Laurent Gornet

A theory of network alteration for the Mullins effect

This paper reports on the development of a new network alteration theory to describe the Mullins effect. The stress-softening phenomenon that occurs in rubber-like materials during cyclic loading is analysed from a physical point of view. The Mullins effect is considered to be a consequence of the breakage of links inside the material. Both filler-matrix and chain interaction links are involved in the phenomenon. This new alteration theory is implemented by modifying the eight-chains constitutive equation of Arruda and Boyce (J. Mech. Phys. Solids 41 (2) (1993) 389). In the present method the parameters of the eight-chains model, denoted C-R and N in the bibliography, become functions of the maximum chain stretch ratio. The accuracy of the resulting constitutive equation is demonstrated on cyclic uniaxial experiments for both natural rubbers and synthetic elastomers.

Modeling of Nomex honeycomb cores, linear and nonlinear behaviours

The purpose of this study is to develop tools dedicated to the design of sandwich panels involving Nomex® honeycomb cores. Special attention is paid to the ability to perform full three dimensional calculations up to failure of such structures. In the first part, the determination of effective elastic properties of Nomex® honeycomb cores is carried out thanks to strain based periodic homogenization technique. Using an equivalence in energy between a real honeycomb and a fictitious continuous medium, it becomes possible to evaluate the elastic behavior of Nomex® cores, starting from the knowledge of the behavior of the constitutive paper. Next, relying on experimental observations, the strengths of Nomex® honeycomb cores are evaluated with a linear Eulers buckling analysis. Results are compared with data coming from manufacturers, and give satisfaction. In order to carry out these two first studies, the NidaCore software has been developed using the finite element code Cast3M from CEA. The last part deals with the modeling of the nonlinear compressive response of Nomex® cores. A model based on the thermodynamics of irreversible process is proposed and the identification technique detailed. Good agreement between experimental data and computed values is obtained.

High Cycle Fatigue Damage Model for Delamination Crack Growth in CF/Epoxy Composite Laminates

This article presents the development of a fatigue damage model which helps to carry out simulation of the evolution of delamination in the laminated composite structures under cyclic loadings. A classical interface damage evolution law, which is commonly used to predict the static debonding process, is modified further to incorporate fatigue delamination effects due to high cycle loadings. An improved formulation is also presented to incorporate the ‘R’ ratio effects. The proposed fatigue damage model is identified using fracture mechanics tests like double cantilever beam, end-notched-flexure and mixed-mode bending. Then a non-monotonic behavior is used to predict the fatigue damage parameters able to carry out delamination simulations for different mode mixtures. Linear Paris plot behaviors of the above-mentioned fracture mechanics tests are successfully compared with available experimental data on HTA/6376C and AS4/PEEK unidirectional materials.

A Rate Dependent Constitutive Model for Carbon-Fiber Reinforced Plastic Woven Fabrics

This paper deals with the modelling until rupture of composite structures made of carbon-fiber/epoxy-resin woven fabrics submitted to dynamic loadings. The model is built at the mesoscale of the elementary ply. It takes into account the slightly nonlinear brittle behavior of the fibers under tensile solicitations, their nonlinear behavior in compression as well as the strongly nonlinear and irreversible behavior of the ply in shear. Strain rate effects are also introduced and special attention is paid to the objectivity of the model in the context of finite element calculation. Therefore the choice of a delayed damage mesomodel coupled with viscoplasticity is made. In order to identify the values of the parameters of the model, an optimization procedure based on a gradient-free direct search method has been developed. As a logical procedure to this study, the models ability to avoid strain localization and mesh dependence is then checked on simple uniaxial examples. The last part of this paper is devoted to structural calculation. The results of the simulations of both the impact on composite plate and the crushing of thin-walled tube demonstrate the capability of the model to reproduce observed physical phenomena.

Inelastic Interface Damage Modeling with Friction Effects: Application to Z-Pinning Reinforcement in Carbon Fiber Epoxy Matrix Laminates:

This article presents the implementation of a new inelastic damage model able to carry out simulation of initiation and evolution of damage in the Z-pinned laminated composite structures with friction effects. The classical elastic damage model is modified to an inelastic model with friction effects obeying the simple Coulomb friction criterion. The main idea is the modification of strain energy parameter by introducing sliding and friction parameters. The simulations of single Z-fiber pull tests highlight the effectiveness of the proposed model for micro-scale predictions.

Numerical modelling of Nomex® honeycomb cores : Failure and effective elastic properties

The aim of the present study is to propose and develop the numerical determination of the effective stress-strain behaviour of Nomex® honeycomb cores made from aramid paper material. This study highlights the determination of the hexagonal and rectangular over-expanded core materials. These honeycombs are extensively used in the manufacturing of aeronautic structures and of oceanic multihull sailing race boats. These sandwich structures are made of carbon-fiber epoxy-matrix composite laminate skins and Nomex® cores. The understanding of the behaviour and eventually failure of honeycombs are extremely important for the design of these engineering composite sandwich structures. Honeycomb cores predictions are directly related to the structural integrity and safety requirements of the entire composite structure. Since the pioneering work numerous studies on the effective properties of cellular sandwich cores have been published [1]–[2]. In the past, core behaviours were studied under strength of material assumptions. In this context a software dedicated to Nomex® honeycombs was developed at the Laboratory in order to predict the failure conditions of these cores [2]. Our software NidaCore has been developed to determine the three dimensional mechanical core properties. The elastic mechanical properties have been determined by a three-dimensional Finite Element model that involves periodic homogenization techniques. For the homogenisation of the honeycomb microstructure, a strain energy-based concept is used which assumes macroscopic mechanical equivalence of a Representative Volume Element for the given microstructure with a similar homogeneous volume element. The software has been developed using the Finite Element structure analysis program Cast3M-CEA. Numerical predictions are compared with the mechanical properties given by the Euro-Composites company. The present study confirms that for honeycombs under consideration the Representative Volume Element symmetries lead to orthotropic homogenized mechanical properties. The key point of the modeling is that the RVE buckling modes conduct to determine the ultimate stresses of the homogenized core. Based on buckling modes, numerical analysis reproduces the ultimate stresses experimentally observed on standard test methods. This approach strengthens by experimental results leads to a failure criteria based on the mechanical understanding of local damage effect. In order to go further, the skin effect on the core properties is discussed for T700/M10 carbon-fiber epoxymatrix cross-ply and angle-ply laminates skins. The honeycomb mechanical properties and ultimate stresses are used to model three dimensional reinforcements that we used for the study of the Oceanic sailboat structures.

Prediction of delamination crack growth in carbon/fiber epoxy composite laminates using a non-local cohesive zone modeling

The global behavior of composite materials is strongly influenced by the quality of adhesion between different components. A component can be single phase, like fibers or particles used as reinforcement in a homogenous matrix, or a multiphase material like a layer in long-fiber laminate. In the latter case the degradation of adhesion implies the separation of the layers, known as delamination. Among all different failure mechanisms, Delamination is considered to be the most prominent mode of failure in fiber-reinforced laminates as a result of their relatively weak inter-laminar strength. When laminated structures are subjected to static, dynamic or cyclic loadings, the inter-laminar adhesion strength between individual plies tends to deteriorate significantly and act as the origin of the final failure. Therefore, an efficient and reliable design tool capable of predicting delamination could improve the durability for composite laminates. There exist damage mechanics based formulations capable of simulating the delamination crack growth in carbon/glass fiber epoxy based composite laminates. The present study is focused on taking a step forward in this respect. At first, already existed local interface models effectiveness is tested and results are successfully compared with available experimental data for UD IMS/924 Carbon/fiber epoxy composite laminate. Next, a non-local integral-type regularization scheme is introduced to overcome the spurious localization problem associated to the existing local model. Basic concepts and mathematical modeling of Non-Local damage evolution law are comprehensively studied and presented in this study. Finite Element simulation results based on proposed model are discussed in detail and are compared with experimental results.

A Rate Dependent Constitutive Model for Carbon-Fibre/Epoxy-Matrix Woven Fabrics Submitted to Dynamic Loadings

This paper deals with the modelling until rupture of composite structures made of carbon/epoxy woven fabrics and submitted to dynamic loadings.

Modelling and Simulation of the Three-Dimensional Hydrodynamic Problem

This paper deals with slamming phenomenon (impact between bow ship and water free surface). Slamming loads on ship may be sufficiently important so as to create plastic deformations of the hull external structure. In extreme cases, they have been recognised for being responsible for the loss of ships. The problem to solve is transient and highly non-linear due to the character of the flow. In the present paper, the three-dimensional Wagner problem is solved numerically using a variational formulation together with a Finite Element Method. Three-dimensional results for simple rigid bodies such as a cone and an ellipsoid are successfully compared with analytical results. Results for deformable structure will be presented.

Numerical Modelling of the Three-Dimensional Slamming Problem

This paper deals with the slamming phenomenon for deformable structures. In a first part, a three-dimensional hydrodynamic problem is solved numerically with the Finite Element Method. The results for a rigid body are successfully compared to the analytical solutions. After the numerical analysis, an experimental investigation is presented. It consists in series of free fall drop-tests of rigid, deformable cones shaped models with different deadrise angle and thickness. Distribution of the pressure and its evolution are analyzed. Numerical and experimental results are compared and present good agreement.