Influence of shear strains on the phase of light transmitted through single-mode fiber optic strain sensors

David W. JensenBrigham Young University, Provo, UT 84602andSuresh P. PalThe Pennsylvania State University, State College, PA 16802INTRODUCTIONSince the well-known demonstration of a fiber-optic strain gage by Butter and Hocker [1] in 1978,significant refmements have been made in the area offiber optic sensing, enabling the measurement ofmany different physical quantities, including strain,displacement, linear and circular acceleration,temperature, degree of cure in plastics, chemicalcompositions, pressure, acoustic waves, and fluidflow rates [2-10]. Optical fibers are particularlysuitable for use as embedded strain sensors incomposite structures because oftheir small size, lightweight, compatibility with composite materials,flexibility, fast response, and high sensitivity andreliability [2]. Distributed fiber-optic strain sensorsprovide an additional advantage in their ability tomonitor perturbations in the strain field over largeareas [3]. This is ofparticular interest in applicationssuch as thin-walled composites, where theoccurrence of localized out-of-plane deformation isquite likely. Out-of-plane deformations reduce theeffective in-plane stiffness and can, ultimately, leadto buckling instabilities. Research has shown thatintegrated fiber-optic strain sensors can be embeddedin composites to discern the initiation of localbuckling [4]. The localized deformations exertsignificant bending and transverse stresses on theembedded sensors. These stresses in turn change thepath length and refractive index ofthe optical fiber,which can be discerned using interferometrictechniques [4]. In this manner, embedded opticalfibers can be used to monitor large deformations ofthin-walled composite structures.Both analytical and experimental efforts havecontributed to our current understanding of therelationship between the elongation of a host mediumand phase changes in the light passing through anoptical fiber [1,11,12]. This paper describes researchwhich partially fills in the remaining gap byquantifying the influence of shear strains on the phasechange of light passing through an embedded opticalfiber. In this experiment, optical fibers wereembedded in 18-inch long by 2.25-inch diametercomposite tubes. Three tubes were fabricated withaxial fibers and one with a helical fiber, using a handlayup fabrication technique. These tubes were alsoinstrumented with two strain gage rosettes. The tubeswere subj ected to pure torsional loads while thesurface strains and the fiber-optic phase changes weremeasured. A modified all-fiber Mach-Zehnderinterferometer with active homodyne feedback wasused to determine the phase changes in the opticalfibers due to the applied strains [1]. The phasechanges were also predicted using fundamentalconcepts of structural mechanics and existing phase-strain models.EXISTING PHASE-STRAIN RELATIONSHIPSExperimental attempts to characterize theresponse of distributed fiber-optic strain sensorssubjected to various strain states have generally beencorrelated to mechanical strains measured byconventional surface-mounted strain gages [12, 13].For obvious reasons, these studies have been limitedto uniform uniaxial (e.g., tension and compression)and linearly varying (e.g., cantilever bending) strainfields. While the sensor response has been found tobe highly sensitive and linearly proportional to theintegrated axial strain along the embedded length ofthe sensor [13], the factors modulating light in theoptical fibers have been accounted for only within the"black-box" of calibration constants and/or withsimple phase-strain relationships.The most widely accepted phase-strain modelsare the original model for surface-mountedinterferometric fiber-optic strain sensors developedby Butter and Hocker [1] and the extension toarbitrary strain fields and sensor configurations bySirkis and Haslach [11]. The original theory includedthe contributions of length change, birefringence andwave guide dispersion to the total phase shift ofcoherent light in a straight fiber subjected to a linearstrain field. Applying a strength of materials analysis40/SPIE Vol. 2574