Polytetramethylene glycol-modified polycyanurate matrices reinforced with nanoclays: synthesis and thermomechanical performance

The outstanding improvement in the physical properties of cyanate esters (CEs) compared with those of competitor resins, such as epoxies, has attracted appreciable attention recently. Cyanate esters undergo thermal polycyclotrimerization to give polycyanurates (PCNs). However, like most thermo setting resins, the main draw back of CEs is brittleness. To over come this disadvan tage, CEs can be toughened by the introduction of polytetramethylene glycol (PTMG), a hydroxyl-terminated polyether. How ever, PTMG has a detrimental impact on Young’s modulus. To simultaneously enhance both the ductility and the stiffness of CE, we added PTMG and an organoclay (mont morillonite, MMT) to it. A series of PCN/PTMG/MMT nanocomposites with a constant PTMG weight ratio was pre pared, and the resulting nanophase morphology, i.e., the degree of filler dispersion and distribution in the composite and the thermomechanical properties, in terms of glass-transition behaviour, Young’s modulus, tensile strength, and elongation at break, were examined using the scanning elec tron micros copy (SEM), a dynamic mechanical analysis (DMA), and stress–strain measurements, re spectively. It was found that, at a content of MMT below 2 wt.%, MMT nanoparticles were distributed uniformly in the matrix, suggesting a lower degree of agglomeration for these materials. In the glassy state, the significant increase in the storage modulus revealed a great stiffening effect of MMT due to its high Young’s modulus. The modification with PTMG led to a 233% greater elongation at break compared with that of neat PCN. The nanocomposites exhibited an invariably higher Young’s modulus than PCN/PTMG for all the volume factors of organoclay examined, with the 2 wt.% material displaying the most pronounced in crease in the modulus, in agreement with micros copy results. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 255–268, March–April, 2009.     

Elastic properties of two-dimensional two-phase composites with isotropic phases

Formal series of powers of Fourier coefficients for the effective elastic constants of a heterogeneous material (Herring’s series) are considered. It is demonstrated that, on their basis, all the known exact solutions of an elastic problem for a two-dimensional two-phase composite can be found. It is also shown how a full renormalization of the series for the inverse bulk modulus can be carried out. A general expression for Young’s modulus is deduced, leading to considerable simplifications in some special cases. All results have been obtained without any restrictions on the Fourier coefficients of local parameters of the composite.     

Finite-element investigation of the stress-strain state of an inhomogeneous rectangular plate

With the use of the finite-element method, the generalized plane stressed state of a rectangle of isotropic functionally gradient materials under the action of normal load is investigated. A finite-element model is constructed by the Bubnov–Galerkin method. The domain of the body is split into rectangular gradient elements that take into account dependences of Young’s modulus and Poisson’s ratios on coordinates. Numerical calculations are performed for the case where Young’s modulus is a polynomial function. The influence of the material gradientness and the sizes of the rectangle on its stress-strain state is analyzed.     

A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites

A literature review on the prediction of Young’s modulus for carbon nanotubes, from both theoretical and experimental aspects, is presented. The discrepancies between the values of Young’s modulus reported in the literature are analyzed, and different trends of the results are discussed. The available analytical and numerical simulations for predicting the mechanical properties of carbon nanotube composites are also reviewed. A gap analysis is performed to highlight the obstacles and drawbacks of the modeling techniques and fundamental assumptions employed which should be overcome in further studies. The aspects which should be studied more accurately in modeling carbon nanotube composites are identified.     

Strengthening of RC beams with an innovative timber-FRP composite system

The results of a theoretical and experimental research project on the use of an innovative technique for strengthening concrete beams are presented. A spacer element is inserted between the tension side of a beam and the composite material to increase its lever arm and to enhance the over all stiffness of the strengthened beam. The main aim of this exploratory project was to increase the ultimate failure load of strengthened beam specimens, whilst guaranteeing acceptable over all deflections at the serviceability limit states. This resulted into a significant reduction in the amount of FPR required and in a better utilization of the materials employed. A preliminary theoretical study was carried out to investigate the effect of Young’s modulus, failure strain, and thickness of the element to be used as a spacer in order to determine the best possible candidate material. Three tests on 2.5-m-long beams were carried out, and different anchorage techniques were used to try and prevent the debonding of the strengthening system. The results from this pilot study are very promising, as the strengthening system ensures an adequate initial stiffness along with an improved ultimate flexural capacity. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 403–416, May–June, 2008.     

Measuring the tensile and bending properties of nanohoneycomb structures

The mechanical properties, including Young’s modulus, the effective bending modulus, and the nominal fracture strength, of nanohoneycomb structures were measured by using an atomic force microscope (AFM) and a nano-universal testing machine (UTM). Anodic alumina films were taken as the nanohoneycomb structures. Bending tests were carried out on cantilever beams by pressing AFM tips, and the results were compared with three-point bending tests and tensile tests conducted by using the nano-UTM. A new and less damaging method for gripping the specimens was elaborated for the tensile tests. The results obtained can serve as design guidelines in applications of nanohoneycomb structures. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 247–264, March–April, 2006.     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.     

A sharp analog of Young’s inequality on S<Superscript>N</Superscript> and related entropy inequalities

We prove a sharp analog of Young’s inequality on S^N, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This strategy also works for the generalization of Young’s inequality on R^N to more than three functions, and leads to significant new information about the optimizers and the constants.     

Coupling of a structural analysis and flow simulation for short-fiber-reinforced polymers: property prediction and transfer of results

The aim of this paper is to discuss the basic theories of interfaces able to transfer the results of an injection molding analyis of fiber-reinforced polymers, performed by using the commercial computer code Moldflow, to the structural analysis program ABAQUS. The elastic constants of the materials, such as Young’s modulus, shear modulus, and Poisson’s ratio, which depend on both the fiber content and the degree of fiber orientation, were calculated not by the usual method of “orientation averaging,” but with the help of linear functions fitted to experimental data. The calculation and transfer of all needed data, such as material properties, geometry, directions of anisotropy, and so on, is performed by an interface developed. The interface is suit able for midplane elements in Moldflow. It calculates and transfers to ABAQUS all data necessary for the use of shell elements. In addition, a method is described how a nonlinear orthotropic behavior can be modeled starting from the generalized Hooke’s law. It is also shown how such a model can be implemented in ABAQUS by means of a material subroutine. The results obtained according to this subroutine are compared with those based on an orthotropic, linear, elastic simulation. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 367-378, May-June, 2009.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

Identifying the elastic moduli of composite plates by using high-order theories. 2. Theoretical-experimental approach

The identification of elastic properties of laminated composite plates from measured eigenfrequencies has been performed. The elastic moduli of the laminates were determined by using a multilevel modeling and a two-step identification procedure. At the first step, based on a genetic algorithm, the Young’s and shear moduli were found, but at the second one, by minimizing an error function, the values of transverse moduli were refined. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 207–216, March–April, 2008.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

The effect of fullerene fillers on the mechanical properties of polymer nanocomposites

The effect of fullerene and carbon fillers on the mechanical properties of polymer nanocomposites based on thermoreactive (epoxy resin) and thermoplastic (polyamide-12) matrices was investigated. It was found that the introduction of these fillers did not affect the properties of the thermoreactive blends, but Young’s modulus and the tensile strength of the thermoplastic ones increased by about 30-40% upon addition of 0.02-0.08 wt.% fullerene materials. The best results were obtained for a mixture of C ₆₀/C ₇₀.     

Modelling the mechanical behaviour of adhesively bonded and sintered hollow-sphere structures

The mechanical properties of periodic hollow-sphere structures are investigated numerically. Young’s modulus and the Poisson ratio are determined in order to describe their linearly elastic behaviour. The initial compressive yield strength is also calculated. The spheres are located at the nodes of a cubic primitive lattice. The cohesion is achieved by an adhesive concentrated in the minimum gap between neighbouring spheres. The geometry of the structure is discretized based on regular hexahedral elements. This approach is much more time-consuming, but it is important in order to achieve a more accurate simulation of the nonlinear behaviour (e.g., plasticity) of such materials. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 803–816, November–December, 2006.     

Effects of Young’s modulus on response of railway sleeper

As a main part of a railroad system, sleepers have important duty in conveying the load from rails to the ballast. The different situations in which the sleepers should function necessitate making them from different materials, such as various types of wood, reinforced concrete and even steel. In this work, the effects of Young’s modulus on response of railway sleeper are evaluated. As a main consideration, Winkler’s theorem is used to model the behavior of the elastic foundation. First, the response of a sleeper on a Winkler’s foundation is found. To evaluate the results of the closed form solution, a finite element model is used. Good agreement between the results of the closed form solution and the finite element model proves the validity of the results. In the next stage, the Young’s modulus is considered as a variable and the fundamental diagrams of the beam are plotted based on the variation of Young’s modulus.     

Structural elastic and creep models of a UD composite in longitudinal shear

The transient creep of a UD composite with a quadratic arrangement of elastic fibers of quadratic cross section is investigated. The deformational properties of the composite are determined from the known properties of its constituents. A structural model of the UD composite is developed, whose minimal elementary cell contains four elements. The stress-strain state of the elements is assumed homogeneous. Two types of basic and resolving governing equations of transient creep are deduced, which are based on static or kinematic assumptions. In each of the cases, a formula for the longitudinal elastic shear modulus of the composite is found. The stationary solutions of creep equations allow one to obtain formulas of the steady-state creep of the composite in a form similar to Norton’s law. Numerical calculations are also performed, and a comparison of the results with data given in the literature bears witness to the efficiency of the models developed and the solutions obtained. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 437–448, July–August, 2007.     

Ballistic performance of a Kevlar-29 woven fibre composite under varied temperatures

Armours are usually manufactured from polymer matrix composites and used for both military and non-military purposes in different seasons, climates, and regions. The mechanical properties of the composites depend on temperature, which also affects their ballistic characteristics. The armour is used to absorb the kinetic energy of a projectile without any major injury to a person. Therefore, besides a high strength and lightness, a high damping capacity is required to absorb the impact energy transferred by the projectile. The ballistic properties of a Kevlar 29/polyvinyl butyral composite are investigated under varied temperatures in this study. The elastic modulus of the composite is determined from the natural frequency of composite specimens at different temperatures by using a damping monitoring method. Then, the backside deformation of composite plates is analysed experimentally and numerically employing the finite-element program Abaqus. The experimental and numeric results obtained are in good agreement.     

Estimates on polynomial exponential sums

In this paper we establish new bounds on exponential sums of high degree for general composite moduli. The sums considered are either Gauss sums or ‘sparse’ and we rely on earlier work in the case of prime modulus.     

基于变体积约束的阻尼材料微结构拓扑优化研究北大核心CSCD

阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.     

Discrete one-sided nonlinear Lp approximation

Under the local Haar condition, an interpolatory theorem for discrete one-sided nonlinear L_p (p>1) approximation is obtained. Under the strong Young’s condition, a Polya-type theorem with discretization for one-sided nonlinear approximation and a limit (discretization) theorem for one-sided modified L_p (p≥1) approximation are given.