Residual stresses are important by the manufacturing of the most components. The analysis of residual stresses using the holedrilling method is complicated and is based at the moment solely on strain measurement on the surface. Now, an approach is described where the residual stresses can be calculated on the basis of strain measured in several plains.
Bragg grating sensors are fibre optic sensors for strain and temperature investigations with many advantages: the sensors can be embedded in plastic materials or composites and several gratings can be inscribed in one sensor. However, inhomogeneous deformation or transversal loading cause widening and splitting of the reflected wavelength peak of a fibre Bragg grating (FBG) sensor. These effects are shown in a residual stress analysis, in which the hole drilling method is adapted for FBG sensors. Additionally, a four-point bending test on three different notched aluminium beams is used to investigate the widening and splitting of the reflected peaks and their effects on the strain analysis. At each sample, a reference strain gauge sensor and two FBG sensors are applied. The two FBG sensors are loaded with different strain gradients. The unnotched beam and the beam with small strain gradient show the accuracy and reproducibility of the experiment. The beam with medium strain gradient shows no peak splitting, but the widening does influence the strain analysis. The results of the beam with high strain gradient demonstrate the peak splitting and the failure of the strain analysis methods. Initial approaches on how to deal with this widening and splitting are discussed.
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lies a nonlinear inverse problem which appears not to have received much attention in the literature. In this paper, we present this core problem to the mathematical community and provide a first report on opportunities and limitations of a regularization approach. In particular, we show that difficulties arise from nonuniqueness and the absence of established parameter selection rules for nonlinear inverse problems with multiple regularization parameters. Nevertheless, the paper takes a first step toward extracting more information from a single FBG measurement.
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