Wolfgang Sachse

On the determination of phase and group velocities of dispersive waves in solids

A new technique is developed to determine the dispersion relation and the propagational speeds of waves in dispersive solids. The phase spectrum of a broadband pulse is linearly related to the dispersion relation of the dispersive medium. The method is simpler than the continuous‐wave phase comparison technique. Application is made to measure the phase and group velocities of waves in fiber‐reinforced composite materials and in thin wires. This technique is expected to be applicable to measurements of acoustic or electromagnetic wave speeds in other dispersive media.

Optimal determination of the elastic constants of composite materials from ultrasonic wave‐speed measurements

A method is described to optimally determine the elastic constants of anisotropic solids from wave‐speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree‐three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double‐iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Determination of the elastic constants of anisotropic materials using laser‐generated ultrasonic signals

This paper presents the solution of the materials characterization problem in which the elastic constants of an anisotropic material are determined from ultrasonic wavespeed measurements made in nonprincipal directions of a specimen. The ultrasonic waves were generated via the point‐source/point‐receiver technique using a pulsed laser as a source and a miniature, point‐like transducer as a receiver. Data were acquired during a scan of the source along one of the principal acoustic axes of symmetry of the material. In each waveform the arrivals of the quasi‐longitudinal and the two quasi‐shear bulk modes were measured and the elastic constants of the material were then recovered using an optimization algorithm. Experimental results are presented for a transversely isotropic, unidirectional fiberglass/polyester and a single crystal specimen of silicon. It was found that the nonlinear fit between the measured and the recovered longitudinal slowness values is excellent. Some discrepancies are observed in the ...

An acoustic emission technique for measuring fiber fragment length distributions in the single-fiber-composite test

Abstract This paper describes the application of an acoustic emission (AE) technique for locating the positions of fiber breaks, and thus determining the lenght distribution of the fiber fragments resulting when a composite specimen containing a single fiber is loaded to failure. By means of a micromechanical model, it is possible to determine from the fragmentation lenghts a measure of the interfacial shear strength between the fiber and the matrix. The AE technique also provides a means for characterizing the statistics of fiber strength, particularly for lengths less than 100 fiber diameters. In contrast to existing optical techniques, the acoustic measurements can be automated and are usable with non-transparent matrices. The technique is demonstrated with E-glass fibers embedded in two epoxy blends. A comparison is made of the statistics for the fragment aspect ratios and resulting interfacial shear strength values determined by acoustic emission and optical techniques. Good agreement is found between the results obtained from these two measurement methods.

Ammonia plasma treatment of ultra-high strength polyethylene fibres for improved adhesion to epoxy resin

A study of the effect of plasma treatments on the mechanical properties and adhesion of ultra-high strength polyethylene fibres to epoxy resin is reported. Fibres were treated with ammonia plasma under various time and power conditions. The fibre/matrix interfacial shear strength was measured using load and fibre pull-out data obtained in a single-fibre pull-out test. The debonding was optically as well as acoustically monitored. Optical birefringence patterns were visible at the fibre debond region. Acoustic emission signals generated from debonding and stick-slip processes were also detected. A more than four-fold increase in the interfacial shear strength was achieved by plasma treating the fibres at the discharging condition of 30 W and 0.5 torr for 1 min. The birefringence patterns showed, qualitatively, that the shear in the matrix around the fibres increased for treated fibres and extended further into the matrix material. Surface topography of the pulled out fibres showed that the failure mode was unchanged by the treatment.

Acoustic emission source location on plate‐like structures using a small array of transducers

A small non-colinear transducer array for omnidirectional acoustic emission monitoring is disclosed. The small transducer array consists of four piezoelectric sensor elements of sufficiently small diameter as to function as essentially point receivers and of sufficient frequency response as to be sensitive to the signals to be detected. The sensor elements of the transducer array are close together and are non-colinear so that the signals received by them can be used for determining the group velocity of acoustic waves on solid plates and on plate-like structures such as shells and pipes, and to permit determination of both the source direction and distance. The array is designed to monitor the region exterior to the area enclosed by the array, and the ratio of the smallest distance between sensors to the radius of a single transducer element is relatively large in order to minimize measurement errors introduced by undertainties in transducer element positions caused by large transducer sizes with respect to the acoustic waves being received.

Quantitative acoustic emission and failure mechanics of composite materials

Abstract This Paper considers quantitative acoustic emission (AE) techniques with real and simulated sources as powerful tools for investigating failure processes in composite materials. Using a simulated source acting as a point source and one or more point receivers whose characteristics are known, one has the necessary components of a materials and structure testing system. Examples are shown in which a composite materials attenuation and wavespeeds can be determined as a function of frequency and propagation direction. It is demonstrated that this testing procedure permits the ultrasonic characterization of ultra-attenuative and irregular shaped, high performance composite materials. The principles of quantitative AE source characterization procedures are also reviewed and applications are demonstrated in which the time characteristics of several simple sources are recovered.

Sensitivity of inversion algorithms for recovering elastic constants of anisotropic solids from longitudinal wavespeed data

Abstract This paper discusses the sensitivity of inversion algorithms for recovering the elastic constants of moderately anisotropic solids using only ultrasonic longitudinal wavespeed data measured for various directions in a medium. This investigation is motivated, in part, by experience with the recently developed point source/point receiver technique, in which longitudinal wave arrivals are clearer and easier to measure accurately than the later transverse wave arrivals. A perturbation method is presented which shows that for a medium of triclinic symmetry, the longitudinal wavespeeds are most sensitive to the partial set of elastic constants C11, C22, C33, (C12 + 2C66), (C23 + 2C44) and (C13 + 2C55), and it is these constants which can therefore be most accurately recovered from longitudinal wavespeed data. A number of illustrative numerical examples are presented which demonstrate the lack of sensitivity to certain constants and illustrate the recovery of elastic constants from simulated longitudinal mode data. These show that there is good convergence for the partial set of elastic constants, whereas the remaining elastic constants are much less accurately recovered.

Interpretation of time records and power spectra of scattered ultrasonic pulses in solids

Experiments were conducted to investigate the scattering of a wide bandwidth pulse by a fluid‐filled cylindrical cavity in an elastic solid. The pulse amplitude‐time record and the corresponding Fourier power spectra of the scattered pulses are analyzed. The sequence of pulses received by a transducer is identified by applying the theory of geometric acoustics and the pulse arrival times are related to the cavity diameter and the wave speed in the fluid. The power spectrum is interpreted in terms of the resonance of the fluid inclusion, the natural frequencies of which also depend on the size and property of the inclusion. Investigations show that both pulse‐time record and power spectrum can be utilized to detect the size and the wave speed of a fluid inclusion in a solid.

Transient elastic waves in a transversely isotropic plate

The elastodynamic response of thick plate, with the axis of transverse isotropy normal to the plate surface, is calculated by double numerical inverse transforms, a method particularly well-suited for calculations of responses in the near field of layered structures. Applications of these calculations include point-source/point-receiver ultrasonics, quantitative acoustic emission measurements, and seismology. The singularities of the integrand are eliminated by the introduction of a small, but nonzero, imaginary part to the frequency. We discuss issues of numerical efficiency and accuracy in the evaluation of the resulting integrals. The method can be generalized to calculate the responses in materials of more general symmetry, in viscoelastic materials and to include the effects of finite aperture sources and receivers. The calculated responses are compared to those measured in a single crystal specimen of zinc.