Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Uncertainty analysis based on sensitivity applied to angle-ply composite structures

This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.

From local to global importance measures of uncertainty propagation in composite structures

The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Comparative analysis of drills for composite laminates

The characteristics of carbon fiber-reinforced plastics allow a very broad range of uses. Drilling is often necessary to assemble different components, but this can lead to various forms of damage, such as delamination which is the most severe. However, a reduced thrust force can decrease the risk of delamination. In this work, two variables of the drilling process were compared: tool material and geometry, as well as the effect of feed rate and cutting speed. The parameters that were analyzed include: thrust force, delamination extension and mechanical strength through open-hole tensile test, bearing test, and flexural test on drilled plates. The present work shows that a proper combination of all the factors involved in drilling operations, like tool material, tool geometry and cutting parameters, such as feed rate or cutting speed, can lead to the reduction of delamination damage and, consequently, to the enhancement of the mechanical properties of laminated parts in complex structures, evaluated by open-hole, bearing, or flexural tests.

Numerical and experimental analyses of biocomposites reinforced with natural fibres

n the last decades the biocomposites have been widely used in the construction, automobile and aerospace industries. Not only the interface transition zone (ITZ) but also the heterogeneity of natural fibres affects the mechanical behaviour of these composites. This work focuses on the numerical and experimental analyses of a polymeric composite fabricated with epoxy resin and unidirectional sisal and banana fibres. A three-dimensional model was set to analyze the composites using the elastic properties of the individual phases. In addition, a two-dimensional model was set taking into account the effective composite properties obtained by micromechanical models. A tensile testing was performed to validate the numerical analyses and evaluating the interface condition of the constitutive phases.

Feasibility of the extended finite element method for the simulation of composite bonded joints

Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.

Development of a new pultrusion equipment to manufacture thermoplastic matrix composite profiles

This paper describes the design and manufacture of a low-cost full scale pultrusion prototype equipment and discusses the production and obtained mechanical properties of polypropylene/glass (GF/PP) reinforced composite ba rs fabricated by using the prototype equipment. Three different GF/PP pre-impregnated ra w-materials, a commercial GF/PP comingled system from Vetrotex, a GF/PP powder coat ed towpreg [1-3] and, a GF/PP pre- consolidated tape (PCT) produced in our laboratorie s, were used in the production of composite bars that were subsequently submitted to mechanical testing in order to determine the relevant mechanical properties and quantify the consolidation quality. Samples of the different composite profiles were also observed und er SEM microscopy.

Strength prediction of adhesively-bonded scarf repairs in composite structures under bending

This work reports on the experimental and numerical study of the bending behaviour of two-dimensional adhesively-bonded scarf repairs of carbon-epoxy laminates, bonded with the ductile adhesive Araldite 2015®. Scarf angles varying from 2 to 45º were tested. The experimental work performed was used to validate a numerical Finite Element analysis using ABAQUS® and a methodology developed by the authors to predict the strength of bonded assemblies. This methodology consists on replacing the adhesive layer by cohesive elements, including mixed-mode criteria to deal with the mixed-mode behaviour usually observed in structures. Trapezoidal laws in pure modes I and II were used to account for the ductility of the adhesive used. The cohesive laws in pure modes I and II were determined with Double Cantilever Beam and End-Notched Flexure tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures of the carbon-epoxy components also occurred in some regions, cohesive laws to simulate these failure modes were also obtained experimentally with a similar procedure. A good correlation with the experiments was found on the elastic stiffness, maximum load and failure mode of the repairs, showing that this methodology simulates accurately the mechanical behaviour of bonded assemblies.

Experimental and numerical evaluation of composite repairs on wood beams damaged by cross-graining

An experimental and Finite Element study was performed on the bending behaviour of wood beams of the Pinus Pinaster species repaired with adhesively-bonded carbon–epoxy patches, after sustaining damage by cross-grain failure. This damage is characterized by crack growth at a small angle to the beams longitudinal axis, due to misalignment between the wood fibres and the beam axis. Cross-grain failure can occur in large-scale in a wood member when trees that have grown spirally or with a pronounced taper are cut for lumber. Three patch lengths were tested. The simulations include the possibility of cohesive fracture of the adhesive layer, failure within the wood beam in two propagation planes and patch interlaminar failure, by the use of cohesive zone modelling. The respective cohesive properties were estimated either by an inverse method or from the literature. The comparison with the tests allowed the validation of the proposed methodology, opening a good perspective for the reduction of costs in the design stages of these repairs due to extensive experimentation.

Drilling tool geometry evaluation for reinforced composite laminates

In this work, a comparative study on different drill point geometries and feed rate for composite laminates drilling is presented. For this goal, thrust force monitoring during drilling, hole wall roughness measurement and delamination extension assessment after drilling is accomplished. Delamination is evaluated using enhanced radiography combined with a dedicated computational platform that integrates algorithms of image processing and analysis. An experimental procedure was planned and consequences were evaluated. Results show that a cautious combination of the factors involved, like drill tip geometry or feed rate, can promote the reduction of delamination damage.

Interlaminar fracture characterization of a carbon-epoxy composite in pure mode II

The interlaminar fracture toughness in pure mode II (GIIc) of a Carbon-Fibre Reinforced Plastic (CFRP) composite is characterized experimentally and numerically in this work, using the End-Notched Flexure (ENF) fracture characterization test. The value of GIIc was extracted by a new data reduction scheme avoiding the crack length measurement, named Compliance-Based Beam Method (CBBM). This method eliminates the crack measurement errors, which can be non-negligible, and reflect on the accuracy of the fracture energy calculations. Moreover, it accounts for the Fracture Process Zone (FPZ) effects. A numerical study using the Finite Element Method (FEM) and a triangular cohesive damage model, implemented within interface finite elements and based on the indirect use of Fracture Mechanics, was performed to evaluate the suitability of the CBBM to obtain GIIc. This was performed comparing the input values of GIIc in the numerical models with the ones resulting from the application of the CBBM to the numerical load-displacement (P-) curve. In this numerical study, the Compliance Calibration Method (CCM) was also used to extract GIIc, for comparison purposes.

Benchmark exact solutions for the static analysis of multi-layered piezoelectric composite using PVDF

The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.

Design of a laminated composite multi-cel structure subjected to torsion

Laminate composite multi-cell structures have to support both axial and shear stresses when sustaining variable twist. Thus the properties and design of the laminate may not be the most adequate at all cross-sections to support the torsion imposed on the cells. In this work, the effect of some material and geometric parameters on the optimal mechanical behaviour of a multi-cell composite laminate structure is studied when torsion is present. A particle swarm optimization technique is used to maximize the multi-cell structure torsion constant that can be used to obtain the angle of twist of the composite laminate profile.

Optimization of magneto-electro-elastic composite structures using differential evolution

Magneto-electro-elastic structures are built from materials that provide them the ability to convert in an interchangeable way, magnetic, electric and mechanical forms of energy. This characteristic can therefore provide an adaptive behaviour to a general configuration elastic structure, being commonly used in association with any type of composite material in an embedded or surface mounted mode, or by considering the usage of multiphase materials that enable achieving different magneto-electro-elastic properties. In a first stage of this work, a few cases studies will be considered to enable the validation of the model considered and the influence of the coupling characteristics of this type of adaptive structures. After that we consider the application of a recent computational intelligence technique, the differential evolution, in a deflection profile minimization problem. Studies on the influence of optimization parameters associated to the problem considered will be performed as well as the adoption of an adaptive scheme for the perturbation factor. Results are also compared with those obtained using an enhanced particle swarm optimization technique. (C) 2013 Elsevier Ltd. All rights reserved.