Jackie Li

Effective elastic moduli of composites reinforced by particle or fiber with an inhomogeneous interphase

The solution of the strain energy change of an infinite matrix due to the presence of one spherical particle or cylindrical fiber surrounded by an inhomogeneous interphase is the basis of solving effective elastic moduli of corresponding composites based on various micromechanics models. In order to find out the strain energy change, the composite sphere or cylinder, i.e., the spherical particle or cylindrical fiber together with its interphase, is replaced by an effective homogeneous particle or fiber. Independent governing differential equations for each modulus of the effective particle or fiber are derived by extending the replacement method [J. Mech. Phys. Solids 12 (1964) 199]. As far as the strain energy changes of the infinite matrix subjected to various far-field stress systems are concerned, the present model is simple. Meanwhile, FEM analysis is carried out for a verification, which shows that the model can lead to rather accurate results for most practical interphases. Besides, to check the validity of the model further when the interactions among composite cylinders exist, the two problems of an infinite matrix containing two composite cylinders and the effective moduli of composites with the equilateral triangular distribution of composite cylinders are analyzed using FEM. The FEM results show that the model is still rather accurate, especially for the case of interphase properties varying between those of fiber and matrix. Therefore, composite spheres or cylinders are assumed as the effective homogeneous particles or fibers and simple expressions of the effective moduli of composites containing the composite spheres or cylinders are obtained. Furthermore, the present model is compared with some existing models that are based on very complicated derivations.

Elastic field of a thin-film/substrate system under an axisymmetric loading

This paper presents the elastic solution of a layered half space with perfect interfacial bonding under an axisymmetrical compressive loading on the plane surface. The analysis is intended to model the nano-indentation of thin-film coating/substrate systems. Unlike most of the existing work of which the substrate is assumed as rigid and the numerical results are obtained by finite element analysis, the present paper presents theoretical solutions for the elastic coating/substrate systems. The surface displacement profiles and the stress fields are shown to be sensitive to the thickness of the coating layer and the ratio of the elastic modulus of the coating material to that of the substrate. When the film thickness is comparable to the loading contact radius, the film elastic property cannot be accurately determined by using Sneddons half-space indentation solution. Furthermore, there are pronounced differences in the stress fields of the hard-coating and the soft-coating systems. When an indentation load is applied to a soft-thin-film/hard-substrate system, most the stress components are compressive. But for a hard-thin-film/soft-substrate system, the radial and hoop stresses in the film near the film/substrate interface change from tension to compression as the film thickness decreases. The normal and shear stress results are compared with those obtained from finite element analysis (Jayachandran, R., Boyce, M. C. and Argon, A. S. (1995) Mechanics of the indentation test and its use to assess the adhesion of polymeric coatings. In Adhesion Measurement of Films and Coatings, ed. K. L. Mittal. VSP, pp. 189–215) for the rigid substrate system. Also, the load-indentation depth results are compared with the experimental data of Oliver and Pharr (Oliver, W. C. and Pharr, G. M. (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Material Research7(6), 1564–1583) for tungsten subjected to elastic indentation. The agreement is quite satisfactory. Implications of the elastic field on the failure mechanisms of coating/substrate systems are also discussed.

Strain-Rate Sensitivity, Relaxation Behavior, and Complex Moduli of a Class of Isotropic Viscoelastic Composites

A micromechanical principle is developed to determine the strain rate sensitivity, relaxation behavior, and complex moluli of a linear viscoelastic composite comprised of randomly oriented spheoidal inclusions. First, by taking both the matrix and incluions as Maxwell or Voigt solids, it is found possible to construct a Maxwell or a Voigt composite when the Poisson ratios of both phases remain constant and the ratios of their shear modulus to shear viscosity (or their bulk counterparts) are equal; such a specialized composite can never be attained if either phase is purely elastic. In order to shed some light for the obtained theoretical structure, explicit results are derived next with the Maxwell matrix reinforced with spherical particles and randomly oriented disks. General calculations are performed for the glass/ED-6 system, the matrix being represented by a four parameter model

A Micromechanics-Based Hysteresis Model for Ferroelectric Ceramics

Based on the mechanics of domain switch and irreversible thermodynamics, a micromechanics-based model that incorporates the effect of polarization strain and electric polarization in the switched domain is developed to predict the evolution of new domain and the associated hysteresis loops of a ferroelectric ceramic. The new domain concentration c r associated with the remanent polarization P r , and the new domain concentration c c at the coercive field E c , are also found in terms of the saturation polarization P s , the coercive field E c , and the dielectric permittivity of the parent domain. The theory is developed with a homogenization technique for a coupled, dual-phase electromechanical system with an evolving microstructure, whose driving force arises from the reduction of Gibbs’ free energy and whose resistance force comes from the energy dissipation due to domain wall movement. The developed theory is applied to a lanthanum doped lead zirconate titanate (PLZT), first for the calculation of its hysteresis electric displacement versus electric field (D vs. E) relation and the butterfly-shaped longitudinal strain versus electric field (∊ vs. E) relation, and then for its nonlinear compressive stress-strain relation and nonlinear depolarization. The results are shown to provide the essential features of the hysteresis behavior and found to be in quantitative accord with the experimental data.

Effect of a viscoelastic interphase on the creep and stress/strain behavior of fiber-reinforced polymer matrix composites

The influence of a viscoelastic interphase on the overall creep compliances and stress/strain relationships of fiber-reinforced polymer-matrix composites under a constant stress and a constant strain-rate loading are examined. The fibers are taken to be elastic but the matrix is also viscoelastic. Evaluation of the overall property is based upon the composite cylinder assemblage and the generalized self-consistent scheme. It is found that, except for the axial tensile behavior, which is fiber-dominated, the creep and stress/strain responses under transverse tension, transverse shear, axial shear, and plane-strain biaxial tension, are all significantly influenced by the interphase. A detailed examination of these effects in the light of the interphase property and volume concentration is carried out, and the results reveal that, when the interphase is viscoelastically softer than the matrix, its presence will cause a very pronounced influence on the creep strength and load-carrying capacity of the three-phase system.

A unified approach from elasticity to viscoelasticity to viscoplasticity of particle-reinforced solids

Abstract This paper presents a novel approach to determine the overall elastic-viscoplastic behavior of a particle-reinforced metal-matrix composite. It is built upon the linkage from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity by means of the concept of secant viscosity and an energy approach. Albeit approximate, this theory is analytically tractable, and capable of delivering the stress-strain relations of the composite sittem under various applied strain rates. The theory embodies the nonlinear, rate-dependent, and work-hardening nature of the constitutive equations of the ductile matrix, as well as the elasticity of both matrix and inclusions. The influence of particle concentration, elastic stiffness, and applied strain rate on the overall dilatational and deviatoric stress-strain behaviors are examined in detail. The theory is finally applied to predict the response of a silicon-carbide/aluminum system and the result is found to be in accord with experimental observations.

Intrinsic dielectric frequency dependent spectrum of a single domain tetragonal BaTiO3

The intrinsic dielectric frequency dependent spectrum of single domain barium titanate (BaTiO3) at room temperature is investigated by considering the vibration of phonons and the conductivity of the tetragonal system in a wide frequency range up to THz. The proposed model combines Debye type of dissipation, soft mode theory, and the influence of conductivity on the dielectric loss to obtain a more precise dielectric frequency spectrum. The calculated results were compared with experimental data on single domain nanocrystals of BaTiO3, both free standing and suspended in a low dielectric medium. The comparisons provide insight into the mechanism for the dielectric behavior, which can be extended to apply to a range of composites that comprise single domain dielectrics embedded in continuous media. At the lower frequency range, conductivity plays a dominant role in the contribution to the dielectric loss along both a- and c-axes, while the phonon vibration controls the dielectric behavior of the system at ...

Time-dependent creep of a dual-phase viscoplastic material with lamellar structure

Abstract Exact solutions for the time-dependent creep behavior of a two-phase material with a lamellar microstructure are derived as a function of volume concentration and the properties of its constituents. Each phase is taken to be elastic–viscoplastic, exhibiting work-hardening characteristics. The derivation takes advantage of the condition of interfacial discontinuities over the interfaces, with a result given in a rate form for the general combined loading. Specific overall creep strains are presented along five distinctive loading directions for two kinds of viscoplastic composites: one involving an elastic and a viscoplastic phases and the other with dual viscoplastic phases. In addition to providing insightful information for the overall time-dependent creep, the exact nature of the results can also serve as a bench mark to test the accuracy of the approximate theories. In this light a secant-viscosity approach recently developed for a particle-reinforced solid ( Li and Weng (1997) . A secant-viscosity approach to the time-dependent creep of an elastic–viscoplastic composite. J. Mech. Phys. Solids , 45 , 1069) is extended to a lamellar structure and the results are tested against these exact solutions. Comparison between the two indicates that the secant-viscosity concept is a sufficiently accurate one and it can be applied to composites with other types of microgeometries.

Investigation of orientation effects on the electro-mechanical coupling behavior of 1-3 piezoelectric composites under compression

The electro-mechanical responses of 1–3 piezoelectric composites with PZT5A1 fibers embedded in an epoxy matrix are investigated under compressive loading. When the applied loading direction is not parallel to the polarization and fiber directions of the PZT fibers, the corresponding electrical and mechanical responses can be dramatically affected. Here both experimental testing and theoretical modeling are carried out to study such orientation effects on 1–3 piezoelectric composites. The testing results indicate that, as the loading direction changes from 0°, to 30°, 45°, 60° and finally 90° to the initial poling direction (which is also the PZT fiber direction), the magnitude of the electric displacement and mechanical strain of the system all decrease and the electrical response will diminish to zero at 90°. On the other hand, a two-level micromechanics theory based on irreversible thermodynamics and the physics of domain switching is applied to predict such orientation dependency of the electro-mechanical coupling behavior of the composite system. The first level is based on PZT fibers only which consist of parent and switched domains due to external loading, and the second level is based on a larger scale consisting of PZT fibers and an electrically inactive polymer matrix. The theoretical results are found to be in reasonable agreement with our experimental data.

A homogenization theory for the overall creep of isotropic viscoplastic composites

SummaryA field-fluctuation method is introduced into the secant-viscosity framework to evaluate the homogenized effective stress of the heterogeneously deformed elastic-viscoplastic matrix in an isotropic composite. Two microgeometries are considered here: one is reinforced with spherical particles and the other with randomly oriented thin discs. The time-dependent creep strains of the elastic-viscoplastic composites are then calculated as a function of inclusion volume concentration. As these two microgeometries are known to provide the lower and upper bounds of the effective moduli in elasticity, the creep strains associated with these two inclusion shapes are believed to set the upper and lower ranges of the overall creep strain for all inclusion shapes. Detailed comparison with a previously developed direct work-rate method is also made. While the effective stress of the ductile matrix-and therefore the overall creep strain of the composite-are higher by the direct work-rate method, the difference between the two is found to be small. However, when the Laplace inversion of the effective secant viscosities of the viscoelastic comparison composite can be cast in an explicit form, the field-fluctuation method will provide a complete evaluation of the effective stress, and is also substantially simpler than the direct work-rate method.