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Levi Richardson
Levi Richardson

Crack V4 Update 2 Sims 4 [TOP]

Several researchers have made contributions on characteristics extracted from crack propagation in aluminum alloy structures with FBG sensors. Yuan [6] extracted the crack initiation factor (CIF) and propagation factor (CPF) from the frequency analysis of the FBG spectrum with wavelet analysis. Opoka [7] extracted the damage parameter as a damage indicator by a root mean square deviation (RMSD) estimator and the smoothed frequency spectrum of the strain data. Peters [8] discussed the spectra of the FBG as a possible basis for the resolution of an arbitrary applied strain distribution. However, it lacked physical interpretations of their evaluation results.

crack v4 update 2 sims 4

When the sensor is subjected to uniform changes in strain, all grating periods experience changes synchronously, resulting in a shift of the Bragg wavelength without modification of the spectrum shape and, consequently, the spectrum was symmetric and smooth due to the uniformity of the strain distribution along the grating, as the red curve in Figure 3 shows. Furthermore, Figure 3 shows the spectral intensity shift toward a higher wavelength with a decrease of the crack tip-FBG distance from 1.6 mm to 1.2 mm, which indicates an increase of tensile strain in the grating. Thus, the central wavelength enlarges from 1529.5 nm to 1530.7 nm, and the spectrum width broadened from 0.3 nm to 0.8 nm.

Variety of physical parameters with different crack lengths. (a) The global curve at different crack lengths; and (b) the subordinate peaks with a 3 db decline near the main peak.

It is worth noting that the spectrum persistently enlarges at the crack tip-FBG distance of 1.2 mm, which indicates a chirp, and the region of the subordinate peaks appeared in the higher wavelength between 1530.9 nm and 1531.1 nm, without subordinate peaks appearing in the lower wavelength, as the blue curve in Figure 3a shows.

It is well known that the deformation of the reflected FBG spectrum is generally subjected to the strain gradient distribution along the FBG sensors [13,14]. In fact, the strain gradient ahead of the crack tip along the grating corresponded with the crack tip-FBG distance. While a broadening is anticipated due to the strain field, which changes along the grating, leading to a chirp, one would also expect an increase in wavelength. Thus, the number of the subordinate peaks increased, the spectrum wavelength enlarged from 1530.7 nm to 1530.9 nm, and the spectrum width broadened from 0.8 nm to 1.2 nm. In addition, the subordinate peaks are more obvious, which are located at a higher wavelength, illustrated by comparing the blue and green curves in Figure 3b.

The subordinate peak, as the red curve in Figure 4a has shown, initially appeared in the lower wavelength at the crack tip-FBG distance of 0.5 mm, and the local amplification of the subordinate peak is shown in Figure 4b. The primary grating sensed the uniformity strain without the complex plastic deformation ahead of the crack tip. Thus, the dominant wavelength decreased from 1530.7 nm to 1530.3 nm. However, the grating terminal, approaching the crack tip zone, could sense complex plastic deformation in this area. This means that the grating period chirped at the initial part of the grating. Literature [15] indicates that the spectrum deformation in this case might be the result of a change in the optical properties of the FBG.

The crack propagates perpendicular to the grating under cyclic loading, and when the crack approaches the observation point (FBG), a highly non-uniform strain field is applied along the initial part of the grating; thus, the spectrum oscillation appeared at a crack length of 4.0 mm with a clear subordinate peak, and the spectra are not symmetrical, as the blue curve in Figure 4a illustrates.

At the crack tip, the singular element was used to improve the accuracy of the strain distribution around the crack tip, and C3D8R eight-node linear hexahedral elements were used for the other grid. The substrate mesh size was 2 mm, and in order to ensure the accuracy of the calculation, the stress concentration parts were refined, and the mesh size of the crack is 0.5 mm, as shown in Figure 5.

The FEM is employed to compute the strain distribution along the grating for various crack sizes, such as 2.8 mm, 3.3 mm, 3.5 mm, and 4.0 mm. Figure 6 shows that the monotonic plastic zone ahead of the crack tip is sensed by the sub-region of the grating at the crack tip-FBG distance of 1.2 mm. The strain distribution along the axis of the grating was mainly quadratic, as shown in Figure 7.

Figure 8 shows the cyclic plastic zone at the crack tip accesses the sub-region of the grating at the crack tip-FBG distance of 0.7 mm. Heterogeneous strain distribution in this area is more severe than the monotonic plastic zone, which is mainly quadratic, as shown in Figure 9. This is the extent of the subordinate peak that is observable.

The improved transfer matrix method (T-matrix method) was used to construct the reflection intensity spectrum of the FBG from the simulation profile along the grating of the FBG. The strain distributions along the grating at different cracks have been calculated in Section 4.1, as shown in Figure 12 and Figure 13. The simulation analysis was as follows: the main strains sensed by the adhered FBG were axial and lateral strains, but was more sensitive to axial strain. The FBG sensor profiles depend on the axial strain distribution ε(x), in which x denotes the axial direction of the FBG, as shown in Equation (1):

Due to the local elastic-plastic material behavior, Ellyin [19] recognized the three different regions in the crack tip area, namely the monotonic plastic zone, cyclic plastic zone, and process zone. The stress ratio, Rδ in the crack tip region is decreased gradually from the process zone to the monotonic plastic zone. Kara [8] developed an experimental calibration of non-homogenous strain distribution along the grating. It reveals that a cubic strain distribution can be sensed by FBG.


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