Identification par recalage modal et fréquentiel des propriétés constitutives de coques en matériaux composites

Fibre-reinforced composites are being increasingly used as alternatives for conventional materials primarily because of their high strength, specific stiffness, light weight and adjustable properties. However, before using this type of material with confidence in industrial applications such as marine, automotive or aerospace structural components, a thorough characterization of the constituent material properties is needed. Because of the number and the inherent variability of the constitutive properties of composite materials, the experimental characterization is quite cumbersome and requires a large number of specimens to be tested. An elegant way to circumvent this lack consists in using mixed numerical-experimental methods which constitute powerful tools for estimating unknown constitutive coefficients in a numerical model of a composite structure from static and/or dynamic experimental data collected on the real structure. Starting from the measurement of quantities such as the natural frequencies and mode shapes, these methods allow, by comparing numerical and experimental observations, the progressive refinement of the estimated material properties in the corresponding numerical model. In this domain, dynamic mixed techniques have gained in importance owing to their simplicity and efficiency. In this work, a new mixed numerical-experimental identification method based on the modal response of thick laminated shells is presented. This technique is founded on the minimisation of the discrepancies between the eigenvalues and eigenmodes computed with a highly accurate composite shell finite element model with adjustable elastic properties and the corresponding experimental quantities. In the case of thick shells, the constitutive parameters that can be identified are the two in-plane Young's moduli E1 and E2, the in-plane Poisson's ratio ν12 and the in-plane and transverse shear moduli G12, G13 and G23. To determine these six parameters, a typical set of 10 to 15 measured eigenfrequencies and eigenmodes is selected, and the over-constrained optimisation problem is solved with a nonlinear least squares algorithm. In order to maximize the quality of the identification, free-free boundary conditions and a non-contacting modal measurement method are chosen for the experimental determination of the eigenparameters. To obtain optimal experimental conditions, the specimens are suspended by thin nylon yarns and excited by a calibrated acoustic source (loudspeakers) while the dynamic response is measured with a scanning laser vibrometer. The measured frequency response functions are then treated in a modal curve fitting software to obtain a high quality set of modal data (mode shapes and frequencies). As the accuracy of this inverse method directly depends on the precision of the finite element model, a family of very efficient thick laminated shell finite elements based on a variable p-order approximation of the through-the-thickness displacement with a full 3D orthotropic constitutive law has been developed. In these elements, varying the degree of approximation of the model allows to adjust the needs in accuracy and/or computation time. It is shown that for thick and highly orthotropic plates, the formulation exhibits a good convergence on the eigenfrequencies with p = 3 and a nearly exact solution for p = 7. In comparison to other 3D solid or thick shell elements, such as layerwise models, the presented elements show an equivalent precision of the computed eigenfrequencies and are computationally less expensive for laminates with more than 8 plies. A classical Levenberg-Marquardt nonlinear least squares minimisation algorithm is used to solve the inverse problem of finding the elastic constitutive parameters which are best matching the experimental modal data. Original multiple objective functions are used for comparing the computed and measured values. They are based upon the relative differences between the eigenfrequencies, upon the diagonal and off-diagonal terms of the so-called modal assurance criterion norm on the mode shapes, and upon geometrical properties of the mode shapes such as the nodal lines. In this work, the convergence properties of the minimisation algorithm are also investigated. It can be observed that usually the minimisation requires between 3 and 6 iterations to reach a residual error of less than 0.2 %. Finally, real identification examples are presented, for various thin to thick unidirectional carbon fiber plates and for a relatively thick cross-ply glass – polypropylene specimen. The robustness and the convergence of the present identification method are studied and the identification results are compared to those obtained with classical static tests. It can be concluded that overall, when the test specimens are moderately thick, the present identification method can accurately determine the in-plane Young's and shear moduli as well as the transverse shear moduli and the in-plane Poisson's ratio. It is also seen that the stability of the method is excellent as long as the number of measured modes is reasonably larger than the number of parameters to be identified

Representative Volume Element Size of Elastoplastic and Elastoviscoplastic Particle-Reinforced Composites with Random Microstructure

With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is representative of many metal matrix composites of technical interests. A large parametric study based on 3D finite element microstructural models is carried out to study the dependence of the Representative Volume Element (RVE) size on the mechanical properties of the constituents, the reinforcement volume fraction and the average strain level. The results show that RVE size mainly depends on the reinforcement volume fraction and on the macroscopic strain level. The estimated RVE size for elastoplastic composites with 5% to 10% volume fraction of reinforcements is found in the range of 5-6 times the average size of reinforcement particles, while for higher volume fraction, e.g. 15% to 25%vol., the RVE size increases rapidly to 10 to 20 times the reinforcement size. Moreover insights on the influence of mesh refinement and boundary conditions on finite element homogenization analysis are obtained

Influence of the moisture content on the fracture characteristics of welded wood joint. Part 2: Mode II fracture

As a second part of this series, the present study also addresses the water resistance of joints obtained by friction welding. Here, the mode II fracture is in focus, that is, 4-points end-notched flexure specimens (4-ENF) were investigated with various moisture contents (MCs). The critical energy release rate was decreasing at higher MCs. The maximal shear strength of the joining material, as determined by torsion tests, was also affected by high MCs. The experimental data were implemented in a finite element model (FEM) based on the cohesive law to simulate the behavior of welded connection in 4-ENF tests. The FEM results describe well the experimental load-displacement curve

Influence of the moisture content on the fracture characteristics of welded wood joint. Part 1: Mode I fracture

Friction welding is a joining technique for wood materials. The positive aspects of this technique are the speed of processing and the absence of chemical or mechanical agents, but the welded joints are not water resistant. To understand better the effect of moisture on the fracture behavior of welded joints, their fracture characteristics have been investigated. The double cantilever beam specimens were tested, which permit to compute the mode I energy release rate of a welded joint. The results confirm the negative effect of moisture on the fracture properties of the joint. The data concerning the maximal tensile strength of the joining material were collected by uniaxial tests and implemented in a finite element model to establish a cohesive law, which describes the behavior of welded pieces in terms of moisture conten

L'Hydroptère: A story of a dream

In 2009, l’Hydroptère broke the symbolic barrier of 50 knots and became the world fastest sailing boat over both 500 meters and 1 nautical mile. This major achievement relied on the high skills of the sailing team but also on technical advances of the boat, resulting from long years of studies and development. This achievement is also an open window to a new goal: flying around the world. In the present article, we present this long and incredible story, highlighting the different steps, the technology involved, and the background of that project.

Representative volume element size of elastoplastic and elastoviscoplastic particle-reinforced composites with random microstructure

With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is representative of many metal matrix composites of technical interests. A large parametric study based on 3D finite element microstructural models is carried out to study the dependence of the Representative Volume Element (RVE) size on the mechanical properties of the constituents, the reinforcement volume fraction and the average strain level. The results show that RVE size mainly depends on the reinforcement volume fraction and on the macroscopic strain level. The estimated RVE size for elastoplastic composites with 5% to 10% volume fraction of reinforcements is found in the range of 5-6 times the average size of reinforcement particles, while for higher volume fraction, e.g. 15% to 25%vol., the RVE size increases rapidly to 10 to 20 times the reinforcement size. Moreover insights on the influence of mesh refinement and boundary conditions on finite element homogenization analysis are obtained

Influence of the moisture content on the fracture characteristics of welded wood joint. Part 2: Mode II fracture

As a second part of this series, the present study also addresses the water resistance of joints obtained by friction welding. Here, the mode II fracture is in focus, that is, 4-points end-notched flexure specimens (4-ENF) were investigated with various moisture contents (MCs). The critical energy release rate was decreasing at higher MCs. The maximal shear strength of the joining material, as determined by torsion tests, was also affected by high MCs. The experimental data were implemented in a finite element model (FEM) based on the cohesive law to simulate the behavior of welded connection in 4-ENF tests. The FEM results describe well the experimental load-displacement curve

Mixed mode fracture behavior of welded wood joints investigated with the Arcan test

Friction welding of wood is an assembly method that is still under investigation and development. A possible application for welded wood joints is the fabrication of multi-layered panels (i.e., cross-laminated panels). In an effort to model the behavior of such products, work is needed to characterize the mechanical strength and fracture properties of welded joints produced with parallel and crossgrain orientations. The present work addresses combined experimental and numerical investigations into the strength and fracture characterization of welded wood joints. The Arcan test setup is used for the experimental mechanical characterization. Numerical and experimental strength analyses are carried out to investigate the effect of the wood’s fiber orientation and in-plane loading direction on the joint strength and fracture toughness. The results show that the orientation of the fibers does not affect the tensile and shear strength (2.3 and 7 MPa, respectively). In the case of fracture, the virtual crack closure technique is used in a finite element model to determine the critical values of energy release rate in pure and mixed modes. A mixed mode fracture criterion of the welded joint is determined

Numerical And Statistical Estimates Of The Representative Volume Element Of Elastoplastic Random Composites

In many applications elastoplastic composites are used in limited amounts, therefore it is important to have estimates of the size of their representative volume element both for modeling and experimental purposes. In this work the tensile response of particle reinforced random composites is simulated by microstructural finite element models. Several microstructural realizations are considered for each composition and volume, and the scatter in the response is used as representativeness metric. The microstructural morphology is characterized using methods and statistical descriptors that can be employed with micrographs of real materials. Numerical results show that the representative volume element dimensions can be estimated by verifying either the consistency of the stress-strain curve for single microstructural realizations and increasing material volume sizes or the convergence of the response of several microstructural realizations at the same material volume size. The analysis of the stress-strain state at the microstructural level shows that the plastic strain and the hydrostatic pressure in the matrix material depend hyperbolically on the interparticle distance. Microstructural analyses show that the matrix coarseness is correlated to the scatter in the mechanical response and therefore can be used to have approximate estimates of the representative volume element size