Rule Of Mixing Research Articles

Study of hygrothermal environment impact on the vibration behavior of thick nanocomposite beams reinforced with multilayer Graphene Nanoplatelet

This paper aims to investigate the free vibration of a multilayer piezo-electric beam strengthened with functionally graded graphene platelets (FG-GPLRC) and subjected to a consistent increase in temperature and humid external loads. Graphene platelets (GPLs) are supposed to be dispersed either uniformly or layerwise form in the polymeric matrix, with a variety of patterns configurations taken into consideration. The rule of mixing is employed to evaluate Poisson's ratio and mass density features. In order to estimate the efficient Young's modulus, the modifier Halpin-Tsai model has been employed. The whole system of governing equations for motion were achieved by exploiting Hamilton’s concept based on Timoshenko beam theory (TBT). After that, these equations were solved using the Navier analytical solution-based Fourier series with high accuracy. Next, to examine the effects of several elements, including graphene weight percentage and their distribution shape, length by thickness ratio, externally provided thermal-humidity fields, on the dynamic of nanocomposite reinforced beams.

Effect of Porosity and Gradient Parameters on Compressive Mechanical Properties of Sheet Gyroid Gradient Porous Structures and Construction of Mechanical Properties Prediction Model

A series of uniform porous structures and radial stepwise and radial linear gradient structures are designed based on sheet‐gyroid to explore the influence mechanism of porosity and gradient parameters on forming quality and compressive mechanical properties. On this basis, mathematical models for predicting mechanical properties of porous structures based on uniform, discrete gradient, and linear gradient porosity distribution are established. The volume fraction deviation of uniform porous structures increases gradually with the increase of porosity. The relative density of porous structures ranges from 96.78 to 98.79%. The influence of porosity on compressive mechanical properties is investigated, and a prediction model of the equivalent elastic modulus and yield strength of porous structures is constructed based on the generalized G‐A model. The elastic modulus of the radial stepwise gradient porous structures is predicted by combining the rule of mixing. The deviation between the predicted results and the experimental results ranges from 0.21 to 2.61%. At the same time, a prediction model of the compressive mechanical properties of the radial linear gradient porous structure is constructed, and it is found that the predicted value is somewhat different from the experimental value, which is related to the synergistic strengthening effect of the gradient porous structure.

Theoretical analysis of perturbative high harmonic wave mixing from plasma surfaces

High harmonic generation modulated by a weakly perturbing laser field enables new wave mixing frequency components, thus allowing in-situ spatiotemporal measurements and wavefront control of attosecond optical pulses. However, perturbative high harmonic wave mixing from plasma surfaces has not been investigated extensively. In this study, we theoretically analyze the plasma high harmonic generation process in the relativistic regime modulated by a perturbing laser field with an arbitrary frequency. New wave mixing frequency components satisfying the conservation laws of photon energy and momentum are observed. The wave mixing component intensities adhere to a power law for the perturbating laser photon number as the perturbing laser intensity increases, thereby revealing perturbative behaviors in the nonperturbative, extremely nonlinear optical process of high harmonic generation. Detailed studies reveal the polarization selection rule and physical mechanism of high harmonic wave mixing. The modulation of the relativistic factor or mass enhancement of electrons on the plasma surface by the perturbing laser field is believed to result in high harmonic wave mixing in the relativistic regime.

Tensile Failure Behaviors and Theories of Carbon/Glass Hybrid Interlayer and Intralayer Composites

Hybrid composites combine various types of fiber that not only provide an effective method to minimize material costs but also enhance the mechanical properties of composites. The tensile fracture behaviors of hybrid composites are more complex than single-fiber composites due to various reinforcing fibers and hybrid effects, and the relationship between tensile behaviors and hybrid structures is not clear. In this paper, various structures of C/G (carbon/glass) interlayer and intralayer hybrid composites were designed, and tensile behaviors were investigated; it revealed that tensile failure is characterized by the synergistic effect and failure acceleration effect. Second, the tensile properties of interlayer and intralayer hybrid composites with various hybrid ratios and stacking structures were systematically analyzed; our results demonstrated that the tensile strength of interlayer and intralayer hybrid composites was predominantly impacted by the hybrid ratio of C/G and increased with the increase in carbon fiber content. For interlayer hybrid composites, with the assistance of the synergistic effect, excellent tensile strength could be obtained for the glass fiber sandwiched carbon fiber structure. For intralayer hybrid composites, the tensile strength was small, while the dispersion degree was high. We compared the tensile properties with theoretically calculated values based on the rule of mixing (ROM) and revealed that the tensile modulus and strength of interlayer and intralayer hybrid composites exhibited a positive hybrid effect. This work serves as a foundation for the structural optimization and potential applications of C/G non-crimp hybrid composites.

Influence of interphase characteristics on the elastic modulus of unidirectional glass-reinforced epoxy composites: a computational micromechanics study

Abstract This article briefly discusses the role of interphase in the elastic moduli of unidirectional fiber-reinforced polymer composite materials. For this unidirectional glass fiber was chosen as reinforcement, and epoxy was selected as the matrix. A hexagonally packed representative volume element is used for the micromechanical analysis. Experimental validation was initially used to verify the accuracy of the established equations of the rule of mixing, Composite Cylinder Assemblage, Chamis, Halpin and Tsai, and Puck. The Chamis equation was found to be the most reasonable. Then the finite element approach in which interphase has been included was used to estimate the elastic moduli. The finite element model without interphase and the experimental result were taken as a reference. The influence of interface ratio and property of interphase on the homogenised elastic properties of the unidirectional fiber-reinforced polymer composites is analysed. A micromechanics plugin in Abaqus software was used to estimate the density and Young’s modulus of the unidirectional fiber-reinforced polymer composites. The interphase properties are varied, having 6.25%, 12.5%, 25% and 50% influence of the fiber phase and the remaining influence of the matrix phase with interface ratios of 0.1, 0.2 and 0.3. The interface ratio of 0.3, having 6.25% fiber phase influence, gave the most reasonable moduli values (with an error <10%) compared to the mean experimental moduli. The study showed interface ratio and interphase properties to critically influence the overall elastic property of the unidirectional fiber-reinforced polymer composites.

Viewing high entropy alloys through glasses: Linkages between solid solution and glass phases in multicomponent alloys

High entropy alloys (HEAs) represent highly promising multicomponent crystals that form concentrated solid solutions (CSSs) and may violate traditional thermodynamic rules of mixing, ultimately leading to excellent physical properties. For a deeper understanding, we investigate seven CSSs, including Co-Cr-Ni-Fe-Mn elements, at experimentally relevant compositions and conditions, through molecular simulations, and we use 1-1 comparisons to corresponding glass state characteristics, attained through rapid cooling protocols. We determine the behavior of various structural features, including the configurational entropy for a set of CSSs in their crystalline and vitreous states numerically. We employ swap Monte Carlo (MC) simulations, in combination with the reversible scaling method, to efficiently compute the configurational entropy (${S}_{\text{conf}}$), and show that the entropic rule of mixing is not always adequate for predicting alloy formation. We study the stability and formability of crystalline solid solutions, as well as glasses, while following the thermodynamics of ${S}_{\text{conf}}$. An apparent entropic similarity between CSSs and corresponding glasses leads us to use a Kauzmann-like ansatz, relating the CSSs at ${S}_{\text{conf}}\ensuremath{\rightarrow}0$ with the emergence of a CSS order-disorder transition, at temperature ${T}_{OD}$. In the context of glasses, a comparison between kinetic and thermodynamic fragilities allows the association of sluggish diffusion onset to a drop in ${S}_{\text{conf}}$ at ${T}_{K}$. Analogously, we classify CSSs as ``strong'' or ``fragile'' in the sense of their ability to migrate across CSS crystal configurations at high temperatures, distinguishing its formability. We argue that the magnitude of ${T}_{OD}$ may be an excellent predictor of CSS single-phase stability, which appears to scale with well-known HEA predictors, in particular we notice that VEC and ${T}_{OD}$ have in relation to the others a significantly large Pearson correlation coefficient, much larger than most other observables (except $\mathrm{\ensuremath{\Delta}}{H}_{\text{mix}}$).

Molecular Insight into 6FD Polyimide-Branched Poly(phenylene) Copolymers: Synthesis, Block Compatibility, and Gas Transport Study

A series of 6FDA-DABA (6FD) polyimide and branched poly(phenylene) (PP) block copolymers and homopolymers were successfully synthesized using Diels–Alder and polycondensation reactions. PP and 6FD homopolymer blends in tetrahydrofuran were immiscible. The result coincides with their large chemical dissimilarity and theoretical solubility parameter differences of 25.47 and 33.17 (MJ/m3)1/2. However, 6FD-PP block copolymer solutions were clear, and thin films were robust and creasable. Densities and fractional free volumes (FFV) (0.162–0.346) largely obeyed the rule of mixing, suggesting a “blend-like” morphology. At moderate PP block lengths, two distinct glass transition temperatures (340 and 420 °C) were evident, while large PP block lengths suppressed first-order polyimide transitions entirely. A small-angle X-ray scattering and atomic force microscopy morphological analysis revealed two distinct domains, with separation lengths increasing with the PP block length. Their gas permeation, diffusion, sorption, and separation properties were thoroughly investigated and exhibited a strong correlation with polymer chemistry, block length, and FFV. A block copolymer had an O2 permeability roughly between 6FD and PP, resulting in a 30% increase in O2/N2 selectivity. The N2/CH4 selectivities ranged from 4.2 to 0.58, suggesting that this 6FD-PP system could be efficiently tuned from highly N2-selective to CH4-selective performance. Five structural models, rule-of-mixture, Maxwell, equivalent box model, laminate, and blend, were used to predict gas transport properties. Compared with experimental data, the miscible blend model provided the best results for the 6FD-PP block copolymer system. Block copolymerization by combining highly selective polyimide and highly permeable branched poly(phenylene) provides an opportunity for gas separation tunability and improvement in selected gas pairs.

The lattice distortion, mechanical and thermodynamic properties of A(Zr0.2Sn0.2Ti0.2Hf0.2Nb0.2)O3 (A = Sr, Ba) high-entropy perovskite with B-site disorder: First principles prediction

High-entropy perovskite oxides are novel high-entropy ceramics developing recently. In this work, the local lattice distortion, mechanical and thermodynamic properties of perovskites A(Zr0.2Sn0.2Ti0.2Hf0.2Nb0.2)O3 (A = Sr, Ba) are explored using the first principle investigation. The equilibrium lattice parameter and bulk moduli of high-entropy perovskites obtained by fitting approximately satisfy the rule of mixture of the components, while the entropy effect of component mixing is very small. The bond length distribution reveals the B-site disorder results in large local lattice distortion. The atomic displacement indicates larger average displacement of O atoms contributes mainly to the wider bond length distribution for most B-O bond. The distortion degree at B-site is naturally associated with A-site. The obtained elastic constants of high-entropy perovskites are also closed to the rule of mixing of the components. Compared with ternary SrTiO3 and BaTiO3 perovskites, B-site mixing for high-entropy perovskites enhances their toughness at expense of strength and stiffness, showing the elastic moduli can be modified and adjusted through multi-component design strategy. Relevant thermodynamic property reveals the B-site disorder is benefit to improve the resistance to softening and suppress volume expansion at high temperature. Electronic structures show the insulator–metal transition takes place, also uncover that the interaction of B-O bond is stronger.

Theoretical Estimation of Elastic Characteristics of Natural Reinforced Composite- A Comparative Analysis

Natural Fiber composites are among the potential materials due to their low cost, biodegradability, environmental concerns, and other merits. This paper investigates various theoretical methods to evaluate the elastic behavior of Bamboo fiber-reinforced Epoxy composite and compare it with available experimental data. To compute elastic properties for different fiber volume fractions, prominent micromechanical models such as the Rule of mixing, Halpin-Tsai, Chamis, Unified Bridging, and Elasticity approach, as well as the most current FE homogenization simulation, are employed. FE simulation results from the advanced ANSYS 21.0 material designer module incorporating different Representative Volume Elements (RVE) (Square, Diamond, and Hexagonal) are compared with these models. Through this, a comparative analysis is provided for the validity of different models in predicting the elastic behavior of similar natural fiber-reinforced composites.

Mechanical characterization of 3D printed continuous carbon fiber reinforced thermoplastic composites

Three dimensional (3D) printing of continuous fiber reinforced composites has attracted great interest in various industrial applications, due to convenient complex geometry manufacturability and material savings. Understanding the mechanical properties of 3D printed composites is required for design and simulation. Hence, this paper aims to carry out a comprehensive study on tension, compression, bend and impact properties as well as failure behavior of 3D printed continuous carbon fiber reinforced thermoplastic (CCFRT) composites. The results show that the print fiber filament fill pattern significantly affect the mechanical properties of CCFRTs. Low strain rate has influence on failure mode and micro failure mechanism, but possesses no strong effect on the tensile elastic modulus and strength. Based on the data from longitudinal (0°) and transverse (90°) specimens, the mechanical properties of cross (0°/90°) specimens for three-point bend and unnotched Charpy impact can be predicted by the rule of mixing. However, it is not suitable for the notched specimens. The notch reduced the impact strength of cross specimens by 61.04%, indicating significant notch sensitivity. This study could provide some insights for testing and applying 3D printed continuous fiber composites.

Thermodynamic Characteristics of Phenacetin in Solid State and Saturated Solutions in Several Neat and Binary Solvents.

The thermodynamic properties of phenacetin in solid state and in saturated conditions in neat and binary solvents were characterized based on differential scanning calorimetry and spectroscopic solubility measurements. The temperature-related heat capacity values measured for both the solid and melt states were provided and used for precise determination of the values for ideal solubility, fusion thermodynamic functions, and activity coefficients in the studied solutions. Factors affecting the accuracy of these values were discussed in terms of various models of specific heat capacity difference for phenacetin in crystal and super-cooled liquid states. It was concluded that different properties have varying sensitivity in relation to the accuracy of heat capacity values. The values of temperature-related excess solubility in aqueous binary mixtures were interpreted using the Jouyban–Acree solubility equation for aqueous binary mixtures of methanol, DMSO, DMF, 1,4-dioxane, and acetonitrile. All binary solvent systems studied exhibited strong positive non-ideal deviations from an algebraic rule of mixing. Additionally, an interesting co-solvency phenomenon was observed with phenacetin solubility in aqueous mixtures with acetonitrile or 1,4-dioxane. The remaining three solvents acted as strong co-solvents.

Effect of structure development on the rheological properties of PVDF/HNBR‐based thermoplastic elastomer and its vulcanizates

ABSTRACTThe present work demonstrates the structure‐rheology relationship of novel polyvinylidene fluoride/hydrogenated nitrile rubber blends with special reference to the effect of mixing time, which has not been amply discussed in the literature. In between 50 and 70 wt% rubber content, a yield in complex viscosity and secondary plateau in storage modulus were discerned due to interconnected droplets‐matrix morphology manifesting the thermoplastic elastomeric nature of the blends (TPEs). Such network‐like structure altered the rheological properties like relaxation time, capillary viscosity, die swell, elastic responses of the TPE with respect to the trend as expected according to the rule of mixing. Interestingly, in the early stages of mixing, when the dispersed size was bigger, the effect of physical network on the rheological properties was suppressed. During dynamic vulcanization (TPV), both lower and higher frequency responses in oscillatory shear flow, steady shear rheological properties, recoverable strain etc. have changed notably with mixing time. For example, although the complex viscosity of the TPV was higher at a lower frequency as compared to its TPE, it was significantly lower at a higher frequency at the beginning of dynamic curing; however, viscosity increased appreciably with time. Temperature‐dependendent rheological properties were also influenced with mixing time of the compositions. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48758.

Application in Cement Soil of Stabilizer in Silt Soft Soil of Wuxi in China

ABSTRACT Lu, X.; Cui, M.; Wang, P., and Li, B., 2018. Application in cement soil of stabilizer in silt soft soil of Wuxi in China. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 316–323. Coconut Creek (Florida), ISSN 0749-0208. Soft silty soils are widespread on floodplains and have a high natural water content, void ratio, weak permeability (10–10 cm/s), high strength, and low compressive engineering characteristics. Therefore, taking necessary action in areas where these soils are present is vital because they pose tremendous risks to the reliability of engineering. In this paper, the intensity variation rule of cement pile mixing in soft soil on the Wicheng Road, in the city of Wuxi, China, was studied under various unconfirmed compression strength tests, and with different stabilizer mixing agents and ages. For convenience to application to solidified soil engineering, we also confirmed a 28 day predictive mod...

Ab initio calculation of thermal expansion with application to understanding Invar behavior in gum metal

A theoretical examination of the thermal expansion behavior of a variety of metals is conducted using a combination of nonlinear elasticity theory and first-principles calculations that is suitable for high throughput computation. Results of this method show good agreement with experimental values. This method is then used to better understand the low thermal expansion behavior of gum metal by comparing the thermal expansion tensor of ${\mathrm{Ti}}_{3}\mathrm{Nb}$ austenitic ($\ensuremath{\beta}$) and martensitic (${\ensuremath{\alpha}}^{\ensuremath{''}}$) gum metal approximants. The thermal expansion coefficient of $\ensuremath{\beta}$ is found to be in agreement with experimental results for that of annealed gum metal. The thermal expansion tensor of the ${\ensuremath{\alpha}}^{\ensuremath{''}}$ phase is shown to be highly anisotropic and exhibit negative thermal expansion along ${\ensuremath{\langle}110\ensuremath{\rangle}}_{\ensuremath{\beta}}$. It is demonstrated that the thermal expansion of the two-phase system, $\ensuremath{\beta}+{\ensuremath{\alpha}}^{\ensuremath{''}}$, can be estimated using the rule of mixing. By applying this averaging scheme and allowing a texturing along $\ensuremath{\langle}110\ensuremath{\rangle}{{001}}_{\ensuremath{\beta}}$ in tandem with the growth of the ${\ensuremath{\alpha}}^{\ensuremath{''}}$ phase, values for the thermal expansion similar to that seen in cold-rolled gum metal are calculated.

A review on the role of interface in mechanical, thermal, and electrical properties of polymer composites

Composite materials and especially polymer composites are widely used in daily life and different industries due to their vastly different properties and design flexibility. It is known that the properties of the composites are strongly related to the properties of its constituents. However, it has been reported in many studies, experimentally and by simulations, that the characteristics of the composites do not follow the rule of mixing. It means that in addition to properties of the constituents, there are other parameters affecting the final physicochemical properties of composites. The interfacial interactions between fillers and host is one of the factors which can strongly affect the properties of the composite. In this review, we summarized the type of interactions between the constituents, their improvement techniques, interaction measurement methods, and the effects of interfacial interactions on thermal, mechanical, and electrical properties of composites.

Radiative corrections to the solar lepton mixing sum rule

The simple correlation among three lepton flavor mixing angles $(\theta^{}_{12}, \theta^{}_{13}, \theta^{}_{23})$ and the leptonic Dirac CP-violating phase $\delta$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule $\theta^{}_{12} \approx \theta^{\nu}_{12} + \theta^{}_{13} \cos \delta$, where $\theta^\nu_{12}$ stems from a constant mixing pattern in the neutrino sector and takes the value of $\theta^\nu_{12} = 45^\circ$ for the bi-maximal mixing (BM), $\theta^\nu_{12} = \tan^{-1}(1/\sqrt{2}) \approx 35.3^\circ$ for the tri-bimaximal mixing (TBM) or $\theta^\nu_{12} = \tan^{-1}\left[2/(\sqrt{5} + 1)\right] \approx 31.7^\circ$ for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of $\delta$ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.

Surface behavior of peptides from E1 GBV-C protein: Interaction with anionic model membranes and importance in HIV-1 FP inhibition

The interaction between a peptide sequence from GB virus C E1 protein (E1P8) and its structural analogs (E1P8-12), (E1P8-13), and (E1P8-21) with anionic lipid membranes (POPG vesicles and POPG, DPPG or DPPC/DPPG (2:1) monolayers) and their association with HIV-1 fusion peptide (HIV-1 FP) inhibition at the membrane level were studied using biophysical methods. All peptides showed surface activity but leakage experiments in vesicles as well as insertion kinetics in monolayers and lipid/peptide miscibility indicated a low level of interaction: neither E1P8 nor its analogs induced the release of vesicular content and the exclusion pressure values (πe) were clearly lower than the biological membrane pressure (24–30mN m−1) and the HIV-1 FP (35mN m−1). Miscibility was elucidated in terms of the additivity rule and excess free energy of mixing (GE). E1P8, E1P8-12 and E1P8-21 (but not E1P8-13) induced expansion of the POPG monolayer. The mixing process is not thermodynamically favored as the positive GE values indicate. To determine how E1 peptides interfere in the action of HIV-1 FP at the membrane level, mixed monolayers of HIV-1 FP/E1 peptides (2:1) and POPG were obtained. E1P8 and its derivative E1P8-21 showed the greatest HIV-1 FP inhibition. The LC-LE phase lipid behavior was morphologically examined via fluorescence microscopy (FM) and atomic force microscopy (AFM). Images revealed that the E1 peptides modify HIV-1 FP–lipid interaction. This fact may be attributed to a peptide/peptide interaction as indicated by AFM results. Finally, hemolysis assay demonstrated that E1 peptides inhibit HIV-1 FP activity.

Solubility of daidzein in propylene glycol plus water cosolvent mixtures

The solubility of daidzein in propylene glycol+water cosolvent mixtures was determined by UV spectrophotometry, and predicted using the Jouyban–Acree model and the mathematical model based on the algebraic rule of mixing. The thermodynamic functions, such as Gibbs energy, enthalpy, and entropy of solution and of mixing and so on, were obtained from these solubility data by using the van’t Hoff and Gibbs equations. The results show that the daidzein solubility increases as propylene glycol proportion increases in the mixtures and the solution temperature increases. The Jouyban–Acree model can be used to predict the solubility of daidzein in propylene glycol+water cosolvent mixtures at different temperatures. The driving mechanism for daidzein solubility in water-rich mixtures is the entropy, probably due to water-structure loss around the drug non-polar moieties by effect of propylene glycol, whereas the driving mechanism is the enthalpy above 0.20 mass fraction of propylene glycol, probably due to daidzein solvation increase by the cosolvent molecules. Non linear enthalpy–entropy compensation with negative slope from water up to 0.20 mass fraction of propylene glycol and positive slope beyond this composition up to pure propylene glycol is found.

Compatibility study of chlorinated polyethylene/ethylene methacrylate copolymer blends using thermal, mechanical, and chemical analysis

ABSTRACTBlends of chlorinated polyethylene (CPE) elastomer and ethylene methacrylate copolymer (EMA) in various compositions were studied for their compatibility using differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and Fourier transform infrared (FTIR) spectroscopy techniques. Irrespective of measurement techniques used, all blends showed a single glass transition temperature (Tg) lying in between the Tg of control polymers in both DSC and DMA. Glass transition temperatures of blends obtained from DSC were in consistency with Couchman–Karasz equation. Also, the Tg obtained from both DSC and DMA are above the “rule of mixing” line of the two control polymers. These results from thermal analysis clearly indicate some compatibility between the two polymers. Furthermore, compatibility of CPE/EMA blends were also been investigated by FTIR spectroscopy and scanning electron microscopic analysis. A shifting of characteristic CCl stretching peak of CPE and CO stretching peak of EMA toward lower wave number indicate the presence of specific interaction between the two polymers. Mechanical properties like tensile strength, modulus at 100% elongation, elongation at break, and hardness were observed above the line of additivity drawn between the two control polymers, which corroborate compatibility between CPE and EMA. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40316.

Thermal expansivity of chicken feather fiber reinforced epoxy composites

AbstractThermal expansivity of chicken feather fibers (CFFs) was studied using thermomechanical analysis for composite applications. CFFs have negative coefficient of thermal expansion (CTE) values in the axial direction at different temperature due to its semicrystalline structure. CFFs have a positive CTE value in the radial direction. The CTE values of epoxy/CFF composites can be predicted by the rule of mixing. CTE values of epoxy/CFF composites in the in‐plane direction at various fiber content and temperature have been fully studied and the results can be used in composite design. We can use CFFs in composite materials to control the overall CTE of the composites to reduce the CTE mismatch between the composites and other components. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013