Non-destructive fatigue damage characterization of laminated thermosetting fibrous composites

The fatigue behaviour of the laminated thermosetting Fiberdux 6376-HTA composite material is studied experimentally for both constant and variable amplitude stress reversal loading. The fatigue-induced material degradation is correlated to non-destructive evaluation data obtained from C-scan graphs through the concept of the damage severity factor ( DSF ). The DSF is able to account for the varying severity of damage at the different specimen locations and is used to quantify the fatigue-induced damage. The concept of the DSF , introduced earlier by the authors for constant amplitude fatigue loading of thermoplastic fibrous composites, is applied to characterize fatigue damage of thermosetting fibrous composites and is extended to account for variable amplitude loading. Constant amplitude fatigue tests at various stress levels were performed to correlate fatigue damage to the change of mechanical properties, such as axial stiffness, residual tensile strength and interlaminar shear strength, and to develop expressions to relate DSF to the degradation of the mechanical properties with increasing fatigue damage. Correlation between DSF evolution and consumed fatigue life is made and fatigue damage functions involving stress amplitude dependency are formulated. These expressions together with a modified rainflow method are then used to assess fatigue life under variable amplitude fatigue loading; computed fatigue lives are compared against experimental results.     

An approach for the reliability based design optimization of laminated composites

This article aims at optimizing laminated composite plates taking into account uncertainties in the structural dimensions. As laminated composites require a global optimization tool, the Particle Swarm Optimization (PSO) method is employed. A new Reliability Based Design Optimization (RBDO) methodology based on safety factors is presented and coupled with PSO. Such safety factors are derived from the Karush–Kuhn–Tucker optimality conditions of the reliability index approach and eliminate the need for reliability analysis in RBDO. The plate weight minimization is the objective function of the optimization process. The results show that the coupling of the evolutionary algorithm with the safety-factor method proposed in this article successfully performs the RBDO of laminated composite structures.     

Reliability-based optimization using bridge importance sampling

This paper introduces an efficient reliability estimation approach to be used in the framework of reliability-based optimization. The key feature of the procedure consists of reusing during the optimization procedure the results of the previous iterations. The reliability analysis is performed subsequently with a reduced number of samples which greatly decreases the computational efforts associated with the reliability-based optimization process. The validity and the advantages of the procedure are demonstrated by means of two reliability-based optimization problems.     

Design and optimization of symmetric laminated composites using a variable neighbourhood search-based model

The development of society is still marked by the need for lighter and stronger structures. The materials that respond best to these needs are composite materials. Designing composite materials is difficult as it involves designing the geometry and their composition. Traditionally, the design tasks have been based on approximate methods; the possibility for creating composite materials is almost unlimited, characterization by testing is very expensive and it is difficult to apply the results to other contexts. This article proposes a variable neighbourhood search-based model for the design of symmetric laminated composites, a general encoding for the design of composites, an evaluation function that has taken into consideration cost and safety criteria in design, the neighbourhood structures and a set of local search operators. The proposed model has been applied to different real-world problems and the results have been compared with other well-known design methods.     

Analytical modelling of laminated composites

A significant number of research papers has been published on the analytical modelling of composite laminates over the past 20 years. The drive for more accurate analysis has led us to techniques which have become computationally more and more burdensome, while the engineering world continues to use simple, first-older shear deformable plate theory as its primary tool. This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the Predictor Corrector technique to extend the simple Mindlin type element to achieve greater accuracy, and the second develops a new Least Squares element which can approximate a C¹ continuous element. The Least Squares element has the capability to incorporate a simplified higher order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to upgrade analysis methods significantly with little additional computational cost. It is hoped that this work can instigate further research into efficient modelling of composite laminates.     

Reliability-based design optimization with progressive surrogate models

Reliability-based design optimization (RBDO) has traditionally been solved as a nested (bilevel) optimization problem, which is a computationally expensive approach. Unilevel and decoupled approaches for solving the RBDO problem have also been suggested in the past to improve the computational efficiency. However, these approaches also require a large number of response evaluations during optimization. To alleviate the computational burden, surrogate models have been used for reliability evaluation. These approaches involve construction of surrogate models for the reliability computation at each point visited by the optimizer in the design variable space. In this article, a novel approach to solving the RBDO problem is proposed based on a progressive sensitivity surrogate model. The sensitivity surrogate models are built in the design variable space outside the optimization loop using the kriging method or the moving least squares (MLS) method based on sample points generated from low-discrepancy sampling (LDS) to estimate the most probable point of failure (MPP). During the iterative deterministic optimization, the MPP is estimated from the surrogate model for each design point visited by the optimizer. The surrogate sensitivity model is also progressively updated for each new iteration of deterministic optimization by adding new points and their responses. Four example problems are presented showing the relative merits of the kriging and MLS approaches and the overall accuracy and improved efficiency of the proposed approach.     

Hierarchic models for laminated composites

The principles governing the formulation of hierarchic models for laminated composites are discussed. The essential features of the hierarchic models described herein are: (a) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness, and (b) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity. Examples are presented.     

Micromodel-based simulations for laminated composites

We develop a calculation strategy for the simulation of a complete microscopic model. This strategy enables one to account for damage mechanisms in laminated composites. The model mixes discrete and continuous approaches by introducing potential rupture surfaces and a damageable continuous medium. This approach requires suitable calculation tools unavailable in industrial analysis codes. The strategy presented is multiscale in space and is based on a decomposition of the domain into substructures and interfaces. This strategy enables one to simulate complex problems with multiple cracks. In practice, to use such a model, the strategy must be improved in order to handle very large numbers of substructures and interfaces and to estimate the rupture criteria for the surfaces introduced into the model. We provide simple examples which demonstrate the capabilities of the microscopic model.     

基于遗传算法的谐波齿轮可靠性优化设计

谐波齿轮具有优异的特性,在传动系统中的应用越来越广泛.针对谐波齿轮,考虑其设计过程中的各种不确定因素,根据其失效形式建立谐波齿轮的可靠性分析模型.在可靠性理论和优化设计方法的基础上,将可靠性设计与遗传算法结合起来;根据应力-强度干涉理论使用一次二阶矩法对谐波齿轮进行了优化设计;使用矩阵微分技术,分析了设计变量对结构可靠性的影响程度,即灵敏度.并使用蒙特卡洛模拟的方法对可靠性进行了验证.在基本随机参数的前二阶矩已知的情况下,通过计算机程序可以迅速准确地得到谐波齿轮可靠性优化设计信息.数值算例表明,所提出的方法是一种实用、有效的方法.     

Reliability-based design and optimization of adaptive marine structures

The objectives of this work are to quantify the influence of material and operational uncertainties on the performance of self-adaptive marine rotors, and to develop a reliability-based design and optimization methodology for adaptive marine structures. Using a previously validated 3D fluid–structure interaction model, performance functions are obtained and used to generate characteristic response surfaces. A first-order reliability method is used to evaluate the influence of uncertainties in material and load parameters and thus optimize the design parameters. The results demonstrate the viability of the proposed reliability-based design and optimization methodology, and demonstrate that a probabilistic approach is more appropriate than a deterministic approach for the design and optimization of adaptive marine structures that rely on fluid–structure interaction for performance improvement.     

Flexural behaviour of hybrid laminated composites

The present paper studies the flexural behaviour of hand manufactured hybrid laminated composites with a hemp natural fibre/polypropylene core and two glass fibres/polypropylene surface layers at each side of the specimen. When compared with full glass fibres reinforced polypropylene laminates, the hybrid composites have economical, ecological and recycling advantages and also specific fatigue strength benefits. Static and fatigue tests were performed in three point bending for both laminates to evaluate flexural strength properties and fatigue behaviour. Fatigue damage was measured in terms of the stiffness loss. Failure sites and mechanisms were evaluated through microscopy studies and a 3D numerical analysis using finite element method.     

Interlaminar shear fracture of laminated composites

The interlaminar fracture toughness in mode II and mode III of a number of advanced composites was studied using beam type test specimens and scanning electron microscopy. Special emphasis was placed on elucidating the material aspects of the fracture process and on quantifying the effect of matrix on fracture energy.The fracture energy in mode II was independent of crack extension while that for mode III exhibited a rather probablistic resistance behavior that was attributed to the effect of fiber bridging. The initiation fracture energy, considered here the true measure of G _IIIC , coincided with G _IIC . For either mode, the interlaminar region ahead of the crack tip exhibited considerable plastic deformations, the severity that is believed to control the laminate toughness. The interlaminar fracture energy in shear, hereby denoted as G _SC (=G _IIC =G _IIIC ), was accurately predicted from a straightforward adhesive joint fracture test provided the adhesive thickness coincide with the thickness of the interlaminar resin layer.

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Résumé On a étudié la rupture par décollement en mode II et en mode III de plusieurs composites évolués, en utilisant des éprouvettes en forme de barreaux et la microscopie électronique à balayage.Un accent particulier a été placé sur la solution d'aspects liés au matériau, portant sur le processus de rupture et sur la quantification des effets de la matrice sur l'énergie de rupture.On a trouvé que l'énergie de rupture en mode II est indépendante de la longueur de fissuration tandis que, pour le Mode III, elle fait état d'un comportement de résistance de caractère plutôt probabilité, attribué à l'effet de pontage entre les fibres.L'énergie d'amorçage de la rupture, que l'on considère ici comme la vraie mesure de G _IIIC , coïncide avec G _IIC .Pour les deux modes de sollicitation, la région de séparation en avant de l'éxtrémité de la fissure fait état d'une déformation plastique importante, dont on pense qu'elle contrôle sérieusement la ténacité due composite.L'énergie de rupture entre couches en cisaillement, que l'on appelle ici G _SC (=G _IIC =G _IIC ), a pu être prédite avec exactitude par des essais de rupture de joints collés, pour autant que l'épaisseur de l'adhésif coïncide de avec celle de la couche de résine entre deux plans du colaminé.

     

Interfacial properties of fibrous composites

The processes for debonding and pull-out in parallel-sided as well as tapered fibre composites are described. Models which can predict and account for all the reported experimental debonding and pull-out behaviour are developed. The effect of the interfacial properties on the plot of maximum pull-out force against fibre embedded length is elucidated. Knowledge of the interfacial parameters of a composite allows proper characterization and leads to better prediction of the mechanical properties.     

Spot welding of metal laminated composites

Composite materials of steel sheets joined by interlayers of zinc or lead- tin, show very good impact and corrosion resistance properties. Resistance spot-weld characteristics of these composite materials made of steel sheets and non-ferrous metals have been tested. Spot welds of composites with both zinc and lead- tin interlayers present good behaviour in peeling tests. Shear tests of the welds also show very high strength, probably as a consequence of simultaneous brazing because of the alloyed layer of non-ferrous material around the weld spot. This good welding behaviour enhances the possibilities of application of this composite.     

基于可靠性的复合材料结构稳定性约束优化设计

基于结构的可靠性, 研究了复合材料结构的稳定性约束优化设计方法。考虑材料及载荷的不确定性, 通过结构可靠性分析的响应面法和有限元法的结合, 对复合材料结构稳定性进行可靠性分析; 利用优化软件iSIGHT集成可靠性分析程序, 实现了以铺层层数及铺层角度为设计变量的复合材料结构稳定性约束问题的可靠性优化方法。对层合板及层合圆柱进行算例分析, 验证了本文中可靠性优化方法的有效性, 为工程实际中的复合材料结构稳定性约束优化设计问题提供借鉴。      

Reliability-based design optimization under stationary stochastic process loads

Time-dependent reliability-based design ensures the satisfaction of reliability requirements for a given period of time, but with a high computational cost. This work improves the computational efficiency by extending the sequential optimization and reliability analysis (SORA) method to time-dependent problems with both stationary stochastic process loads and random variables. The challenge of the extension is the identification of the most probable point (MPP) associated with time-dependent reliability targets. Since a direct relationship between the MPP and reliability target does not exist, this work defines the concept of equivalent MPP, which is identified by the extreme value analysis and the inverse saddlepoint approximation. With the equivalent MPP, the time-dependent reliability-based design optimization is decomposed into two decoupled loops: deterministic design optimization and reliability analysis, and both are performed sequentially. Two numerical examples are used to show the efficiency of the proposed method.     

On heat conduction in laminated composites

A continuum integral theory is developed for heat-conduction in a laminated medium. Based on asymptotic expansions of the microstructure equations in terms of a small parameter given by the ratio of diffusivities of the two constituents, a continuum model is developed in which microstructure effects appear as a consequence of the fact that the current state in a laminated medium is history-dependent.