Christophe Bacon

Finite element predictions for the dynamic response of thermo-viscoelastic material structures

In this paper, constitutive relations are solved in the Fourier domain using a finite-element-based commercial software. The dynamic responses of viscoelastic bars or plates to either thermal or mechanical loads are predicted by considering complex moduli (Young, Poisson, stiffness moduli) as input data. These moduli are measured in the same frequency domain as that which is chosen for modeling the wave propagation. This approach is simpler since it suppresses the necessity of establishing a rheological model. Specific output processing then allows the numerical predictions to be compared to analytical solutions, in the absence of scatterers. The performances of this technique and its potential for simulating more complicated problems like diffraction of waves or for solving inverse problems are finally discussed.

Wave propagation along transversely periodic structures

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

Separation of waves propagating in an elastic or viscoelastic Hopkinson pressure bar with three-dimensional effects

The Split Hopkinson pressure bar technique needs the separation of the waves propagating in opposite directions. The wave separation can be performed whatever the test duration by using the two-point strain measurement method based on the elastic one-dimensional wave propagation theory. If the three-dimensional effects due to the radial inertia are important or if the bar is viscoelastic, wave dispersion and attenuation occur and the previous method cannot be used accurately. This paper presents a new two-point strain measurement method which takes account of the wave dispersion and attenuation. The wave separation is performed in the frequency and time domains. The method is validated with numerical simulations on an elastic bar and experimentally with a viscoelastic PMMA bar.

3D finite element simulations of an air-coupled ultrasonic NDT system

A single-sided, air-coupled ultrasonic NDT system based on the generation and reception of the A0 Lamb mode is used for detecting defects in plates. Transmitting and receiving transducers, being oriented at the appropriate coincidence angle for the generation and detection of the mode, are scanned along a line from one side to the other over the surface of the sample, passing the area with the defect. This contact-less NDT system is modelled in three dimensions with a Finite Element -based method. The air-coupled transmitter is modelled by the normal pressure that it locally applies on the surface of the plate, and the air-coupled receiver by integrating normal displacements over a finite area of appropriate position on the surface of the plate. In this way, beam spreading of both incident and scattered fields is considered. Numerical predictions have successfully been compared with experimental data for a through-thickness hole in an Aluminium plate and also for an impact damage in a composite sample.

Finite element modeling of torsional wave modes along pipes with absorbing materials

This paper describes the implementation of equations of dynamic equilibrium in a finite element (FE) code for modeling, in axisymmetry, the propagation of torsional wave modes along metallic pipes coupled to solid elements. Materials constituting either pipes and/or surrounding elements can be absorbing media, the absorption being caused by either their viscoelasticity or scattering on their internal structure (or both). Complex moduli are used as input data to equations of dynamic equilibrium, which are solved in the frequency domain rather than in the temporal domain. Their real and imaginary parts represent material elasticity and damping, respectively. A new definition of efficient and easy-to-implement absorbing regions that suppress undesired reflections from boundaries is proposed. The resolution of equations in the frequency domain, together with the use of absorbing regions, lead to significant reductions in the number of mesh elements and also in the number of iterations required for describing ...

Methodology for a Hopkinson test with a non-uniform viscoelastic bar

Abstract The conventional Hopkinson pressure bar method needs the use of uniform elastic bars with uniform mechanical characteristics and uniform cross-sectional area. In some particular cases, the impedance may be non-uniform in order to match the specimen impedance or if the bar is heated for high-temperature tests for instance. The method presented allows one to take the impedance variation of elastic or viscoelastic bars into account by using a transfer matrix. This transfer matrix can be predicted theoretically if the variations of the mechanical characteristics and of the cross-sectional area are known. If this is not the case, it is shown that the transfer matrix can be evaluated by a direct experimental method. This method is validated by tests performed on a viscoelastic bar having a significant impedance variation.

Acoustic wave generation in viscoelastic rods by time-gated microwaves

A one-dimensional model is developed to predict the acoustic waves generated in viscoelastic rods by electromagnetic microwave pulses. The wave generation is due to the rapid thermal expansion caused by microwave absorption. The distribution of the temperature rise along the rod is taken to be either uniform or linear. The effects of this distribution and of the microwave pulsewidth are investigated numerically. Some tests are carried out on PVC rods instrumented with accelerometers. The presence of the accelerometer mass at the end of the rod is taken into account in the model. The comparison between the experimental and the theoretical accelerations leads to the evaluation of the maximum temperature rise during one pulse. Although this temperature rise is found to be extremely low, it produces acoustic waves easily detectable with the accelerometer. The inverse problem to estimate the viscoelastic properties of the rod and the temperature rise is approached by means of a numerical minimization technique.

Acoustic waves generated by pulsed microwaves in viscoelastic rods: Modeling and experimental verification

The acoustic wave generation in a specimen irradiated by a pulsed microwave is predicted theoretically. The specimen is a viscoelastic rod inserted into a wave guide. The model is based on Maxwells equations, heat equation and thermoviscoelasticity theory. Computations show the presence of temperature oscillations due to the electromagnetic interferences in the irradiated rod if its electromagnetic absorption is low. An experimental method to infer indirectly the detailed behavior of microwave-generated acoustic waves in polymer rods, including the influence of electromagnetic wave reflection at the rod ends, is presented. The method consists of measuring the oscillations in the particle acceleration detected at the end of the rod that are induced by variations in the polymer rod length. The oscillations are caused by changing electromagnetic standing-wave conditions within the rod. It is found that these oscillations are in agreement in period, amplitude, and phase, with independent values of the complex dielectric constant and complex acoustic slowness of the polyvinyl chloride samples used in the study.

Measurement of complex Young moduli of composite materials by time-gated microwaves

The complex Young’s modulus of composite materials made of glass/fibers and epoxy matrix is deduced from the measurement of velocities and amplitude of acoustic waves generated by microwaves. A magnetron working at 10 GHz delivers a pulse of 1.2 μs with a power of 5 kilowatts. Acoustic rod modes are generated at both interfaces of the sample that is placed in a waveguide. The acoustic wave generation is due to the rapid thermal expansion caused by microwave absorption. From a unidirectional model the acceleration at any position in the sample can be computed. An accelerometer acquired the acoustic waveform in a low frequency domain (5–25 kHz) at an end of the rod. The comparison between experimental and theoretical accelerations permits to solve the inverse problem of determination of the viscoelastic properties of the rod. The samples are cut out of a plate in various directions to measure the viscoelastic properties along the fibers or in the perpendicular direction. A comparison between complex Young’s...

Finite element modeling of the temperature rise due to the propagation of ultrasonic waves in viscoelastic materials and experimental validation.

The ultrasound stimulated thermography method is usually used to detect the temperature rise at a defect position. The temperature rise can be due to the friction between the edges of the defect and/or the plastic deformation around the defect. This paper presents another aspect of the method when the ultrasounds are propagating in a viscoelastic anisotropic material, such as polymers or fiber-reinforced polymers. The attenuation of the waves produces a distributed temperature field. Therefore, even a defect that does not produce some heat can be detected, the ultrasonic field is modified. A finite element model is used for computing the temperature field and for predicting the possibility for an infrared camera of detecting the temperature rise and its modification due to a defect. The model computes the stress and displacement fields associated with the propagation and the loss of energy. Then the heat equation is solved with this loss as a source of heating. An experiment is done with a sonotrode that excites a PVC plate. The ultrasonic displacement at the top of the plate is measured with a laser velocimeter and introduced in the model. Finally, the model result is compared to the image produced by the camera.