Jean-Jacques Barrau

Torsion of thin-walled composite beams with midplane symmetry

Abstract The optimization of thin-walled beams can lead to the design of structures whose walls have significant differences in stiffness. The stress field resulting from a twisting moment is not correctly modeled by classical analytical theories, so numerical modeling is therefore essential. The analytical theory presented in this study provides us with a simple way of determining stress and stiffness in this type of structure, without having to resort to complex methods of calculation. The walls are made of isotropic or composite materials with midplane symmetry and one orthotropic axis is the longitudinal axis. The section may be open or closed and the constrained warping effect can be taken into account. The results obtained correlate accurately with those obtained from 3D FE modeling.

Failure mechanism analysis under compression loading of unidirectional carbon/epoxy composites using micromechanical modelling

Abstract An experimental study of the compression fracture of unidirectional composites (T300/914, T800/5245C, M40J/913, GY70/V108 and AS4/ PEEK) shows that fibre kinking is the main failure mode. All materials tested exhibited a non-linear elastic behaviour characterized by a continuous decrease of the tangent modulus as soon as the load was applied. A micromechanical model taking into account initial geometric imperfections was developed. Stress evolution in the constituents was analysed and then compared with their strength. Two failure modes were distinguished: failure due to the fracture of fibres and failure due to the fracture of matrix. This model demonstrates that the non-linear behaviour is not due to the initial geometric imperfections. To refine modelling, a numerical analysis using a finite element method with elastoplastic and large displacement hypothesis was developed. This model not only shows the principals governing failure parameters: initial geometric impertions, yield stress of matrix and fibre compressive strength, but also demonstrates two failure mechanisms: fracture of fibres in compression and fibre kinking. This model confirms that the non-linear behaviour is not attributed to the initial geometric imperfections.

Theoretical and experimental analysis of asymmetric sandwich structures

A new technology known as asymmetric sandwich structures is now used for the design of lightweight structures. Static failure tests demonstrate the high performance of this technology and show its original mechanical behavior. Due to this complex mechanical behavior, the use of non-linear finite element models in the pre-project phase is a long, expensive process. This paper presents a specific theory which enables faster design loops. The theory is first validated by comparison to numerical models and is then used to correlate structural tests on asymmetric sandwich plate under combined compression/shear loadings. The tests were conducted on original test equipment designed to investigate the capabilities of this technology.

Analytical theory for an approach calculation of composite box beams subjected to tension and bending

Abstract Optimisation of composite beam behaviour has led to the use of composite materials where one of the constituent orthotropic axes is no longer orthogonal to the cross-section, in order to obtain specific coupling characteristics which enhance the overall performance of the structure. Therefore, theories which were previously valid for traditional beams (where the longitudinal axis is parallel to an orthotropic axis) are no longer applicable. The purpose of this paper is to provide a simple analytical method for calculating stresses and strains existing in thin-walled composite beams formed of orthotropic materials, one of whose orthotropic axes is not necessarily orthogonal to the cross-section. The advantage of such a method is that it does not rely on a cumbersome numerical calculation like, for example, a finite element method. The box beam to be studied is formed of different parts, so that, by using a homogenisation method, each part can be considered as an equivalent homogeneous material. The use of the original hypothesis, together with global equilibrium equations, have enabled us to obtain a set of easy-to-solve linear equations. The solution gives forces and strains in the cross-section. Using this knowledge, stress can be determined in each layer. The suggested method has been validated by comparison with results calculated by a finite element software called MEF-MOSAIC.

Combined shear/compression structural testing of asymmetric sandwich structures

Asymmetric sandwich technology can be applied in the design of lightweight, non-pressurized aeronautical structures such as those of helicopters. A test rig of asymmetric sandwich structures subjected to compression/shear loads was designed, validated, and set up. It conforms to the standard certification procedure for composite aeronautical structures set out in the “test pyramid”, a multiscale approach. The static tests until failure showed asymmetric sandwich structures to be extremely resistant, which, in the case of the tested specimen shape, were characterized by the absence of buckling and failure compressive strains up to 10,000 μ strains. Specimens impacted with perforation damage were also tested, enabling the original phenomenon of crack propagation to be observed step-by-step. The results of the completed tests thus enable the concept to be validated, and justify the possibility of creating a much larger machine to overcome the drawbacks linked to the use of small specimens.

Analytical theory for an approach calculation of non-balanced composite box beams

Abstract For aeroelastic problems, optimization of the behavior of box beams, carried out in composite materials, can lead to the construction of structures whose longitudinal axis is not necessarily the orthotropic axis of the materials. These beams present couplings such as Flexion–Torsion or Traction–Torsion. In this study, we propose an analytical theory which allows these structures to be dimensioned with extreme accuracy and without using complicated calculations. The method developed, based on a weak hypothesis on the field of deformations, makes it possible to obtain from simple analytical calculations, the stresses and displacement in a cross-section for normal load F → x , flexion moments M → y , M z and torsion moments M → x . It is then possible using the laminated plates theory, to determine the stresses in each layer. The results obtained correspond perfectly to those found in a 3D Finite Element model, calculated using CATIA–ELFINI software. On the central part of the beams, the relative differences noticed between these two methods on the calculation of stress, strain and rigidities are negligible. Near the embedded section, warping is very important and the relative error is great.

Discrete Impact Modeling of Inter- and Intra-laminar Failure in Composites

The goal of this study is to initiate a “test-calculation dialogue” on low velocity/low energy impact tests in laminated composites. The different types of impact damage developing during an impact test, i.e. matrix cracking, fiber failure, interface delamination and permanent indentation, are simulated. The bibliography shows a general lack of detailed validation of impact modeling and the originality of this work is to use refined and complementary experimental data to build and validate a numerical model. The good correlation between the model and this refined experimental database gave us relative confidence in the model, despite a few non-standard material parameters.

Buckling optimisation of composite panels via lay-up tables

The strategy to optimise a composite panel is based on a multi-level optimisation. The fust level defmes a thichess law for the skin (thichesses and angle percentages for each uniform area all over the panel) and stiffener properties (height, thichess...). The objective function is the total weight of the panel. The optimisation takes into account strength criteria (in-plane behavior) and stability criteria (out-of-plane behavior). At this level, composite material behavior is modelled as a homogeneous material and effects of lay-up are not taken into account for buckling calculations.

Modeling of Impacts on Sandwich Structures

In aeronautics, passenger safety and reliability of structures are essential aspects. Helicopter blades are particularly sensitive to impact solicitations but modeling these phenomena is still difficult and experimental tests often replace the prediction. This study will be focused on the modeling of an impact on the skin of the blade. It is equivalent in a first approach to an impact on a sandwich panel made up with a foam core and a thin composite skin. The objective is to develop a representative model of the damage kinetics adapted to the modeling of the complete structure. Thus, an F.E. explicit model has been developed. It relies on the development of a multiscale approach. Damage is modeled at an intermediate scale (mesoscopic) in order to reproduce the damage kinetics observed at a microscopic scale. Numerical results obtained are correct and reproduce the behavior of the panel for a static test of indentation and low velocity impact test.

Prediction of the longitudinal crack behavior of stiffened curved panels

Abstract The purpose of this study is to present a simplified semi-analytical methodology to predict the behavior of longitudinal cracks in cracked stiffened curved panels with frames. Pressure loading acting on the longitudinal cracks induces geometrical non-linearity due to large deflection of crack edges. This methodology is based mainly on the applicatin of “bulging” coefficients to stress intensity factors taken from a numerical model of a stiffened cracked flat panel in order to get the crack driving force of the curved panel. This flat model must be geometrically similar to the curved panel. The advantage of the method is the reduced calculation time compared with a numerical model of the cracked stiffened curved panel, including frames. Analysis of the results shows a highly satisfactory correlation between prediction by calculation and experimental data.