We study an innovative experimental approach for the characterization of the elastic response of anisotropic composite materials by ultrasonic immersion tests. In particular, the class of anisotropy and the elastic moduli can be determined starting from measurements of the velocities of ultrasonic waves propagating in suitable directions. To this aim, we have designed and developed a goniometric ultrasonic test bench and a software for the management of the test and the processing of the acquired data. By employing this experimental device, we determine in a non-destructive way the five elastic moduli of a transversely isotropic unidirectional CFRP composite. The experimental analyses are supported by numerical simulations, which are useful for a deeper insight of the propagation phenomena and for enhancing the experimental strategies to be adopted.

Mechanical characterization of CFRP composites by ultrasonic immersion tests: Experimental and numerical approaches

The reconstruction of all nine unknown elastic moduli of orthotropic plate structures has been achieved using a single-transmitter-multiple-receiver (STMR) compact structural health monitoring (SHM) array. This method uses the velocity measurement of the fundamental guided Lamb wave modes (S0 and A0), generated from a central transmitter, and received by a sparse array of receivers that encircle the transmitter. The measured velocities are then used in an inversion algorithm based on genetic algorithms. A prototype compact STMR array was developed and used in the measurement. Simulated data were used to demonstrate the feasibility of the technique. Experiments were conducted on 3.15 mm graphite–epoxy composite plate using a PZT based STMR array as well as laser vibrometer based displacement measurement. Experimental Lamb wave velocity data were used to validate the present technique. This technique finds application in the areas of material characterization and SHM of anisotropic plate-like structures used in aerospace and automobile components made using fiber reinforced composites.

http://iopscience.iop.org/article/10.1088/0964-1726/16/5/017/pdf

Genetic algorithm based reconstruction of the elastic moduli of orthotropic plates using an ultrasonic guided wave single-transmitter-multiple-receiver SHM array

This paper reports a Genetic Algorithm (GA) based reconstruction procedure to determine the elastic constants of an orthotropic plate from ultrasonic velocity data Phase velocity measurements are carried out using ultrasonic back-reflection technique on laminated unidirectional graphite–epoxy (0)16 and quasi-isotropic graphite–epoxy (+45, −45, 0, 90)7s fiber reinforced composite plates A forward model to generate the slowness curves from elastic constants has been used to verify the quality of the reconstruction The sensitivity of the chosen GA parameters is studied As expected, out of 9 orthotropic elastic constants to be determined, the C23 and C44 found to be insensitive The GA based reconstruction using data obtained from multiple planes were evaluated and it is shown that the single plane reconstruction at a non-symmetric plane was sufficient for the computation of the seven elastic constants

Genetic algorithm reconstruction of orthotropic composite plate elastic constants from a single non-symmetric plane ultrasonic velocity data

Destructive identification approaches are no longer in favor since the advent of nondestructive evaluation approaches, as they are accurate, rapid, and cheap. Researchers are devoted to improving the accuracy, rate of convergence, and cost of such approaches, which depend greatly on the types of vibrational experiments conducted and the types of forward and inverse methods used in numerical section. Therefore, this article presents a review on the development of nondestructive vibrational evaluation approaches in identifying the elastic constants of composite plates, in experimental and numerical manners in order to enlighten researchers with the current trends of nondestructive vibrational approaches.

Identification of material properties of composite materials using nondestructive vibrational evaluation approaches: A review

Our work is focused on a new experimental approach for the comparison between Quasi Static Indentation (QSI) damage and Low-Velocity Impact (LVI) damage in polymer composites starting from the results of ultrasonic goniometric immersion tests. In particular, the comparison is performed through the analysis of the additional anisotropy induced by the damage in unidirectional Glass Fiber-Reinforced Polymer (GFRP) composites due to QSI and LVI damage tests performed with a low level of the employed energy. To this aim, we ultrasonically reconstruct the acoustic curves (velocity curves and slowness curves) before and after the damage. Ultrasonic experiments are performed by using a goniometric ultrasonic immersion device designed and built at our laboratory, aimed at the mechanical characterization of anisotropic materials. We highlight differences and similarities between QSI and LVI damage starting from the analysis of the variations of the acoustic behavior and by using a suitable anisotropic damage model developed in the framework of the Continuum Damage Mechanics theory. The proposed experimental approach can be suitably developed for in situ investigations on low-velocity impact damage in polymer composite components.

Quantitative analysis of QSI and LVI damage in GFRP unidirectional composite laminates by a new ultrasonic approach

Ultrasonic goniometry immersion techniques for the measurement of elastic moduli

The ultrasonic benchmark problem requires models to predict, given a reference pulse waveform, the pulse echo response of cylindrical voids of various radii located in an elastic solid for various incidence angles of a transducer immersed in water. We present a conceptually simple yet reliable numerical technique to determine these internal fields in any region of interest within the elastic solid for the specified angles made by the transducer in water. The technique, equivalent to evaluating the Rayleigh‐Sommerfeld integral but through a computationally less demanding procedure, regards the transducer as made of elemental rectangular/square patches and uses the well‐known expression for the radiation pattern of an elemental patch to obtain the total transducer radiation field. A ray‐based method is adopted to propagate the elementary radiation field across a fluid‐solid interface. The FBH is treated in terms of explicit patch element reflectors, its response is evaluated and validated with measurements. The P‐wave scattering charactieristics of spherical voids are evaluated using the exact separation of variables method and the patch model for the transducer is used to determine their response. The advantages of the patch model for the transducer in the context of the benchmark problems in particular and non‐destructive evaluation in general are indicated.

Patch Element Model for the Evaluation of Displacement Fields Within an Elastic Solid from a Non-Contact Immersion Transducer: Application to the 2004 Ultrasonic Benchmark Problem

The measurement of Stress Gradients with Depth using an analytical ultrasonic Raleigh wave dispersion relationship inversion procedure is discussed in this paper Ultrasonic Surface (Raleigh) waves become dispersive when propagating on non‐uniformly stressed media In the light of this, the Acoustoelastic effect on their propagation in deformed but initially isotropic materials has been investigated in the past, using an energy perturbation approach that considerably reduces the complexity in the treatment of the Acoustoelastic effect Inversion of the perturbation relation offers an advantageous route to obtaining the stress gradients This paper presents a new mechanism for effecting this inversion Crucial use is made of the fact that Raleigh waves diminish rapidly beyond a depth equaling the wavelength, and the governing integral equation, a Fredholm Integral equation of the first kind, is reduced to a Volterra integral equation of the first kind The conditions of the problem allow a further conversion into the more stable and tractable Volterra Integral equation of the second kind, which is easily solvable by conventional analytical or numerical iterative techniques

A New Approach to Inversion of Surface Wave Dispersion Relation for Determination of Depth Distribution of Non‐Uniform Stresses in Elastic materials

Measurements and numerical experiments are reported for a sub‐set of the problems defined as the Ultrasonic Benchmark 2002 by the World Federation of Nondestructive Evaluation Centers. The backscatter from cylindrical voids of 0.125, 0.5, 1.0, 2.0, and 4 mm radii in an Aluminum block for an incident plane longitudinal elastic wave has been numerically evaluated using one exact and one approximate solution and compared. The exact solution is based on the separation of variables method. The approximate solution is based on Kirchoff’s approximation. Within the Thomson‐Gray measurement model and the paraxial approximation for the transducer beam, the peak‐to‐peak voltage is computed as a function of void radius using the exact and approximate backscatter solutions. Using a prescribed reference RF signal waveform, the backscattered RF flaw signals are predicted. Within the Kirchoff’s approximation, the backscatter from partially illuminated cylindrical voids is evaluated as a function of the fractional area illuminated. RF signal waveforms were measured for cylindrical voids of 0.5, 1.0, 2,0 and 4.0 mm radii in an Aluminum block under a normal incidence immersion method. The RF signals were also measured, as the transducer was scanned perpendicular to the cylindrical void axis. Measurements were also carried out to obtain the backscatter from solid cylinders of various radii immersed in water. Comparisons between predicted peak‐to‐peak voltages and measurements are made. Attention is drawn to the transition from 2D backscatter to 3D backscatter encountered when seeking comparisons between predictions and measurements.

Ultrasonic Benchmark Problem 2002: Measurements and Numerical Experiments

The 2004 ultrasonic benchmark problem requires models to predict, given a reference pulse waveform, the pulse echo response of cylindrical voids of various radii located in an elastic solid for various incidence angles of a transducer immersed in water. We present the results of calculations based on the patch element model, recently developed at CNDE, to determine the response of an SDH in aluminum for specific oblique incidence angles. Patch element model calculations for a scan across the SDH, involving a range of oblique incidence angles, are also presented. Measured pulse‐echo scans involving the SDH response under oblique incidence conditions are reported. In addition, through transmission measurements involving a pinducer as a receiver and an immersion planar probe as a transmitter under oblique incidence conditions are also reported in a defect‐free Aluminum block. These pinducer‐based measurements on a defect‐free block are utilised to characterize the fields at the chosen depth. Comparisons are made between predictions and measurements for the pulse‐echo response of a SDH.

M. Shankar

Papers

Ultrasonic goniometry immersion techniques for the measurement of elastic moduli

Patch Element Model for the Evaluation of Displacement Fields Within an Elastic Solid from a Non-Contact Immersion Transducer: Application to the 2004 Ultrasonic Benchmark Problem

A New Approach to Inversion of Surface Wave Dispersion Relation for Determination of Depth Distribution of Non‐Uniform Stresses in Elastic materials

Ultrasonic Benchmark Problem 2002: Measurements and Numerical Experiments

The 2004 Ultrasonic Benchmark Problem - SDH Response Under Oblique Incidence: Measurements and Patch Element Model Calculations