Infoscience

Thesis

Application des réseaux de Bragg à la détermination des déformations distribuées dans les matériaux composites

The behaviour of brittle matrix fibre reinforced-composites is dependent of the properties of its constituents (fibre, matrix and fibre-matrix interface) and is affected by the mechanical and environmental loads. The fracture of a unidirectional composite material is the result of various micro-mechanisms (matrix and/or fiber fractures, crack fibre interactions, interface failure, delamination, …) that generally occur simultaneously. Among these, one distinguishes the failure by fibre-matrix debonding and the frictional sliding along the composite interfaces. The initiation and debonding growth are influenced by the specimens' geometry, the loading conditions, the nature of the constituent materials, the residual stress and the fibre-matrix interface. Several works have been carried out that deal with theoretical and experimental aspects of micro-mechanisms of fracture. However, a complete understanding is still lacking due to the difficulties to characterise quantitatively the individual contribution of these different micro-mechanisms. In the recent past, optical Fibre Bragg Grating (FBG) have been used as embedded strain sensors. They are particularly adapted to polymer composites where they can provide accurate internal strain measurements at selected locations. Until today, short FBGs have been often used in uniform loading conditions. In such cases, the grating parameters do not vary along the grating length and when uniform variations in strain and/or temperature occur, the FBG spectral response exhibits a simple shift of the Bragg peak without modification of the spectrum shape. This wavelength shift has been used extensively as a global indicator of internal strain in classical sensing applications. This approach however is not realistic when the FBG is found near damage, i.e. crack, delamination, residual strain field, etc. To achieve non-uniform strain measurements using long gauge FBG sensors, a new Optical Low-Coherence Reflectometry (OLCR-based) technique has been developed and tested in order to study crack-fiber interaction and the interface between the glass fibre and epoxy matrix material during composite damage process. When a long FBGs is subjected to non-homogeneous distributed strains, the grating parameters are position-dependent. Due to the extensive grating length, the optical sensor undergoes substantial non-uniform variation along the fibre direction. Inhomogeneity of the grating is a result of the application of a non-uniform strain or temperature field in the interface region and/or the FBG writing process (manufacture). The coupled-mode formalism provides a mathematical tool to describe the interaction of light propagation. This analysis leads to the introduction of a unique complex coupling coefficient to be determined from the FBG complex impulse response. A novel optical low coherence reflectometry acquisition system, designed at EPFL, allows precise measurement of the FBG complex impulse response with high precision and low noise (generally below -120dB). The working principle of the apparatus is well documented elsewhere (93). The OLCR-based method enabled us to obtain the local Bragg wavelength along the grating located in the core of the optical fibre. In this study, epoxy is used as the main material. An established standard protocol is followed with a couple of D.E.R. 330/732 Dow Epoxy Resins (70%/30% mass weight) and a D.E.H. 26 curing agent (+13%). Once the polymerization process is well advanced (24h@28°C), the specimen is removed from its mould and placed in an oven for the post curing phase (10h@70°C). The specimen is left to cool inside the oven until ambient temperature was reached. Three main experiments are conducted with a centrally located long FBG (14 to 25mm length): one on a Double Edge Notch Specimen (DENS) in order to investigate and validate the newly-developed OLCR method and two pull-out tests on two different single fibre cylindrical specimens (with or without fibre protective acrylate coating). The last experiments are conducted in order to describe the interface behavior. Thus, the optical fibre plays the role of fibre-reinforcement and strain sensor. Various Finite Element Models are developed in order to understand better the phenomena and analyse the experimental results. All materials are considered to be linear elastic and with isotropic properties. To model the matrix shrinkage effect the problem is considered analogous to a thermo-elastic one. A shrinkage function, evaluated experimentally, from the FBG response is introduced in the general strain-stress relations. Displacement boundary conditions are applied to the fibre end and the epoxy to simulate the loading conditions. The first set of simulations is dedicated to the stress analysis of the DENS and the comparison of the OLCR data with those of the simulations. The other set allows to identify the properties of the fiber/matrix for weak (glass-acrylate) or strong interfaces (acrylate-epoxy or glass-epoxy) respectively. In particular for the weak interface, interaction between the glass fibre and the coating is described using the regularized Coulomb friction model. That defined the critical shear stress as a fraction of the contact pressure. Higher than this limit, the contact surfaces start sliding relative to one another. Except of the friction coefficient μ, an elastic slip parameter γlim is also introduced into the model to take into account the interface stiffness in the elastic regime (i.e. the sticking stiffness). For the strong interface, interaction between the glass fibre and the epoxy resin is described using the energy release rate G parameter. The observed interface crack grow is used as an input to simulate evolution during debonding propagation. The J-integral equivalent is numerically calculated around the crack tip for different crack lengths during the test. A G(z) distribution along the glass-epoxy interface is identified as possible criterion for adhesion rupture. A single Coulomb identification model μ is proposed to describe the behavior of the interface once it fails. The main results of the simulations are given bellow: The redistribution of the axial stress is obtained for two interfaces and at different force levels. The strain data show that residual stress effects due to epoxy matrix shrinkage and positive strains reveal the presence of the interfacial crack propagation when the fibre is in tension. Numerical models are compared with experimental results of the fibre pull-out tests. The overall experimental results are reproduced for the proposed parameter values although discrepancies exist when the load is released. Two parameter models explain the data very well. At the glass-acrylate weak interface: two interface parameters μ and γlim are identified. At the glass-epoxy strong interface: a constant friction coefficient μ and a distributed energy release rate G(z) are estimated. In this study, a mixed experimental-numerical approach is developed to investigate the strain response of long-gauge FBG and the interface of glass-epoxy and glass-acrylate epoxy. This work demonstrated the potential of the FBG sensor associated with OLCR technique to understand micromechanics damage in fracture.

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