Pseudo-percolation: Critical volume fractions and mechanical percolation in polymer nanocomposites

Polymer nanocomposites offer a basis for the design and manufacture composite materials with greatly enhanced properties at relatively low volume fractions of the included phase. One underlying mechanism, thought to contribute to these properties is the presence of an interfacial region, ∼15 nm thick, between the polymer matrix and included particles. The size of the interface makes relatively little contribution to the effective properties of composites with micro-sized particles but, because its thickness is comparable to the size of the nanoscaled included phase, its potential impact within nanocomposites is much greater. In particular, percolated nano-microstructures may result at volume fractions below theoretical thresholds, due to connectivity achieved through rod-interface-rod, or ‘pseudo-percolation’, contact. In this work the influence of the interface layer is incorporated into estimates of critical volume fraction through an excluded volume model. Results show a significant reduction in the range of critical volume fractions. These values are incorporated into a mean-field micromechanics model to illustrate mechanical percolation through changes in predicted effective elastic composite properties.     

An enhanced FEM model for particle size dependent flow strengthening and interface damage in particle reinforced metal matrix composites

By incorporating the dislocation punched zone model, the Taylor-based nonlocal theory of plasticity, and the cohesive zone model into the axisymmetric unit cell model, an enhanced FEM model is proposed in this paper to investigate the particle size dependent flow strengthening and interface damage in the particle reinforced metal matrix composites. The dislocation punched zone around a particle in the composite matrix is defined to consider the effect of geometrically necessary dislocations developed through a mismatch in the coefficients of the thermal expansion. The Taylor-based nonlocal theory of plasticity is applied to account for the effect of plastic strain gradient which produces geometrically necessary dislocations due to the geometrical mismatch between the matrix and the particle. The cohesive zone model is used to consider the effect of interfacial debonding. Lloyd’s experimental data are used to verify this enhanced FEM model. In order to demonstrate flow strengthening mechanisms of the present model, we present the computational results of other different models and evaluate the strengthening effects of those models by comparison. Finally, the limitations of present model are pointed out for further development.     

Coefficients of thermal expansion for single crystal piezoelectric fiber composites

Piezoelectric fiber composites were developed to overcome drawbacks of typical monolithic piezoceramic (PZT) actuators. Although piezoelectric fiber composites had many improvements over the monolithic PZT, there are still improvements. Thus, the single crystal piezoelectric fiber composite actuator is proposed. Single crystal piezoelectric materials such as PMN-PT have larger piezoelectric strain constants, higher bandwidth and higher energy density than polycrystalline counterparts. Piezoelectric fiber composites can improve the performance of various structures, and can be subject to wide temperature range where the thermoelastic behavior is important. Therefore, this paper studies the coefficients of thermal expansion (CTE) for single crystal piezoelectric fiber composites. The Macro Fiber Composite (MFC) as the piezoelectric fiber composite is considered. To calculate the effective properties of two orthotropic layers of the MFC, PMN-PT(or PZT)/epoxy and copper/epoxy layers, the rule of mixture is adopted. With the effective properties known for each layers, the two CTE of the MFC actuator are obtained from the classical lamination theory considering thermal effects. The difference of the CTE between the single crystal MFC and the standard MFC is studied.     

Estimation of thermal conductivity for polypropylene/hollow glass bead composites

The thermal conductivity of hollow glass bead (HGB)-filled polypropylene (PP) composites was estimated using the thermal conductivity equation of inorganic hollow microsphere-filled polymer composites published in the previous paper. The estimations were compared with the measured data of the PP composites filled with two kinds of HGB with different size (the mean diameter was respectively 35 μm and 70 μm). The results showed that the predictions of the thermal conductivity were in good agreement with the measured data except to individual data points. Furthermore, both the estimated and measured thermal conductivity decreased roughly linearly with increasing the HGB volume fraction when the HGB volume fraction was less than 20%; the influence of the particle diameter on the thermal conductivity was insignificant.     

In-plane thermal enhancement behaviors of Al matrix composites with oriented graphite flake alignment

Oriented graphite flakes (G_f)/Si/Al composites were fabricated to study their thermal enhancement behaviors. The in-plane thermal conductivity (TC) of the composites increases with the increase of G_f volume fraction. At a given volume fraction, a larger G_f size can achieve a higher in-plane TC of the composites. Microstructural characterization revealed a clean and Al₄C₃-free interface between the side surface of G_f and the Al matrix. Based on the observed microstructures, an analytical model was presented to predict the in-plane TC of the composites with oriented G_f alignment by incorporating interfacial thermal resistance within the framework of effective medium approach (EMA). Comparisons of the present model predictions with the experimental data of the as-fabricated G_f/Si/Al and previously reported G_f/Al and G_f/polymer (polyvinyl butyral, PVB) composites show good agreement. The results indicate that our model can well predict the in-plane thermal enhancement behaviors of the composites at different effective phase contrasts (i.e. the ratio between effective TC of the G_f and TC of the matrix).     

Effect of interface debonding on the thermal conductivity of microencapsulated-paraffin filled epoxy matrix composites

Microcapsules containing phase change materials (microPCMs) can be filled in polymeric matrix forming smart temperature-controlling composites. The aim of this study was to investigate the effect of interface debonding on the thermal conductivity of microPCMs containing paraffin/epoxy composites. The shell thickness and average size of microPCMs were controlled by regulating the core/shell ratios and emulsion stirring rates. Test results indicated that the thermal conductivity (K_e) of all composites decreased after a thermal shock treatment. SEM and thermography measurements were applied to observe the interface behaviors of composites after a violent thermal treatment process. It was proved that the interface debonding was generated because of the mismatch of expansion coefficient between shell and epoxy. A modeling analysis of the relative thermal conductivity (K_r) indicated that the effective approach to decrease the debonding is to enhance the molecule tangling degree between shell and matrix.     

Thermoreversible and remendable glass-polymer interface for fiber-reinforced composites

Adhesion of the reinforcement to the polymer matrix is essential for load transfer from the polymer matrix to the reinforcement material in fiber-reinforced composites. The reversible Diels-Alder reaction between a furan-functionalized epoxy-amine thermosetting matrix with a maleimide-functionalized glass fiber was used to impart remendability at the polymer-glass interface for potential application in glass fiber-reinforced composites. At room temperature the Diels-Alder adduct is formed spontaneously and above 90 °C the adduct breaks apart to reform the original furan and maleimide moieties. Healing of the interface was investigated with single fiber microdroplet pull-out testing. Following complete failure of this interface, significant healing was observed, with some specimens recovering over 100% of the initial properties. Healing efficiency was not affected by the distance of displacement, with an overall average of 41% healing efficiency. Up to five healing cycles were successfully achieved. It is expected that a glass fiber-reinforced composite of maleimide-sized glass within a furan-functionalized network will demonstrate extension of fatigue life.     

Effect of coating on the microstructure and thermal conductivities of diamond-Cu composites prepared by powder metallurgy

Diamond-Cu composites from the direct combination of diamond and Cu show low thermal conductivities due to weak interface and high thermal resistance as a result of chemical incompatibility. In this paper, a new method is proposed to strengthen interfacial binding between diamond and Cu by coating strong carbide-forming elements, e.g., Ti or Cr on the surface of the diamond through vacuum micro-deposition. Interfacial thermal resistance of diamond-Cu composites is greatly decreased when diamond particles are coated by a Cr or Ti layer of a certain thickness before combining with Cu. Thermal conductivity is also increased several times. Cr coating can reduce more effectively interface thermal resistance between diamond and Cu than Ti coating. Moreover, it has a smaller negative impact on the thermal conductivity of the Cu matrix, resulting in higher thermal conductivity of Cr-coated diamond-Cu composites. Through the vacuum micro-deposition technology, Cr on the diamond particle surface is present in the form Cr₇C₃ near diamond and a pure Cr outer layer at 2:1. The optimum thickness is within 0.6-0.9 μm; at this depth, the thermal conductivities of 70 vol% diamond-Cu composites can be increased four times and reach as high as 657 W/m K. In this work, an original theoretical model is proposed to estimate the thermal conductivities of composite materials with an interlayer of a certain thickness. The predicted values from this model are in good agreement with the experimental values.     

Predicting the thermal conductivity of composite materials with imperfect interfaces

This paper compares the predicted values of the thermal conductivity of a composite made using the equivalent inclusion method (EIM) and the finite element method (FEM) using representative volume elements. The effects of inclusion anisotropy, inclusion orientation distribution, thermal interface conductance, h, and inclusion dimensions have been considered. Both methods predict similar overall behaviour, whereby at high h values, the effective thermal conductivity of the composite is limited by the inclusion anisotropy, while at lower h values, the effect of anisotropy is greatly diminished due to the more dominant effect of limited heat flow across the inclusion/matrix interface. The simulation results are then used to understand why in those cases where it has been possible to produce CNF reinforced Cu matrix composites with a large volume fraction of well dispersed CNFs, the measured thermal properties of the composite have failed to meet the expectations in terms of thermal conductivity, with measured conductivities in the range 200–300 W/m K. The simulation results show that, although degradation of the thermal properties of the CNFs and a poor interfacial thermal conductance are very likely the reasons behind the low conductivities reported, great care should be taken when measuring the thermal conductivity of this new class of materials, to avoid misleading results due to anisotropic effects.     

Multivariable dependency of thermal shrinkage in highly aligned polypropylene tapes for self-reinforced polymer composites

Self-reinforced composites offer a unique combination of properties such as high specific strength, high impact resistance, and recyclability by incorporating highly aligned fibers within a random matrix of the same polymer. However, high temperatures will shrink the system to recover randomness in the aligned segments, compromising the composite thermal stability during processing as self-reinforced tapes are consolidated into the final composite through heating and pressure. Hence, the dynamic nonlinear multivariable (i.e., time, temperature, stress) shrinkage exhibited by self-reinforced polypropylene (SRPP) tapes was measured and modeled at the maximum shrinkage limit achieved in the proximity of the composite processing temperature [∼140 to160 °C]. At high stress (∼7.5 MPa) the thermal shrinkage of the SRPP tapes was reduced and a parallel creep mechanism was activated. The modeling, and prediction of the main factors governing the thermal shrinkage expand and diversify the dynamic design window for new SRPP composites.     

Mechanical and thermal properties of chicken feather fiber/PLA green composites

Chicken feather fiber (CFF)/reinforced poly(lactic acid) (PLA) composites were processed using a twin-screw extruder and an injection molder. The tensile moduli of CFF/PLA composites with different CFF content (2, 5, 8 and 10 wt%) were found to be higher than that of pure PLA, and a maximum value of 4.2 GPa (16%↑) was attained with 5 wt% of CFF without causing any substantial weight increment. The morphology, evaluated by scanning electron microscopy (SEM), indicated that an uniform dispersion of CFF in the PLA matrix existed. The mechanical and thermal properties of pure PLA and CFF/PLA composites were compared using dynamic mechanical analysis (DMA), thermomechanical analysis (TMA) and thermogravimetric analysis (TGA). DMA results revealed that the storage modulus of the composites increased with respect to the pure polymer, whereas the mechanical loss factor (tan δ) decreased. The results of TGA experiments indicated that the addition of CFF enhanced the thermal stability of the composites as compared to pure PLA. The outcome obtained from this study is believed to assist the development of environmentally-friendly composites from biodegradable polymers, especially for converting agricultural waste – chicken feather into useful products.     

On the Lewis–Nielsen model for thermal/electrical conductivity of composites

Several models have been proposed in the literature to describe the thermal and electrical conductivities of particulate composites. Among the proposed models, the Lewis–Nielsen model appears quite attractive as it is simple to use and it predicts the correct behavior when filler concentration () approaches the maximum packing concentration (_m). In this paper, the Lewis–Nielsen model is evaluated in light of a vast amount of experimental data available on thermal and electrical conductivities of particulate composites. The Lewis–Nielsen model is found to describe the experimental data for both thermal and electrical conductivities reasonably well.     

Modeling of the thermal conductivity and thermomechanical behavior of diamond reinforced composites

Semi-analytical Mori-Tanaka methods and numerical models for studying the overall thermal conduction behavior of metal matrix composites reinforced by diamond particles are presented, special emphasis being put on the effects of finite interfacial conductances. Good agreement between the simulation approaches is obtained and the influence of particle shapes and homogeneous vs. inhomogeneous interfacial conductances on local and global responses is studied. Analogous methods are applied to modeling the elastic and thermoelastoplastic behavior of diamond reinforced metals.     

Multiscale progressive failure analysis of textile composites

The experimental determination of stiffness and strength of textile composites is expensive and time-consuming. Experimental tests are only capable of delivering properties of a whole textile layer, because a decomposition is not possible. However, a textile layer, consisting of several fiber directions, has the drawback that it is likely to exhibit anisotropic material behavior. In the presented paper a finite element multiscale analysis is proposed that is able to predict material behavior of textile composites via virtual tests, solely from the (nonlinear) material behavior of epoxy resin and glass fibers, as well as the textile fiber architecture. With these virtual tests it is possible to make predictions for a single layer within a textile preform or for multiple textile layers at once. The nonlinear and pressure-dependent behavior of the materials covered in the multiscale analysis is modeled with novel material models developed for this purpose. In order to avoid mesh-dependent solutions in the finite-element simulations, regularization techniques are applied. The simulations are compared to experimental test results.     

The influence of interface and thermal conductivity of filler on the nonisothermal crystallization kinetics of polypropylene/natural protein fiber composites

The nonisothermal crystallization kinetics of polypropylene/down feather fiber composites were investigated using a Differential Scanning Calorimeter at five different cooling rates. The Avrami and Liu models were able to satisfactorily describe the crystallization behavior of composites, which indicated the entirely unique mechanism. It was found that fiber/matrix interface and thermal conductivity of fiber had key roles for the crystallization behavior of composites and had a close relationship with the properties of the industrial product reinforced with natural protein fiber. The nucleation activity and activation energies were also calculated by different theoretical models and also proved the experimental results.     

Effect of tungsten addition on thermal conductivity of graphite/copper composites

Graphite/copper composites with high thermal conductivity were fabricated by tungsten addition, which formed a thin tungsten carbide layer at the interface. The microstructure and thermal conductivity of the composite material were studied. The results indicated that the insertion of tungsten carbide layer obviously suppressed spheroidization of copper coating on the graphite particles during the sintering process, and decreased the interfacial thermal resistance of the composites. Compared with the graphite/copper composites without tungsten, the thermal conductivity of the obtained composites was increased by 43.6%.     

Gradient of nanomechanical properties in the interphase of cellulose nanocrystal composites

The nanoscale transitional zone between a nanofiber and surrounding matrix (interphase) defines the ultimate mechanical characteristics in nanocomposite systems. In spite of this importance, one can hardly find quantitative data on the mechanical properties of this transitional zone in the cellulose–nanofiber composites. In addition, most of the theoretical models to predict the mechanical properties of interphase are developed with the assumption that this transitional zone is independent of the nanofiber size. In the current study, we show that the mechanical properties of interphase in cellulose nanocrystal (CNC) composites can be quantitatively characterized and the correlation with the size of CNCs can be mapped. The peak force tapping mode in atomic force microscope (AFM) was used to characterize deformation, adhesion, and modulus gradient of the interphase region in poly(vinyl alcohol) (PVA)–poly(acrylic acid) (PAA)–cellulose nanocrystal (CNC) composites. In comparison to the polymer matrix, the adhesion force of CNC was lower. The average elastic modulus in the interphase varied from 12.8 GPa at the interface of CNC to 9.9 GPa in PVA–PAA matrix. It was observed that the existence of PAA increased the gradient of mechanical and adhesion properties of the interphase zone. This occurs due to the variation in the ester linkage density from the CNC interface to the polymer matrix. Finally, it is shown that interphase thickness is higher for CNCs with larger diameter.     

Bounds on effective magnetic permeability of three-phase composites with coated spherical inclusions

An effective model is developed to bound the effective magnetic permeability of three-phase composites with coated spherical inclusions. In the present model, the trial magnetic potential for the upper bound and the trial magnetic induction field for the lower bound are constructed to satisfy continuity interface conditions. According to the variational principle, the upper and lower bounds on the effective magnetic permeability of three-phase composites with coated spherical inclusions are derived. In this paper, trial magnetic potentials with different function forms are taken and the optimal upper bound is obtained for the trail magnetic potential corresponding to the third-order function. When the three-phase model degenerates into the composite spheres assemblage model [1], it is interesting that the optimal upper and lower bounds are the same. The effects of the volume fraction of coated spherical inclusions and the thickness and magnetic permeability of coated layers between the matrix and spherical inclusions on the effective magnetic permeability of composites are analyzed. The upper and lower bounds are finite non-zero values when the magnetic permeability of spherical inclusions tends to ∞$\infty$ and 0, respectively.     

Statistical continuum theory for the effective conductivity of fiber filled polymer composites: Effect of orientation distribution and aspect ratio

Effective conductivity of polymer composites, filled with conducting fibers such as carbon nanotubes, is studied using statistical continuum theory. The fiber orientation distribution in the matrix plays a very important role on their effective properties. To take into account their orientation, shape and distribution, two-point and three-point probability distribution functions are used. The effect of fibers orientation is illustrated by comparing the effective conductivity of microstructures with oriented and non-oriented fibers. The randomly oriented fibers result in an isotropic effective conductivity. The increased fiber orientation distribution can lead to higher anisotropy in conductivity. The effect of fiber’s aspect ratio on the effective conductivity is studied by comparing microstructures with varying degrees of fiber orientation distribution. Results show that the increase in anisotropy leads to higher conductivity in the maximum fiber orientation distribution direction and lower conductivity in the transverse direction. These results are in agreement with various models from the literature that show the increase of the aspect ratio of fibers improves the electrical and thermal conductivity.     

Meshfree modeling and homogenization of 3D orthogonal woven composites

In this paper, evaluation of 3D orthogonal woven fabric composite elastic moduli is achieved by applying meshfree methods on the micromechanical model of the woven composites. A new, realistic and smooth fabric unit cell model of 3D orthogonal woven composite is presented. As an alternative to finite element method, meshfree methods show a notable advantage, which is the simplicity in meshing while modeling the matrix and different yarns. Radial basis function and moving kriging interpolation are used for the shape function constructions. The Galerkin method is employed in formulating the discretized system equations. The numerical results are compared with the finite element and the experimental results.