Design of Fibre Reinforced Composite Structures Subjected to High Strain Rates Using Finite Element Analysis

A finite element analysis of fibre reinforced plastic tubes subjected to a dynamic internal pressure pulse is performed using the ABAQUS finite element program. The effects of strain rate on the ply properties, the nonlinearity of the stress-strain curves, failure and post-failure theories are incorporated in the analysis. The results of the analysis show good agreement with the experimental stress-strain and strain-time results for 45° and 65° Kevlar fibre reinforced epoxy (KRP) tubes.     

Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading

Transverse cracking behaviour in a quasi-isotropic glass/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°/90°/–45°/45°] _S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the neutral axis position and the residual curvature as a function of the transverse crack density and the in-situ ply stress at first ply failure. Experimental results are obtained with the use of the applied moment – strain data in four-point flexural tests and compared with predictions. Time-dependent behaviour of the residual curvature is also investigated.The theoretical predictions are in reasonably good agreement with the experimental results. It is found that the decrease in the residual curvature after unloading is mainly ascribed to viscoelasticity of the material.     

Simultaneous determination of in-plane shear and transverse moduli of unidirectional composite laminae at different strain rates and temperatures

A semi-empirical method is proposed for the extraction, simultaneously, of the transverse tensile and in-plane shear moduli of unidirectional laminae, at various strain rates and temperatures, from tests on symmetric and balanced ±65 ° angle-ply composite laminates. The extraction method is applied to data obtained from tests on Kevlar-49/epoxy and carbon/ epoxy filament-wound tubes which were subjected to internal pressure loading at three key temperatures of −45, 20 and 70 °C at different strain rates of up to 80/s. The combined effect of strain rate and temperature on these extracted properties is studied by applying strain rate temperature equivalence principles. It is found that the variation of the mechanical properties of the two materials with strain rate and temperature can be adequately described by semi-empirical equations similar to the Arrhenius and Williams-Landel-Ferry relationships, usually used for homogeneous solids.     

铺层拼接层合板的抗拉强度

针对复合材料结构设计中遇到含铺层拼接的层合板强度预测问题,本文设计了含铺层交错拼接区的碳/双马复合材料层合板试件,采用拉伸试验方法测定了该材料的力学性能,得到了不同拼接长度层合板的抗拉强度。试验结果表明,铺层拼接状态差异对复合材料层合板的承载能力有显著影响,文中根据试验结果建立了抗拉强度随拼接长度变化的经验公式,为复合材料层合板结构的铺层设计和强度分析提供了理论依据。     

Effect of Temperature on the Tensile Strength and Failure Modes of Angle Ply Aramid Fibre (KRP) Tubes Under Hoop Loading

A comprehensive study was undertaken to characterise Kevlar reinforced plastic (KRP) angle ply filament wound tubes at different temperatures. Quasi-static burst tests were performed on tubes of 25°, 55° and 75° winding angle. The tubes were burst under internal radial pressure with minimum end constraints. An experimental rig and two conditioning tanks were designed and built to test the specimens at three temperatures; –46°C (low temperature) and +20°C (room temperature) and +70°C (high temperature). For each test the internal pressure and the strains in both circumferential and longitudinal directions were recorded on suitable digital processing equipment.For a particular batch of tubes tested at three different temperatures, an increase in ultimate hoop strain and a decrease in hoop modulus of the 55° tubes with increasing temperatures was recorded; the temperature effect was less pronounced on the corresponding properties of 25° and 75° tubes. The use of a non-structural thin liner during the tests led to a higher ultimate strength of 55° tubes but had negligible effect on the behaviour of 25° and 75° tubes. The 75° tubes failed in a catastrophic fibre fracture under all test conditions. The mode of failure of 55° changed from weeping at 70°C to fibre fracture at –46°C. The 25° tubes failed by weeping with matrix cracking. The matrix cracking was particularly severe when a liner was used.     

Investigating the transverse behavior of Glass–Epoxy composites under intermediate strain rates

In this study, the strain rate effects on transverse tensile and compressive properties of unidirectional Glass fiber reinforced polymeric composites are investigated. To demonstrate strain rate effects, the tensile and compressive composite specimens with identical configuration are fabricated and tested to failure in the transverse direction at quasi-static strain rate of approximately 0.001 s⁻¹ and intermediate strain rates of 1–100 s⁻¹. The tensile and compressive tests are performed using a servo-hydraulic testing apparatus equipped with strain rate increasing mechanisms. For performing the practical tests, a jig and a fixture and other test supplies are designed and manufactured. The performance of the test jig is evaluated and showed that it is adequate for composites testing under tension and compression loads. The effects of strain rate on mechanical properties (maximum strength, modulus, and strain to failure) are considered. The characteristic results for the transverse properties indicate that damage evolution is strain-rate-dependent for the examined material. Also, a strain-rate-dependent empirical material model associated with different regression constants is proposed based on the experimental results obtained to characterize the rate dependent behavior of Glass/Epoxy composite material.     

The static and high strain rate behaviour of a commingled E-glass/polypropylene woven fabric composite

In this paper the effect of strain rate on the tensile, shear and compression behaviour of a commingled E-glass/polypropylene woven fabric composite over a strain rate range of 10⁻³–10² s⁻¹ is reported. The quasi-static tests were conducted on an electro-mechanical universal test machine and a modified instrumented falling weight drop tower was used for high strain rate characterisation. The tensile and compression modulus and strength increased with increasing strain rate. However, the shear modulus and strength were seen to decrease with increasing strain rate. Strain rate constants for use in finite element analyses are derived from the data. The observed failure mechanisms deduced from a microscopic study of the fractured specimens are presented.     

Transverse ply cracking strains in (0°/90°) and (±θ°/90°) laminates

Comparisons have been made between experimental data on transverse ply cracking in various types of (0°/90°) and (°/90°) laminates and the predictions of the constrained cracking and strain field theory. Generally it is observed that the predictions of the strain field theory are in closer agreement with the experimental data over a wider range of experimental conditions than those of the constrained cracking model. It is shown that reasonable agreement with the observed transverse ply cracking strains of various laminates produced from similar material can be obtained through the use of a standard set of material property values.     

Characterization of the in-situ non-linear shear response of laminated fiber-reinforced composites

A simple procedure to determine the non-linear in-plane lamina shear response of laminated composites is presented. Using the ±45° symmetric laminate tensile test results, in conjunction with computational micromechanics, a method was developed and validated to characterize the lamina shear response and the in-situ matrix shear response. Load, and axial and transverse strains measured in the tests were used to calculate the non-linear shear stress–shear strain response of the composite. From this result, the in-situ matrix equivalent stress–strain response was obtained, with some simplifying assumptions, and subsequently used in a micromechanics-based representative finite element (FE) model of the ±45° symmetric laminate tensile test to determine the accuracy of the non-linear response of the in-situ matrix. Results from the FE model of a representative cell (RC) that depicts fiber diameter, fiber volume fraction (V_f) and angled fiber packing of the ±45° symmetric laminate were found to match the tests result well. Thus, the procedure to extract the non-linear lamina shear response and the non-linear in-situ matrix response from the ±45° symmetric laminate tensile test was validated.     

The Effect of Crack Spacing Distribution on Stiffness Reduction of Cross-ply Laminates

The effect of transverse crack distribution on the effective mechanical properties of cross-ply laminates is considered. Young’s modulus and Poisson’s ratio dependence on the transverse ply crack density is obtained experimentally for glass fiber/epoxy laminates of lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s subjected to uniaxial tensile loading. Crack spacing distributions at the edge of the specimen are also measured at a predefined applied strain. Mechanical property reduction is evaluated for two crack spacing distributions: uniform spacing routinely considered in theoretical derivations and the experimental crack spacing distribution; the results are compared with test data.     

Effect of temperature and strain rate on tensile mechanical properties of ARALL-1 laminates

The combined effect of temperature and strain rate of the mechanical properties for unidirectional 3/2 ARALL^®-1 laminates was studied. In this paper, the effect of strain rates from 0.00083–0.833 min^–1 on tensile behaviour at temperatures up to 250°F (121 °C) has been conducted. It is demonstrated that tensile strength, tensile modulus, and fracture strain are found to depend on temperature and strain rate. However, the effect of strain rates at 75 °F (24 °C) and 180 °F (82 °C) was found to be insignificant except the lowest strain rate at 180 °F. It was also observed that the tensile yield strength decreased as the strain rate decreased. The tensile properties were moderately reduced at high temperatures and were higher at high strain rates than at low strain rates. The temperature effect is more significant than that due to the strain rate. Scanning electron photomicrographs of the fracture surfaces observed in the aramid/epoxy layer of ARALL-1 laminates at the lowest strain rate are shown to be significantly different only at 250 °F (121 °C). But this phenomenon is not obvious when the highest strain rate is employed.     

Monitoring local strains in cracked cross-ply composites using an embedded aramid fibre strain sensor

Single aramid fibre strain sensors have been embedded in transparent glass-fibre reinforced epoxy resin cross-ply laminates. The sensors, located at the 0°/90°/0° ply interfaces, were interrogated by a remote laser Raman microprobe which enabled the changes in the longitudinal strain in the 0° plies caused by transverse cracking in the 90° ply to be monitored. Strain magnifications of up to about 6 were measured in the crack plane, 10 m from the 0°/90° ply interface, and it is estimated that the region of enhanced strain extends to a distance of about 40 m from the interface. Crack interactions were seen to occur for crack spacings of less than two transverse ply thicknesses.     

Effects of Shear‐Transverse Coupling and Plasticity in the Formulation of an Elementary Ply Composites Damage Model,Part I: Model Formulation and Validation

Abstract: Continuum damage mechanics (CDM) models have been employed successfully in the literature to predict the response of laminated composite materials. Some sophisticated models can include the effects of non‐linear shear and transverse damage progression, plasticity and shear‐transverse damage coupling. However, these models require non‐standard test data for calibration that may not always be available to a modeller. In this two‐part study, we examine the effect of neglecting plasticity parameters, and also the effect of neglecting both plasticity and shear‐transverse coupling parameters in simplified CDM models for predicting monotonic tensile strength. In part I, we develop simplified versions of the CDM model and test their ability to accurately predict the failure response of angle‐ply laminates. In part II, we provide details of the experimental test series carried out to determine the input parameters for the models. It was found that neglecting plasticity requires some approximations in the damage development laws, but the resulting model can predict well the response of the angle‐ply laminates tested under monotonic loading to failure. Neglecting shear‐transverse coupling is acceptable for the some materials.     

Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.     

An acoustic emission energy analysis and its use to study damage in laminated composites

A new technique which uses the output of a true RMS voltmeter to measure the acoustic emission energy output of a transducer is presented. To demonstrate its use in a typical case, this procedure is used to measure acoustic emission energy during tensile tests on [0°/±30°/90°]_s glass-epoxy laminate uniaxial and 10° off-axis tensile coupons. The test results were compared with numerical predictions of laminate response and acoustic emission energy. The experiments indicate that acoustic emission energy can be used to indicate the onset of ply and interlaminar failure.     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

A novel 3D mixed finite‐element model for statics of angle‐ply laminates

Analysis of angle‐ply laminates becomes critical and computationally involved because of the presence of extension–shear coupling. A refined three‐dimensional, mixed, 18‐node finite element (FE) model has been developed to analyse angle‐ply laminates under static loading. The minimum potential energy principle has been used for the development of the mixed FE model, where the transverse stress components (τ_xz, τ_yz and σ_z, where z is the thickness direction) have been incorporated as the nodal degrees of freedom, in addition to the three displacement fields. Further, continuity of transverse stress fields through the thickness of the plate and layerwise continuity of displacement fields have been enforced in the formulation. Because all the constitutive and the compatibility conditions have been ensured within the continuum, the present formulation is unique amongst the family of mixed FE models. Results have been obtained for various angle‐ply laminates and compared with analytical and finite‐element solutions, which have been found to be in good agreement with them. Some new results on angle‐ply with clamped–clamped support condition have also been presented to serve as benchmark results. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of cooling rate on the high strain rate properties of boron steel

In this work, the effect of cooling rate on the high strain rate behavior of hardened boron steel was investigated. A furnace was used to austenize boron sheet metal blanks which were then quenched in various media. The four measured cooling rates during the solid state transformation were: 25 (compressed air quench), 45 (compressed air quench), 250 (oil quench) and 2200 °C/s (water quench). Micro-hardness measurements and optical microscopy verified the expected as-quenched microstructure for the various cooling rates. Miniature dog-bone specimens were machined from the quenched blanks and tested in tension at a quasi-static rate, 0.003 s⁻¹ (Instron) and a high rate, 960 s⁻¹ (split Hopkinson tensile bar). The resulting stress vs. strain curves showed that the UTS increased from 1270 MPa to 1430 MPa as strain rate increased for the specimens cooled at 25 °C/s, while the UTS increased from 1615 MPa to 1635 MPa for the specimens cooled at 2200 °C/s. The high rate tests showed increased ductility for the 25, 45 and 250 °C/s specimens, while the specimens cooled at 2200 °C/s showed a slight decrease. The Hollomon hardening curve was fit to the true stress vs. true strain curves and showed that the mechanical response of the high rate tests exhibited a greater rate of hardening prior to fracture than the quasi-static tests. The hardening rate also increased for the specimens quenched at higher cooling rates. Optical micrographs of the fractured specimens showed that the failure mechanism transformed from a ductile-shear mode at the lower cooling rates to a shear mode at the high cooling rates.     

Thermo-mechanical characterisation of AA 6056-T4 and estimation of its material properties using Genetic Algorithm

This paper presents an experimental investigation of thermo-mechanical material properties of AA 6056-T4, which is used extensively in aeronautic applications. Monotonic tensile tests have been carried out on the dog-bone type specimens at temperatures ranging from room temperature (16 °C) to high temperature (450 °C) with two different strain rates; viz. high strain rate (∼0.002 s⁻¹) and low strain rate (∼0.0002 s⁻¹). Specimens were heated with the help of Joule heating system using Gleeble® 3500 machine at a temperature rate of 25 °C/s. Material properties which were investigated include the Young’s modulus, yield strength at 0.1% plastic strain and hardening modulus.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.