Stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in cross-ply plates and validity of St. Venant’s principle in the presence of interacting singularities

Effects of localized elliptical (circular being a special case) cylindrical surface flaws in laminated composite plates are investigated by using C°-type triangular composite plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST). Numerical results for a cross-ply laminate compromised by the presence of an external part-through elliptical/circular cylindrical slot indicate the existence of severe cross-sectional warping in the vicinity of the surface flaw and plate boundaries. Furthermore, three-dimensional nature of the stress concentration factor in the neighborhood of the elliptical or circular cylinder shaped surface flaw boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the surface flaw. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening laminated composite plates, are numerically assessed, because of their role in crack initiation. Finally, the interaction of this singularity with free edge stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of St. Venant’s principle) in regards to testing of laminated composite specimens are thoroughly investigated.     

Application of a Viscoelastic Model to simulate the Interface of a Metal/Fibre-Reinforced Polymer Joint

A viscoelastic model with the Lemaitre-type damage is applied to simulate an interfacial adhesive zone in light weight engineering structures, like aluminum/fiber-reinforced polymer specimens. The evolution of irreversible deformation and damage progression are investigated. The joint of aluminium alloy 5754 (AA5754) and carbon fibre reinforced thermoplastic composite CF-PA66 is manufactured by means of an epoxy (1K) adhesive. The adhesive zone is considered as an interface material. The aim of the research is to study the influence of the interface geometry on the mechanical characteristics of the structure. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A 4D Composite Reinforced along Cube Diagonals with a Small Content of Yarns under Large Tensile Deformations

The deformation behavior of a 4D composite reinforced along cube diagonals under large tensile deformations is examined. The investigation is based on an applied theory which allows one to perform a macromechanical analysis of composite materials with small volume contents of reinforcing yarns with an accuracy sufficient in practice. It is found that, under large deformations, the properties of composites reinforced along cube diagonals differ qualitatively from their properties under small deformations. The evolution of the structural geometry of the deformed composite material is traced.     

Computing a composite reinforced shell structure by finite-element method

We consider a composite reinforced shell which contains a plate reinforced by longitudinal and transverse members. A special feature of the structure is the presence of cutouts. Finite-element analysis of the stressstrain state of the structure for four load configurations identifies the stress concentration zones.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 77–81, 1987.     

Braided reinforced composite rods for the internal reinforcement of concrete

This paper reports on the development of braided reinforced composite rods as a substitute for the steel reinforcement in concrete. The research work aims at understanding the mechanical behaviour of core-reinforced braided fabrics and braided reinforced composite rods, namely concerning the influence of the braiding angle, the type of core reinforcement fibre, and preloading and postloading conditions. The core-reinforced braided fabrics were made from polyester fibres for producing braided structures, and E-glass, carbon, HT polyethylene, and sisal fibres were used for the core reinforcement. The braided reinforced composite rods were obtained by impregnating the core-reinforced braided fabric with a vinyl ester resin. The preloading of the core-reinforced braided fabrics and the postloading of the braided reinforced composite rods were performed in three and two stages, respectively. The results of tensile tests carried out on different samples of core-reinforced braided fabrics are presented and discussed. The tensile and bending properties of the braided reinforced composite rods have been evaluated, and the results obtained are presented, discussed, and compared with those of conventional materials, such as steel. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 327–338, May–June, 2008.     

A 4D Composite Reinforced along Cube Diagonals with a Small Content of Yarns under Large Shear Deformations

The deformation behavior of a 4D composite reinforced along cube diagonals under large shear deformations is examined. The investigation is based on an applied theory which allows one to perform a macromechanical analysis of composite materials with small volume contents of reinforcing yarns to an accuracy sufficient in practice. Qualitative differences between the properties of such composites under large and small shear deformations are revealed. The evolution of the structural geometry of the deformed composite material is traced.     

Electrostrictive stresses near crack-like flaws

Slit cracks in purely dielectric material systems do not perturb any applied uniform electric field. Furthermore, when the dielectric is unconstrained and does not support any conducting plates or mechanical loads, there are no additional mechanical stresses generated in the material upon introduction of the crack. This situation applies to both electrostrictive and piezoelectric materials. However, flaws which have finite thickness such as thin elliptical or ellipsoidal voids will cause severe inhomogeneous concentration of the electric field. In turn, this can generate substantial mechanical stress from electrostrictive or piezoelectric sources. The effect of an elliptical through flaw in an infinite isotropic body is considered. It is found that, in the case of thin ellipses, the near flaw tip mechanical stresses approximate the singular stresses near a slit crack with an equivalent stress intensity factor. In that sense, the flaw may be considered as a slit crack and treated in terms of linear elastic fracture mechanics. However, except for impermeable and conducting flaws, the value of the equivalent stress intensity factor depends on the aspect ratio of the flaw. As the aspect ratio of the flaw diminishes, the magnitude of the equivalent stress intensity factor falls and disappears in the limit of a slit crack. The results are used to show that a flaw-like crack in a material with a very high dielectric constant can be treated by fracture mechanics as an impermeable slit crack when the flaw aspect ratio is an order of magnitude greater than the ratio of dielectric permittivities (flaw value divided by the value for the surrounding material).     

Nonlinear in-plane buckling of fixed shallow functionally graded graphene reinforced composite arches subjected to mechanical and thermal loading

The nonlinear in-plane buckling analysis for fixed shallow functionally graded (FG) graphene reinforced composite arches which are subjected to uniform radial load and temperature field is presented in this paper. The arch is composed of multiple graphene platelet reinforced composite (GPLRC) layers with gradient changes of concentration of graphene platelets (GPLs) in each layer. The principle of virtual work, combined with the effective materials properties estimated by the Halpin-Tsai micromechanics model for GPLRC layer, is used to derive the nonlinear buckling equilibrium equations of the FG-GPLRC arch, and then the analytical solutions for the limit point and bifurcation buckling loads are obtained. Comprehensive parametric studies are conducted to explore the effects of various distribution patterns and geometries of GPL, temperature field and arch geometry on the nonlinear equilibrium path and buckling behavior of the composite arch. The influence of temperature on the geometric parameters which are defined as switches between limit point buckling, bifurcation buckling and no buckling are also discussed. It is found that a higher temperature field can increase the buckling loads of the FG-GPLRC arch but reduce the value of the minimum geometric parameters that switching the buckling modes. The results also show that even a small amount of GPLs filler content can increase the buckling loads of the FG-GPLRC arch considerably, and distributing more GPLs near the surface layers is the best pattern to enhance the buckling performances of FG-GPLRC arches.     

Impact response of a cracked layer embedded in a composite

The impact response of a laminate composite with a crack or flaw normal to the interface is studied in terms of the intensification of the dynamic stresses around the crack border. Analytically, the laminate is modeled by a single layer with the crack sandwiched between two other layers of dissimilar material. Fourier and Laplace transforms are employed such that the problem reduces to the solution of a system of dual integral equations. Numerical results for the dynamic stress intensity factor are obtained by solving a Fredholm integral equation. The dynamic stress intensity factors are shown to fluctuate as a function of time, reaching a maximum that depends on the elastic properties of the composite and the flaw size.Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennysylvania 18015. Published in Mekhanika Polimerov, No. 5, pp. 835–840, September–October, 1978.     

纤维增强复合材料螺接接头挤压强度的估算方法

一些研究者采用比较简单有效的工程方法来估算纤维增强复合材料螺接接头的强度,但是这些方法均未考虑由于螺栓拧紧后对螺栓强度的影响。本文在对试验结果观察分析的基础上提出一种单孔螺接接头的临界挤压强度的估算方法,考虑了螺栓拧紧的效应。计算结果与碳/环氧迭层试验结果有较好的一致性。     

预测复合材料开裂方向的比应变能密度准则

本文提出预测复合材料中裂纹方向的比应变能密度准则,并将Tsai-Hill与Norris准则扩展来预测复合材料中的开裂方向.用这三个准则预测了具有各种不同纤维方向的单向纤维复合材料的裂纹扩展方向,预测结果与现有的比正应力准则和应变能密度准则进行了对比.     

A solid-shell finite element for fibre reinforced composites

Fibre reinforced composites consisting of several layers, each of which is composed of a woven fabric embedded in a matrix material, are investigated in this paper. Such materials are characterized by a complex anisotropic behavior, which necessitates a fully three-dimensional formulation of the constitutive equations. On the other hand, they are frequently used in thin shell-like applications. In order to account for the three-dimensional material law while still providing the suitable shape for thin structures, a solid-shell finite element for fibre composite materials is presented herein. Locking phenomena are treated by both the enhanced assumed strain (EAS) concept and the assumed natural strain concept (ANS). Using reduced integration together with hourglass stabilization leads to high computational efficiency. The anisotropic constitutive behavior of the composites is reflected by a micromechanically motivated continuum model, which –together with the solid-shell formulation– allows for an accurate representation of the through-the-thickness stress distribution even for thin structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

预测纤维增强复合材料层压板固有频率振型及模态阻尼的有限元算法

本文提供了预测纤维增强复合材料层压板固有频率、振型及模态阻尼的理论计算方法,此方法是综合了有限元法和阻尼单元模型,并考虑了横向剪应变和转动惯量的影响,本文给出了对称铺层石墨纤维及玻璃纤维复合材料层压板的理论计算结果,并给出实验数据进行对比.本文还提出一种预测复合材料层压板固有频率和阻尼的简易方法.     

Shear of orthogonally reinforced spherofibrous composites

The problem of determining the shear characteristics and interphase stress concentration of fibrous composites with spherical inclusions is examined on the basis of a three-phase model. Stress fields caused by diffusion interaction of phases are neglected. The elastic moduli of the composite are investigated and compared with those obtained from a two-phase model. The general formula for determination of the shear modulus of triorthogonally reinforced compsites is derived using previously investigated relationships for averaged stress fields. The matrix of these compsites contained spherical cavities. The dependence of integral characteristics of three-phase composites on their bulk phase concentration was investigated. The stresses between phases were studied as a function of composite structure.A. A. Blagonravov Machine-Science Institute, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, 104–111, January–February, 1997.     

Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects

Local scale effects for linear continuous media are investigated as applied to the composites reinforced by nanoparticles. A mathematical model of the interphase layer is proposed that describes the specific nature of deformations in the neighborhood of the interface between different phases in an inhomogeneous material. The characteristic length of the interphase layer is determined formally in terms of the parameters of the mathematical model. The local stress state in the neighborhood of the phase boundaries in the interphase layer is examined. This stress can cause a significant change of the integral macromechanical characteristics of the material as a whole if the interphase boundaries are long. Such a situation is observed in composite materials reinforced by microparticles and nanoparticles even when the volume concentration of the inclusions is small. A numerical simulation of the stress state is performed on the basis of the block analytical-numerical multipole method with regard for the local effects related to the special nature of the deformation of the interphase layer in the vicinity of the interface.     

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.     

Limiting stresses in spatially reinforced composites with components-having different structural geometries nd elastic properties

A model which is proposed for calculating structural stresses in spatially reinforced composites and an invariant-polynomial criterion for evaluating their limiting values are used to predict the effect of the elastic and strength properties of the components and their relative content on the limiting stress-strain state of composites of different structures. Emphasis is given to tri-orthogonal and 4D cubic structures, in addition to structures with hexagonal and angle-ply fiber reinforcement schemes in the plane and perpendicular to it. The types of composite loading typical of standard tests are examined in separate numerical experiments for shear, tension, compression, and their proportional combination. A computational variant of a criterional estimate of the limiting stresses is substantiated for an anisotropic composite of variable strength. The limiting-stress surface is obtained along with contour maps showing stress isolines as a function of the properties of the components and the geometry of the structure. The maps are suitable for practical use. The cases of maximum resistance to shear, tension, compression, and combination loading of 3D and 4D composites are compared to the analogous cases for two-dimensional structures.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 616–639, September–October, 1995.     

Boundary element method for calculation of effective elastic moduli in 3D linear elasticity

A boundary integral formulation of the linear elasticity problem for a multi‐component composite is given. The fast BEM solver based on the adaptive cross approximation is then obtained by the data‐sparse representation of the resulting Galerkin matrices. The solver is used to obtain effective elastic moduli of fibre and particle reinforced composites in three dimensions by means of the strain energy equivalence principle. Copyright © 2009 John Wiley & Sons, Ltd.