Zhuping Huang

A scaling law for properties of nano-structured materials

In this brief communication, we identify intrinsic length scales of several physical properties at the nano-scale and show that, for nano-structures whose characteristic sizes are much larger than these scales, the properties obey a simple scaling law. The underlying cause of the size-dependence of these properties at the nano-scale is the competition between surface and bulk energies. This law provides a yardstick for checking the accuracy of experimentally measured or numerically computed properties of nano-structured materials over a broad size range and can thus help replace repeated and exhaustive testing by one or a few tests.

Constitutive relation of particulate-reinforced viscoelastic composite materials with debonded microvoids

Abstract In this paper, the constitutive relation of particulate-reinforced viscoelastic composite materials is studied by considering the evolution of microvoids. Owing to the difference in mechanical properties between matrix and second phase particles, debonding of particle-matrix interface may occur under the condition of high stress triaxiality. This kind of damage will lead to the nucleation and growth of microvoids. The reinforcing effect due to rigid particles and the weakening effect due to microvoids caused by debonding on the overall mechanical properties of particulate-reinforced composites are investigated. Using the energy criterion of interfacial debonding, an expression for the nucleation rate of microvoids is suggested. Then, the growth of these voids is studied by means of Eshelby’s equivalent inclusion method. It is shown that the strain of the microvoids depends not only on the remote strain history but also on their nucleation time. By considering the effect of nucleation time, a new definition of an average strain of microvoids is given. According to the Mori–Tanaka scheme, a macroscopic constitutive relation of the composite material is finally derived. The results show that macroscopic strain rate, particle-size dispersity, relaxation time of matrix, and interface adhesive strength all play key roles in the overall mechanical properties of particulate-reinforced composites.

Stress fields of a spheroidal inhomogeneity with an interphase in an infinite medium under remote loadings

This paper presents the elastostatic solution of the problem of an arbitrarily oriented spheroidal inhomogeneity with an interphase embedded in an infinite medium. The latter is under a remote axisymmetric loading. The complete solution of this problem requires three fundamental solutions, which are obtained by the Papkovich–Neuber displacement potentials and the expansion formulae for spheroidal harmonics. New displacement potentials are given when the remote loading is a longitudinal shear. The influence of the orientation and aspect ratio of the inhomogeneity, and of the remote stress ratio on the stress concentrations at the interfaces and the von Mises equivalent stress in the inhomogeneity, are studied. It is found that the interphase between the inhomogeneity and the surrounding medium significantly alters the stress distribution in, and around, the inhomogeneity. In addition to the general solution for an inhomogeneity with an interphase, the stress field exterior to a spheroidal inhomogeneity without an interphase (the Eshelby problem) is presented in a simple form. It is pointed out that the solution of a spheroidal inhomogeneity with an interphase in an infinite medium subjected to an arbitrary uniform eigenstrain, or a combination of a uniform eigenstrain and an arbitrary remote mechanical loading, can be obtained using the procedure developed in this paper.

Explicit expressions for bounds for the effective moduli of multi-phased composites by the generalized self-consistent method

The weak point of the generalized self-consistent method (GSCM) is that it does not have a simple form of solution for the effective shear modulus. This is inconvenient for engineering applications. To obtain an explicit form of solution, a new three-phase configuration, i.e. embedding a composite sphere with a spherical inclusion core surrounded by the matrix shell in an infinite yet-known comparison medium instead of in an as-yet-unknown composite material, is proposed in this paper. For this new configuration, explicit forms of upper and lower bounds for GSCM estimation of the effective moduli for two-phase and three-phase composites are obtained for the first time. According to the proposed criteria the best simplified model is suggested. Comparisons with existing theoretical and experimental results demonstrate that the suggested model is sufficiently accurate to predict the effective moduli of multiphase composites. Furthermore, the present solutions can be expressed in a simple explicit form and are very convenient for applications. Moreover, the interesting difference and connection between GSCM and the Mori–Tanaka method (MTM) is revealed under a unified micromechanical framework.

Interface effect on the mechanical behaviour of rigid particle filled polymer

Glass beads, non-modified and modified separately with two different coupling agents, were incorporated in high density polyethylene to prepare composite materials with different interfacial adhesion strengths. Tensile tests show that the mechanical behaviour of the materials is sensitive to the strain rates. The strong interfacial adhesion can delay the occurrence of damage and so increase the load- bearing ability under both monotonic and cyclic loading. In situ tensile tests give damage mechanisms mainly induced by the interfacial debonding. The stronger the interfacial adhesion, the lower the number of glass beads debonded from the matrix under a given stress. The degree of microdamage defined as the percentage of debonded particles is obtained as a function of the applied load. # 2001 Society of Chemical Industry

The role of the interfacial strength in glass bead filled HDPE

The interface plays an important role not only in fiber reinforced composites, but also in particle filled ones. Therefore, much research work was carried out to study the interfacial properties. Some experimental methods were developed to measure the interfacial strength of fiber reinforced composites [1]. By contrast, little experimental work was undertaken to determine the interfacial strength of particle filled composites. The difficulty comes from the fact that the load cannot be applied directly onto the particle. While, for fiber reinforced composites, it is possible to apply the force onto the fiber such as pull-out and push-out tests. Therefore, for particle filled composites, the mechanical tests can only be carried out on bulk composites and one has to find a method to deduce the interfacial properties from the experimental results. The theoretical models were developed to describe the strength of particle reinforced composites as a function of fiber size, shape and volume fraction, etc. [2, 3]. It is well know that adding rigid particles into polymer can substantially increase the elastic modulus [4, 5]. While the effect of the particle on the strength is complex and sometimes the adverse results were obtained [6]. In this letter, in situ tensile tests were carried out under a scanning electronic microscope (SEM). The critical external stress at the moment of the interfacial debonding was measured and the interfacial bonding strength was estimated. It was found that good interfacial adhesion can increase the tensile strength of the composite materials compared to pure matrix materials. The mechanisms of the nucleation and evolution of the damage induced by the interfacial debonding were also studied. Commercial high density polyethylene (HDPE) and glass beads with an average radius of 30 μm are respectively used as the matrix material and the filler. Four groups of materials are studied. The compositions and the interfacial connections of these materials are given in Table I. It can be seen from Table I that the use of different coupling agents results in differ-

Dynamic void growth in rate-sensitive plastic solids

A dynamic void growth model in rate-sensitive plastic materials is derived. The constitutive relation of the matrix is in the overstress form proposed by Perzyna. When the rate of deformation sensitive parameter tends to zero, the Gurson model is retrieved. When the porous material element is under triaxial tension, the Carroll-Holt and Johnson models are retrieved. The normality condition of the plastic rate of deformation to the dynamic loading surface at constant equivalent rates of deformation (with the volumetric part also taken into account) is discussed, and it is shown that the normality rule no longer exists in general. Finally, an approximate expression of the dynamic loading surface that may be convenient for engineering applications is suggested.

Surface Energy Effect on Damage Evolution in a Viscoelastic Nanocomposite

In this article, the surface energy effect on damage evolution in a linear viscoelastic material filled with second phase nano-particles is studied. Because of the difference in mechanical properties between the matrix material and second phase particles, the progressive debonding of particle—matrix interface may occur under high stress triaxiality, and hence the damage evolution may be described by the nucleation and growth of these debonded voids. In order to study the surface energy effect on this kind of damage evolution, an energy criterion of interfacial debonding under spherically symmetrical loading is proposed, and an expression of the growth of debonded voids in a viscoelastic matrix material is derived, in which the effect of surface tension is also taken into account. Thus, a macroscopic constitutive model of the considered nanocomposite is presented. It is shown that the overall mechanical properties of such a nanocomposite are size dependent, due to the existence of the surface/interface energy effect.

Nonlinear Mechanics of Solids Containing Isolated Voids

The ductile fracture of many materials is related to the nucleation, growth, and coalescence of voids. Also, a material containing voids represents an extreme case of heterogeneous materials. In the last few decades, numerous studies have been devoted to the local deformation mechanisms and macroscopic overall properties of nonlinear materials containing voids. This article presents a critical review of the studies in three interconnected topics in nonlinear mechanics of materials containing isolated voids, namely, the growth of an isolated void in an infinite medium under a remote stress; the macroscopic mechanical behavior of these materials predicted by using a cell model; and bounds and estimates of the overall properties of these materials as a special case of nonlinear composite materials. Emphasis are placed upon analytical and semianalytical approaches for static loading conditions. Both the classical methods and more recent approaches are examined, and some inadequacies in the existing methods are pointed out. In addition to the critical review of the existing methods and results, some new results, including a power-law stress potential for compressible nonlinear materials, are presented and integrated into the pertinent theoretical frameworks. This review article contains 118 references.

The damage evaluation of rigid particle filled polymer

In this paper, the rigid particle filled polymer is studied in the hope to understand the real damage mechanisms. Two damage parameters were introduced and measured. One is the macro-damage of the materials calculated from the modulus measured, another is micro-damage describing the interfacial debonding or the percentage of the particle debonded from the matrix. The damage rate of the macro damage decreases, while the micro damage increases with the applied stress.