alkali Phosphomolybdate Glasses

Ultrasonic velocities at 10 MHz have been measured in two series of lithium, sodium, and potassium phosphomolybdate glasses with two fixed P2O5 concentrations. Elastic moduli, Poisson's ratio, and Debye temperature have been calculated. The composition dependence of most of the properties of lithium glasses exhibits a trend opposite to that of potassium glasses. Properties of sodium glasses lie between the other two alkali systems. Alkali oxide modification is suggested to be accompanied by ring reformation in lithium and sodium glasses. Ring size effects have been shown to account for all of the composition dependence.

Elastic properties of phosphotungstate glasses

Elastic properties of potassium and lead phosphotungstate glasses have been investigated using ultrasonic velocity measurements. The composition dependence of elastic moduli in WO3-K2O-P2O5 glasses suggests that at low alkali oxide concentrations the atomic ring size increases by network modification, which results in the decrease of elastic moduli. In the highly modified regime, due to the presence of coulombic interaction, the rate of decrease of elastic moduli is reduced. In the WO3-PbO-P2O5 glasses the behaviour of elastic moduli suggests that PbO behaves both as a network former and network modifier. The incorporation of PbO into the network is quantitatively determined by the concentration of P2O5 in the system. The results are consistent with the structural model proposed earlier, based on characterization studies.

Coherence factors in excitonic insulators

Results of a theoretical study on ultrasonic attenuation and NMR relaxation in excitonic insulators are reported. The transition rates derived have anomalous temperature dependence owing to the occurrence of coherence factors analogous to the case of superconductors. It is found that these coherence factors are characteristically different for the interband and the intraband scattering processes. It is suggested that experimental observation of these temperature-dependent coherence factors may help identify the existence of an excitonic phase.