Shiro Biwa

Wave attenuation in particulate polymer composites: independent scattering/absorption analysis and comparison to measurements

Abstract Attenuation characteristics of ultrasonic longitudinal waves in particle-reinforced polymer-matrix composites are considered. The spatial decay of a plane wave in the composite is evaluated within the independent scattering/absorption theory valid for dilute particle concentrations, with the absorption loss in the viscoelastic matrix accounted for explicitly. Numerical analysis is carried out for longitudinal wave attenuation in glass-particle reinforced epoxy composite and rubber-particle toughened poly(methyl methacrylate) (PMMA) blend. In the glass/epoxy composite, wave attenuation is due to absorption in the matrix and scattering by the particles, while in the rubber/PMMA blend, attenuation is additionally caused by absorption in the particles. The influence of matrix viscoelasticity on the low-frequency scattering characteristics of a particle is demonstrated, which show certain deviation from the classical Rayleigh scattering behavior. The frequency and particle-radius dependence of the scattering, absorption and the resulting attenuation characteristics are illustrated. Numerical results are discussed in comparison to existing experimental data of longitudinal wave attenuation in the two composites, and the predicting capability of the theory is found to be satisfactory.

Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation

Abstract Ultrasonic measurements and micromechanical models are used to evaluate elastic properties of rubber particles dispersed in toughened polymers. Ultrasonic phase velocities and attenuation spectra of rubber-toughened poly(methyl methacrylate) (PMMA) with different rubber particle fractions are measured for longitudinal as well as transverse waves. The ultrasonic properties of rubber-toughened PMMA are found to depend markedly on the rubber particle fraction. The bulk and shear moduli determined from the measured velocities are in turn used to estimate those moduli of the particles based on existing micromechanics models, namely the three-phase model and the Hashin–Shtrikman upper and lower bounds. The bulk modulus of the particle estimated by the three-phase model is found to be in close agreement with the result of previous investigators. Implications of the Hashin–Shtrikman bounds for the particle moduli are also examined.

Analysis of wave attenuation in unidirectional viscoelastic composites by a differential scheme

Abstract Wave attenuation characteristics of unidirectional fiber-reinforced polymer composites are analyzed theoretically by a micromechanical differential (incremental) scheme for their macroscopic acoustic properties. In this approach, the effect of neighboring fibers on the wave scattering by a single fiber is accounted for in an approximate and averaged sense. The analysis also takes into account the viscoelastic nature of the matrix, so it yields the attenuation of the composite due to both wave scattering loss and the viscoelastic absorption loss. As an example, frequency-dependent attenuation coefficients of the longitudinal and transverse waves are computed for unidirectional carbon/epoxy composites. The computed results are favorably compared to the experimental data regarding their dependence on the frequency and the fiber volume fraction. The analysis shows that the attenuation in these composites is principally governed by the wave absorption of the epoxy matrix for a practical frequency range.

Independent scattering and wave attenuation in viscoelastic composites

A theoretical model for ultrasonic attenuation in viscoelastic composite materials is examined which is based on the evaluation of scattering as well as absorption losses. The theoretical formulation explicitly takes into account the viscoelastic nature of the matrix. The model gives an expression for the attenuation coefficient of the plane wave propagating in the composite in terms of the scattering and absorption cross-sections of a single inclusion and the attenuation properties of the matrix. To gain first insight into the problem, the single and independent scattering approximation is considered, although extension to a more elaborate scheme is briefly discussed. The model is applied to a special case of shear horizontal waves in a unidirectional fiber reinforced viscoelastic composite. In particular, the frequency dependence is demonstrated for the scattering cross-section of an elastic fiber embedded in a viscoelastic matrix. In contrast to the classical Rayleigh scattering where the normalized cross-section of a fiber scales to the third power of the normalized frequency, it is found that the frequency dependence of a lower order is possible when viscoelasticity of the matrix is accounted for. Shear wave attenuation spectrum of the viscoelastic composite is also illustrated, for which the contributions of scattering and absorption are discussed.

Inelastic flattening of rough surfaces

Abstract When rough surfaces are impressed, the electrical, thermal and mechanical contact properties will originally be imperfect as compared to smooth surfaces. Here the initial mechanical contact at inelastic materials is analysed for residual plastic strain-hardening and creep deformation when two rough surfaces are approached. First a self-consistent micro-mechanical analysis is carried out for general viscoplastic impression of a single asperity based on self-similarity and stationary contact. Probabilistic models of surface topography are then employed to determine the macroscopic flattening behaviour for a distribution of asperities. Relations between contact area, impression depth and loading are determined with high accuracy and their validity compared with earlier significant experimental findings. In particular it is shown that the contact pressure–area connection is nonlinear. Estimates are given for the degree of roughness required for flattening to be essentially plastic. A prototype model based on fractal surface geometry is outlined using scale-independent parameters and its virtues and shortcomings discussed.

A variational method for unidirectional fiber-reinforced composites with matrix creep

Abstract A variational method is developed for analyzing the matrix creep induced time-dependent change in fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress rate is presented by supposing a fiber broken in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying an incremental differential equation based on the shear lag assumption. Then, the stationary function is approximately determined by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to analytical solutions for the time-dependent change in fiber stress profiles. The solutions are verified on the basis of an energy balance equation and a finite difference computation. Moreover, it is shown that the solution for the fiber pull-out model agrees well with an experiment on a single carbon fiber/acrylic model composite if the initial slip at fiber/matrix interface is taken into account. In addition, the solution for the fiber breakage model is used for evaluating the characteristic time in long-term creep rupture of unidirectional composite.

Modeling of Ultrasonic Attenuation in Uni‐Directional Fiber Reinforced Composites Combining Multiple‐Scattering and Viscoelastic Losses

A model coupling viscoelastic and multiple‐scattering losses is developed to predict ultrasonic attenuation in unidirectional fiber reinforced composite of high fiber volume fraction. Complex‐valued stiffness constants accounting for viscoelasticity are inserted in classical multiple‐scattering theory. Waves of various polarities (SH, SV, L) relatively to the fiber direction are considered. SH waves only require a scalar treatment, whereas the others require a vector treatment accounting for mode‐conversions. Comparisons of predicted attenuation coefficients with experimentally measured ones validate the model.

Evaluation of time-dependent change in fiber stress profiles during long-term pull-out tests at constant loads using Raman spectroscopy

Constant-load pull-out tests were carried out on single-fiber model composite specimens for 500 to 1,000 hours in order to investigate the time-dependent change in fiber axial stress profiles resulting from matrix creep in unidirectional continuous fiber-reinforced composites. Three resins used as the matrix materials, in which single carbon fibers were embedded, were normal epoxy, a blend with a more flexible epoxy, and UV-curable acrylic. The time-dependent change in fiber stress profiles in the constant-load pull-out tests was measured using Raman spectroscopy, and creep and relaxation tests for the matrix resins themselves were performed. It was observed that the normal epoxy matrix composite exhibited only a negligible change in the fiber stress profile with time whereas the flexible epoxy and UV-curable acrylic matrices allowed, respectively, considerable and significant changes. These observations were shown to be consistent with the creep and stress relaxation test results of the matrix resins. It was also found that the time-dependent change in fiber stress was much slower in the experiment than in the prediction based on perfect bonding at the fiber/matrix interface. The interfacial slip that occurred in the composites tested could be responsible for the gradual variation in fiber stress profiles.

Ultrasonic measurements and micromechanical evaluation of constituent properties for rubber-toughened polymers

Ultrasonic phase velocities and attenuation spectra of rubber-toughened poly(methyl methacrylate) (PMMA) with different rubber particle fractions are measured for longitudinal as well as transverse waves by means of digitized spectrum analysis. The ultrasonic characteristics of rubber-toughened PMMA depend markedly on the particle fraction. Using a micromechanical model, the bulk and shear moduli of dispersed rubber particles are evaluated. The ultrasonic attenuation behavior is also examined in the light of scattering theory.

Wave Scattering and Attenuation in Polymer-Based Composites: Analysis and Measurements

Polymer-based composite materials are widely used in application, including various particulate and fibrous composites. In this regard, evaluation of their dynamical properties as well as monitoring of their manufacturing processes become highly important. Ultrasonic waves offer useful means to this purpose [1]. Especially, the velocity measurements have long been practiced to assess elastic properties of composites. In addition, there has been growing interest in complementing the evaluation with the attenuation measurements of ultrasound. There is certain advantage in utilizing the attenuation for material characterization in that the changes in material properties appear more sensitively in the attenuation than in the velocity. Attenuation properties have been explored for polymer-based composites to monitor their processing, and to evaluate their deterioration due to mechanical/thermal loading as well as moisture absorption [2–4]. In order to enhance nondestructive characterization and smart monitoring of polymer-based composites by ultrasonic attenuation, however, it is important to understand the propagation of ultrasound in these composites and to interpret the measured attenuation qualitatively as well as quantitatively.