Modeling of the residual stresses acting on a low-birefringence fiber Bragg grating sensor embedded in an epoxy matrix

An optical fiber Bragg grating (FBG) embedded in an epoxy matrix is indubitably subjected to non-negligible residual stresses arising from the cure, especially for a strong fiber-matrix interface. The spectral response of the FBG sensor is clearly influenced by the presence of the residual non-homogeneous strain field along the grating and results in a distortion (chirp) of the reflected spectrum. Direct applications for distributed strain sensing, without taking the residual field into account, can lead to inaccurate results. In the present work the reflected spectrum of a single FBG sensor embedded in an epoxy specimen at the end of the post-curing process is recorded and characterized using an analytical model which accounts for a distributed residual strain profile along the axial direction of the fiber. In addition an equivalent thermo-elastic problem for the matrix material is considered in finite elements simulations of the actual specimen. Both approaches show good agreement for the axial field, with some differences in the radial direction, presumably due to the simplifications introduced by the shear lag simplifications in the adopted analytical model. A level of about 20 MPa of compressive residual stresses is found in the vicinity of the fiber matrix interface.