Tensile strength of ABS/PA6 composites reinforced with HNO<Subscript>3</Subscript>-treated carbon fibers

In this study, an acrylonitrile-butadiene-styrene (ABS) terpolymer was reinforced with HNO₃-treated short carbon fibers (SCFs). The effects of SCF concentration on the tensile properties of the composites were examined. Increasing the SCF concentration in the ABS matrix from 10 to 30 wt.% raised its tensile strength and tensile modulus. To obtain a strong interaction at the fiber-matrix interface, polyamide-6 (PA6) at varying concentrations was introduced into the ABS/10 wt.% SCF composite. The incorporation and increasing the amount of PA6 in the ABS/PA6/SCF systems upgraded their tensile properties due to the improved adhesion at the fiber-matrix interface, which was confirmed by the growing tensile strength. These results were also supported by scanning electron micrographs of the ABS/PA6/SCF composites, which exhibited an enhanced adhesion between the SCFs and the ABS/PA6 matrix.     

The effect of carbon fibers and carbon nanotubes on the mechanical properties of polyimide composites

In this experimental work, the influence of carbon fibers (CFs) added to polyimide (PI) composite plastics was investigated. Also, the effect of carbon nanotubes (CNTs) on the fiber-matrix interface was studied. The results obtained show that the mechanical properties of CF/CNT/PI nanocomposites are superior to those of CF/PI composites.     

Influence of nano-SiO<Subscript>2</Subscript> and carbon fibers on the mechanical properties of POM composites

Polyoxymethylene/carbon fiber(POM/CF)composites containing nano-SiO₂ were prepared, and their mechanical properties were investigated. At a content of 1-5 vol.%, the nano-SiO₂ exerted an obvious reinforcing effect on POM, leading to an increase in the elastic modulus and stiffness of the composites.     

Environmental degradation of carbon nanotube-modified composite laminates: a study of electrical resistivity

The environmental durability of carbon nanotube (CNT)-modified carbon-fibre-reinforced polymers (CFRPs) is investigated. The key problem of these new-generation composites is the modification of their polymer matrix with nanoscaled fillers. It was recently demonstrated that the damage tolerance of these materials, as manifested by their fracture toughness, impact properties, and fatigue life, can be improved by adding CNTs at weight fractions as low as 0.5%. This improvement is mainly attributed to the incorporation of an additional interfacial area between the CNTs and the matrix, which is active at the nanoscale. However, this additional interface could have a negative effect on the environmental durability of the aforementioned systems, since it is well known that the moisture absorption ability of a matrix is enhanced by the presence of multiple interfaces, which serve as an ingress route to water. To examine this problem, CNT-modified CFRPs were exposed to hydrothermal loadings. At specified intervals, the composites were weighted, and the water uptake vs. time was recorded for both the modified and a reference systems. The electrical conductivity of the composites was registered at the same time intervals. After the environmental exposure, the interlaminar shear properties of the conditioned composite systems were measured and compared with those of unmodified composites, as well as with the shear properties of unexposed laminates. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 31–48, January–February, 2009.     

Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [0₂/90₁₂/0₂] and quasi-isotropic [(±45/0/90)₄] _s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.     

The effect of C<Subscript>60</Subscript> fullerene on the toughening of epoxy compositions

The effect of C₆₀ fullerene on the mechanical properties of epoxy resins has been investigated. It is found that this filler affects the tensile modulus and tensile strength of epoxy compositions only slightly, but their impact strength at a 0.01–0.12 wt.% content of C₆₀ increases by about 100–200%. A molecular mechanism of the toughening effect of C₆₀ on epoxy resins is suggested.     

Dual-phase-lag analysis of CNT–MoS2–ZrO2–SiO2–Si nano-transistor and arteriole in multi-layered skin

The numerical simulation of non-Fourier dual-phase-lag heat conduction in three-dimensional bio and nano media has been investigated with two developed solvers using the OpenFOAM C++ finite-volume libraries. Despite the rapid growth in the use of non-Fourier heat transfer model, most researchers conduct simulations over simple geometries due to numerical restrictions. The developed solvers have been verified for four benchmark cases. After that, two complex geometries have been selected to show the accuracy of the solvers for complicated geometries. The first case is the temperature distribution in the human hand skin in the presence of a circular arteriole, while the second case is the thermal analysis of a newly constructed CNT–MoS₂ transistor with 1 nm gate length. Both cases are multilayered structures with curved boundaries. The computed temperature rises in the blood vessel and in the transistor are 63°C after 15 s and 16 °C after 10 ps, respectively. It is found that considering the temperature-dependent electrical properties of ZrO₂ and CNT is essential to present an accurate mathematical model.     

Computational study of compressive loading of carbon nanotubes using quasi-continuum method

A reduced-order general continuum method is used to examine the mechanical behavior of single-walled carbon nanotubes (CNTs) under compressive loading and unloading conditions. Quasi-static solutions are sought where the total energy of the system is minimized with respect to the spatial degrees of freedom. The obtained continuum solution is mapped back to the lattice structure of CNTs. We then provide a detailed analysis of buckled configurations for four different types of CNTs on the lattice level and show that, among the cases studied, the armchair CNT has the strongest resistance to the compressive loading. It is also shown that the buckled CNT will significantly lose its structural strength with the zigzag lattice structure. The post-buckling unloading of CNTs demonstrates that, after the occurrence of buckling, the CNT can return to its original state, making its use desirable in fields such as synthetic biomaterials, electromagnetic devices, or polymer composites.     

<Emphasis Type="Italic">A</Emphasis><Subscript>2</Subscript>-continued fraction representation of real numbers and its geometry

We study the geometry of representations of numbers by continued fractions whose elements belong to the set A ₂ = {α₁, α₂} (A ₂-continued fraction representation). It is shown that, for α₁α₂ ≤ 1/2 , every point of a certain segment admits an A ₂-continued fraction representation. Moreover, for α₁α₂ = 1/2, this representation is unique with the exception of a countable set of points. For the last case, we find the basic metric relation and describe the metric properties of a set of numbers whose A ₂-continued fraction representation does not contain a given combination of two elements. The properties of a random variable for which the elements of its A ₂-continued fraction representation form a homogeneous Markov chain are also investigated.     

Properties of a composite prepared using a concentrate of carbon nanotubes in polyethylene

Results of an investigation into the properties of polyethylene (PE) with small, no more than 5 wt.%, additions of multiwall carbon nanotubes (CNTs) are reported. Specimens of the composite were prepared using a concentrate containing 31.6 wt.% of nanotubes in the polyethylene matrix. The concentrate was fabricated by a patent in situ polymerization method. Experimental data on the influence of CNT additions on the thermograms of differential scanning calorimetry, the crystallinity of the polyethylene matrix, and the indices of mechanical properties (yield stress, strength, elastic modulus, ultimate elongation, and long-term creep) of PE/CNT composite are obtained. A theoretical analysis of elastic properties of the PE/CNT composite was carried out by using the Mori–Tanaka theory of an equivalent medium. The calculation results are compared with experimental data.     

Coincidence points of multivalued mappings in (<Emphasis Type="Italic">q</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">q</Emphasis><Subscript>2</Subscript>)-quasimetric spaces

The properties of (q₁, q₂)-quasimetric spaces are examined. Multivalued covering mappings between (q₁, q₂)-quasimetric spaces are investigated. Given two multivalued mappings between (q₁, q₂)-quasimetric spaces such that one of them is covering and the other satisfies the Lipschitz condition, sufficient conditions for these mappings to have a coincidence point are obtained. A theorem on the stability of coincidence points with respect to small perturbations in the considered mappings is proved.     

Theory of (<Emphasis Type="Italic">q</Emphasis> <Subscript>1</Subscript>, <Emphasis Type="Italic">q</Emphasis> <Subscript>2</Subscript>)-quasimetric spaces and coincidence points

We introduce (q₁, q₂)-quasimetric spaces and examine their properties. Covering mappings between (q₁, q₂)-quasimetric spaces are investigated. Sufficient conditions for the existence of a coincidence point of two mappings acting between (q₁, q₂)-quasimetric spaces such that one is a covering mapping and the other satisfies the Lipschitz condition are obtained.     

Regularity for weakly (K<Subscript>1</Subscript>, K<Subscript>2</Subscript>)-quasiregular mappings

In this paper, we first give the definition of weakly (K₁,K₂-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Hölder inequality, we obtain their regularity property: For anyq ₁ that satisfies\(0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1\), there existsp ₁=p ₁(n,q ₁,K ₁,K ₂)>n, such that any (K₁, K₂)-quasiregular mapping\(f \in W_{loc}^{1,q_1 } (\Omega ,R^n )\) is in fact in\(W_{loc}^{1,p_1 } (\Omega , R^n )\). That is, f is (K₁,K₂)-quasiregular in the usual sense.     

SOME PROPERTIES OF STRONGLY MONOTONICALLY T2 SPACES

This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.     

Strength of glass laminates at low temperatures and high strain rates

The tensile strengths of glass laminates of various compositions under standard, high-speed and impact loading have been experimentally investigated in relation to the effect of low-temperature and stress raisers. As the loading rate increases (from 0.7 to 253 · 10³ kgf/cm². · sec) and the temperature falls to –196° C, the effective stress concentration coefficient decreases, which indicates that the glass laminates will perform adequately under these conditions.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 836–841, September–October, 1970.     

The effect of introduction of carbon nanotubes on the physicomechanical properties of polyvinylacetate

The physicomechanical properties of polyvinylacetate (PVA) with small, no more than 2 wt.%, additions of carbon nanotubes (CNTs) are investigated. Data on the influence of CNT concentration on the differential scanning calorimetry thermograms, thermal destruction, electrical resistance, water vapor sorption, as well as indices of the mechanical properties of PVA/CNT (yield stress, strength, elastic modulus, ultimate elongation, and short-term creep) are reported. A variant of calculation of the elastic constants of the nanocomposite is considered with account of the effect of nanotube agglomeration.     

Frequency analysis of carbon and silicon nanosheet with surface effects

Silicon-based microelectromechanical system (MEMS) and nanoelectromechanical systems (NEMS) have been used to design and fabricate sensitive sensors and actuators. Recent research trends show that graphene and carbon nanotubes (CNTs) have been used to change the surface properties of silicon-based MEMS and NEMS to improve different mechanical, optical and electrical properties of silicon-based composites. In this paper, we focus on analyzing the vibrational characteristics of silicon-based devices when the surface of silicon is coated with single-layer graphene and horizontally aligned carbon nanotubes (HACNTs). To perform the analysis, we use multi-scale finite element approach for developing graphene–silicon nanocomposites (GSNCs) and carbon nanotube-silicon nanocomposites (CSNC) composites in which interface layer of silicon with graphene or CNT is modeled using bonded contact element. Subsequently, we performed modal analysis to find the first transverse mode frequency of GSNC and CSNC composites for beam with smaller as well as longer lengths. The numerical model is compared with classical beam theory with and without surface effect. For GSNCs composites, we take a fixed-free case with lengths in the range of (20 Å–120 Å) and (400 Å–2000 Å), respectively. For CSNC composites, CNT diameter is varied from (5 Å–30 Å) for single walled nanotube. Subsequently, we analyze the influence of HACNTs-on-silicon on its vibrational characteristics. The analysis presented in the paper demonstrate that GSNCs offer a higher bending stiffness compared to single layer graphene (SLGs) and isolated silicon nanosheet which lead to higher natural frequency. A similar trend is found in the case of HACNTs on silicon NS when the number of tubes increases.     

A Remark on the sl<Subscript>2</Subscript> Approximation of the Kontsevich Integral of the Unknot

The Kontsevich integral of a knot K is a sum over all chord diagrams with suitable coefficients. Here A_n is the space of chord diagrams with n chords. A simple explicit formula for the coefficients a_D is not known even for the unknot. Let E₁, E₂,... be elements of A = ⊕_n A_n. Say that the sum is an sl₂ approximation of the Kontsevich integral if the values of the sl₂ weight system W_sl2 on both sums are equal: W_sl2 (I(K)) = W_sl2 (I′(K)). For any natural n fix points a₁,..., a_2n on a circle. For any permutation σ ∈ S_2n of 2n elements, one defines the chord diagram D(σ) with n chords as the diagram with chords formed by pairs a_{σ (2-1)} and a_σ(2i), i = 1,...,n. It is shown that

On the distribution of Satake parameters of GL<Subscript>2</Subscript> holomorphic cuspidal representations

We prove that for a fixed non-archimedean place v of a totally real number field F, the traces of the associated Langlands classes of holomorphic cuspidal representations of GL₂(A) with trivial central character and of prime levels is equidistributed with respect to the measure