Configuration of a genetic algorithm used to optimise fibre steering in composite laminates

In a previous study, a genetic algorithm (GA) was applied to define the optimum orientation of fibres in a unidirectional laminate in which the fibre orientations were allowed to vary continuously across the domain. The results were positive, but computation time was excessively long. The present study was undertaken to address this issue. The elements used by the GA (encoded representation, fitness criterion, operators affecting the population) were examined and optimised to reduce computation time. It was found that the use of a strain-based fitness criterion was better than use of a stress-based criterion, regardless of whether the load was above or below the elastic limit. A good balance of elitism and mixing was necessary in the GA parameters to obtain the fastest convergence. Automatic imaging of the GA output was achieved using the SAMCEF software package.     

Poisson's ratios in glass fibre reinforced plastics

The characterisation of the mechanical properties of an orthotropic composite material generally requires nine interdependent elastic constants: three Young's moduli, three shear moduli and three Poisson's ratios. In most papers it is the practice to quote only two orthogonal axial moduli, a shear modulus and a Poisson's ratio in the plane of the laminate. However, the value of Poisson's ratio is a function of the orientation of the loading axis relative to the principal axis of the reinforcement fibres, both in and through the plane of the laminate. In an earlier paper, the correlation of experimental and theoretically predicted Poisson's ratios was reported around the angles in the plane of the laminate. Both unidirectional and woven roving fibreglass panels were tested. Accurate prediction of Poisson's ratio was shown to be critically dependent on the value of shear modulus used. This paper reports an extension of the previous work to consider the through-plane properties and will examine the results in the context of the Lempriere constraints.     

The environmental fatigue behaviour of carbon fibre reinforced polyether ether ketone

The fatigue behaviour of carbon fibre/PEEK composite is compared with that of carbon/ epoxy material of similar construction, particularly in respect of the effect of hygrothermal conditioning treatments. Laminates of both materials were of 0/90 lay-up, and they were tested in repeated tension at 0° and at 45° to the major fibre axis. The superior toughness of the polyether ether ketone and its better adhesion to the carbon fibres results in composites of substantially greater toughness than that of the carbon/epoxy material, and this is reflected in the fatigue behaviour of the carbon fibre/PEEK. The tougher PEEK matrix inhibits the development of local fibre damage and fatigue crack growth, permitting a 0/90 composite with compliant XAS fibres to perform as well in fatigue as an epoxy laminate with stiffer HTS fibres. Hygrothermal treatments have no effect on the fatigue response of either material in the 0/90 orientation. The fatigue response of a cross-plied carbon/PEEK laminate in the ±45° orientation is much better than that of equivalent carbon/epoxy composites, again because the superior properties of the thermoplastic matrix.     

Optimization of hybrid laminated composites using the multi-objective gravitational search algorithm (MOGSA)

The multi-objective gravitational search algorithm (MOGSA) technique is applied to hybrid laminates to achieve minimum weight and cost. The investigated laminate is made of glass–epoxy and carbon–epoxy plies to combine the economical attributes of the first with the light weight and high-stiffness properties of the second in order to make the trade-off between the cost and weight as the objective functions. The first natural flexural frequency was considered as a constraint. The results obtained using the MOGSA, including the Pareto set, optimum stacking sequences and number of plies made of either glass or carbon fibres, were compared with those using the genetic algorithm (GA) and ant colony optimization (ACO) reported in the literature. The comparisons confirmed the advantages of hybridization and showed that the MOGSA outperformed the GA and ACO in terms of the functions’ value and constraint accuracy.     

Off-axis fatigue cracking behaviour in notched fibre metal laminates

The off‐axis fatigue cracking behaviour of notched fibre metal laminates under constant amplitude loading conditions was investigated experimentally and numerically. It was found that the off‐axis fatigue crack initiation life decreased as the off‐axis angles increased. This indicated that the off‐axis laminates raised the applied stress level in the aluminium (Al) layer and subsequently resulted in earlier cracking in the Al layer. The off‐axis fatigue crack initiation lives of notched fibre metal laminates were predicted using lamination theory and an energy‐based critical plane fatigue damage analysis from the literature. After a crack initiated in the Al layer, it was observed that the crack path angles of the off‐axis specimens were neither perpendicular to the fibre nor to the loading direction. A finite‐element model was established for predicting the crack path angles.     

Mechanical analysis of bi-component-fibre nonwovens: Finite-element strategy

In thermally bonded bi-component fibre nonwovens, a significant contribution is made by bond points in defining their mechanical behaviour formed as a result of their manufacture. Bond points are composite regions with a sheath material reinforced by a network of fibres’ cores. These composite regions are connected by bi-component fibres — a discontinuous domain of the material. Microstructural and mechanical characterization of this material was carried out with experimental and numerical modelling techniques. Two numerical modelling strategies were implemented: (i) traditional finite element (FE) and (ii) a new parametric discrete phase FE model to elucidate the mechanical behaviour and underlying mechanisms involved in deformation of these materials. In FE models the studied nonwoven material was treated as an assembly of two regions having distinct microstructure and mechanical properties: fibre matrix and bond points. The former is composed of randomly oriented core/sheath fibres acting as load-transfer link between composite bond points. Randomness of material’s microstructure was introduced in terms of orientation distribution function (ODF). The ODF was obtained by analysing the data acquired with scanning electron microscopy (SEM) and X-ray micro computed tomography (CT). Bond points were treated as a deformable two-phase composite. An in-house algorithm was used to calculate anisotropic material properties of composite bond points based on properties of constituent fibres and manufacturing parameters such as the planar density, core/sheath ratio and fibre diameter. Individual fibres connecting the composite bond points were modelled in the discrete phase model directly according to their orientation distribution. The developed models were validated by comparing numerical results with experimental tensile test data, demonstrating that the proposed approach is highly suitable for prediction of complex deformation mechanisms, mechanical performance and structure-properties relationships of composites.     

Reliability-based optimization of fibrous laminated composites

This paper is concerned with the optimum design of multiaxial fiber reinforced laminate systems under probabilistic conditions of loads and material properties. A multiaxially laminated composite is treated as a structural system with each ply contained in the composite as one element. The Tsai-Wu failure criterion is adopted as the limit state function of a unidirectional ply. It is assumed that the system failure occurs when any one of the plies in a laminate system fails. The multiple-check-point method is successfully applied to evaluate the system reliabilities of multiaxial laminates under probabilistic in-plane stresses. An optimization problem is defined to find the optimal number of fiber orientation axes, optimum orientation angles, and optimum ply ratios which yield the highest system reliability.     

On the structure and mechanical properties of beetle shells

Rose chafer beetle shells are composites of chitin fibres and proteinaceous matrix in an orthogonal plywood-like laminate. Fibre layers are connected by unique inter and intra-ply cross-links that afford a novel solution to shear and crack-propagation resistance.The elastic and plastic properties of both isolated fibres and the composite shell were investigated in terms of orientation and state of hydration. It appears that beetle shell design is based on attaining reasonable functional isotropy from an inherently tough anisotropic fibrous structure.     

The thermal conductivity of Kevlar fibre-reinforced composites

The thermal conductivities of a series of blocks consisting of Shell DX210/BF₃400 resin reinforced with Kevlar 49 fibre are reported in the approximate temperature range 180–270 K. The results are used to calculate the thermal conductivities of the fibres in directions parallel and perpendicular to their length. Varying the angle between the principal fibre directions of bidirectional laminates produced in-plane results that varied in a manner which was quantitatively consistent with expectation. The out-of-plane results proved to be independent of fibre orientation, as expected. In-plane and out-of-plane results for a Kevlar 49 fabric reinforced laminate proved to be essentially similar to results for a laminate reinforced with unwoven fibres of the same type, arranged in a 90° cross-plied disposition at the same fibre volume density.     

引入减基法的压电层合板瞬态响应分析

摘要：用减基法（RBM）结合有限元法、傅里叶变换和Newmark直接积分法,研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散,得到时间域内的运动方程,通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势,并在Newmark法求解过程嵌入减基法,构造减基空间,把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶,得到减缩的Newmark增量式,从而快速求解得到原结构波数域响应,通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明,求解过程引入减基法能更快得到结构的瞬态响应,并保证了精度。     

Strength and failure modes in resistance welded thermoplastic composite joints: Effect of fibre–matrix adhesion and fibre orientation

The strength and failure modes of resistance welded thermoplastic composites were investigated. Special attention was paid to the effect of basic characteristics of the adherends such as fibre–matrix adhesion and fibre orientation. 8HS woven GF/PEI composites were resistance welded. Intralaminar failure was found to be the major failure mechanism for the well welded joints, consisting of either fibre–matrix debonding or laminate tearing. An improved fibre–matrix adhesion was found to result in significantly higher lap shear strength. Besides, the main apparent orientation of the fibres on the welding surfaces was found to have an effect on the strength of the joints.     

Interlaminar Stress Determination in Carbon Fibre Epoxy Composites with the Embedded Strain Gauge Technique

Abstract: In order to determine interlaminar stresses, strain gauges have been embedded in carbon fibre/epoxy composites. Insulation problems occurring because of the electrical conductivity of the carbon fibres were successfully resolved with the help of special foils. Measurements on unidirectional and angle‐ply laminates were in good agreement with calculations based on the classical laminate theory. Moreover, the laminate strength was not significantly affected by the embedded strain gauges. The technique may also be applied to residual stress determination in composite components.     

Numerical analysis of the notch effect and the behaviour of notch crack in adhesively bonded composite laminates

In this study the finite element method is used to analyse the notch effect and the behaviour of notch cracks in adhesively composite laminate under tension by computing respectively the stress concentration factor at the notch tip which characterize the notch strength and the stress intensity factor at the crack tip which characterize the resistance to the crack propagation. The effects of the adhesive properties and fiber orientation on the variation of both stress concentration and stress intensity factors are highlighted. The obtained results show that the notch strength is reduced in the layer of the laminate of which the fiber orientation is in the applied load direction; the resistance to the crack propagation is also reduced in this type of layer. The stress intensity factor at the tip of notch crack exhibits an asymptotic behaviour as the crack length increases.     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

基于两尺度代表体元的含孔隙复合材料单层板弹性常数预测

为预测含孔隙复合材料单层板的弹性常数,以单向纤维增强复合材料单层板为研究对象,首先,基于细观力学方法,提出了一种基于两尺度代表体元的含孔隙复合材料单层板弹性常数预测方法;然后,基于纤维排列和孔隙特征,建立了纤维-基体尺度的代表体元模型和含孔隙复合材料单层板的代表体元模型,并采用有限元方法求解弹性常数;接着,采用周期对称边界条件,在纤维-基体尺度先进行第1步等效,得到不含孔隙复合材料单层板的弹性常数;最后,在含孔隙复合材料单层板的代表体元模型上进行第2步等效,完成了含孔隙复合材料单层板弹性常数的预测。结果显示:应用该方法得到的计算结果与试验数据吻合较好;结合纤维、基体弹性常数及孔隙形态的模型,该方法可以反映各因素对复合材料单层板弹性常数的影响。      

Microtexture and structure of boron nitride fibres by transmission electron microscopy, X-ray diffraction, photoelectron spectroscopy and Raman scattering

Continuous boron nitride fibres have been fabricated by melt spinning and pyrolysis of poly[2,4,6-tris(methylamino)borazine]. The longitudinal mechanical properties depend on mechanical stress and temperature applied during the conversion process. High-performance and low-performance fibres were characterized in order to find relationship between structure and physical properties. In all the cases, photoelectron spectroscopy (XPS) analysis proves that the chemical composition of the fibre is close to stoichiometric BN. The crystallite sizes were measured by means of X-ray diffraction (XRD) and Raman techniques. Cross-sections of separated fibres were investigated by high-resolution electron microscopy (HREM) and transmission electron microscopy (TEM). All the BN fibres have a hexagonal turbostratic structure. With increasing stress and temperature, the tensile strength and the elastic modulus increase. In the high-performance fibres, the 002 layers with an increased distance (about 0.35 nm) showed a mean stacking sequence near to graphite and a preferred orientation of the 002 layers parallel to the fibre axis.     

Flexural properties of hybrid composites reinforced by S-2 glass and T700S carbon fibres

A study on the flexural properties of hybrid composites reinforced by S-2 glass and T700S carbon fibres is presented in this paper. Specimens were manufactured following the hand lay-up process in an intra-ply configuration with varying degrees of glass fibres added to the surface of a carbon laminate. These specimens were then tested in the three point bend configuration in accordance with ASTM D790-07 at a span to depth ratio of 32. The failure modes were examined under an optical microscope, and the results show that the dominant failure mode is compressive failure. The flexural modulus, flexural strength and strain to failure were also predicted by finite element analysis. It is seen that flexural modulus decreases with increasing percentage of S-2 glass fibres. Both the experiments and FEA suggest that positive hybrid effects exist by substituting carbon fibres with glass fibres.     

The damage and failure of GRP laminates by underwater explosion shock loading

This paper examines the development of microstructural damage in a glass-reinforced polymer (grp) laminate subjected to explosive shock loading in water. GRP is commonly used in small naval vessels, and may be subjected to underwater explosions. In the experiments, the laminates were exposed to increasing amounts of shock loading produced by underwater explosions. The laminates were backed with either water or air to modify the amount of bending experienced under loading, with the air-backed laminates having the higher amount of bending. Examination of the grp microstructure by optical and scanning electron microscopy after shock testing failed to reveal any damage to either the polymer matrix or glass fibres when the laminate was backed with water. In contrast, when the laminate was backed with air, small cracks were produced in the polymer matrix at low shock pressures. Raising the shock pressure above a threshold limit caused complete failure of the laminate by cracking in the polymer matrix, cracking of the glass fibres, and delamination of the glass fibres from the polymer. The differences in the shock resistance of the water- and air-backed grp are discussed. Measurements of the residual tensile fracture strength of the laminates after shock loading are also presented. The fracture strength of the water-backed laminate was not affected by shock, but the fracture strength of the air-backed laminate deteriorated with the onset of glass fibre breakage and delamination in the grp microstructure.     

Distribution of steel fibres in rectangular sections

In this paper a calculation method is explained to predict the total number of fibres crossing a rectangular section. The largest part of the paper deals with the theoretical calculation of an orientation factor. The orientation factor is defined here as the average length of the projection on the longitudinal axis of all fibres crossing a section, divided by the fibre length. Once the orientation factor is found, a simple calculation gives the number of fibres crossing a crack. Since the proposed approach is to a large extent new, there is a need for verification with test results. For this reason a fibre counting was done on 107 Rilem beam specimens, involving different fibre types. The comparison with the calculated number of fibres shows that the model provides good predictions of the number of fibres crossing a section.     

A mechanically fastened composite laminate joint and progressive failure analysis

A comprehensive procedure for a mechanically fastened composite laminate joint (ASTM D5961 Proc. A, B) is demonstrated from fixture design to analysis of test results. The ASTM tests are applied to evaluate the standard laminate properties and the composite joints. Composite laminate mechanical joints were analyzed using the finite element method (FEM), and the results were compared to test results. A progressive failure analysis (PFA) was applied to the FEM to predict the overall failure behavior of the test specimens. Three laminate failure theories – maximum stress, maximum strain, and Tsai–Wu – were applied to the PFA to predict the test failure load, displacement and strength. The PFA method was suitable to predict the initial test range of test and maximum test load except for the excessive failure area.