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ABSTRACT4This paper investigates the use of embedded optical fiber Bragg gratings to measure strain near a stress concentration within a solid structure. Due to the nature of a stress concentration (i.e., the strong nonuniformity of the strain field), the assumption that the grating spectrum in reflection remains a single peak with a constant bandwidth is not valid. Compact tension specimens including a controlled notch shape are fabricated, and optical fiber Bragg gratings with different gage lengths are embedded near the notch tip. The form of the spectra in transmission varies between gages that are at different distances from the notch tip under given loading conditions. This variation is shown to be due to the difference in the distribution of strain along the gage length. By using the strain field measured using electronic speckle pattern interferometry on the specimen surface and a discretized model of the grating, the spectra in transmission are then calculated analytically. For a known strain distribution, it is then shown that one can determine the magnitude of the applied force on the specimen. Thus, by considering the nonuniformity of the strain field, the optical fiber Bragg gage functions well as an embedded strain gage near the stress concentration.KEY WORDS--Optical fiber sensor, Bragg grating, embedded sensor, strain distribution, nondestructive evaluationThe use of optical fiber gages to measure temperature, strain, or even detect fracture in a material has great potential due to their relatively small size, sensitivity and immunity to electrical fietds.l Surface-mounted optical fibers, for example, have been used in a variety of strain gage applications. 2 Furthermore, due to their dimensions, optical fiber gages can be embedded unobtrusively into materials, particularly composites already containing fiber reinforcements. However, once an optical fiber is embedded, the interpretation of the gage response becomes more complex due to the effects of May 20, 1999. Final manuscript received: October 10, 2000 interface between the fiber and the material, as well as the multiple components of strain applied to the fiber. 3-6 The problem is further complicated when the strain field surrounding the gage is not sufficiently uniform with respect to the scale of the gage length.As an example, the optical fiber Bragg grating (OFBG) sensor permits the localized measurement of axial strain in an optical fiber. In comparison with a simple optical fiber displacement gage, the response of the OFBG sensor is only affected by the strain (or temperature) field at the location of the grating and not along other portions of the opticai fiber. This property makes the OFBG sensor especially useful for measuring localized phenomena such as the strain conditions near a region of fracture. 7The conventional treatment of the OFBG as a strain gage assumes that the reflected spectrum is a single distinct peak whose shift is linearly proportional to the applied strain. Naturally, this assumption is only valid if the gage le...

This study examined the time-dependent response of bovine periodontal ligament (PDL). Applying linear viscoelastic theory, the objective was 1) to examine the linearity of the PDL's response in terms of its scaling and superposition property and 2) to generate the phase lag-vs.-frequency spectrum graph. PDL specimens were tested under three separate straining conditions: 1) tension ramp tests conducted at different strain rates, 2) pulling step-straining to 0.3 in discrete tests and to 0.3 and 0.6 in one continuous run, and 3) tension-compression sinusoidal oscillations. To this effect, bar-shaped specimens of bovine roots that comprised portions of dentin, PDL tissue, and alveolar bone were produced and strained in a microtensile machine. The experimental data demonstrated that neither the scaling nor the superposition properties were verified and that the viscoelastic response of the PDL was nonlinear. The PDL's elastic response was essentially stiffening, and its viscous component was pseudoplastic. The tangent of the PDL's strain-stress phase lag was in the 0-0.1 range in the tensile direction and in the 0.35-0.45 range in the compressive direction. In line with other biological tissues, the phase lag was largely independent of frequency. By use of the data generated, a mathematical model is outlined that reproduces both the elastic stiffening and viscous thinning of the PDL's response.

This study is part of a research program that aims to develop a constitutive three-dimensional model of the periodontal ligament (PDL) through the identification of pertinent material parameters. As part of this program, bovine PDL was utilized to establish stress-strain responses under tensile and compressive loading conditions. Fresh bovine molars were secured, frozen and prepared to appropriate dimensional specifications. Bar-shaped specimens that comprised portions of dentine, PDL and bone were produced. Push-pull tests were conducted using a specifically constructed loading machine. Full range monotonic stress-strain diagrams were generated. The effect of a rate increase on cyclic S-E diagrams was also determined. The influence of specimen thickness was expressed in terms of modulus of elasticity, strength, uniaxial maximizer strain, and strain energy density. The overall load-response was heavily hysteretic in compression. On the tensile side, after a steep rise, the curve tended to flatten out asymptotically. Variations in rate that spanned four orders of magnitude had no effect on reciprocal load responses. The E-modulus was in the 4-8 MPa range, the strength of the PDL was 1-2 MPa, the maximizer strain was at 45-60% and the strain energy density ranged between 0.3 and 0.4 MPa.