An electromechanical higher order model for piezoelectric functionally graded plates

Bidirectional flexure analysis of functionally graded (FG) plate integrated with piezoelectric fiber reinforced composites (PFRC) is presented in this paper. A higher order shear and normal deformation theory (HOSNT12) is used to analyze such hybrid or smart FG plate subjected to electromechanical loading. The displacement function of the present model is approximated as Taylor’s series in the thickness coordinate, while the electro-static potential is approximated as layer wise linear through the thickness of the PFRC layer. The equations of equilibrium are obtained using principle of minimum potential energy and solution is by Navier’s technique. Elastic constants are varying exponentially along thickness (z axis) for FG material while Poisson’s ratio is kept constant. PFRC actuator attached either at top or bottom of FG plate and analyzed under mechanical and coupled mechanical and electrical loading. Comparison of present HOSNT12 is made with exact and finite element method (FEM).     

A bimodal plasticity theory of fibrous composite materials

Summary It is shown that elastic-plastic response of metal matrix composites reinforced by aligned continuous fibers can be described in terms of two distinct modes. In the matrix-dominated mode, the composite deforms primarily by plastic slip in the matrix, on planes which are parallel to the fiber axis. In the fiber-dominated mode, both phases deform together in the elastic and plastic range. Constitutive equations are derived for the matrix-dominated mode of deformation in composites with elastic-perfectly plastic matrices. Response in the fiber-dominated mode is approximated by the self-consistent and Voigt models. The two deformation modes give different branches of the overall yield surface which identify the state of stress that activates a particular mode, and indicate the conditions for mode transition in a given composite system. The matrix-dominated mode is found to exist in systems reinforced by fibers of large longitudinal shear stiffness, such as boron or silicon carbide. Systems reinforced by more compliant fibers, such as graphite, appear to deform exclusively in the fiber-dominated mode. The results show good agreement with experimental data, and with predictions obtained from a more accurate material model. They also help to reconcile several different plasticity theories of fibrous composites, and suggest limits of their validity.With 9 FiguresPrepared for the Symposium on Plasticity: Foundations and Future Directions. In Memory of Aris Phillips. January 28–30, 1987. University of Florida, Gainesville, U.S.A.     

Calculation of effective coefficients for piezoelectric fiber composites based on a general numerical homogenization technique

Numerical unit cell models for 1–3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method (FEM) and it allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method (AHM) for different fiber volume fractions.     

The influence of the elastic properties and dimensions of coatings on the stiffnes of encapsulated fiber composites

The effect of coating around fibers embedded in an isotropic matrix on the stiffness of the composite, due to the variation of the coating thickness and rigidity, is examined in this paper. The model of the representative volume element (RVE) of the composite consisted of a cylindrical fiber coated by an annular layer, the encapsulated fiber being embedded in a matrix annulus enveloped by an infinite region of an equivalent composite, which constitutes the rest of the composite. This model constitutes an extension of the Christensen and Kerner models. By varying the rigidity and the thickness of the encapsulation, the longitudinal, transverse and shear elastic moduli of the composite were determined. Interesting results concerning the composite stiffness were established by selecting types of composite having different rigidities for the constituent phases. Furthermore, specific examples of encapsulated fiber composites usually encountered in applications were considered where the properties of the composite are changed by the sizing effect due to encapsulations.     

Microstructure and mechanical properties of Al–2Mg alloy base short steel fiber reinforced composites prepared by vortex method

Fabrication and characterization of cast Al–2Mg alloy matrix composites reinforced with short steel fibers are dealt with in the present study. Three types of steel fiber were used: uncoated, copper coated and nickel coated. All the composites were prepared by the liquid metal route using vortex methods. When tested in tension, all composites exhibited improvement in strength due to high relative strength of steel fibers. The ductility was lowered except for the composite with copper coated fibers. Copper coated fiber reinforced composites gave the highest strength. Higher strength accompanied with appreciable ductility demonstrated by composites with copper coated fibers is attributed to the solid solution and fiber strengthening as well as good bonding at the interface. Composites reinforced with uncoated and Ni coated steel fibers did not exhibit strengthening to the level exhibited with copper coated fibers because brittle intermetallic phases are formed at the interface. These phases promote initiation and facilitate propagation of cracks. The observed fracture mechanism of composites was dimple formation, fiber breakage and pullout of fibers. Fracture surface of uncoated and Ni coated composites showed extensive pull out of fibers as well as fiber breakage confirming the above inference. In case of the copper coated composites dimple formation and coalescence was more extensive. EDX analysis showed a build up Cu, Ni, and Fe at the interface.     

Constitutive relations for the thermomechanical behavior of fiber-reinforced inelastic laminates

The thermomechanical behavior of laminated composites in which every lamina is unidirectional fiber-reinforced thermoinelastic material is determined by a micromechanical analysis followed by a macromechanical one. In the micromechanical analysis, effective constitutive relations are derived for unidirectional fibrous materials in which the matrix and fiber phases are thermoelastic in the linear region and thermoinelastic in the nonlinear region. The derivation is based solely on the material properties of fibers and matrix and amount of reinforcement. By a macromechanics analysis the gross behavior of the laminated composite in stretching and bending deformation is determined. Applications are given for the deformation field developed in cooling and reheating of graphite/aluminium laminated plates.     

Enhanced polarization in zirconia-P(VDF-TrFE) laminar composite dielectrics

Zirconia-P(VDF-TrFE) double-layered laminar composites are experimentally investigated to understand inorganic–organic interfacial effects in composite dielectrics. The DC and AC electrical response of the individual phases were characterized in addition to the zirconia-P(VDF-TrFE) composite. The measured real part of permittivity for the laminar composite is found to be higher than theoretically calculated values using series mixing rules for zirconia and P(VDF-TrFE). Additional polarization of the composite structure can be attributed to either the presence of interfacial polarization of zirconia and P(VDF-TrFE) or modification of polymer. Impedance spectroscopy has shown that dielectric properties of laminar composites are dominated by zirconia thin films in low frequency region. The impedance spectroscopy shows that zirconia blocks charge carrier motion and hence partially contribute towards additional interfacial polarization in the laminar composite. The dielectric response of the laminar composite was also modeled through a Maxwell–Wagner interfacial polarization mechanism, which was found to inadequately describe the polarization response. Equivalent circuit modeling of the composite has revealed an additional interfacial circuit element for the additional polarization, suggesting a structurally modified polymer at the interface.     

Dual scale non-linear stress analysis of a fibrous metal matrix composite

Precise estimation of local stress profiles in individual phases of a fiber reinforced metal matrix composite is a crucial concern for design of composites. Stress profiles are significantly affected by plastic relaxation of soft matrix. In this work, an analytical model was developed to compute local stress profiles in individual phases of fibrous metal matrix composites. To this end, embedded cell cylindrical composite model was applied in which a layered concentric cylinder consisting of a fiber-, matrix- and homogenized composite layers was used. Mean field micromechanics was integrated into the conventional elasticity solution process so that micro-macro dual scale analysis could be performed. The algorithm was formulated in an iterative incremental structure which was able to perform plastic analysis. This also allows temperature dependence of flow stress to be considered. Taking copper-SiC system as a reference composite, stress profiles were obtained for mechanical and thermal loading cases. For comparison, independent finite element analyses were carried out for two different unit cell models. Excellent agreement between analytical and numerical solutions was found for the mechanical loading case even for plastic range. In the case of thermal loading, however, plastic solutions revealed notable difference in quantity, especially for the axial stress component.     

Experimental and Numerical Investigations on the Ballistic Performance of Polymer Matrix Composites Used in Armor Design

Ballistic properties of two different polymer matrix composites used for military and non-military purposes are investigated in this study. Backside deformation and penetration speed are determined experimentally and numerically for Kevlar 29/Polivnyl Butyral and Polyethylene fiber composites because designing armors for only penetration is not enough for protection. After experimental ballistic tests, a model is constructed using finite element program, Abaqus. The backside deformation and penetration speed are determined numerically. It is found that the experimental and numeric results are in agreement and Polyethylene fiber composite has much better ballistic limit, the backside deformation, and penetration speed than those of Kevlar 29/Polivnyl Butyral composite if areal densities are considered.     

氧化铝短纤维增强铝基复合材料的蠕变破坏行为

研究了挤压铸造Al₂O₃短纤维增强铝基复合材料在350℃恒应力条件下的蠕变行为。蠕变试验过程中采用中断实验的方法对复合材料的显微组织进行观察,发现复合材料在蠕变过程中纤维发生断裂,弱界面发生破坏以及基体合金在应力作用下发生变形。根据复合材料在蠕变三个阶段中显微组织的变化情况,对其宏观蠕变行为进行了分析,认为位错在复合材料中滑移和攀移控制整个蠕变过程,并提出了短纤维增强金属基复合材料的蠕变断裂机理,合理地解释了复合材料的蠕变过程。      

Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors

A benchmark three-dimensional (3D) exact piezoelasticity solution is presented for free vibration and steady state forced response of simply supported smart cross-ply circular cylindrical shells of revolutions and panels integrated with surface-bonded or embedded monolithic piezoelectric or piezoelectric fiber reinforced composite (PFRC) layers. The effective properties of PFRC laminas for the 3D case are obtained based on a fully coupled iso-field model. The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends. These equations with variable coefficients are solved using the modified Frobenius method, wherein the solution is constructed as a product of an exponential function and a power series. The unknown constants of the general solution are finally obtained by employing the transfer matrix method across the layers. Results for natural frequencies and the forced response are presented for single layer piezoelectric and multilayered hybrid composite and sandwich shells of revolution and shell panels integrated with monolithic piezoelectric and PFRC actuator/sensor layers. The present benchmark solution would help assess 2D shell theories for dynamic response of hybrid cylindrical shells.     

国产碳纤维增强树脂基复合材料应变不变量性能

应变不变量失效理论是一种新型的基于物理失效模式的复合材料强度理论, 广泛应用于复合材料结构失效分析。根据该理论, 建立了碳纤维增强树脂基复合材料微观力学模型, 获取树脂基体和纤维不同位置的机械应变放大系数和热应变放大系数。对国产复合材料CCF300/5228、CCF300/5428和T700/5428不同铺层角单向层合板进行拉伸试验, 并根据试验结果得到对应复合材料的应变不变量性能。分析了增强体纤维和树脂基体对复合材料应变不变量性能的影响; 并将应变不变量失效理论应用于国产复合材料失效分析。结果表明碳纤维增强树脂基复合材料应变不变量性能中的第一应变不变量和基体Von-Mises应变临界值取决于树脂, 而纤维Von-Mises应变临界值取决于增强体纤维; 应变不变量失效理论能够用于国产复合材料失效分析。      

How to improve mechanical properties of polylactic acid with bamboo fibers

Bamboo fibers (BF) were mixed in polylactic acid (PLA) to improve its mechanical properties: impact strength and heat resistance. Three different types of BF were extracted from raw bamboo by either sodium hydroxide (NaOH) treatment or steam explosion in conjunction with mechanical processing. They were designated as “short fiber bundle,” “alkali-treated filament” and “steam-exploded filament,” respectively. Composite samples were fabricated by injection molding using PLA/BF pellets prepared by a twin-screw extruding machine. Among them, the highest bending strength was obtained when steam-exploded filaments were put into PLA matrix. Impact strength of PLA was not greatly improved by addition of short fiber bundles as well as both filaments. In order to improve the impact strength of PLA/BF composites, PLA composite samples were alternatively fabricated by hot pressing using medium length bamboo fiber bundles (MFB) to avoid the decrease in fiber length at fabrication. Impact strength of PLA/MFB composite significantly increased, in which long fiber bundles were pulled out from the matrix. The addition of BF improves thermal properties and heat resistance of PLA/BF composites due to the constraint of deformation of PLA in conjunction with crystallinity promoted by anneal (at 110 °C for 5 h).     

Creep behavior of SiC fiber-reinforced hot-pressed Si3N4 composites

The creep response of SiC fiber-reinforced Si₃N₄ composites has been measured using four-point flexural loading at temperatures of 1200–1450°C and stress levels ranging from 250 to 350 MPa. Parameters characterizing the stress and temperature dependence of flexural creep strain rates were determined. A numerical analysis was also performed to estimate the power-law creep parameters for tensile and compressive creep from the bend test data. The incorpoporation of SiC fiber into Si₃N₄ resulted in substantial improvements in creep resistance even at very high stresses. The steady-state creep deformation mechanism, determined to be subcritical crack growth in the unreinforced matrix, changed to a mechanism in the composites of repeated matrix stress relaxation-fiber rupture-load dispersion by the matrix. Multiple fiber fracture rather than multiple matrix cracking resulted. The tertiary creep in the composite resulted from the rapid growth of the microcracks which initiated from the fiber rupture sites. Fiber strength, matrix cracking stress and interfacial shear strength have been identified as the key microstructural parameters controlling the creep behavior of the composite.     

Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate

In this paper, the problem of interfacial stresses in steel beams strengthened with bonded hygrothermal aged composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach developed by Tounsi (Int. J. Solids Struct. 43:4154–4174, 2006) where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the steel beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient ξ is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.     

Effect of Reactive Graphitic Nanofibers (r-GNFs) on Tensile Behavior of UHMWPE Fiber/Nano-Epoxy Bundle Composites

Ultra-high molecular weight polyethylene (UHMWPE) fibers have good mechanical and physical properties and effective radiation shielding functions, which are significant for aerospace structures. In our previous work, nano-epoxy matrices were developed based on addition of reactive graphitic nanofibers (r-GNFs) in a diluent to form a blend. It is found that improved wettability and enhanced adhesion of the matrices to UHMWPE fibers can be obtained. In this study, a series of nano-epoxy matrices with different concentrations of r-GNFs (up to 0.8 wt%) and different weight ratios of r-GNFs to a reactive diluent (1:4, 1:6, 1:7, and 1:9) were prepared. Composite bundle specimens of UHMWPE fiber/nano-epoxy were fabricated and their tensile behavior was investigated. All load-displacement curves of the UHMWPE/nano-matrix bundle composites under tensile loading showed three regions corresponding to the three deformation and failure stages of the materials: 1) elastic deformation stage, 2) plateau stage, and 3) UHMWPE fiber failure stage. The nano-epoxy with 0.3 wt% of r-GNFs and with 1:6 ratio of r-GNFs to the diluent proved to be the best matrix for UHMWPE fiber composites with enhanced tensile properties. For the resulting composite, the load level and consumed energy in the plateau stage were increased by 8% and 30% over the UHMWPE fiber/pure-epoxy specimens, respectively. This UHMWPE fiber composite with the optimized nano-epoxy matrix also possesses the highest initial stiffness and ultimate tensile strength among all the resulting UHMWPE fiber composites. These results laid a foundation for us to fabricate UHMWPE fiber reinforced composite laminates in the near future.     

弹道防护用先进复合材料弹道响应的研究进展

本文对弹道防护用先进复合材料的弹道响应研究及其在工程领域的应用现状进行了综述。首先,基于工程应用研究的试验结果,对超高分子量聚乙烯(UHMWPE)纤维、对位芳香族聚酰胺(PPTA)纤维、芳Ⅲ纤维、聚对苯撑苯并双噁唑(PBO)纤维和聚酰亚胺(PI)纤维等高性能纤维的防弹性能及其复合材料在弹道防护工程领域的应用现状进行了概述,近年来先进复合材料的防弹性能随着纤维力学性能的突破而逐渐提高;其次,讨论了先进复合材料弹道响应的影响因素及其作用机制,发现先进复合材料的塑性拉伸变形是其抵挡弹丸侵彻的主要防弹机制;最后,对弹道防护用先进复合材料的研究方向进行了展望。      

Thermomechanical analysis of elastic–plastic fibrous composites comprising an inhomogeneous interphase

An analytical approach is presented to investigate thermomechanical response of composites consisting of a transversely isotropic fiber, an inhomogeneous interphase and an elastic–plastic matrix. Using the existing cubic variation to describe the continuous change of the material properties of the interphase and dividing the interphase into a number of subdomains, the continuously varying material properties of the interphase are approximated by the constant ones of these subdomains, and the deformations and stresses of the interphase are described with the same formulae as those of transversely isotropic fibers. The analytical expressions of elastic–plastic deformations and stresses of the matrix are obtained from the basic equations of axisymmetric problems in elasticity, the assumption of generalized plane strain, the linear strain–hardening stress–plastic strain relation, Tresca’s yield condition, the associated flow rule and impressibility of plastic deformation. The boundary conditions of the composites and the continuities of the radial displacement and stress between different components are used to determine all the unknown constants and the obtained analytical solution is applied to thermomechanical analysis of the composites. The effects of the inhomogeneity of the interphase, and the plasticity and material properties of the matrix on the thermomechanical response of the composites are investigated.     

Magnetoelectric coupling and cross-property connections in a square array of a binary composite

Effective elastic, dielectric, magnetic, piezoelectric, piezomagnetic and magnetoelectric properties for the anti-plane shear magnetoelectroelastic state are determined. This properties are calculated by means of the Asymptotic Homogenization Method for a composite material with unidirectional cylindrical fiber periodically distributed in a square array. Closed-form formulae are obtained for the effective properties. The formulae exhibit explicitly the dependence on (i) the geometry through fiber volume fraction, (ii) the periodicity of the array through its lattice sums, and finally (iii) the material properties of the phases. Anti-plane property calculations are carried out for BaTiO₃/CoFe₂O₄ composite. The local problem is solved using potential methods of a complex variable. The solution involves double periodic Weierstrass elliptic and related functions. The shear modulus experiments a stiffening due to the coupling piezoelectric and piezomagnetic effect. Both exact and empirical cross-property connections are found for these composites. For the empirical case, the knowledge of the anti-plane effective dielectric property, ε₁₁, experimentally or otherwise, yields the remaining ones, “plane and anti-plane”, with good accuracy within a wide range of fiber volume fractions. The magnetoelectric effect results from the mechanical interaction between constituents. Hence, in order to maximize the magnetoelectric coefficient during composite design, matrix plane shear modulus must be as higher as possible than plane bulk modulus.