Stress transfer between fibrillated polyalkene films and cement matrices

Experimental results indicate that the ‘average bond’ strength between polyalkenes and cement increases with increasing film volume fraction. It is suggested that this dynamic transfer of stress from fibril to matrix is achieved because of the misfit between fibril and matrix resulting from the non-uniform cross-section of the fibrils. This mechanism is equally applicable to both fibrillated films and monofilaments.     

Some results on crack propagation in media with spatially varying elastic moduli

Energy release rates are calculated for cracks propagating in media with spatially varying elastic moduli, this variation being in a direction perpendicular to the crack growth direction. Results are given for transient problems of semi-infinite cracks in infinite media for certain special forms of the variation in shear modulus. Steady state crack propagation in a displacement loaded strip is also considered and it is shown by the use of a certain path independent integral that a simple formula for the energy release rate can be obtained for quite general variations in clastic moduli provided these variations are in a direction perpendicular to the crack. Other path independent integrals are derived which may be of use for transient crack tip stress analysis in strips in a similar way to that used in [4] for the homogeneous elastic problem.     

Calculating the elastic moduli of steel-fiber reinforced concrete using a dedicated empirical formula

The equivalent inclusion method (EIM) is adopted to study the characteristics of the equivalent material properties of steel-fiber reinforced concrete as a function of the volume fraction and the length to diameter ratio of the fibers. It is found that the equivalent material moduli of concrete reinforce with randomly orientated and distributed fibers are insensitive to the length to diameter ratio of the steel fibers. A set of empirical formulae is then proposed for the purposes of engineering applications. The proposed empirical model can simplify the calculation of the equivalent material moduli. Verifications of the proposed empirical formulae with the EIM model and with experimental data are performed with two examples. The first is a compression test. The second is 4 point bending test. The empirical formulae, based on the equivalent inclusion method proposed in this study, represent an alternative means of quickly calculating the effective elastic modulus of steel-fiber reinforced concrete materials.     

A buckling-based metrology for measuring the elastic moduli of polymeric thin films

As technology continues towards smaller, thinner and lighter devices, more stringent demands are placed on thin polymer films as diffusion barriers, dielectric coatings, electronic packaging and so on. Therefore, there is a growing need for testing platforms to rapidly determine the mechanical properties of thin polymer films and coatings. We introduce here an elegant, efficient measurement method that yields the elastic moduli of nanoscale polymer films in a rapid and quantitative manner without the need for expensive equipment or material-specific modelling. The technique exploits a buckling instability that occurs in bilayers consisting of a stiff, thin film coated onto a relatively soft, thick substrate. Using the spacing of these highly periodic wrinkles, we calculate the film's elastic modulus by applying well-established buckling mechanics. We successfully apply this new measurement platform to several systems displaying a wide range of thicknessess (nanometre to micrometre) and moduli (MPa to GPa).     

Quasi-static and dynamic mechanical elastic moduli of alkaline aged pultruded fibre reinforced polymer composite rebar

Due to the increased use of glass fibre reinforced polymer composite (GFRP) rebar in concrete structures, the durability performance of GFRP rebar has been an important research topic in recent years. This paper presents elastic modulus of alkaline environment (pH ≈ 13) aged pultruded GFRP rebar as evaluated by three different methods, namely, quasi-static tensile, quasi-static flexural and dynamic mechanical thermal tests. It was found that elastic modulus of the GFRP rebar samples did not change significantly due to exposure in alkaline environment at 60 °C for 1, 2, 3, 4, 6 and 14 months when compared with that of control sample. Elastic modulus was found to be in the range of 52.5–56.5 GPa irrespective to testing methods and ageing time. In addition, it was estimated from the long time projected results that quasi-static tensile, quasi-static flexural and dynamic mechanical moduli will be retained by about 93%, 95% and 85%, respectively, after 100 years in alkaline environment at 60 °C. Microscopic analysis indicated that quasi-static tensile and flexural failure was mainly due to matrix cracking and shear failure of fibre/matrix interface.     

Prediction of elastic moduli of solids with oriented porosity

There have been no simple equations available to predict the effects of arbitrarily shaped voids over the entire range of porosity encountered in real materials. Empirical expressions have been proposed, but they agree neither with appropriate theoretical analyses nor with extensive experimental data. Theoretical predictions have been linear in porosity and thus predict an insufficient reduction. Only a few analyses account for void shapes other than spherical. The present work represents a semi-empirical approach to fill these information deficiences.     

Effective elastic moduli of syntactic foams

An analytical approach to compute the effective elastic moduli of syntactic foams is presented. Using the concentric spherical model, the effective elastic constants are estimated, and compared with other theories and experimental data. The computed effective elastic moduli are within the lower and upper bounds, and agree with the experimental data.     

Porosity dependence of material elastic moduli

A new equationE =E ₀(1+aP+bP ²)/(1+cP), whereE andE ₀ are Young's moduli at porosityP and zero, respectively, anda, b, c are constants, has been derived. Our theoretical derivation is based on the dependence of sound velocity on the Young's modulus of the material.     

Determining elastic moduli of tungsten nanowires

The elastic properties of tungsten nanowires (NWs) grown by the carbothermal reduction of nickel tungstate (NiWO₄) have been studied using atomic force microscopy (AFM). Based on the AFM data, the elastic moduli of NWs with various dimensions have been calculated. It is concluded that the elastic properties of tungsten NWs are determined by grain boundaries.     

The elastic moduli of tellurite glasses

The elastic moduli of two tellurite glasses have been measured as functions of both temperature and pressure. The results indicate that these glasses are normal in their behaviour and this contrasts with the anomalous behaviour of silica-based glasses. The coordination number seems to be the parameter which decides the elastic characteristics of glasses.     

Effective elastic moduli of porous solids

The principles of continuum mechanics can be extended to porous solids only if the effective moduli are known. Although the effective bulk modulus has already been determined by approximating the geometry of a porous solid to be a hollow sphere, bounds could only be established for the other moduli. This problem of indeterminacy of the moduli is solved in this study using a particular model from the variation of the effective Poisson's ratio. In addition to this, the results are extended for the hollow sphere to real geometry by introducing a porositydependent factor. These results are compared with experimental data and the agreement is found to be good. As the effective Poisson's ratio cannot be determined accurately using experiments, the derived equation is verified using finite element analysis.     

Connection between elastic moduli and thermal conductivities of anisotropic short fiber reinforced thermoplastics: theory and experimental verification

Cross-property connections for two phase composites derived recently by the authors are specified for short fiber reinforced thermoplastics. They are verified by comparison with experimental data on glass fiber reinforced composites available in literature. The comparison demonstrates a good agreement for the entire set of nine orthotropic constants with the exception of C₃₃. The results make it possible to estimate anisotropic elastic constants from the conductivity measurements.     

Multi-scale modelling of elastic moduli of trabecular bone

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results.     

Distributions of elastic moduli in mechanically percolating composites

Power-law percolation models contain very little mechanics other than the theoretical or simulated value of a percolation threshold, the volume fraction where a connected microstructure forms. For mechanical percolation these theoretical values do not correspond well to experimental results and so the models are commonly used empirically; results are correlative rather than predictive. In recent work, the effective elastic properties of a model polymer nanocomposite were approximated using a computational micromechanics model within a Monte Carlo framework. Significantly, the statistical averages resulting from these simulations displayed distinct percolation-like behavior. Of equal interest is the distribution of properties that resulted from the randomly simulated microstructures. This strongly suggests that mechanical percolation in nanocomposites is the result of a combination of microstructural mechanisms. Analysis aimed at determining which microstructure produces what response is a challenging task if microstructure is the random variable. In this work, the effective composite properties are considered as the random variable; probability distribution functions (PDFs) of the properties at discrete volume fractions are developed using the Principle of Maximum Informational Entropy. The evolution of these PDFs with increasing volume fraction helps visualize and track the significant property changes that result from microstructural randomness.     

Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions

A higher-order micromechanical framework is presented to predict the overall elastic deformation behavior of continuous fiber-reinforced composites with high-volume fractions and random-fiber distributions. By taking advantage of the probabilistic pair-wise near-field interaction solution, the interacting eigenstrain is analytically derived. Subsequently, by making use of the Eshelby equivalence principle, the perturbed strain within a continuous circular fiber is accounted for. Further, based on the general micromechanical field equations, effective elastic moduli of continuous fiber-reinforced composites are constructed. An advantage of the present framework is that the higher-order effective elastic moduli of composites can be analytically predicted with relative simplicity, requiring only material properties of the matrix and fibers, the fiber?Cvolume fraction and the microstructural parameter ??. Moreover, no Monte Carlo simulation is needed for the proposed methodology. A series of comparisons between the analytical predictions and the available experimental data for isotropic and anisotropic fiber reinforced composites illustrate the predictive capability of the proposed framework.     

Effective elastic moduli of two-phase transversely isotropic composites with aligned clustered fibers

Summary In this paper, we address the issue of the effective elastic moduli of transversely isotropic composites reinforced with aligned clustered continuous fibers. Clustering implies that there are portions of the matrix with a dense reinforcement of fibers and other portions with a sparse reinforcement. The clustering effect is characterized by a probability density distribution in local fiber volume fractions, obtained from the Dirichlet tessellation of a microstructure. Using a combination of Christensen and Lo's solution of a 3-phase boundary value problem and Hill's self-consistent method, the effective moduli are derived in terms of the probability density distribution function. It is shown that a unimodal distribution (representative of a random microstructure) has a modest effect on the effective moduli whereas a bimodal distribution (representative of a clustered microstructure) has a significant effect over a wide range of inclusion/matrix properties. A parametric study demonstrates that clustering has a significant effect on the shear moduli and the plane strain bulk modulus of the transversely isotropic composite and has a negligible effect on the longitudinal Young's modulus and the major Poisson's ratio. The theory has been compared with the Hashin-Rosen [1] bounds (appropriately modified for the clustered microstructure) and the classical Hashin-Shtrikman [2] bounds, and the theoretical predictions have been found to be bracketed by both bounds. In addition, the plane strain bulk modulus of a sample clustered periodic microstructure is computed by the developed theory and also by the finite element analysis, and the modulus computed by both approaches demonstrates a sensitivity to clustering.     

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.