Elastic stability of skew laminated composite plates subjected to biaxial follower forces

The present study investigates the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces by the finite element method. The plate is assumed to follow first-order shear deformation plate theory (FSDPT). The kinetic and strain energies of skew laminated composite plate and the work done by the biaxial inplane follower forces are derived by using tensor theory. Then, by Hamilton's principle, the dynamic mathematical model to describe the free vibration of this problem is formed. The finite element method and the isoparametric element are utilized to discretize the continuous system and to obtain the characteristic equations of the present problem. Finally, natural vibration frequencies, buckling loads (also the instability types) and their corresponding mode shapes are found by solving the characteristic equations. Numerical results are presented to demonstrate the effects of those parameters, such as various inplane force combinations, skew angle and lamination scheme, on the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces.     

Strength of composite laminates under biaxial loads

Five well known failure criteria and one simple progressive model have been used in conjunction with laminate theory, which allows for nonlinear lamina shear behaviour, to predict the initial and final failure strengths of filament wound composite tubes. The predictions have been compared with experimental leakage and fracture stresses for ±75°, ±55° and ±45° filament wound GRP tubes subjected to a wide range of biaxial stress systems including biaxial compression. In some cases the fracture strengths were a factor of 10 higher than the initial failure predictions. The simple progressive failure theory predictions gave the best agreement with the experimental results.©British Crown Copyright 1996, Defence Evaluation and Research Agency published by Kluwer Academic Publishers with permission.     

A continuum damage mechanics model with the strain-based approach to biaxial low cycle fatigue failure

A continuum damage mechanics model for low cycle fatigue failure of initially isotropic materials under biaxial loading conditions is presented. The expression for the equivalent strain in the fatigue damage evolution equation contains the three material parameters, and the strain intensity as well as the maximum principal strain and the volume strain for amplitudes. It is shown how these material parameters can be determined from a series of basic experiments using a cruciform specimen. Particular expressions for the equivalent strain with a smaller number of material parameters and invariants are obtained. Model predictions are found to be in satisfactory agreement with the experimental low cycle fatigue data under full ranged biaxial loadings obtained in the test using a cruciform specimen.     

Biaxial deformation of Ti-6Al-4V and Ti-6Al-4V/TiC composites by transformation-mismatch superplasticity

Gas-pressure bulge forming of unreinforced Ti-6Al-4V and TiC-reinforced Ti-6Al-4V was performed while cycling the temperature around the allotropic transformation range of the alloy (880–1020 °C). The resulting domes exhibited very large strains to fracture without cavitation, demonstrating for the first time the use of transformation-mismatch superplasticity under a biaxial state of stress for both an alloy and a composite. Furthermore, much faster deformation rates were observed upon thermal cycling than for control experiments performed under the same gas pressure at a constant temperature of 1000°C, indicating that efficient superplastic forming of complex shapes can be achieved by transformation-mismatch superplasticity, especially for composites which are difficult to shape with other techniques. However, the deformation rate of the cycled composite was lower than for the alloy, most probably because the composite exhibits lower primary and secondary isothermal creep rates. For both cycled materials, the spatial distribution of principal strains is similar to that observed in domes deformed by isothermal microstructural superplasticity and the forming times can be predicted with existing models for materials with uniaxial strain rate sensitivity of unity. Thus, biaxial transformation-mismatch superplasticity can be modeled within the well-known frame of biaxial microstructural superplasticity, which allows accurate predictions of forming time and strain spatial distribution once the uniaxial constitutive equation of the material is known.     

Biaxial testing of high strength carbon fiber composite cylinders for pulsed magnet reinforcement

A methodology is introduced to test carbon-fiber-reinforced, hoop-wound composite cylinders for their biaxial mechanical properties under axial compression and hoop tension. The understanding of the behavior of these composites under biaxial loads is extremely important in the design of pulsed magnets. These composites are used as reinforcements for both the inner conducting layers and as an overall exterior reinforcement. Testing of actual pulsed magnets to ascertain design change effects of composite reinforcement schemes on the maximum attainable field can be expensive; hence, a standard biaxial testing method is desirable which is relevant to the design of pulsed magnets. In this investigation, an attempt was made to produce a standard testing procedure aimed at measuring the biaxial mechanical properties (elastic, plastic, and failure envelope) of composite materials. This methodology was applied to two different carbon/epoxy based composites. The results of these tests (elastic properties and failure points) are compared with theoretical predictions, specifically those due to Tsai-Wu.     

A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis

A simple model based on experimental observations of the yarn-parallel biaxial extension of PVC-coated polyester fabric cruciform specimens is proposed. In situ loading conditions are considered. The material behaviour is assumed to be plane stress orthotropic for a particular load ratio, while the elastic properties can vary with the load ratio in order to represent the complex interaction between warp and fill yarns. A linear relationship is experimentally found between elastic moduli and normalized load ratios for a wide range of PVC-coated polyester (Type I to Type IV). Two new parameters corresponding to the moduli variations are introduced to complement the existing plane stress orthotropic model. Theoretical results show that only five biaxial tests are required to accurately describe the material response with the proposed material model. Finally, the model was integrated in a commercial finite element software. It is shown that the proposed material model significantly increases the accuracy of the finite element predictions compared to the standard orthotropic linear material model with almost identical computation times.     

三维机织碳/碳复合材料双轴压缩载荷下的力学行为

基于三维机织碳/碳复合材料的细观结构特征, 设计平板十字形试样, 在材料双轴力学性能试验机上开展了复合材料单轴、 双轴加载压缩试验, 对比分析了三维机织碳/碳复合材料在双轴压缩载荷下的力学行为。研究表明: 三维机织碳/碳复合材料的压缩行为表现为非线性、 脆性断裂; 双轴载荷作用下非线性特征更为显著, 压缩模量随应力的增加而增大, 强度与模量相较于单轴有较大幅度增加, 双轴压缩载荷作用下材料的强化效应显著; 试样破坏位置并未出现在试样中心区, 而是发生在试样的加载端部或十字形试样的加载分枝根部, 主要表现为基体开裂、 纤维断裂和层间脱粘, 碳布及其层间界面剪切强度的强弱直接影响材料的压缩强度。     

A thermo-micro-mechanical modeling for smart shape memory alloy woven composite under in-plane biaxial deformation

This paper presents a theoretical study of the in-plane behavior of Smart Shape Memory Alloy Woven Composites (SSMAWC) under biaxial loading by developing an integrated micromechanical constitutive model. The model studied in this research is established on the geometric parameters of fibers, metal layers, unit cell, the material constants of composite constituents, and the orientation of fibers, in which the fibers in one direction are SMA ones. The Helmholtz free energy of a Shape Memory Alloy, in 3-Dimensional and 1-Dimensional applications is derived. Using mechanical energy of matrix and elastic yarns, the constitutive relations are developed with the use of strain energy approach and energy variation theorem. The kinetic relations of SMA depicted by Brinson is coupled with the final governing equation of the composite to predict the stress history in smart shape memory alloy woven composites. The deflection of the structure, subjected to uniform biaxial loading is studied numerically. It is found that the effect of Shape Memory Effect (SME) of the SMA wires on the behavior of plain woven flexible fabric composite is significant.     

A micromechanical characterization of graphite-fiber/epoxy composites containing a heterogeneous interphase region

An improved micromechanical model based on the method of cells is introduced in order to describe three-phase, continuous-fiber composite materials containing a heterogeneous interphase region. The model's capability represents a significant improvement over that of the previous version (which is applicable to a homogeneous interphase) in that additional microstress information is obtained within the interphase region. A critical assessment of the model demonstrates that the predictions are consistent with data reproduced by using other micromechanical models. The study includes a parametric simulation in which the effective properties and the mechanical stresses associated with model graphite-fiber/epoxy composites are predicted as a function of the dimensions and Young's modulus of the interphase. Three different interphases are modeled such that the Young's modulus varies between that of the fiber and the matrix according to a generalized parabolic function of the radial coordinate. The parabolic functions are specified such that two of the model composites possess an interphase whose effective Young's modulus is above that of the matrix. The third interphase is specified such that its effective Young's modulus is below that of the matrix. The data indicate that the interphase dimensions and the functional form describing the interphase Young's modulus significantly influence the composite microstresses. These data may be used to help identify optimum material combinations during composite material synthesis.     

Biaxial experimental determination of in-plane matrix fracture envelope of unidirectional composite

A test procedure for the determination of the in-plane fracture envelope of unidirectional fibre reinforced polymers (FRP) is presented. In particular, the determined fracture envelope covers combined in-plane shear and transverse (perpendicular to the fibre direction) matrix strength. The proposed test procedure allows the manufacture of specimens for material fracture characterisation in the same way that real composite structures are usually produced for the automotive industry. The biaxial testing is performed using a custom-made dual actuator test machine and keeping the ratio of transverse and shear load constant until fracture. The experimentally obtained transverse–shear strength relation can be well represented by the matrix fracture model by Puck. It is shown that the stress concentrations in the gauge section of the flat biaxial specimens can be avoided by the introduction of a thickness reduction, whereas the stress concentrations within biaxial specimens without such a thickness reduction lead to significantly lower strength.     

Nonlinear Analysis of Woven Fabric-Reinforced Graphite/PMR-15 Composites under Shear-Dominated Biaxial Loads

An elastic-plastic, time-independent, macroscopic, homogenous model of an 8HS woven graphite/PMR-15 composite material has been developed that predicts the nonlinear response of the material subjected to shear-dominated biaxial loads. The model has been used to determine the response of woven composite off-axis and Iosipescu test specimens in nonlinear finite element analyses using a multilinear averaging technique. The numerically calculated response of the specimen was then compared to experimentally obtained data. It has been shown that the numerically calculated stress - strain diagrams of the off-axis specimens are very close to the experimentally obtained curves. It has also been shown that the numerically determined shear stress - strain and load-displacement curves of the woven Iosipescu specimens are close to the experimentally obtained curves up to the point of significant interlaminar damage initiation and propagation. The results obtained in this study clearly demonstrate that the nonlinear material behavior of the graphite/polyimide woven composites subjected to shear-dominated biaxial loading conditions cannot be ignored and should be considered in any stress analysis. The linear-elastic approach grossly overestimates the loads and stresses at failure of these materials in the off-axis and Iosipescu tests. It can be assumed that the same discrepancies will arise in the numerical analysis of the woven composites tested under other biaxial shear-dominated loading conditions using other biaxial test methods.     

Thermoviscoelastic models for polyethylene thin films

This paper presents a constitutive thermoviscoelastic model for thin films of linear low-density polyethylene subject to strains up to yielding. The model is based on the free volume theory of nonlinear thermoviscoelasticity, extended to orthotropic membranes. An ingredient of the present approach is that the experimentally inaccessible out-of-plane material properties are determined by fitting the model predictions to the measured nonlinear behavior of the film. Creep tests, uniaxial tension tests, and biaxial bubble tests are used to determine the material parameters. The model has been validated experimentally, against data obtained from uniaxial tension tests and biaxial cylindrical tests at a wide range of temperatures and strain rates spanning two orders of magnitude.     

Modelling of the mechanical behaviour of a 2-D SiC-SiC composite at a meso-scale

An original meso-model of the mechanical behaviour of a 2-D SiC-SiC composite is proposed. In order to take into account the main elementary constituents of the composite (which govern the material damage), the composite material and the damage mechanisms are described at an intermediate scale referred to as the meso-scale. The laminate meso-model is defined with an arrangement of one ‘inter-tow matrix and pores’ ply and four ‘unidirectional composite’ plies. The model is validated on the basis of comparisons between numerical simulations of the mechanical behaviour of the composite under both off-axis tensile (or biaxial stress state) testing conditions, and experimental data.     

A solution for the problem of load introduction in biaxial fatigue tests

The concept of introduction of biaxial loads in a specimen made of sheet material using soft clamps of unidirectional aramid composite sheet is presented. Using this concept it is possible to generate realistic biaxial tensile stress states in specimens made of sheet materials without the introduction of unwanted fatigue critical areas.     

Application of the biaxial Iosipescu method to mixed-mode fracture of unidirectional composites

In this paper the biaxial Iosipescu test method has been used, employing specimens with a central precrack placed along the notch-root axis, to study the intralaminar failure properties of a unidirectional carbon/epoxy composite under mixed-mode (dominated by shear) loadings. A linear finite element analysis has been performed to determine the energy release rates and stress intensity factors for the central crack under various biaxial loading conditions. In addition, a series of simple and biaxial fracture experiments have been performed on the composite material. Numerical results indicate that the method is capable of generating a wide range of mixed-mode loading conditions at the crack tip for various loading angles and crack lengths. Using the numerical results, in conjunction with experimental data, the biaxial intralaminar failure process in the cracked Iosipescu specimens has been explained.     

编织复合材料弹性性能的细观分析及试验研究

基于细观分析与体积平均法建立了二维编织/RTM复合材料刚度的理论分析方法,该分析方法针对工程应用,具有计算量较小、计算精度高等优点,完成了相应的软件分析工具,并在此基础上对编织复合材料的弹性性能进行分析研究,得到了结构参数对编织复合材料整体力学性能的影响。通过与实验数据的对比表明,分析结果精度高,能够满足工程结构设计和理论分析的需要,为二维编织复合材料的设计、分析和减少试验件提供了理论分析方法。      

Modeling of smart composites on account of actuation,thermal conductivity and hygroscopic absorption

The asymptotic homogenization models for smart composite materials are derived and effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients for smart structures are obtained. The actuation coefficients characterize the intrinsic transducer nature of active smart materials that can be used to induce strains and stresses in a coordinated fashion. Examples of such actuators employed with smart composite material systems are derived from piezoelectric, magnetostrictive, and some other materials. The pertinent mathematical framework is that of asymptotic homogenization. The objective is to transform a general anisotropic composite material with a regular array of reinforcements and/or actuators into a simpler one that is characterized by some effective coefficients; it is implicit, of course, that the physical problem based on these homogenized coefficients should give predictions differing as little as possible from those of the original problem. The effectiveness of the derived models is illustrated by means of two- and three-dimensional examples.     

Analytical model for prediction of load capacity of RC columns confined with CFRP under uniaxial and biaxial eccentric loading

This paper presents an analytical model for prediction of the load carrying capacity of reinforced concrete (RC) columns confined with carbon fiber reinforced polymers (CFRP) under uniaxial and biaxial eccentric loading. The model is based on realistic material laws and accounts for the non-linear stress–strain behavior of both unconfined and CFRP-confined concrete. Under uniaxial eccentric loading, the column cross-section is discretized into finite layers along the section depth. For a symmetric square cross-section subjected to biaxial eccentric loading with equal eccentricity about each principal axis, the column cross-section is discretized into finite layers along the diagonal of the column cross-section. For a given strain distribution in a direction perpendicular to the neutral axis, the sectional forces are integrated numerically and the load capacity of the column is predicted using an iterative process. For rectangular and non-symmetric square cross-sections subjected to biaxial eccentric loading, the load capacities under uniaxial eccentric loading along each principal axis are first derived independently. The column load capacity under concentric axial loading is calculated. The determined distribution of the column load capacities under uniaxial eccentric loading and concentric loading are then utilized to compute the load capacity under biaxial eccentric loading using the reciprocal load equation. An experimental study was carried out to examine the effectiveness of the CFRP-confinement to improve the load capacity and ductility of RC columns under biaxial eccentric loading. The accuracy of the proposed analytical model was demonstrated by comparing the model predictions to results of the current experimental study in addition to experimental data published in the literature.     

Normalisation of biaxial bias extension test results considering shear tension coupling

A theoretical background is proposed for the normalisation of biaxial bias extension results for rate-independent fabrics, whose shear compliance depends on both the shear angle and the fibre tension within the fabric. The theory is used to predict the form of biaxial bias extension results from known shear force–shear angle–fibre tension behaviours. Hypothetical data sets are used to perform a parametric study of the likely influence of the nature of the shear–tension coupling on the form of the biaxial bias extension test results. The theory is then used in implementing an iterative numerical code designed to retrieve the underlying material response from biaxial bias extension test results and examples predictions are given. A discussion of the information required in order to perform the normalisation, and the methods by which this information can be obtained, is presented. Finally, assumptions behind the theory are outlined and critically assessed.     

Beyond plain weave fabrics – I. Geometrical model

In response to the large variety of weaving styles offered by the textile industry, a new general approach for the geometrical modeling of 2D biaxial orthogonal woven fabric reinforcements for composite materials is proposed here. New geometrical parameters are introduced in order to describe general families of twill and satin woven patterns, and a new classification of woven fabrics is proposed based on these parameters. Generation of the 3D internal geometry of the woven fabric families is achieved based on new geometrical functions that consider the actual configuration of the composite material in all its complexity. The proposed geometrical model is intended as the foundation for further analytical or numerical modeling of the mechanical properties of the composite materials reinforced with these fabrics.