The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 2. Experimental Results

Background

This paper is Part 2 of a study on the scope of the ultrasonic Surface Reflection Method (SRM). Part 1 deals with the theoretical conditions for a satisfactory usage of this method.

Objective

This second part validates the practical feasibility and reliability of the SRM method by comparison with the conventional Transmission Method (TM) in cases where the latter is applicable.

Methods

Two experimental devices (one for SRM and one for TM) are developed and measurements of shear and bulk moduli are carried out at ultrasonic frequency (610 kHz) and at room temperature.

Results

The experimental conditions in terms of sample geometry, pulse characteristics and interfacial transmission required to obtain a given accuracy on the measurement are stated. The SRM is then validated against other experimental methods and is used to determine the shear modulus of a carbon black filled neoprene at ambient temperature (T?=?21 °C) and ultrasonic frequency.

Conclusions

The benefit brought by this method is well demonstrated: a unique measurement allows the determination of all the moduli of a highly damping isotropic material (carbon black filled neoprene) not achievable by other methods.

     

High-speed planar thermometry and velocimetry using thermographic phosphor particles

Simultaneous gas-phase temperature and velocity imaging using micrometer-size thermographic phosphor particles seeded into the flow is demonstrated at a 3 kHz repetition rate. The velocity field is measured using a standard particle image velocimetry approach, while the temperature is determined from the temperature sensitive phosphorescence emission of the particles following excitation at 355 nm. Since the particles are very small, they rapidly assume the temperature and velocity of the surrounding gas. A single shot temperature precision of better than 5 % was achieved at 500 K. Time-resolved measurements in the wake of a heated cylinder are presented, demonstrating the utility of these imaging diagnostics to observe transient, coupled heat and mass transfer phenomena.     

Cavitation criterion for rubber materials: A review of void‐growth models

The principal criteria used to predict cavitation in rubber materials are reviewed, and experimental evidence is recalled for three different configurations: in the bulk, in the vicinity of a rigid particle, and in small rubber particles embedded in a rigid polymer matrix. Two major classes of cavitation criteria are defined, those based on an elastic instability (i.e., related to a stress state and finite strains) and those based on the energy balance (i.e., involving surface energies). The different criteria, in which various hyperelastic behavior laws are considered, are compared in numerical applications, and the tendencies are derived. The particular case of accounting for the surface tension of the rubber, a parameter common to the stress state and the energy balance, is treated in detail. It appears that the understanding of the genesis of a microcavity in a rubber material, when no pre‐existing flaw is assumed, still constitutes a difficulty for the analysis of mechanical damage in polymers containing a rubber phase. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2081–2096, 2001     

Simulated glass-forming polymer melts: Glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T _g and for the elastic properties of the glassy state are presented. We find that T _g increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T _g is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T _g via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T _g from below, the shear modulus μ displays a much stronger decrease near T _g. From the present simulation data it is not possible to decide whether μ takes a finite value at T _g, as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.     

Experimental investigations and modeling of volume change induced by void growth in polyamide 11

Polymers are known to be sensitive to hydrostatic pressure. The influence of stress triaxiality ratio on cavitation and damage has been highlighted in numerous studies. This paper proposes experimental investigations allowing the control of both the stress triaxiality ratio and the void distribution via microscopic observations of microtome-cut surfaces from interrupted tests. With the help of a finite element code, the Gurson–Tvergaard–Needleman model was calibrated by using these multi-scale experimental data. Then comparison between both numerical and analytical models and experimental data was performed. Bridgman formulae were reported to be valid up to the peak load. Moreover, a better understanding of the time evolution of significant parameters such as the porosity (volume change) and the stress triaxiality ratio (hydrostatic pressure), was highlighted.     

Compliant rubber domains in a rigid polymer matrix: Shape and orientation factors related to cavitation and plastic dissipation

The hydrostatic stress in compliant rubber inclusions embedded in a rigid polymer matrix is evaluated for various shapes and orientations of the rubber domains and triaxialities of the remote stress tensor to determine the propensity of the inclusions to undergo cavitation. The first section analyzes the case of rubber particles of an ellipsoidal shape assuming linear elasticity of the matrix and small strains. It is shown that flat shapes, of which the long axis lies perpendicular to the direction of the maximum principal stress, are subjected to the highest levels of hydrostatic stress. The pressure induced by the deviatoric part of the remote stress tensor in the compliant rubber domains depends strongly on their shape and orientation, whereas the pressure induced by the hydrostatic part of the tensor is almost insensitive to the shape and orientation of the compliant domains. The second section examines the stress concentrations for elastoplasticity and plastic dissipation in the matrix. It is found that spherical inclusions ensure the best compromise between the early occurrence of plasticity and large amounts of plastic dissipation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1476–1486, 2004     

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 1. A Theoretical Analysis

Background

This paper deals with the possible field of application of ultrasonic Surface Reflection Method (SRM) to achieve the mechanical characteristics of isotropic materials. This method is based on the measurement of the amplitude of the reflected wave at the interface between reference material and the material to be characterised. Objective: The purpose of Part 1 of this paper is to establish the theoretical conditions for the applicability of SRM.

Methods

First, the theoretical formulas necessary to obtain the mechanical properties of the material to be tested will be established. Then, on the basis of these analytical formulas, the validity of the results for the material to be studied will be discussed according to the choice of the mechanical properties of the reference material through uncertainty calculations. The measurand error of SRM is then compared to that of traditional methods (transmission, transmission in water bath, pulse-echo).

Results

The analytical solution to the inverse problem (the mechanical characteristics of the tested medium based on those of the reference medium and the waves’ amplitude) will be given. From this analytical solution, an analysis of the measurand error will be performed and a method for choosing the reference material will be proposed.

Conclusions

It appears that SRM is better suited than traditional methods in two specific cases: measurement of small deviations of mechanical properties from a reference material or characterisation of high damping materials. In Part 2 of this paper, the practical conditions of applicability of the method are described and then applied to different kinds of materials.

     

A dynamic programming approach to the maximum principle of distributed-parameter systems

This paper provides a dynamic programming approach to the maximum principle for the optimal control of systems with distributed parameters. The process of the systems under consideration is governed by a partial differential equation.This paper is based on Chapter 2 of the author's PhD Thesis under the supervision of Professor S. E. Dreyfus to whom the author wishes to express his appreciation.