Mohanraj Prabhugoud

Modified transfer matrix formulation for bragg grating strain sensors

This paper presents a formulation for the application of the transfer matrix method to Bragg grating strain sensors. A modified T-matrix representation is detailed for the sensor problem based on an effective period derived from the coupling coefficients. This modified T-matrix formulation is shown to converge to the coupled-mode equations solution for a large number of grating segments, even in the presence of significant strain gradients. Several numerical examples are presented to demonstrate the importance of inclusion of the strain gradient in the calculation. In addition, the current formulation is validated by application to previously published experimental data.

Finite element model for embedded fiber Bragg grating sensor

This paper presents an integrated formulation for the calculation of the spectral response of a fiber Bragg grating sensor embedded in a host material system, as a function of the loading applied to the host structure. In particular, the calculation of the transverse strain sensitivity of a fiber Bragg grating sensor through the calculation of the change in effective index (or indices) of refraction of the fiber cross-section due to the applied load is presented in detail. For the calculation of the fiber propagation constants, a two-step finite element formulation is used incorporating the optical, geometric and material properties of the cross-section. Once the propagation constants and principal optical axes are known along the fiber, a modified transfer matrix method is applied to calculate the spectral response of the FBG. It is shown that the FE formulation yields close agreement with previous methods for benchmark diametrical compression cases. However, the current method provides the potential to evaluate the effects of high strain gradients across the optical fiber core present in some loading applications.

Global-local Assessment of Low-velocity Impact Damage in Woven Composites

Global measurements from low-velocity impact experiments and local strain measurements from embedded and surface mounted optical fiber Bragg grating (FBG) sensors were used to obtain failure maps for two- and three dimensional woven composites. These maps delineated five distinct regimes spanning behavior from initial impact to complete penetration. Sensor and host damage were separated by signal intensity and the evolution of Bragg peaks due to repeated impact loads. The results indicate that a local-global framework can be used to monitor damage progression in different host materials, and hence it can be potentially used to mitigate damage.

Efficient simulation of Bragg grating sensors for implementation to damage identification in composites

A computationally efficient method is proposed to interpret optical fiber sensor data collected from Bragg grating sensors embedded in composites. The method divides the composite into remote field and critical field regions with respect to any developed damage. These regions are defined via non-uniformities in the sensor response. The remote field response is treated via an optimal shear-lag theory first presented by Mendels and Nairn. This formulation provides a rapid solution of the average fiber axial stress at the location of each sensor. The critical field region is modeled via a finite element sensor model including the effects of multi-axis loading on the sensor and an optical loss due to local fiber curvature. The response of the Bragg grating sensor to the effects of axial, bending and shear loading are simulated for inclusion in the model. The bending loss response as a function of fiber curvature is experimentally measured. The application of this method is demonstrated through a numerical example, simulating the response of sensors embedded in a lamina to the presence of a transverse crack.

Finite element analysis of multi-axis strain sensitivities of bragg gratings in PM fibers

This article presents a numerical analysis of the sensitivity of fiber Bragg grating (FBG) sensors written into polarization maintaining fibers to transverse and thermal loading. These sensors are typically applied for the measurement of multiple strain components for the monitoring of civil structures. The finite element analysis includes both the optical and mechanical variations in the optical fiber. Five fiber types typically used in FBG sensors (elliptical core, D-fiber, elliptical core SAP, Bow-Tie, and Panda) are compared. It is shown that when only the fiber geometry is considered while the material parameters are approximately the same, the D-fiber demonstrates the highest sensitivity to transverse loading. In addition, it is shown that reducing the fiber cladding diameter significantly improves the sensitivities of the FBG sensor to transverse loads. All fiber types exhibit approximately the same sensitivity to thermal loading.

Failure and damage identification in woven composites with fiber bragg grating sensors

In this study, measurements from low-impact velocity experiments and embedded and surface mounted optical fiber Bragg grating (FBG) sensors were used to obtain detailed information pertaining to damage progression in two-dimensional laminate woven composites. The woven composites were subjected to multiple strikes at 2m/s until perforation occurred, and the impactor position and acceleration were monitored throughout each event. From these measurements, we obtained dissipated energies and contact forces. The FBG sensors were embedded and surface mounted at different critical locations near penetration-induced damaged regions. These FBG sensors were used to obtain initial residual strains and axial and transverse strains that correspond to matrix cracking and delamination. The transmission and the reflection spectra were continuously monitored throughout the loading cycles. They were used, in combination with the peak contact forces, to delineate repeatable sensor responses corresponding to material failure. From the FBG spectra, fiber and matrix damage were separated by an analysis based on signal intensity, the presence of cladding modes, and the behavior of individual Bragg peaks as a function of evolving and repeated impact loads. This provided an independent feedback on the integrity of the Bragg gratings. A comparison by number of strikes and dissipated energies corresponding to material perforation indicates that embedding these sensors did not affect the integrity of the woven systems and that these measurements can provide accurate failure strains.

Modified transfer matrix model for Bragg grating strain sensors

Optical fiber Bragg gratings are unique among strain sensors due to their potential to measure strain distributions over gage lengths of a few centimeters with a spatial resolution of a few nanometers. The application of these sensors requires modeling of the grating output spectrum due to an applied axial strain profile. The most computationally efficient method for this calculation is the transfer-matrix model (T-matrix) derived originally for chirped gratings. This approach models a grating with varying properties as a series of smaller grating segments with constant parameters. Huang and colleagues first applied the T-matrix approach to model the inverse problem of a grating subjected to non-uniform strain by varying the period of each segment. The current work shows that, in the presence of strain gradients, this approach does not converge to the numerical solution of the grating coupled mode equations in the limit of a large number of segments. A modified T-matrix representation is then derived for the sensor problem and is shown to approach the coupled mode solutions for a large number of segments. Finally, the application of the modified T-matrix model to Bragg grating sensors is outlined, including inversion of the grating spectrum via a genetic algorithm.

In situ failure identification in woven composites throughout impact using fiber Bragg grating sensors

In this study, measurements from low-impact velocity experiments and surface mounted optical fiber Bragg grating (FBG) sensors were used to obtain detailed information pertaining to damage progression in two-dimensional laminate woven composites. The woven composites were subjected to multiple strikes at 2m/s until perforation occurred, and the impactor position and acceleration were monitored throughout each event. From these measurements, we obtained dissipated energies and contact forces. The FBG sensors were surface mounted at different critical locations near penetration-induced damaged regions. These FBG sensors were used to obtain initial residual strains and axial and transverse strains that correspond to matrix cracking and delamination. The transmission and the reflection spectra were continuously monitored throughout the loading cycles. They were used, in combination with the peak contact forces, to delineate repeatable sensor responses corresponding to material failure. From the FBG spectra, fiber and matrix damage were separated by an analysis based on the behavior of individual Bragg peaks as a function of evolving and repeated impact loads. This provided an independent feedback on the integrity of the Bragg gratings. Thus, potential sources of error such as sensor debonding were eliminated from the strain data throughout the measurements. A comparison by number of impact strikes and dissipated energies corresponding to material perforation indicates that these measurements can provide accurate failure strains.

Transverse strain sensitivity of fiber Bragg grating sensors

This article presents an integrated formulation for the calculation of the spectral response of a fiber Bragg grating sensor embedded in a host material system, as a function of the loading applied to the host structure. In particular, the calculation of the transverse strain sensitivity of a fiber Bragg grating sensor through the calculation of the change in effective index (or indices) of refraction of the fiber cross-section due to the applied load is presented in detail. For the calculation of the fiber propagation constants, a two-step finite element formulation is used moeling the optical, geometric and material properties of the cross-section. Once the propagation constants and principle optical axes are known along the fiber, a modified transfer matrix method is applied to calculate the spectral response of the FBG. It is shown that the inclusion of the change in index of refraction throughout the cross-section yields close agreement with previous methods. However the current method provides the potential to evaluate the effects of high strain gradients across the optical fiber core for some loading applications.

Birefringence and Transverse Strain Sensitivity in Bragg Grating Sensors

This article presents the derivation of a finite element formulation for the calculation of the spectral response of a fiber Bragg grating sensor embedded in a host material system. The formulation is based on a 3D/2D element for which the local fiber propagation constants are calculated from the optical and geometric properties in the plane perpendicular to light propagation. Afterwards, a modified transfer matrix can be applied to calculate the Bragg wavelength shifts in each of the principle optical axes for the grating. The effects of axial strain, transverse strain, and fiber curvature can be implemented into the formulation. This novel approach permits the prediction of the sensor response when the sensor is embedded in a complicated material system for which analytical or approximate solutions do not accurately predict the strain state in the sensor. A numerical example demonstrating the response of the senor to diametrical compression is presented to verify the formulation.