Residual stress characterization in a single fibre composite specimen by using FBG sensor and the OLCR technique

The purpose of this thesis is to characterize internal strains in polymeric materials due to consolidation. In view of this, optical Fiber Bragg Grating sensors are an excellent non-destructive tool for internal strain characterization and damage detection in composite materials and structures. Fiber Bragg Gratings (FBG), have become increasingly used in engineering applications because of their inherent advantages with respect to traditional sensors. They can provide an important tool in experimental mechanics to perform key experiments that are difficult or impossible with other standard techniques. In this respect, they are ideally suited as strain measuring devices in composites, where they can be embedded non-invasively during fabrication. In view of this, the main goal of this thesis is the development of an experimental methodology to characterize the residual stresses that are generally present in many materials and is a complex problem to solve in micro-mechanics. The work is presented in three interrelated parts. Long-gauge-FBGs (Bragg grating of ∼ 24 mm) are introduced in cylindrical specimens of epoxy. In this configuration the fiber is simultaneously a reinforcement and a sensor in a single fiber composite. Because the epoxy matrix shrinks during the polymerization process, the optical sensor undergoes substantial non-uniform strain along the fiber. The response of the FBG to a non-uniform strain distribution is investigated by using an Optical Low-Coherence Reflectometry (OLCR) based technique which allows a direct reconstruction of the optical period along the grating without any a priori assumption about the strain field. A comparison with the most common reconstruction inverse technique T-Matrix is also proposed, showing that it generally introduces greater errors without ensuring the uniqueness of the solution. The OLCR permits in fact the direct measurement of the axial evolution of the residual strain along the core of the reinforcing fiber, thus providing important information on the internal state of stress of the specimen at a given stage of its preparation and, later on, during its service life. In addition, the measured strain distribution evolves along the fiber direction following a fourth-order function, which clearly presents a plateau over a 20 mm range at the center of the specimen. In particular, the maximum strain level reached after the matrix solidification is –2000 με which increases up to –6000 με at the end of the post-curing process of the resin. This value is consistent with the volume reduction of the free resin provided by the producer and equal to 2 %. This strain corresponds to -450 MPa axial compressive stress on the embedded reinforcing fiber. The implementation of FBG sensors to study the changes in the stress field when a crack is present in the sample is addressed next. Bragg wavelength distributions have been measured as a function of the depth of machined circular cracks in the radial direction of the cylinder. Three different crack depths (namely 7.5 mm, 11 mm and 12 mm) have been machined in the central section of the specimen. First, these measurements give an indication about the zone of influence of the reinforcing fiber on the residual stresses and, secondly, they permit the characterization of the effect of a mechanically induced crack on the initial residual stress state. In particular, only the stress relaxation due to the introduction of the deepest transversal crack significantly affects the FBG response with a related wavelength variation of 3 nm. These data are used as input to deduce the radial evolution of the stress field by adapting and improving the Crack Compliance (C.C.M) inverse Method to retrieve the stress field within a composite starting from a measurement of strain. A rigorous analytical approach to predict the residual stress field is described and verified numerically and experimentally. A very good agreement is found between experimental and numerical values, thus proving the reliability of the experimental approach. As last topic in this work, the response of a long FBG to the transverse crack propagation is monitored experimentally by using the OLCR and modeled numerically. Firstly, a Compact-Tension specimen submitted to a cyclic fatigue test is chosen with the FBG glued on its back-face and normal to the crack direction. A simple analytical model predict the FBG response as the crack advances. Secondly, long- FBG is embedded in a Compact-Tension specimen of the same dimensions. In particular when the natural crack overpasses the fiber, the grating can be used to measure the bridging forces between fracture surfaces and/or to measure the relative opening of the crack. Reconstruction of the FBG signal with T-matrix indicate problems associated to stress distributions due to highly non-uniform strain field. In this way, the FBG becomes the excellent candidate to study a number of interesting problems in the field of the fracture mechanics applications.

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