Luc Piché

A robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media

An improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media. Generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half‐space and problems associated with numerical stability are solved efficiently. The formulation is applicable to longitudinal and shear input waves alike, at arbitrary incidence angles and for any sequence of solid or fluid layers. Also, allowance is made for viscoelastic behavior by means of relaxation functions in the Laplace transform domain. Finally, the response to arbitrary incident pulse shapes and beam profiles is described through application of two‐dimensional numerical Laplace inversion.

Application of Ultrasonic Sensors in the Study of Physical Foaming Agents for Foam Extrusion

The extrusion foaming process involves several critical steps, in which the physical foaming agent plays a significant role: plasticization, solubility, nucleation and bubble growth. Although these aspects can be studied by different techniques, a novel method based on ultrasonic sensors has proven to provide valuable information with respect to the thermoplastic foaming process. This technique can be either used off-line as a characterization tool to improve our understanding of the foaming agent characteristics, or it can be installed in-line, on the extrusion line, as a control device. Review of the different applications of this technique will be covered in this paper, with numerous examples given to the mixture of PS with CO2. The degree of plasticization of the polymer as a function of the blowing agent concentration will be addressed first, followed by the detection of the conditions prone to induce nucleation, in terms of pressure, temperature, type of nucleating agents and flow conditions. The evaluation of the kinetics of bubble growth will also be explored.

Ultrasonic measurement of relaxation behavior in polystyrene

We report measurements of the temperature and pressure dependence of ultrasonic modulus and specific volume in polystyrene between 50 and 280°C and applied pressures up to 775 bar. The volumetric glass transition temperature is found to vary linearly with pressure. Furthermore, it coincides with the temperature at which the velocity of sound and the attenuation in the material show pronounced change from solid-like to liquid-like behavior. The storage and loss moduli are analyzed within the Havriliak-Negami model and very good agreement is found over the entire temperature and pressure ranges. Using the Vogel-Tammann-Fulcher equation for the relaxation time, the Kauzmann temperature T h and the fragility parameter D of polystyrene were determined from fits to the data. T k is also a linear function of pressure, but D is constant over the whole pressure range. The value of D allows us to classify polystyrene among the fragile-glass formers.

Flame propagation in random media.

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration {ital c}{gt}{ital c}{sup *}{gt}0, while its vanishing at {ital c}{sup *} is consistent with mean-field percolation theory. For {ital c}{gt}{ital c}{sup *}, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.

SCALING, PROPAGATION, AND KINETIC ROUGHENING OF FLAME FRONTS IN RANDOM MEDIA

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with meanfield theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time-dependent width and equal-time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.

Phenomena related to the propagation of ultrasound in polymers (a paradigm for disordered materials)

The author studies the propagation of ultrasonic waves in polymers in relation to their state of structural organization in the transformation range from solid to liquid. Because of the disordered nature of the structure, the equation of state for polymers is determined by pressure (p), volume (V), temperature (T), and time (t), leading to the concept of thermodynamic history (p, V, T, t). A novel technique is presented that measures the velocity and attenuation and controls thermodynamic history from T=-150 degrees C to 400 degrees C, and up to p=200 MPa, and which incorporates simultaneous measurement of specific volume to characterize the thermodynamic state. The author investigates amorphous polymers with respect to anharmonicity, the glass transition phenomenon at the glass transition temperature evidencing irreversible structural rearrangements, and linear viscoelasticity associated with free-volume and configurational entropy. Semicrystalline polymers where collapse of the modulus correlates to melting of the crystalline phase and critical transformation to the liquid state are examined.<<ETX>>

ON-LINE ULTRASONIC CHARACTERIZATION OF POLYMER FLOWS

Although ultrasonic techniques have proven useful for investigating elasticity of solids and viscosity of fluids and gases1, they have seldom been used for polymer studies. Notwithstanding, all reports2,3,4 point out the distinctive behavior of ultrasound in polymers and suggest numerous prospects for fundamental studies, and industrial applications5,6. Thermomechanical properties of polymers are usually measured at low frequencies between 0.01 and 100 Hz, with deformations e ≈ 10-4, while ultrasonic techniques involve frequencies in the MHz range and strains near e ≈ 10-7. Whilst rheology measures global properties associated to long range diffusion of molecules, ultrasonic waves probe the mobility of short chain segments. In an attempt to relate the different measurements, we described experiments7,8 using an apparatus9 that measures the complex ultrasonic modulus with close control of the thermodynamic history. Although successful, the technique involves no macroscopic flow of molecules.

Investigation of Stress Relaxation in Filled Elastomers by XPCS with Heterodyne Detection

XPCS with heterodyne detection (HD‐XPCS) is a new original method that gives information about the dynamics of filler aggregates during stress relaxation and its relation to the macroscopic mechanical behavior measured in situ.

Dynamics and effective thermodynamics of a model structural glass

The authors use Monte Carlo methods to investigate a purely dynamical model for structural glasses. They observe stretched exponential decays of the equilibrium autocorrelation function and measure the late-time relaxation times tau . These diverge with temperature following a Vogel-Fulcher law. They also study systems which are quenched deeply and then re-heated. This gives a peak in the effective specific heat with properties matching those of the glass transition. The model thus reproduces the main phenomenology of glasses and the glass transition.

Characterization of Isotropic Composites Containing Inclusions of Specified Shapes by use of Ultrasonics In The Long Wavelength Limit

The presence of an additional heterogeneous phase, dispersed in a matrix can bring about important improvements in the properties of the original material and make it appropriate for more specific purposes. Most engineering needs require the optimization of the strength to weight ratio of materials and from this point of view, polymer composites offer excellent characteristics. This factor and others such as versatility, ease of fabrication and cost effectiveness are some of the reasons why composite plastics are rapidly gaining ground over the more usual engineering materials.