Continuum theory of carbon phases

We constructed a continuum theory of carbon phases based on the Landau theory of phase transitions. Our theory ties up many seemingly unrelated data on the carbon system. Transformations between graphite, diamond, and liquid-carbon are described by the Landau-Gibbs free-energy which depends on two order parameters: crystallization and structural. The barrier-height and gradient-energy coefficients were calculated from the nucleation data obtained in the studies of diamond/graphite and diamond/liquid-carbon systems. The boundary of the absolute stability of the graphitic phase was interpreted as the spinodal point of the free-energy, which allowed us to calculate the pressure dependence of the barrier-height coefficient. The continuum model yielded a value of 1.66 J/m² for the graphite/liquid-carbon interface energy, which continues the trend of the elements of Group IV. We also analyzed stability of nanostructured amorphous carbon and interpreted it as the transition state of the free-energy function. This conjecture helped us to explain results of the experiments on the focused ion-beam irradiation of CVD-diamond nanofilms. The present theory may be used for the large-scale modeling of graphite and diamond crystallization; it can also be extended to include other structural modifications of carbon or an entirely different element such as silicon.     

A New Extension of Cauchy–Born Rule for Monolayer Crystal Films

By combining with the physical concept of inscribed surface, the standard Cauchy–Born rule (CBR) is straightly extended to have a rigorous and accurate atomistic continuum theory for the monolayer crystal films. Resorting to using Tersoff–Brenner potential, the present theory to graphite sheet and single-walled carbon nanotubes (SWCNTs) is applied to evaluate the mechanical properties. The results are validated by the comparison with previously reported studies.     

Effects of conductive graphite filler loading on physical properties of high‐density polyethylene composite

High‐density polyethylene (HDPE)/graphite nanocomposites containing up to 30 vol% of graphite powder filler were prepared by melt mixing in a Brabender Plasticorder at 180°C for 15 min. The nanocomposites were characterized for their rheological, dynamic mechanical, crystallographic, and electrical properties as a function of graphite loading. The results indicated that graphite loading affects storage modulus, loss modulus, complex viscosity, and conductivity of HDPE matrix. The storage modulus increases while the graphite loading increases in the studied concentration range (up to 30%). When the graphite loading was increased to 30%, storage modulus at room temperature was about 300% higher than that of pure HDPE. Also, the composites containing 20 and 30% graphite shows more conductivity than the others. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Stress simulation of carbon nanotubes in tension and compression

Based on a continuum shell model, a structural mechanics approach is presented to simulate stress-strain behavior of carbon nanotubes (CNTs). The nanoscale continuum theory is established to directly incorporate the Morse potential function into the constitutive model of CNTs. According to the present model, the mechanical properties of both zigzag and armchair tubes are investigated. The result shows that the atomic structures of CNTs have a significant influence on the stress-strain behavior. The armchair zigzag tube exhibits larger stress-strain response than the zigzag tube under tensile loading, but its relationship turns over between the tension and compression deformations. The theoretical approach supplies a set of very simple formulas and able be serve as a good approximation on the mechanical properties for CNTs.     

等静压石墨的研究与探讨

等静压石墨是一种新型石墨材料。由于它具有一系列优良特性，从而使它与当今的高新技术，国防尖端技术紧密相联。它是制造单晶硅炉，金属连铸的石墨结晶器、电火花加工用石墨电极等不可替代的材料。更是制造火箭的点火极、激励极、喷嘴和舵板以及石墨核反应堆的减速材料和反射材料的绝好材料。     

Improvement in thermal conductivity and mechanical properties of ethylene‐propylene–diene monomer rubber by expanded graphite

Thermally conductive fillers are usually employed in the preparation of rubber composites to enhance thermal conductivity. In this work, ethylene‐propylene‐diene monomer rubber (EPDM)/expanded graphite (EG) and EPDM/graphite composites with up to 100 phr filler loading were prepared. Compared to EPDM/graphite compounds with the same filler loading, stronger filler network was demonstrated for EPDM/EG compounds. Thermal conductivity and mechanical properties of EPDM/graphite and EPDM/EG composites were compared and systematically investigated as a function of the filler loading. The thermal conductivity of both EPDM/graphite and EPDM/EG composites increased with increasing volume fraction of fillers, and could be well fitted by Geometric Mean Model. The thermal conductivity as high as 0.910 W · m⁻¹ · K⁻¹ was achieved for the EPDM/EG composite with 25.8 vol% EG, which was ∼4.5 times that of unfilled EPDM. Compared to EPDM/graphite composites, EPDM/EG composites exhibited much more significant improvement in thermal conductivity and mechanical properties, which could be well correlated with the better filler‐matrix interfacial compatibility and denser structure in EPDM/EG composites, as revealed in the SEM images of tensile fracture surfaces. POLYM. COMPOS., 38:870–876, 2017. © 2015 Society of Plastics Engineers     

An improved model for adhesively bonded DCB joints

An improved analytical model is proposed for characterizing the fracture behavior of an adhesively bonded double cantilever beam joint under Mode I loading. Novel interfacial normal stress distribution function is used with a key parameter c that is determined using continuum mixture theory. In addition to the mechanical and sectional properties of the adherends, crack length, and overlap area, the model also incorporates the adhesive thickness and material properties as well as the crack tip rotation. Model prediction of the fracture toughness of the joint is entered into finite element analysis to simulate crack propagation under peel loading. The effect of various parameters on the joint fracture properties is discussed. Results show that the proposed model provides better correlation with published experimental data.     

Polypropylene-graphite nanocomposites made by solid-state shear pulverization: Effects of significantly exfoliated, unmodified graphite content on physical, mechanical and electrical properties

Nanocomposites made from polypropylene and as-received graphite were prepared by solid-state shear pulverization (SSSP) as a function of graphite loading (0.3-8.4 wt%). X-ray diffraction indicates that SSSP employing harsh pulverization conditions yields substantial graphite exfoliation at 0.3-2.7 wt% graphite content with less exfoliation being achieved at higher graphite content. With increasing graphite content, thermal degradation temperature and non-isothermal onset crystallization temperature increase substantially (by as much as 35 and 23 °C relative to neat polypropylene) while isothermal crystallization half-time decreases dramatically. In contrast, Young’s modulus and tensile yield strength exhibit maxima (∼100% and ∼60% increases, respectively, relative to neat polypropylene) at 2.7 wt% graphite content, with all nanocomposites retaining high elongation at break values except at the highest filler loading. Electrical conductivity measurements indicate percolation of graphite at 2.7 wt% and higher graphite content, consistent with rheology measurements showing the presence of a solid-like response of melt-state shear storage modulus as a function of frequency. Significant tunability of graphite exfoliation and property enhancements is demonstrated as a function of SSSP processing.     

石墨改性交联聚乙烯导热复合材料性能研究

用石墨填充硅烷接枝可交联聚乙烯，制备导热高分子复合材料。研究了基体种类及填料含量对复合材料热性能的影响，交联前后材料力学性能、热性能的变化规律。结果表明，基体导热性能的差异在复合材料中将得到数倍甚至数十倍的扩大，填充20vt％以上石墨后材料导热性能才能得到较大提升，较高石墨含量下，材料力学性能在交联前后没有明显变化，导热性能随交联程度增加略有提高。     

Non-classical continuum theories for solid and fluent continua and some applications

ABSTRACT

This paper presents two specific thermodynamically consistent non-classical continuum theories for solid and fluent continua. The first non-classical continuum theory for solid continua incorporates Jacobian of deformation in its entirety in the conservation and the balance laws and the derivation of the constitutive theories. The second non-classical continuum theory for solid continua considers Jacobian of deformation in its entirety as well as the Cosserat rotations in the conservation and balance laws as well as the constitutive theories. The first non-classical continuum theory for fluent continua presented here considers velocity gradient tensor in its entirety. The second non-classical continuum theory for fluent continua considers velocity gradient tensor in its entirety as well as Cosserat rotation rates in the derivation of the conservation and balance laws and the constitutive theories. Since the non-classical continuum theories for solid and fluent continua considered here incorporate additional physics of deformation due to rotations and rotation rates compared to classical continuum mechanics, the conservation and balance laws of classical continuum mechanics are shown to require modification as well as a new balance law balance of moment of moments is required to accommodate the new physics due to rotations and rotation rates. Eringen’s micropolar, micromorphic and microstretch theories, couple stress theories and nonlocal theories are also discussed within the context of the non-classical theories presented here for solid and fluent continua. Some applications of these theories are also discussed.     

石墨凝胶注模工艺研究

采用凝胶注模成型工艺制备了石墨浆料,研究了石墨粉体类型、pH值、分散剂加入量和固相含量对浆料粘度的影响,浆料温度对凝胶固化时间的影响,以及乙酰丙酮对素坯强度的影响.实验结果表明:当采用等静压石墨粉,pH值为7,分散剂加入量为4wt%,固相含量为50vol%时,可制备流动性良好的石墨浆料;浆料温度为3 ℃时,凝胶固化时间为5.6 min;当乙酰丙酮加入量为0.6wt%时,素坯强度达到15.8 MPa.     

紫外光固化法制备漆酚/石墨复合导电涂料的研究

以漆酚为基体,石墨为导电填料,利用紫外光固化法制备漆酚/石墨复合导电涂料,讨论了涂膜中石墨的含量以及固化方式等对漆膜导电性能的影响,并测试了漆膜的常规物理机械性能。结果表明,在紫外光辐照下,漆酚/石墨混合物涂膜可快速固化。当石墨含量达到25%(wt%)时,漆膜的表面电阻率为442Ω.cm,硬度为6H,附着力2级,冲击强度为45kg.cm。     

Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading

Brittle fracture of polycrystalline graphite under torsion loading is studied experimentally and theoretically using axisymmetric specimens weakened by sharp and rounded-tip V-notches. The main purpose is twofold. First, to provide a new set of experimental data from notched samples made of isostatic polycrystalline graphite with different values of notch opening angles and root radii, which should be useful to engineers engaged with static strength analysis of graphite components. At the best of authors’ knowledge, data from notch specimens under torsion are not available in the literature for this material. Second, to apply to the torsion loading case a fracture criterion based on the strain energy density (SED) averaged over a well-defined control volume surrounding the notch tip, extending what was made by the present authors for in-plane tension-shear loading conditions in notched graphite specimens. Good agreement is found between the experimental data related to the critical loads to failure and the theoretical assessments based on the constancy of the mean SED over the material-dependent control volume.     

Electrical properties of exfoliated-graphite filled polyester based composites

Work has been done to develop and optimize a procedure for the preparation of electrically conductive exfoliated-graphite filled unsaturated polyester composites. The exfoliated graphite flakes impart excellent electrical properties to the polyester composite. EMI (electromagnetic interference) shielding effectiveness, comparable to that of exfoliated graphite alone, has been observed over a frequency range of 0 to 1000 MHz with composite samples containing as little as 4 weight percent of exfoliated graphite. The resistivities approached the value for exfoliated graphite in the c-direction (0.03 μ-cm) at a graphite loading of 11 weight percent. It has been observed that the mechanical integrity of the composite remained good up to graphite loadings of some 17 weight percent. The polyester readily wets the graphite and penetrates most of the graphite open pore volume during processing. Flow visualization measurements have been made in a transparent compression molding apparatus. No effect of the flow conditions on the apparent electrical properties has been found.     

Theory of yield of cohesive powders

In many problems in process technology, the influence of the adhesion forces on the mechanics of fine powders plays a considerable role. The existing knowledge is characterized by intensive experimental and theoretical investigations into the mechanism of adhesion for single particle contacts without consolidation by external forces. On the other hand, the mechanical behaviour of cohesive powders has been investigated mainly on the basis of continuum mechanics.For science and technology, it is useful to combine the particles approach and the continuum approach in order to provide a better understanding of the mechanical properties of cohesive powders. A theoretical model has therefore been developed which takes into account the forces acting in interparticle contacts. The theory especially considers the increase in the adhesion forces transmitted in interparticle contacts with increasing consolidation. Contrary to the commonly used phenomenological view, this theory yields a physically based understanding of the effective yield locus for steady-state flow which is reduced to material properties of the solid particles and is therefore shown to be an invariant of a respective powder.The opinion found in the literature that a single yield locus uniquely belongs to one consolidation locus is shown to be not valid. The microstructural view of a cohesive powder is able to show that, contrary to the continuum mechanical view, in the general case a cohesive powder is mechanically anisotropic due to its loading history.     

Kinetics and thermodynamics of intercalation of bromine in graphite—II. Theory

A theory that describes the diffusion of an intercalate within graphite in a multiphase situation is presented. The theory was applied to the intercalation of bromine in graphite. Single-phase diffusion represents the intercalation of bromine in graphite as well as multiphase diffusion due to the dominance of the final stage.     

A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers

A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress-strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.     

聚丙烯／石墨复合材料的导电与阻燃性能研究

制备了以膨胀石墨和可膨胀石墨为填料、聚丙烯为基体的兼具导电与阻燃性能的复合材料。确定了膨胀石墨和可膨胀石墨的表面处理剂及其最佳用量，研究了复合材料的导电性能和阻燃性能。结果表明，固定可膨胀石墨含量为10％（质量分数，下同），当膨胀石墨含量达到12％时，复合材料的导电网络基本形成；固定膨胀石墨含量为8％，当可膨胀石墨含量达到25％时，复合材料的导电网络也基本形成。结果表明，复合材料的导电性主要靠膨胀石墨起作用，但可膨胀石墨也能发挥一定的导电作用。膨胀石墨对于复合材料的阻燃性贡献甚微，阻燃效应主要靠可膨胀石墨起作用。     

The influence of carbon black on the extrusion characteristics and rheological properties of elastomers: Polybutadiene and butadiene–styrene copolymer

An experimental study of the influence of carbon black loading, particle size, and structure on the extrusion characteristics of polybutadiene and butadiene–styrene copolymer synthetic rubber is described. The development of extrudate distortion and its mechanisms are considered. The viscosity and die swell have been related to black loading, particle size, and structure. Generally, it is found that black surface area and structure acts to increase viscosity and decrease elastic memory. This situation is analyzed in terms of the theory of nonlinear viscoelasticity. Two mechanistic theories are described which may explain this behavior. One theory is based on the continuum mechanics analysis of suspensions of particles in viscoelastic media. The rheological behavior of the black compounds is explained in terms of the increased severity of deformation in the polymer matrix surrounding the particle agglomerates. The second theory is based on the view of an entanglement network containing black particles. Polymer chains may be adsorbed onto the surface giving rise to increased entanglement densities.